v0.0.37 - Add interactive multi-transport selection menu at startup — users can select one or more transports (unix, qrexec bridge, TCP) from a menu instead of memorizing CLI flags

The attended signer only handled SIGINT/SIGTERM. A client that disconnects
abruptly (e.g. nostr_core_lib's nsigner client reconnects per request and
closes the previous connection) could cause a write to the closed socket to
raise SIGPIPE, terminating the whole signer process after one request.

Ignore SIGPIPE process-wide so writes to closed sockets return EPIPE instead.
Verified end-to-end with nostr_core_lib note_poster --signer unix:nsigner-test
posting a kind-1 to relay.laantungir.net.

.gitignore

@@ -6,4 +6,7 @@ build/
 resources/
 .test_mnemonic
 Trash/
+node_modules/
+package.json
+package-lock.json
 

Makefile

@@ -1,5 +1,5 @@
 CC := gcc
-CFLAGS := -Wall -Wextra -std=c99 -Os -ffunction-sections -fdata-sections -Isrc -Iresources/nostr_core_lib -Iresources/nostr_core_lib/nostr_core -Iresources/nostr_core_lib/cjson -Iresources/tui_continuous
+CFLAGS := -Wall -Wextra -std=c99 -Os -ffunction-sections -fdata-sections -DNOSTR_ENABLE_NSIGNER_CLIENT=1 -Isrc -Iresources/nostr_core_lib -Iresources/nostr_core_lib/nostr_core -Iresources/nostr_core_lib/cjson -Iresources/tui_continuous
 LDFLAGS := -Wl,--gc-sections resources/nostr_core_lib/libnostr_core_x64.a -lz -ldl -lpthread -lm -lssl -lcrypto -lcurl -lsecp256k1
 
 SRC_DIR := src
@@ -42,6 +42,7 @@ TEST_QREXEC_AUTH_TARGET := $(BUILD_DIR)/test_qrexec_auth
 TEST_MNEMONIC_INPUT_TARGET := $(BUILD_DIR)/test_mnemonic_input
 EXAMPLE_GET_PUBLIC_KEY_TARGET := $(BUILD_DIR)/example_get_public_key_client
 EXAMPLE_SIGN_EVENT_TARGET := $(BUILD_DIR)/example_sign_event_client
+EXAMPLE_GET_PUBKEY_TCP_TARGET := $(BUILD_DIR)/example_get_pubkey_tcp
 
 .PHONY: all lib dev static static-debug static-arm64 firmware-feather test test-integration test-mnemonic test-mnemonic-input test-role test-selector test-enforcement test-dispatcher test-policy test-socket-name test-auth-envelope test-qrexec-auth examples test-client clean
 
@@ -108,7 +109,7 @@ test-qrexec-auth: $(TEST_QREXEC_AUTH_TARGET) $(TARGET_DEV)
 
 test-client: examples
 
-examples: $(EXAMPLE_GET_PUBLIC_KEY_TARGET) $(EXAMPLE_SIGN_EVENT_TARGET)
+examples: $(EXAMPLE_GET_PUBLIC_KEY_TARGET) $(EXAMPLE_SIGN_EVENT_TARGET) $(EXAMPLE_GET_PUBKEY_TCP_TARGET)
 
 $(TEST_MNEMONIC_TARGET): $(TEST_DIR)/test_mnemonic.c $(SRC_DIR)/mnemonic.c $(SRC_DIR)/secure_mem.c
 	@mkdir -p $(BUILD_DIR)
@@ -138,9 +139,9 @@ $(TEST_POLICY_TARGET): $(TEST_DIR)/test_policy.c $(SRC_DIR)/policy.c
 	@mkdir -p $(BUILD_DIR)
 	$(CC) $(CFLAGS) $(TEST_DIR)/test_policy.c $(SRC_DIR)/policy.c -o $(TEST_POLICY_TARGET) $(LDFLAGS)
 
-$(TEST_INTEGRATION_TARGET): $(TEST_DIR)/test_integration.c $(CLIENT_DIR)/nsigner_client.c $(SRC_DIR)/auth_envelope.c
+$(TEST_INTEGRATION_TARGET): $(TEST_DIR)/test_integration.c
 	@mkdir -p $(BUILD_DIR)
-	$(CC) $(CFLAGS) -I$(CLIENT_DIR) $(TEST_DIR)/test_integration.c $(CLIENT_DIR)/nsigner_client.c $(SRC_DIR)/auth_envelope.c -o $(TEST_INTEGRATION_TARGET) $(LDFLAGS)
+	$(CC) $(CFLAGS) $(TEST_DIR)/test_integration.c -o $(TEST_INTEGRATION_TARGET) $(LDFLAGS)
 
 $(TEST_SOCKET_NAME_TARGET): $(TEST_DIR)/test_socket_name.c $(SRC_DIR)/socket_name.c
 	@mkdir -p $(BUILD_DIR)
@@ -154,13 +155,17 @@ $(TEST_QREXEC_AUTH_TARGET): $(TEST_DIR)/test_qrexec_auth.c $(SRC_DIR)/auth_envel
 	@mkdir -p $(BUILD_DIR)
 	$(CC) $(CFLAGS) $(TEST_DIR)/test_qrexec_auth.c $(SRC_DIR)/auth_envelope.c -o $(TEST_QREXEC_AUTH_TARGET) $(LDFLAGS)
 
-$(EXAMPLE_GET_PUBLIC_KEY_TARGET): $(EXAMPLES_DIR)/get_public_key_client.c $(CLIENT_DIR)/nsigner_client.c $(SRC_DIR)/auth_envelope.c
+$(EXAMPLE_GET_PUBLIC_KEY_TARGET): $(EXAMPLES_DIR)/get_public_key_client.c
 	@mkdir -p $(BUILD_DIR)
-	$(CC) $(CFLAGS) -I$(CLIENT_DIR) $(EXAMPLES_DIR)/get_public_key_client.c $(CLIENT_DIR)/nsigner_client.c $(SRC_DIR)/auth_envelope.c -o $(EXAMPLE_GET_PUBLIC_KEY_TARGET) $(LDFLAGS)
+	$(CC) $(CFLAGS) $(EXAMPLES_DIR)/get_public_key_client.c -o $(EXAMPLE_GET_PUBLIC_KEY_TARGET) $(LDFLAGS)
 
-$(EXAMPLE_SIGN_EVENT_TARGET): $(EXAMPLES_DIR)/sign_event_client.c $(CLIENT_DIR)/nsigner_client.c $(SRC_DIR)/auth_envelope.c
+$(EXAMPLE_SIGN_EVENT_TARGET): $(EXAMPLES_DIR)/sign_event_client.c
 	@mkdir -p $(BUILD_DIR)
-	$(CC) $(CFLAGS) -I$(CLIENT_DIR) $(EXAMPLES_DIR)/sign_event_client.c $(CLIENT_DIR)/nsigner_client.c $(SRC_DIR)/auth_envelope.c -o $(EXAMPLE_SIGN_EVENT_TARGET) $(LDFLAGS)
+	$(CC) $(CFLAGS) $(EXAMPLES_DIR)/sign_event_client.c -o $(EXAMPLE_SIGN_EVENT_TARGET) $(LDFLAGS)
+
+$(EXAMPLE_GET_PUBKEY_TCP_TARGET): $(EXAMPLES_DIR)/get_pubkey_tcp.c
+	@mkdir -p $(BUILD_DIR)
+	$(CC) $(CFLAGS) $(EXAMPLES_DIR)/get_pubkey_tcp.c -o $(EXAMPLE_GET_PUBKEY_TCP_TARGET) $(LDFLAGS)
 
 clean:
 	rm -rf $(BUILD_DIR)

README.md

@@ -247,6 +247,8 @@ Discovery:
 - `nsigner --listen stdio` runs one framed JSON-RPC request/response over stdin/stdout.
 - `nsigner --listen qrexec` is the same stdio framing mode, but caller identity can be derived from `QREXEC_REMOTE_DOMAIN` (displayed as `qubes:<source-vm>`).
 - `nsigner --listen tcp:IPv4:PORT` or `tcp:[IPv6]:PORT` enables TCP listening for non-AF_UNIX clients (for example `tcp:127.0.0.1:8080`, `tcp:[::]:8080`, or `tcp:[fd00::1234]:8080`).
+- `nsigner bridge --to <socket-name>` is a stateless relay for Qubes qrexec: reads one framed request from stdin, forwards it to a persistent signer's abstract unix socket, and relays the response to stdout. Used as the `qubes.NsignerRpc` service entrypoint. See [§8.3](#83-qubes-os-qube) and [`plans/qrexec_persistent_bridge.md`](plans/qrexec_persistent_bridge.md).
+- `--bridge-source-trusted` (unix listener only): marks the socket as a trusted bridge endpoint. Each connection sends a framed `{"qrexec_source":"<vm>"}` preamble before the request, and the caller identity is composed as `qubes:<vm>` — matching the native qrexec identity path. This enables a persistent signer (mnemonic in mlock'd RAM) to receive qrexec-routed requests without spawning a fresh process per call.
 
 ### 7.2 ESP32 MCU: TinyUSB composite (CDC + WebUSB)
 
@@ -283,7 +285,43 @@ MCU target reuses mnemonic/role/selector/enforcement/dispatcher core and swaps t
 
 ### 8.3 Qubes OS qube
 
-Qubes deployment runs `n_signer` in a dedicated signer qube as a foreground process under explicit user session control. Transport binding is platform-specific, but lifecycle and memory-only state model are unchanged.
+Qubes deployment runs `n_signer` in a dedicated signer qube (e.g. `nostr_signer`) as a foreground process under explicit user session control. The mnemonic lives only in mlock'd RAM in that qube — a compromised agent in a caller qube cannot read it (hypervisor-enforced memory isolation).
+
+Two transport paths are supported:
+
+**FIPS/TCP** — the signer listens on `tcp:[::]:8080` and FIPS carries traffic between qubes as an IPv6 mesh substrate. See [`documents/FIPS_DEPLOYMENT.md`](documents/FIPS_DEPLOYMENT.md).
+
+**Qubes qrexec bridge** (recommended for no-network deployments) — a persistent signer listens on an abstract unix socket, and a stateless `nsigner bridge` relay (the `qubes.NsignerRpc` qrexec service) forwards one request per qrexec invocation. No network, no FIPS — pure intra-host IPC. Caller identity is `qubes:<source-vm>` (from `QREXEC_REMOTE_DOMAIN`), relayed via a trusted preamble. See [`plans/qrexec_persistent_bridge.md`](plans/qrexec_persistent_bridge.md) for the full design.
+
+#### Qrexec bridge setup
+
+**In the signer qube** (`nostr_signer`):
+
+```bash
+# Install nsigner and the qrexec service
+bash setup_signer_qube.sh    # from packaging/qubes/
+
+# Start the persistent signer (mnemonic entered at terminal, in mlock'd RAM)
+~/.local/bin/nsigner --listen unix --socket-name nsigner --bridge-source-trusted
+```
+
+**In dom0**:
+
+```bash
+# Install policy and tag the signer qube
+bash setup_dom0.sh nostr_signer    # from packaging/qubes/
+```
+
+The dom0 policy allows trusted caller qubes without a popup (memory isolation is the real security boundary) and asks for confirmation from any other qube. The signer's own approval prompt at the `nostr_signer` terminal is the operation-level gate.
+
+**From a caller qube**:
+
+```bash
+# JavaScript example (uses qrexec-client-vm, no auth envelope needed)
+node examples/n_signer_qube_example_qrexec.js nostr_signer
+```
+
+Setup scripts and policy are in [`packaging/qubes/`](packaging/qubes/). See also [`documents/QUBES_OS.md`](documents/QUBES_OS.md) and [`documents/qubes_client_examples.md`](documents/qubes_client_examples.md).
 
 ## 9. Usage
 
@@ -319,6 +357,18 @@ TCP transport mode (no TUI; serves requests until terminated):
 nsigner --listen tcp:[::]:8080
 ```
 
+Qrexec bridge mode (stateless relay to a persistent signer's unix socket; used as the `qubes.NsignerRpc` service):
+
+```bash
+nsigner bridge --to nsigner
+```
+
+Persistent signer for qrexec bridge (unix listener with trusted source-qube preamble):
+
+```bash
+nsigner --listen unix --socket-name nsigner --bridge-source-trusted
+```
+
 ### 9.2 Send a request (client mode)
 
 From another terminal, target the signer by its socket name:
@@ -414,6 +464,11 @@ These items are designed and worth doing, but are not in the current implementat
 - [`documents/CLIENT_IMPLEMENTATION.md`](documents/CLIENT_IMPLEMENTATION.md): client integration contract and framing behavior
 - [`documents/QUBES_OS.md`](documents/QUBES_OS.md): Qubes OS deployment/integration checklist for dedicated signer qubes
 - [`documents/FIPS_DEPLOYMENT.md`](documents/FIPS_DEPLOYMENT.md): Tier-1 FIPS deployment runbook using loopback TCP listener
+- [`plans/qrexec_persistent_bridge.md`](plans/qrexec_persistent_bridge.md): design for the qrexec → unix-socket bridge transport (persistent signer, no mnemonic on disk)
+- [`packaging/qubes/`](packaging/qubes/): qrexec service script, dom0 policy, and setup scripts for Qubes deployment
+- [`examples/n_signer_qube_example_qrexec.js`](examples/n_signer_qube_example_qrexec.js): JavaScript caller example using qrexec (no network, no auth envelope)
+- [`examples/n_signer_qube_example_fips.js`](examples/n_signer_qube_example_fips.js): JavaScript caller example using FIPS/TCP with auth envelope
+- [`examples/get_pubkey_tcp.c`](examples/get_pubkey_tcp.c): C caller example using TCP transport with auth envelope
 - [`plans/nsigner.md`](plans/nsigner.md): implementation plan and sequencing
 - [`plans/seed_phrase_uses.md`](plans/seed_phrase_uses.md): seed phrase domain/use catalog and caveats
 - [`firmware/feather_s3_tft`](firmware/feather_s3_tft): Feather ESP32-S3 Reverse TFT firmware (TinyUSB composite CDC + WebUSB signer PoC)

client/README.md

@@ -1,47 +1,44 @@
-# n_signer C Reference Client
+# n_signer C Client — migrated to `nostr_core_lib`
 
-This directory provides a minimal copy/paste-friendly C client for `n_signer`.
+The hand-rolled `nsigner_client.{c,h}` that previously lived in this directory
+has been **removed**. n_signer now uses the shared, transport-pluggable client
+stack that lives in [`nostr_core_lib`](../resources/nostr_core_lib):
 
-## Files
+- [`nostr_core/nsigner_transport.{h,c}`](../resources/nostr_core_lib/nostr_core/nsigner_transport.h) —
+  pluggable transport vtable (unix-abstract / tcp / usb-cdc serial / fds) + discovery.
+- [`nostr_core/nsigner_client.{h,c}`](../resources/nostr_core_lib/nostr_core/nsigner_client.h) —
+  heap-allocated client: 4-byte length-prefixed framing, kind-27235 auth envelope
+  (self-contained), JSON-RPC verbs, cJSON result parsing, RPC error mapping.
+- [`nostr_core/nostr_signer.{h,c}`](../resources/nostr_core_lib/nostr_core/nostr_signer.h) —
+  high-level `nostr_signer_t` abstraction (local + remote backends, 6 verbs).
 
-- `nsigner_client.h` / `nsigner_client.c`:
-  - Unix abstract socket connect helper
-  - length-prefixed frame send/receive
-  - generic request API
-  - helpers for `get_public_key` and `sign_event`
-  - optional TCP auth envelope attachment via `auth_envelope_build_for_request()`
+This is the single source of truth for the n_signer wire contract. See
+[`nostr_core/NSIGNER_INTEGRATION.md`](../resources/nostr_core_lib/nostr_core/NSIGNER_INTEGRATION.md)
+for the full integration contract.
 
-## API at a glance
+## What moved where
 
-```c
-nsigner_client_t client;
-nsigner_client_init(&client);
+| Old (`client/`) | New (`nostr_core_lib`) |
+|---|---|
+| `nsigner_client_t` (stack) | `nsigner_client_t*` (heap) or `nostr_signer_t*` |
+| `nsigner_client_init` / `connect_unix` / `close` | `nsigner_transport_open_unix` + `nsigner_client_new` / `nsigner_client_free` |
+| `nsigner_client_get_public_key` | `nostr_signer_get_public_key` or `nsigner_client_call(..., "get_public_key", ...)` |
+| `nsigner_client_sign_event` | `nostr_signer_sign_event` or `nsigner_client_call(..., "sign_event", ...)` |
+| `nsigner_client_set_auth` | `nsigner_client_set_auth` or `nostr_signer_nsigner_set_auth` |
+| `nsigner_client_request` / `request_raw` | `nsigner_client_call` (returns parsed cJSON result) |
 
-nsigner_client_connect_unix(&client, "nsigner", 5000);
+## Consumers (updated)
 
-char *resp = NULL;
-nsigner_client_get_public_key(&client, "1", "", &resp);
-free(resp);
+- [`examples/get_public_key_client.c`](../examples/get_public_key_client.c) — uses `nsigner_transport_open_unix` + `nsigner_client_new` + `nsigner_client_call`.
+- [`examples/sign_event_client.c`](../examples/sign_event_client.c) — same pattern.
+- [`tests/test_integration.c`](../tests/test_integration.c) — same pattern; cJSON-based assertions.
 
-nsigner_client_close(&client);
-```
+The `nsigner ... client '<json>'` subcommand in [`src/main.c`](../src/main.c) is
+unaffected — it has its own raw framing pass-through and never used this directory.
 
-## Auth envelope usage
+## Why
 
-If transport requires auth envelopes (for TCP mode), set a private key once:
-
-```c
-unsigned char privkey[32] = { /* caller key */ };
-nsigner_client_set_auth(&client, privkey, "example-client");
-```
-
-Subsequent requests automatically include an `auth` object.
-
-## Ownership rules
-
-- Any `out_response_json` returned by the API must be freed by caller using `free()`.
-- `nsigner_client_close()` only closes the socket; it does not free the client struct itself.
-
-## License
-
-Source files in this directory use SPDX `0BSD` headers for permissive reuse in external projects.
+Per [`plans/nsigner_integration_plan.md`](../resources/nostr_core_lib/plans/nsigner_integration_plan.md)
+(Phase 7): retire per-project hand-rolled clients in favor of the shared module
+in `nostr_core_lib`, so the wire contract has one implementation and downstream
+projects get unix/tcp/serial/fds transports for free.

client/nsigner_client.c

@@ -1,369 +0,0 @@
-/*
- * SPDX-License-Identifier: 0BSD
- */
-
-#define _GNU_SOURCE
-
-#include "nsigner_client.h"
-
-#include <arpa/inet.h>
-#include <errno.h>
-#include <stdarg.h>
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <sys/socket.h>
-#include <sys/types.h>
-#include <sys/un.h>
-#include <time.h>
-#include <unistd.h>
-
-#include <cJSON.h>
-
-#include "auth_envelope.h"
-
-#define NSIGNER_CLIENT_MAX_FRAME (65536U)
-
-static void client_set_error(nsigner_client_t *client, const char *fmt, ...) {
-    va_list ap;
-
-    if (client == NULL) {
-        return;
-    }
-
-    va_start(ap, fmt);
-    vsnprintf(client->last_error, sizeof(client->last_error), fmt, ap);
-    va_end(ap);
-}
-
-static int write_full(int fd, const void *buf, size_t len) {
-    const unsigned char *p = (const unsigned char *)buf;
-    size_t off = 0;
-
-    while (off < len) {
-        ssize_t n = write(fd, p + off, len - off);
-        if (n < 0) {
-            if (errno == EINTR) {
-                continue;
-            }
-            return -1;
-        }
-        off += (size_t)n;
-    }
-
-    return 0;
-}
-
-static int read_full(int fd, void *buf, size_t len) {
-    unsigned char *p = (unsigned char *)buf;
-    size_t off = 0;
-
-    while (off < len) {
-        ssize_t n = read(fd, p + off, len - off);
-        if (n == 0) {
-            return -1;
-        }
-        if (n < 0) {
-            if (errno == EINTR) {
-                continue;
-            }
-            return -1;
-        }
-        off += (size_t)n;
-    }
-
-    return 0;
-}
-
-static int send_framed(int fd, const char *payload) {
-    uint32_t len;
-    uint32_t be_len;
-
-    if (payload == NULL) {
-        return -1;
-    }
-
-    len = (uint32_t)strlen(payload);
-    be_len = htonl(len);
-
-    if (write_full(fd, &be_len, sizeof(be_len)) != 0) {
-        return -1;
-    }
-    if (write_full(fd, payload, len) != 0) {
-        return -1;
-    }
-
-    return 0;
-}
-
-static int recv_framed(int fd, char **out_payload) {
-    uint32_t be_len;
-    uint32_t len;
-    char *payload;
-
-    if (out_payload == NULL) {
-        return -1;
-    }
-
-    *out_payload = NULL;
-
-    if (read_full(fd, &be_len, sizeof(be_len)) != 0) {
-        return -1;
-    }
-
-    len = ntohl(be_len);
-    if (len == 0 || len > NSIGNER_CLIENT_MAX_FRAME) {
-        return -1;
-    }
-
-    payload = (char *)malloc((size_t)len + 1U);
-    if (payload == NULL) {
-        return -1;
-    }
-
-    if (read_full(fd, payload, len) != 0) {
-        free(payload);
-        return -1;
-    }
-
-    payload[len] = '\0';
-    *out_payload = payload;
-    return 0;
-}
-
-static int sleep_ms(int ms) {
-    struct timespec ts;
-    ts.tv_sec = ms / 1000;
-    ts.tv_nsec = (long)(ms % 1000) * 1000000L;
-    return nanosleep(&ts, NULL);
-}
-
-void nsigner_client_init(nsigner_client_t *client) {
-    if (client == NULL) {
-        return;
-    }
-
-    memset(client, 0, sizeof(*client));
-    client->fd = -1;
-    client->timeout_ms = 5000;
-}
-
-void nsigner_client_close(nsigner_client_t *client) {
-    if (client == NULL) {
-        return;
-    }
-
-    if (client->fd >= 0) {
-        close(client->fd);
-        client->fd = -1;
-    }
-}
-
-int nsigner_client_connect_unix(nsigner_client_t *client,
-                                const char *socket_name,
-                                int timeout_ms) {
-    struct sockaddr_un addr;
-    socklen_t addr_len;
-    int elapsed = 0;
-
-    if (client == NULL || socket_name == NULL || socket_name[0] == '\0') {
-        return -1;
-    }
-
-    timeout_ms = (timeout_ms > 0) ? timeout_ms : 5000;
-    nsigner_client_close(client);
-
-    memset(&addr, 0, sizeof(addr));
-    addr.sun_family = AF_UNIX;
-    addr.sun_path[0] = '\0';
-    strncpy(&addr.sun_path[1], socket_name, sizeof(addr.sun_path) - 2);
-    addr.sun_path[sizeof(addr.sun_path) - 1] = '\0';
-    addr_len = (socklen_t)(sizeof(sa_family_t) + 1 + strlen(socket_name));
-
-    while (elapsed < timeout_ms) {
-        int fd = socket(AF_UNIX, SOCK_STREAM, 0);
-        if (fd < 0) {
-            client_set_error(client, "socket failed: %s", strerror(errno));
-            return -1;
-        }
-
-        if (connect(fd, (struct sockaddr *)&addr, addr_len) == 0) {
-            client->fd = fd;
-            client->timeout_ms = timeout_ms;
-            client_set_error(client, "ok");
-            return 0;
-        }
-
-        close(fd);
-        sleep_ms(100);
-        elapsed += 100;
-    }
-
-    client_set_error(client, "connect timeout: %s", strerror(errno));
-    return -1;
-}
-
-int nsigner_client_set_auth(nsigner_client_t *client,
-                            const unsigned char privkey[32],
-                            const char *label) {
-    if (client == NULL || privkey == NULL) {
-        return -1;
-    }
-
-    memcpy(client->auth_privkey, privkey, 32);
-    client->auth_enabled = 1;
-
-    if (label == NULL) {
-        label = "";
-    }
-    strncpy(client->auth_label, label, sizeof(client->auth_label) - 1);
-    client->auth_label[sizeof(client->auth_label) - 1] = '\0';
-
-    return 0;
-}
-
-const char *nsigner_client_last_error(const nsigner_client_t *client) {
-    if (client == NULL) {
-        return "invalid_client";
-    }
-    return client->last_error;
-}
-
-int nsigner_client_request_raw(nsigner_client_t *client,
-                               const char *request_json,
-                               char **out_response_json) {
-    char *response_json = NULL;
-
-    if (client == NULL || request_json == NULL || out_response_json == NULL) {
-        return -1;
-    }
-    if (client->fd < 0) {
-        client_set_error(client, "not connected");
-        return -1;
-    }
-
-    *out_response_json = NULL;
-
-    if (send_framed(client->fd, request_json) != 0) {
-        client_set_error(client, "send failed");
-        return -1;
-    }
-
-    if (recv_framed(client->fd, &response_json) != 0) {
-        client_set_error(client, "receive failed");
-        return -1;
-    }
-
-    *out_response_json = response_json;
-    client_set_error(client, "ok");
-    return 0;
-}
-
-int nsigner_client_request(nsigner_client_t *client,
-                           const char *id,
-                           const char *method,
-                           const cJSON *params,
-                           char **out_response_json) {
-    cJSON *root = NULL;
-    cJSON *params_copy = NULL;
-    cJSON *auth = NULL;
-    char *request_json = NULL;
-    int rc = -1;
-
-    if (client == NULL || id == NULL || method == NULL || out_response_json == NULL) {
-        return -1;
-    }
-
-    root = cJSON_CreateObject();
-    if (root == NULL) {
-        client_set_error(client, "out of memory");
-        goto cleanup;
-    }
-
-    cJSON_AddStringToObject(root, "id", id);
-    cJSON_AddStringToObject(root, "method", method);
-
-    if (params != NULL) {
-        params_copy = cJSON_Duplicate((cJSON *)params, 1);
-    } else {
-        params_copy = cJSON_CreateArray();
-    }
-
-    if (params_copy == NULL) {
-        client_set_error(client, "failed to create params");
-        goto cleanup;
-    }
-    cJSON_AddItemToObject(root, "params", params_copy);
-
-    if (client->auth_enabled) {
-        if (auth_envelope_build_for_request(id,
-                                            method,
-                                            params_copy,
-                                            client->auth_privkey,
-                                            client->auth_label,
-                                            time(NULL),
-                                            &auth) != 0) {
-            client_set_error(client, "failed to build auth envelope");
-            goto cleanup;
-        }
-        cJSON_AddItemToObject(root, "auth", auth);
-        auth = NULL;
-    }
-
-    request_json = cJSON_PrintUnformatted(root);
-    if (request_json == NULL) {
-        client_set_error(client, "failed to serialize request");
-        goto cleanup;
-    }
-
-    rc = nsigner_client_request_raw(client, request_json, out_response_json);
-
-cleanup:
-    cJSON_Delete(root);
-    cJSON_Delete(auth);
-    free(request_json);
-    return rc;
-}
-
-int nsigner_client_get_public_key(nsigner_client_t *client,
-                                  const char *id,
-                                  const char *selector,
-                                  char **out_response_json) {
-    cJSON *params = cJSON_CreateArray();
-    int rc;
-
-    if (params == NULL) {
-        return -1;
-    }
-
-    cJSON_AddItemToArray(params, cJSON_CreateString((selector != NULL) ? selector : ""));
-    rc = nsigner_client_request(client, id, "get_public_key", params, out_response_json);
-    cJSON_Delete(params);
-    return rc;
-}
-
-int nsigner_client_sign_event(nsigner_client_t *client,
-                              const char *id,
-                              const char *event_json,
-                              const char *role,
-                              char **out_response_json) {
-    cJSON *params = cJSON_CreateArray();
-    cJSON *opts = cJSON_CreateObject();
-    int rc;
-
-    if (params == NULL || opts == NULL || event_json == NULL) {
-        cJSON_Delete(params);
-        cJSON_Delete(opts);
-        return -1;
-    }
-
-    cJSON_AddItemToArray(params, cJSON_CreateString(event_json));
-    if (role != NULL && role[0] != '\0') {
-        cJSON_AddStringToObject(opts, "role", role);
-    }
-    cJSON_AddItemToArray(params, opts);
-
-    rc = nsigner_client_request(client, id, "sign_event", params, out_response_json);
-    cJSON_Delete(params);
-    return rc;
-}

client/nsigner_client.h

@@ -1,56 +0,0 @@
-/*
- * SPDX-License-Identifier: 0BSD
- */
-
-#ifndef NSIGNER_CLIENT_H
-#define NSIGNER_CLIENT_H
-
-#include <stddef.h>
-#include <stdint.h>
-
-#include <cJSON.h>
-
-typedef struct {
-    int fd;
-    int timeout_ms;
-    unsigned char auth_privkey[32];
-    int auth_enabled;
-    char auth_label[64];
-    char last_error[128];
-} nsigner_client_t;
-
-void nsigner_client_init(nsigner_client_t *client);
-void nsigner_client_close(nsigner_client_t *client);
-
-int nsigner_client_connect_unix(nsigner_client_t *client,
-                                const char *socket_name,
-                                int timeout_ms);
-
-int nsigner_client_set_auth(nsigner_client_t *client,
-                            const unsigned char privkey[32],
-                            const char *label);
-
-const char *nsigner_client_last_error(const nsigner_client_t *client);
-
-int nsigner_client_request_raw(nsigner_client_t *client,
-                               const char *request_json,
-                               char **out_response_json);
-
-int nsigner_client_request(nsigner_client_t *client,
-                           const char *id,
-                           const char *method,
-                           const cJSON *params,
-                           char **out_response_json);
-
-int nsigner_client_get_public_key(nsigner_client_t *client,
-                                  const char *id,
-                                  const char *selector,
-                                  char **out_response_json);
-
-int nsigner_client_sign_event(nsigner_client_t *client,
-                              const char *id,
-                              const char *event_json,
-                              const char *role,
-                              char **out_response_json);
-
-#endif

documents/QUBES_OS.md

@@ -160,6 +160,58 @@ Includes:
 - missing policy -> deny path
 - missing `QREXEC_REMOTE_DOMAIN` -> fallback identity path
 
+## 5.5 USB keyboard firmware workflows in a PCI-USB-controller qube
+
+When a full USB controller is assigned directly to a qube via PCI passthrough, HID input does **not** flow through `sys-usb` input proxy policy. In this setup, keyboard-class USB blocking is usually caused by `usbguard` inside the owning qube.
+
+### Scope check (dom0)
+
+```bash
+qvm-prefs AI klass
+```
+
+- `StandaloneVM`: service state changes in the qube root filesystem persist.
+- `AppVM`: root filesystem state resets at reboot; use `/rw/config/rc.local` for per-qube persistence.
+
+### Disable usbguard immediately (inside AI qube)
+
+```bash
+sudo systemctl disable --now usbguard
+sudo systemctl mask usbguard
+```
+
+### Persist behavior across reboot
+
+- **StandaloneVM**: the mask persists as-is.
+- **AppVM**: persist with `/rw/config/rc.local`:
+
+```bash
+sudo tee /rw/config/rc.local >/dev/null <<'EOF'
+#!/bin/sh
+systemctl stop usbguard 2>/dev/null || true
+systemctl mask usbguard 2>/dev/null || true
+EOF
+sudo chmod +x /rw/config/rc.local
+```
+
+### Restart + verify
+
+```bash
+# dom0
+qvm-shutdown --wait AI && qvm-start AI
+
+# inside AI qube
+systemctl is-enabled usbguard
+lsusb
+ls /dev/ttyACM*
+```
+
+Expected result: `usbguard` is `masked`, the keyboard-class device enumerates, and serial/WebUSB workflows remain usable.
+
+### Security trade-off
+
+Disabling `usbguard` removes an important BadUSB defense for that qube. Keep this configuration limited to a dedicated hardware-development qube and avoid using it for general browsing or untrusted USB devices.
+
 ---
 
 ## 6. Security requirements

examples/get_pubkey_tcp.c

@@ -0,0 +1,195 @@
+/*
+ * get_pubkey_tcp.c — connect to a running n_signer over TCP and call
+ * get_public_key for nostr_index 0 and 1, printing both hex pubkey and
+ * bech32 npub for each.
+ *
+ * This is a cross-qube test client for Qubes OS: the signer runs in the
+ * nostr_signer qube listening on tcp:[::]:8080, and this client runs in
+ * a different qube connecting to the signer's FIPS address.
+ *
+ * Usage:
+ *   ./get_pubkey_tcp <host> <port>
+ *   ./get_pubkey_tcp npub1xxx...fips 8080
+ *
+ * If no arguments are given, defaults to localhost:8080.
+ *
+ * Output: for each index, prints:
+ *   index 0: hex=<64 hex chars>  npub=npub1...
+ */
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "nostr_common.h"
+#include "nsigner_transport.h"
+#include "nsigner_client.h"
+#include "nip019.h"
+#include "../cjson/cJSON.h"
+
+/* Demo caller key (32 bytes). Replace with your stable caller key in real use. */
+static const unsigned char DEMO_PRIVKEY[32] = {
+    1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
+    17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32
+};
+
+static int hex_to_bytes(const char *hex, unsigned char *out, size_t out_len) {
+    size_t len = strlen(hex);
+    if (len != out_len * 2) {
+        return -1;
+    }
+    for (size_t i = 0; i < out_len; i++) {
+        unsigned int byte;
+        if (sscanf(hex + 2 * i, "%2x", &byte) != 1) {
+            return -1;
+        }
+        out[i] = (unsigned char)byte;
+    }
+    return 0;
+}
+
+static int query_pubkey(const char *host, int port, int nostr_index,
+                        char *out_hex, size_t hex_size, char *out_npub, size_t npub_size) {
+    (void)npub_size; /* npub buffer size is enforced by nostr_key_to_bech32 output */
+    nsigner_transport_t *transport = NULL;
+    nsigner_client_t *client = NULL;
+    cJSON *params = NULL;
+    cJSON *opts = NULL;
+    cJSON *result = NULL;
+    const char *hex_pubkey = NULL;
+    unsigned char pubkey_bytes[32];
+    int rc = -1;
+
+    transport = nsigner_transport_open_tcp(host, port, 10000);
+    if (transport == NULL) {
+        fprintf(stderr, "connect failed: cannot open TCP transport to %s:%d\n", host, port);
+        goto cleanup;
+    }
+
+    client = nsigner_client_new(transport);
+    if (client == NULL) {
+        fprintf(stderr, "connect failed: cannot create nsigner client\n");
+        transport->close(transport);
+        goto cleanup;
+    }
+    transport = NULL; /* owned by client now */
+
+    /* Set auth envelope — required for TCP listeners */
+    if (nsigner_client_set_auth(client, DEMO_PRIVKEY, "get_pubkey_tcp") != NOSTR_SUCCESS) {
+        fprintf(stderr, "failed to set auth envelope\n");
+        goto cleanup;
+    }
+
+    /* params: [{"nostr_index": N}] */
+    params = cJSON_CreateArray();
+    if (params == NULL) {
+        fprintf(stderr, "out of memory\n");
+        goto cleanup;
+    }
+    opts = cJSON_CreateObject();
+    if (opts == NULL) {
+        fprintf(stderr, "out of memory\n");
+        goto cleanup;
+    }
+    cJSON_AddNumberToObject(opts, "nostr_index", nostr_index);
+    cJSON_AddItemToArray(params, opts);
+    opts = NULL;
+
+    if (nsigner_client_call(client, "get_public_key", params, &result) != NOSTR_SUCCESS) {
+        fprintf(stderr, "request failed for index %d: %s\n", nostr_index,
+                nsigner_client_last_error(client));
+        params = NULL; /* nsigner_client_call took ownership even on failure */
+        goto cleanup;
+    }
+    params = NULL; /* nsigner_client_call took ownership */
+
+    if (!cJSON_IsString(result)) {
+        fprintf(stderr, "index %d: unexpected result type\n", nostr_index);
+        goto cleanup;
+    }
+
+    hex_pubkey = result->valuestring;
+    if (strlen(hex_pubkey) != 64) {
+        fprintf(stderr, "index %d: unexpected pubkey length: %zu\n", nostr_index, strlen(hex_pubkey));
+        goto cleanup;
+    }
+
+    strncpy(out_hex, hex_pubkey, hex_size - 1);
+    out_hex[hex_size - 1] = '\0';
+
+    /* Convert hex pubkey to npub (bech32) */
+    if (hex_to_bytes(hex_pubkey, pubkey_bytes, 32) != 0) {
+        fprintf(stderr, "index %d: failed to parse hex pubkey\n", nostr_index);
+        goto cleanup;
+    }
+    if (nostr_key_to_bech32(pubkey_bytes, "npub", out_npub) != NOSTR_SUCCESS) {
+        fprintf(stderr, "index %d: failed to convert to npub\n", nostr_index);
+        goto cleanup;
+    }
+
+    rc = 0;
+
+cleanup:
+    cJSON_Delete(opts);
+    cJSON_Delete(params);
+    cJSON_Delete(result);
+    nsigner_client_free(client);
+    return rc;
+}
+
+int main(int argc, char **argv) {
+    const char *host = "127.0.0.1";
+    int port = 8080;
+    char hex0[65], npub0[128];
+    char hex1[65], npub1[128];
+    int failures = 0;
+
+    if (argc > 1) {
+        host = argv[1];
+    }
+    if (argc > 2) {
+        port = atoi(argv[2]);
+        if (port <= 0 || port > 65535) {
+            fprintf(stderr, "Invalid port: %s\n", argv[2]);
+            return 1;
+        }
+    }
+
+    if (nostr_init() != NOSTR_SUCCESS) {
+        fprintf(stderr, "failed to initialize crypto subsystem\n");
+        return 1;
+    }
+
+    printf("Connecting to n_signer at %s:%d\n", host, port);
+    printf("Querying get_public_key for nostr_index 0 and 1...\n\n");
+
+    /* Query index 0 */
+    hex0[0] = '\0';
+    npub0[0] = '\0';
+    if (query_pubkey(host, port, 0, hex0, sizeof(hex0), npub0, sizeof(npub0)) == 0) {
+        printf("index 0: hex=%s  npub=%s\n", hex0, npub0);
+    } else {
+        printf("index 0: FAILED\n");
+        failures++;
+    }
+
+    /* Query index 1 */
+    hex1[0] = '\0';
+    npub1[0] = '\0';
+    if (query_pubkey(host, port, 1, hex1, sizeof(hex1), npub1, sizeof(npub1)) == 0) {
+        printf("index 1: hex=%s  npub=%s\n", hex1, npub1);
+    } else {
+        printf("index 1: FAILED\n");
+        failures++;
+    }
+
+    nostr_cleanup();
+
+    if (failures > 0) {
+        printf("\n%d query(s) failed\n", failures);
+        return 1;
+    }
+
+    printf("\nAll queries succeeded\n");
+    return 0;
+}

examples/get_public_key_client.c

@@ -1,32 +1,100 @@
+/*
+ * get_public_key_client.c — connect to a running n_signer over its abstract
+ * UNIX socket and call get_public_key, using the shared nsigner client from
+ * nostr_core_lib (nostr_core/nsigner_client.h + nostr_core/nsigner_transport.h).
+ *
+ * Usage: ./get_public_key_client [socket_name]
+ *
+ * Output: the raw JSON-RPC response string, e.g.
+ *         {"id":"1","result":"<pubkey hex>"}
+ */
+
 #include <stdio.h>
 #include <stdlib.h>
+#include <string.h>
 
-#include "../client/nsigner_client.h"
+#include "nostr_common.h"
+#include "nsigner_transport.h"
+#include "nsigner_client.h"
+#include "../cjson/cJSON.h"
 
 int main(int argc, char **argv) {
     const char *socket_name = "nsigner";
-    nsigner_client_t client;
-    char *response = NULL;
+    nsigner_transport_t *transport = NULL;
+    nsigner_client_t *client = NULL;
+    cJSON *params = NULL;
+    cJSON *result = NULL;
+    cJSON *response = NULL;
+    char *response_json = NULL;
+    int rc = 1;
 
     if (argc > 1 && argv[1] != NULL && argv[1][0] != '\0') {
         socket_name = argv[1];
     }
 
-    nsigner_client_init(&client);
-
-    if (nsigner_client_connect_unix(&client, socket_name, 5000) != 0) {
-        fprintf(stderr, "connect failed: %s\n", nsigner_client_last_error(&client));
+    if (nostr_init() != NOSTR_SUCCESS) {
+        fprintf(stderr, "failed to initialize crypto subsystem\n");
         return 1;
     }
 
-    if (nsigner_client_get_public_key(&client, "example-1", "", &response) != 0) {
-        fprintf(stderr, "request failed: %s\n", nsigner_client_last_error(&client));
-        nsigner_client_close(&client);
-        return 1;
+    transport = nsigner_transport_open_unix(socket_name, 5000);
+    if (transport == NULL) {
+        fprintf(stderr, "connect failed: cannot open unix transport @%s\n", socket_name);
+        goto cleanup;
     }
 
-    printf("%s\n", response);
-    free(response);
-    nsigner_client_close(&client);
-    return 0;
+    client = nsigner_client_new(transport);
+    if (client == NULL) {
+        fprintf(stderr, "connect failed: cannot create nsigner client\n");
+        /* nsigner_client_new takes ownership of transport on success only */
+        transport->close(transport);
+        goto cleanup;
+    }
+    transport = NULL; /* owned by client now */
+
+    /* params: [] (empty array — server picks the default role) */
+    params = cJSON_CreateArray();
+    if (params == NULL) {
+        fprintf(stderr, "out of memory\n");
+        goto cleanup;
+    }
+
+    if (nsigner_client_call(client, "get_public_key", params, &result) != NOSTR_SUCCESS) {
+        fprintf(stderr, "request failed: %s\n", nsigner_client_last_error(client));
+        goto cleanup;
+    }
+    params = NULL; /* nsigner_client_call takes ownership of params */
+
+    /*
+     * Reconstruct a JSON-RPC response string so the CLI output stays
+     * backward-compatible with the old client example:
+     *   {"id":"<id>","result":"<pubkey hex>"}
+     * nsigner_client_call returns only the parsed `result` element and does
+     * not expose the server-assigned id, so we emit a minimal envelope.
+     */
+    response = cJSON_CreateObject();
+    if (response == NULL) {
+        fprintf(stderr, "out of memory\n");
+        goto cleanup;
+    }
+    cJSON_AddStringToObject(response, "id", "1");
+    cJSON_AddItemReferenceToObject(response, "result", result);
+
+    response_json = cJSON_PrintUnformatted(response);
+    if (response_json == NULL) {
+        fprintf(stderr, "failed to serialize response\n");
+        goto cleanup;
+    }
+
+    printf("%s\n", response_json);
+    rc = 0;
+
+cleanup:
+    free(response_json);
+    cJSON_Delete(response);
+    cJSON_Delete(result);
+    cJSON_Delete(params);
+    nsigner_client_free(client); /* also closes/frees the transport */
+    nostr_cleanup();
+    return rc;
 }

examples/kb2040_hidden_signer_client.py

@@ -0,0 +1,214 @@
+#!/usr/bin/env python3
+"""
+KB2040 Hidden Signer host client (WebUSB/vendor interface via pyusb).
+
+Protocol:
+  4-byte big-endian length + UTF-8 JSON body.
+
+Default target:
+  VID:PID 239a:8104
+
+Examples:
+  python3 examples/kb2040_hidden_signer_client.py status
+  python3 examples/kb2040_hidden_signer_client.py set-mnemonic --mnemonic "abandon ... about"
+  python3 examples/kb2040_hidden_signer_client.py get-public-key
+  python3 examples/kb2040_hidden_signer_client.py sign-event --event '{"kind":1,"content":"hello"}'
+"""
+
+import argparse
+import json
+import struct
+import sys
+import time
+
+try:
+    import usb.core
+    import usb.util
+except ImportError:
+    print("Missing pyusb. Install with: pip install pyusb", file=sys.stderr)
+    sys.exit(2)
+
+
+def find_vendor_interface(dev):
+    cfg = dev.get_active_configuration()
+    for itf in cfg:
+        if itf.bInterfaceClass == 0xFF:
+            ep_out = None
+            ep_in = None
+            for ep in itf:
+                direction = usb.util.endpoint_direction(ep.bEndpointAddress)
+                if direction == usb.util.ENDPOINT_OUT:
+                    ep_out = ep
+                elif direction == usb.util.ENDPOINT_IN:
+                    ep_in = ep
+            if ep_out is not None and ep_in is not None:
+                return itf, ep_out, ep_in
+    return None, None, None
+
+
+def open_device(vid: int, pid: int):
+    dev = usb.core.find(idVendor=vid, idProduct=pid)
+    if dev is None:
+        raise RuntimeError(f"Device {vid:04x}:{pid:04x} not found")
+
+    try:
+        dev.set_configuration()
+    except usb.core.USBError:
+        pass
+
+    itf, ep_out, ep_in = find_vendor_interface(dev)
+    if itf is None:
+        raise RuntimeError("Vendor/WebUSB interface (class 0xFF) not found")
+
+    itf_num = itf.bInterfaceNumber
+    try:
+        if dev.is_kernel_driver_active(itf_num):
+            dev.detach_kernel_driver(itf_num)
+    except (NotImplementedError, usb.core.USBError):
+        pass
+
+    usb.util.claim_interface(dev, itf_num)
+
+    # WebUSB-style connect handshake (CDC SET_CONTROL_LINE_STATE / request 0x22).
+    # Firmware gates IN transfers on this "connected" state.
+    try:
+        dev.ctrl_transfer(0x21, 0x22, 0x0001, itf_num, None)
+    except usb.core.USBError:
+        # Some stacks may not require/implement this; continue and let RPC I/O decide.
+        pass
+
+    return dev, itf_num, ep_out, ep_in
+
+
+def close_device(dev, itf_num: int):
+    try:
+        usb.util.release_interface(dev, itf_num)
+    except usb.core.USBError:
+        pass
+
+
+_rx_remainder = bytearray()
+
+
+def send_frame(ep_out, payload: bytes):
+    frame = struct.pack(">I", len(payload)) + payload
+    ep_out.write(frame)
+
+
+def recv_exact(ep_in, n: int, timeout_ms: int):
+    global _rx_remainder
+
+    out = bytearray()
+
+    # Consume previously over-read bytes first.
+    if _rx_remainder:
+        take = min(n, len(_rx_remainder))
+        out.extend(_rx_remainder[:take])
+        del _rx_remainder[:take]
+
+    deadline = time.time() + max(1.0, timeout_ms / 1000.0)
+    packet_size = max(64, int(getattr(ep_in, "wMaxPacketSize", 64)))
+
+    while len(out) < n and time.time() < deadline:
+        chunk = ep_in.read(packet_size, timeout=timeout_ms)
+        out.extend(bytes(chunk))
+
+    if len(out) < n:
+        raise TimeoutError(f"Timeout while reading {n} bytes (got {len(out)})")
+
+    if len(out) > n:
+        _rx_remainder.extend(out[n:])
+        del out[n:]
+
+    return bytes(out)
+
+
+def recv_frame(ep_in, timeout_ms: int):
+    hdr = recv_exact(ep_in, 4, timeout_ms)
+    body_len = struct.unpack(">I", hdr)[0]
+    if body_len > 64 * 1024:
+        raise ValueError(f"Refusing oversized frame: {body_len}")
+    body = recv_exact(ep_in, body_len, timeout_ms)
+    return body
+
+
+def rpc(dev_args, method: str, params: dict):
+    global _rx_remainder
+
+    dev, itf_num, ep_out, ep_in = open_device(dev_args.vid, dev_args.pid)
+    try:
+        _rx_remainder.clear()
+        req = {"method": method}
+        req.update(params)
+        payload = json.dumps(req, separators=(",", ":")).encode("utf-8")
+        send_frame(ep_out, payload)
+        resp = recv_frame(ep_in, dev_args.timeout_ms)
+        return json.loads(resp.decode("utf-8", errors="replace"))
+    finally:
+        close_device(dev, itf_num)
+
+
+def cmd_status(args):
+    print(json.dumps(rpc(args, "get_status", {}), indent=2))
+
+
+def cmd_set_mnemonic(args):
+    print(json.dumps(rpc(args, "set_mnemonic", {"mnemonic": args.mnemonic}), indent=2))
+
+
+def cmd_set_auto_approve(args):
+    value = args.value.lower() in ("1", "true", "yes", "on")
+    print(json.dumps(rpc(args, "set_auto_approve", {"value": value}), indent=2))
+
+
+def cmd_get_public_key(args):
+    print(json.dumps(rpc(args, "get_public_key", {}), indent=2))
+
+
+def cmd_sign_event(args):
+    event = json.loads(args.event)
+    print(json.dumps(rpc(args, "sign_event", {"event": event}), indent=2))
+
+
+def build_parser():
+    p = argparse.ArgumentParser()
+    p.add_argument("--vid", type=lambda s: int(s, 16), default=0x239A, help="USB VID in hex (default: 239A)")
+    p.add_argument("--pid", type=lambda s: int(s, 16), default=0x8104, help="USB PID in hex (default: 8104)")
+    p.add_argument("--timeout-ms", type=int, default=3000, help="USB read timeout in ms")
+
+    sub = p.add_subparsers(dest="cmd", required=True)
+
+    s = sub.add_parser("status")
+    s.set_defaults(func=cmd_status)
+
+    s = sub.add_parser("set-mnemonic")
+    s.add_argument("--mnemonic", required=True)
+    s.set_defaults(func=cmd_set_mnemonic)
+
+    s = sub.add_parser("set-auto-approve")
+    s.add_argument("--value", required=True, help="true|false")
+    s.set_defaults(func=cmd_set_auto_approve)
+
+    s = sub.add_parser("get-public-key")
+    s.set_defaults(func=cmd_get_public_key)
+
+    s = sub.add_parser("sign-event")
+    s.add_argument("--event", required=True, help="JSON object string")
+    s.set_defaults(func=cmd_sign_event)
+
+    return p
+
+
+def main():
+    parser = build_parser()
+    args = parser.parse_args()
+    try:
+        args.func(args)
+        return 0
+    except Exception as e:
+        print(f"ERROR: {e}", file=sys.stderr)
+        return 1
+
+
+if __name__ == "__main__":
+    sys.exit(main())

examples/n_signer_qube_example_fips.js

@@ -0,0 +1,257 @@
+#!/usr/bin/env node
+/**
+ * n_signer_qube_example.js — connect to a running n_signer over TCP (FIPS mesh)
+ * and call get_public_key for nostr_index 0 and 1, printing both hex pubkey
+ * and bech32 npub for each.
+ *
+ * This is a cross-qube test client for Qubes OS: the signer runs in the
+ * nostr_signer qube listening on tcp:[::]:8080, and this client runs in
+ * a different qube connecting to the signer's FIPS address.
+ *
+ * Usage:
+ *   node n_signer_qube_example.js [host] [port]
+ *   node n_signer_qube_example.js fd56:d7c3:f605:719d:15b:18a0:fb06:982f 8080
+ *
+ * If no arguments are given, defaults to localhost:8080.
+ *
+ * Protocol:
+ *   - 4-byte big-endian length prefix + JSON payload (TCP framing)
+ *   - JSON-RPC: {"id":"...","method":"get_public_key","params":[{"nostr_index":N}],"auth":{...}}
+ *   - Auth envelope: kind 27235 Nostr event with nsigner_rpc, nsigner_method,
+ *     nsigner_body_hash tags. body_hash = sha256(json.dumps(params))
+ *   - Response: {"id":"...","result":"<pubkey hex>"} or {"id":"...","error":{...}}
+ */
+
+const net = require("net");
+const crypto = require("crypto");
+const secp = require("@noble/secp256k1");
+
+// @noble/secp256k1 v3 requires us to provide sync sha256/hmacSha256
+secp.hashes.sha256 = (msg) => new Uint8Array(crypto.createHash("sha256").update(msg).digest());
+secp.hashes.hmacSha256 = (key, msg) =>
+  new Uint8Array(crypto.createHmac("sha256", key).update(msg).digest());
+
+const { schnorr } = secp;
+
+/** Convert a Uint8Array to a hex string. */
+function bytesToHex(bytes) {
+  return Array.from(bytes, (b) => b.toString(16).padStart(2, "0")).join("");
+}
+
+/** Convert a hex string to a Uint8Array. */
+function hexToBytes(hex) {
+  const arr = new Uint8Array(hex.length / 2);
+  for (let i = 0; i < arr.length; i++) {
+    arr[i] = parseInt(hex.substr(i * 2, 2), 16);
+  }
+  return arr;
+}
+
+// Demo caller key (32 bytes). Replace with your stable caller key in real use.
+const DEMO_PRIVKEY = new Uint8Array(Array.from({ length: 32 }, (_, i) => i + 1));
+
+/**
+ * Compute the body hash for a params array.
+ * This must match n_signer's hashing: sha256 of canonical JSON (no spaces).
+ */
+function computeBodyHash(params) {
+  const canonical = JSON.stringify(params);
+  return crypto.createHash("sha256").update(canonical).digest("hex");
+}
+
+/**
+ * Build a kind-27235 auth envelope for the given method and params.
+ * Returns the auth object to include in the JSON-RPC request.
+ */
+function buildAuthEnvelope(privkey, method, params, requestId) {
+  const bodyHash = computeBodyHash(params);
+  const pubkeyHex = bytesToHex(schnorr.getPublicKey(privkey));
+  const createdAt = Math.floor(Date.now() / 1000);
+
+  // nsigner_rpc tag value MUST match the JSON-RPC request "id" field
+  const tags = [
+    ["nsigner_rpc", requestId],
+    ["nsigner_method", method],
+    ["nsigner_body_hash", bodyHash],
+  ];
+
+  const content = "js-example";
+
+  // Serialize the event for signing: [0, pubkey, created_at, kind, tags, content]
+  const serialized = JSON.stringify([
+    0,
+    pubkeyHex,
+    createdAt,
+    27235,
+    tags,
+    content,
+  ]);
+
+  const eventId = crypto.createHash("sha256").update(serialized).digest("hex");
+  const sig = bytesToHex(schnorr.sign(hexToBytes(eventId), privkey, new Uint8Array(32)));
+
+  return {
+    id: eventId,
+    pubkey: pubkeyHex,
+    created_at: createdAt,
+    kind: 27235,
+    tags: tags,
+    content: content,
+    sig: sig,
+  };
+}
+
+/**
+ * Send a framed JSON-RPC request over a TCP socket and receive the response.
+ * Framing: 4-byte big-endian length prefix + JSON payload.
+ */
+function sendRequest(socket, request) {
+  return new Promise((resolve, reject) => {
+    const payload = Buffer.from(JSON.stringify(request), "utf8");
+    const header = Buffer.alloc(4);
+    header.writeUInt32BE(payload.length, 0);
+    socket.write(Buffer.concat([header, payload]));
+
+    let headerBuf = Buffer.alloc(0);
+    let bodyBuf = Buffer.alloc(0);
+    let bodyLen = 0;
+    let state = "header";
+
+    const onData = (chunk) => {
+      if (state === "header") {
+        headerBuf = Buffer.concat([headerBuf, chunk]);
+        if (headerBuf.length >= 4) {
+          bodyLen = headerBuf.readUInt32BE(0);
+          const remaining = headerBuf.subarray(4);
+          headerBuf = Buffer.alloc(0);
+          state = "body";
+          if (remaining.length > 0) {
+            bodyBuf = Buffer.concat([bodyBuf, remaining]);
+          }
+          if (bodyBuf.length >= bodyLen) {
+            finish();
+          }
+        }
+      } else if (state === "body") {
+        bodyBuf = Buffer.concat([bodyBuf, chunk]);
+        if (bodyBuf.length >= bodyLen) {
+          finish();
+        }
+      }
+    };
+
+    function finish() {
+      socket.off("data", onData);
+      socket.off("error", onError);
+      const body = bodyBuf.subarray(0, bodyLen).toString("utf8");
+      try {
+        resolve(JSON.parse(body));
+      } catch (e) {
+        reject(new Error(`Failed to parse response: ${e.message}`));
+      }
+    }
+
+    function onError(err) {
+      socket.off("data", onData);
+      reject(err);
+    }
+
+    socket.on("data", onData);
+    socket.on("error", onError);
+  });
+}
+
+/**
+ * Query get_public_key for a given nostr_index.
+ * Opens a fresh TCP connection for each request (n_signer handles one request
+ * per connection).
+ */
+async function getPublicKey(host, port, nostrIndex, privkey) {
+  const params = [{ nostr_index: nostrIndex }];
+  const requestId = String(nostrIndex);
+  const auth = buildAuthEnvelope(privkey, "get_public_key", params, requestId);
+
+  const request = {
+    id: requestId,
+    method: "get_public_key",
+    params: params,
+    auth: auth,
+  };
+
+  return new Promise((resolve, reject) => {
+    const socket = new net.Socket();
+    socket.setTimeout(15000);
+
+    socket.connect(port, host, async () => {
+      try {
+        const response = await sendRequest(socket, request);
+        socket.destroy();
+        resolve(response);
+      } catch (e) {
+        socket.destroy();
+        reject(e);
+      }
+    });
+
+    socket.on("timeout", () => {
+      socket.destroy();
+      reject(new Error("Connection timed out"));
+    });
+
+    socket.on("error", (err) => {
+      reject(err);
+    });
+  });
+}
+
+/**
+ * Convert a 32-byte hex pubkey to bech32 npub format (NIP-19).
+ */
+function hexToNpub(pubkeyHex) {
+  const { nip19 } = require("nostr-tools");
+  return nip19.npubEncode(pubkeyHex);
+}
+
+async function main() {
+  const host = process.argv[2] || "127.0.0.1";
+  const port = parseInt(process.argv[3] || "8080", 10);
+
+  console.log(`Connecting to n_signer at ${host}:${port}`);
+  console.log("Querying get_public_key for nostr_index 0 and 1...\n");
+
+  let failures = 0;
+
+  for (const index of [0, 1]) {
+    // Small delay between requests to avoid auth nonce collision
+    // (the auth envelope uses created_at as part of the nonce)
+    if (index > 0) await new Promise((r) => setTimeout(r, 1100));
+    try {
+      const response = await getPublicKey(host, port, index, DEMO_PRIVKEY);
+
+      if (response.error) {
+        console.log(`index ${index}: ERROR: ${JSON.stringify(response.error)}`);
+        failures++;
+        continue;
+      }
+
+      const pubkeyHex = response.result;
+      const npub = hexToNpub(pubkeyHex);
+      console.log(`index ${index}: hex=${pubkeyHex}  npub=${npub}`);
+    } catch (e) {
+      console.log(`index ${index}: FAILED - ${e.message}`);
+      failures++;
+    }
+  }
+
+  if (failures > 0) {
+    console.log(`\n${failures} query(s) failed`);
+    process.exit(1);
+  }
+
+  console.log("\nAll queries succeeded");
+}
+
+main().catch((e) => {
+  console.error(e);
+  process.exit(1);
+});

examples/n_signer_qube_example_qrexec.js

@@ -0,0 +1,155 @@
+#!/usr/bin/env node
+/**
+ * n_signer_qube_example_qrexec.js — connect to n_signer in the nostr_signer
+ * qube via Qubes qrexec (qubes.NsignerRpc service) and call get_public_key
+ * for nostr_index 0 and 1, printing both hex pubkey and bech32 npub.
+ *
+ * This uses Qubes OS's built-in secure IPC (qrexec) instead of FIPS TCP.
+ * No network connectivity is required — all traffic stays within the host.
+ *
+ * Prerequisites:
+ *   - The qubes.NsignerRpc service must be installed in the nostr_signer qube
+ *     (see packaging/qubes/install-service.sh)
+ *   - The qrexec policy must be installed in dom0
+ *     (see packaging/qubes/install-policy.sh)
+ *   - The nostr_signer qube must be tagged with 'nsigner-signer'
+ *     (qvm-tags nostr_signer add nsigner-signer)
+ *   - A mnemonic file must exist at /home/user/.nsigner_mnemonic in the
+ *     nostr_signer qube
+ *
+ * Usage:
+ *   node n_signer_qube_example_qrexec.js [target_qube]
+ *   node n_signer_qube_example_qrexec.js nostr_signer
+ *
+ * If no argument is given, defaults to "nostr_signer".
+ *
+ * Protocol:
+ *   - qrexec-client-vm spawns the qubes.NsignerRpc service in the target qube
+ *   - The service runs: nsigner --listen qrexec --allow-all --mnemonic-fd 3
+ *   - We send one framed JSON-RPC request via stdin, receive one framed response via stdout
+ *   - Framing: 4-byte big-endian length prefix + JSON payload
+ *   - Auth: not required in qrexec mode (caller identity is qubes:<source-vm>)
+ */
+
+const { spawn } = require("child_process");
+const { nip19 } = require("nostr-tools");
+
+/**
+ * Frame a JSON-RPC request: 4-byte big-endian length + JSON payload.
+ */
+function frameRequest(obj) {
+  const payload = Buffer.from(JSON.stringify(obj), "utf8");
+  const header = Buffer.alloc(4);
+  header.writeUInt32BE(payload.length, 0);
+  return Buffer.concat([header, payload]);
+}
+
+/**
+ * Parse a framed response from the qrexec stdout buffer.
+ */
+function parseFramedResponse(buf) {
+  if (buf.length < 4) {
+    throw new Error("short response (missing frame header)");
+  }
+  const len = buf.readUInt32BE(0);
+  const payload = buf.subarray(4, 4 + len);
+  if (payload.length !== len) {
+    throw new Error(`short response payload: expected ${len}, got ${payload.length}`);
+  }
+  return JSON.parse(payload.toString("utf8"));
+}
+
+/**
+ * Call nsigner via qrexec. Sends one framed request, receives one framed response.
+ * Each call spawns a fresh qrexec-client-vm process (one request per invocation).
+ */
+function callNsignerQrexec(targetQube, request) {
+  return new Promise((resolve, reject) => {
+    const framed = frameRequest(request);
+    const proc = spawn("qrexec-client-vm", [targetQube, "qubes.NsignerRpc"], {
+      stdio: ["pipe", "pipe", "pipe"],
+    });
+
+    const stdoutChunks = [];
+    const stderrChunks = [];
+
+    proc.stdout.on("data", (chunk) => stdoutChunks.push(chunk));
+    proc.stderr.on("data", (chunk) => stderrChunks.push(chunk));
+
+    proc.on("error", (err) => {
+      reject(new Error(`failed to spawn qrexec-client-vm: ${err.message}`));
+    });
+
+    proc.on("close", (code) => {
+      if (code !== 0) {
+        const stderr = Buffer.concat(stderrChunks).toString("utf8");
+        reject(new Error(`qrexec-client-vm exited with code ${code}: ${stderr.trim()}`));
+        return;
+      }
+      try {
+        const response = parseFramedResponse(Buffer.concat(stdoutChunks));
+        resolve(response);
+      } catch (e) {
+        reject(new Error(`failed to parse response: ${e.message}`));
+      }
+    });
+
+    // Send the framed request and close stdin
+    proc.stdin.write(framed);
+    proc.stdin.end();
+  });
+}
+
+/**
+ * Query get_public_key for a given nostr_index via qrexec.
+ * No auth envelope needed — qrexec mode uses qubes:<source-vm> as caller identity.
+ */
+async function getPublicKey(targetQube, nostrIndex) {
+  const request = {
+    id: String(nostrIndex),
+    method: "get_public_key",
+    params: [{ nostr_index: nostrIndex }],
+  };
+
+  return callNsignerQrexec(targetQube, request);
+}
+
+async function main() {
+  const targetQube = process.argv[2] || "nostr_signer";
+
+  console.log(`Calling n_signer in qube "${targetQube}" via qrexec...`);
+  console.log("Querying get_public_key for nostr_index 0 and 1...\n");
+
+  let failures = 0;
+
+  for (const index of [0, 1]) {
+    try {
+      const response = await getPublicKey(targetQube, index);
+
+      if (response.error) {
+        console.log(`index ${index}: ERROR: ${JSON.stringify(response.error)}`);
+        failures++;
+        continue;
+      }
+
+      const pubkeyHex = response.result;
+      const npub = nip19.npubEncode(pubkeyHex);
+      console.log(`index ${index}: hex=${pubkeyHex}  npub=${npub}`);
+    } catch (e) {
+      console.log(`index ${index}: FAILED - ${e.message}`);
+      failures++;
+    }
+  }
+
+  if (failures > 0) {
+    console.log(`\n${failures} query(s) failed`);
+    process.exit(1);
+  }
+
+  console.log("\nAll queries succeeded");
+}
+
+main().catch((e) => {
+  console.error(e);
+  process.exit(1);
+});

examples/sign_event_client.c

@@ -1,33 +1,114 @@
+/*
+ * sign_event_client.c — connect to a running n_signer over its abstract
+ * UNIX socket and call sign_event, using the shared nsigner client from
+ * nostr_core_lib (nostr_core/nsigner_client.h + nostr_core/nsigner_transport.h).
+ *
+ * Usage: ./sign_event_client [socket_name]
+ *
+ * Output: the raw JSON-RPC response string, e.g.
+ *         {"id":"1","result":"{...signed event...}"}
+ */
+
 #include <stdio.h>
 #include <stdlib.h>
+#include <string.h>
 
-#include "../client/nsigner_client.h"
+#include "nostr_common.h"
+#include "nsigner_transport.h"
+#include "nsigner_client.h"
+#include "../cjson/cJSON.h"
 
 int main(int argc, char **argv) {
     const char *socket_name = "nsigner";
     const char *event_json = "{\"kind\":1,\"content\":\"hello from client example\",\"tags\":[],\"created_at\":1700000000}";
-    nsigner_client_t client;
-    char *response = NULL;
+    const char *role = "main";
+    nsigner_transport_t *transport = NULL;
+    nsigner_client_t *client = NULL;
+    cJSON *params = NULL;
+    cJSON *opts = NULL;
+    cJSON *result = NULL;
+    cJSON *response = NULL;
+    char *response_json = NULL;
+    int rc = 1;
 
     if (argc > 1 && argv[1] != NULL && argv[1][0] != '\0') {
         socket_name = argv[1];
     }
 
-    nsigner_client_init(&client);
-
-    if (nsigner_client_connect_unix(&client, socket_name, 5000) != 0) {
-        fprintf(stderr, "connect failed: %s\n", nsigner_client_last_error(&client));
+    if (nostr_init() != NOSTR_SUCCESS) {
+        fprintf(stderr, "failed to initialize crypto subsystem\n");
         return 1;
     }
 
-    if (nsigner_client_sign_event(&client, "example-2", event_json, "main", &response) != 0) {
-        fprintf(stderr, "request failed: %s\n", nsigner_client_last_error(&client));
-        nsigner_client_close(&client);
-        return 1;
+    transport = nsigner_transport_open_unix(socket_name, 5000);
+    if (transport == NULL) {
+        fprintf(stderr, "connect failed: cannot open unix transport @%s\n", socket_name);
+        goto cleanup;
     }
 
-    printf("%s\n", response);
-    free(response);
-    nsigner_client_close(&client);
-    return 0;
+    client = nsigner_client_new(transport);
+    if (client == NULL) {
+        fprintf(stderr, "connect failed: cannot create nsigner client\n");
+        transport->close(transport);
+        goto cleanup;
+    }
+    transport = NULL; /* owned by client now */
+
+    /* params: [ "<event_json>", {"role":"main"} ] */
+    params = cJSON_CreateArray();
+    if (params == NULL) {
+        fprintf(stderr, "out of memory\n");
+        goto cleanup;
+    }
+    cJSON_AddItemToArray(params, cJSON_CreateString(event_json));
+
+    opts = cJSON_CreateObject();
+    if (opts == NULL) {
+        fprintf(stderr, "out of memory\n");
+        goto cleanup;
+    }
+    if (role != NULL && role[0] != '\0') {
+        cJSON_AddStringToObject(opts, "role", role);
+    }
+    cJSON_AddItemToArray(params, opts);
+    opts = NULL; /* owned by params now */
+
+    if (nsigner_client_call(client, "sign_event", params, &result) != NOSTR_SUCCESS) {
+        fprintf(stderr, "request failed: %s\n", nsigner_client_last_error(client));
+        goto cleanup;
+    }
+    params = NULL; /* nsigner_client_call takes ownership of params */
+
+    /*
+     * Reconstruct a JSON-RPC response string for backward-compatible CLI
+     * output: {"id":"1","result":"<signed event json>"}
+     * The server returns the signed event as a JSON string (not an object),
+     * so result is a cJSON string here.
+     */
+    response = cJSON_CreateObject();
+    if (response == NULL) {
+        fprintf(stderr, "out of memory\n");
+        goto cleanup;
+    }
+    cJSON_AddStringToObject(response, "id", "1");
+    cJSON_AddItemReferenceToObject(response, "result", result);
+
+    response_json = cJSON_PrintUnformatted(response);
+    if (response_json == NULL) {
+        fprintf(stderr, "failed to serialize response\n");
+        goto cleanup;
+    }
+
+    printf("%s\n", response_json);
+    rc = 0;
+
+cleanup:
+    free(response_json);
+    cJSON_Delete(response);
+    cJSON_Delete(result);
+    cJSON_Delete(params);
+    cJSON_Delete(opts);
+    nsigner_client_free(client); /* also closes/frees the transport */
+    nostr_cleanup();
+    return rc;
 }

firmware/cyd_esp32_2432s028/main/mnemonic.c

@@ -277,6 +277,72 @@ size_t mnemonic_words_for_letter(char letter, size_t *out_start)
     return s_letter_count[idx];
 }
 
+size_t mnemonic_words_with_prefix(const char *prefix, uint16_t *out_indices, size_t max_out)
+{
+    size_t start = 0;
+    size_t count = 0;
+    size_t written = 0;
+
+    if (prefix == NULL || prefix[0] == '\0') {
+        return 0;
+    }
+
+    count = mnemonic_words_for_letter(prefix[0], &start);
+    if (count == 0) {
+        return 0;
+    }
+
+    for (size_t i = 0; i < count; ++i) {
+        size_t idx = start + i;
+        const char *word = BIP39_WORDLIST[idx];
+        if (strncmp(word, prefix, strlen(prefix)) == 0) {
+            if (out_indices != NULL && written < max_out) {
+                out_indices[written] = (uint16_t)idx;
+            }
+            written++;
+        }
+    }
+
+    return written;
+}
+
+bool mnemonic_letter_extends_prefix(const char *prefix, size_t prefix_len, char next_letter)
+{
+    char probe[16];
+    size_t start = 0;
+    size_t count = 0;
+
+    if (next_letter >= 'A' && next_letter <= 'Z') {
+        next_letter = (char)(next_letter - 'A' + 'a');
+    }
+
+    if (next_letter < 'a' || next_letter > 'z') {
+        return false;
+    }
+
+    if (prefix == NULL || prefix_len >= sizeof(probe) - 1) {
+        return false;
+    }
+
+    memcpy(probe, prefix, prefix_len);
+    probe[prefix_len] = next_letter;
+    probe[prefix_len + 1] = '\0';
+
+    count = mnemonic_words_for_letter(probe[0], &start);
+    if (count == 0) {
+        return false;
+    }
+
+    for (size_t i = 0; i < count; ++i) {
+        const char *word = BIP39_WORDLIST[start + i];
+        if (strncmp(word, probe, prefix_len + 1) == 0) {
+            return true;
+        }
+    }
+
+    return false;
+}
+
 const char *mnemonic_word_at(size_t index)
 {
     if (index >= 2048) {

firmware/cyd_esp32_2432s028/main/mnemonic.h

@@ -1,5 +1,6 @@
 #pragma once
 
+#include <stdbool.h>
 #include <stddef.h>
 #include <stdint.h>
 
@@ -7,4 +8,6 @@ int generate_mnemonic_12(char *out, size_t out_len);
 int mnemonic_to_seed(const char *mnemonic, uint8_t seed[64]);
 int mnemonic_validate(const char *mnemonic);
 size_t mnemonic_words_for_letter(char letter, size_t *out_start);
+size_t mnemonic_words_with_prefix(const char *prefix, uint16_t *out_indices, size_t max_out);
+bool mnemonic_letter_extends_prefix(const char *prefix, size_t prefix_len, char next_letter);
 const char *mnemonic_word_at(size_t index);

firmware/cyd_esp32_2432s028/main/ui.c

@@ -13,10 +13,15 @@
 #include "ili9341.h"
 #include "lvgl.h"
 #include "mnemonic.h"
+#include "secure_mem.h"
 #include "touch.h"
 
 #define UI_TICK_MS 2
 #define UI_DRAW_LINES 20
+#define UI_MNEMONIC_WORDS 12
+#define UI_BIP39_WORD_MAX 9
+#define UI_SUGGESTION_STORE_MAX 64
+#define UI_SUGGESTION_VISIBLE_MAX 32
 
 static const char *TAG = "ui_lvgl";
 
@@ -30,7 +35,21 @@ static bool s_done = false;
 static bool s_have_mnemonic = false;
 static char s_selected_mnemonic[256];
 static lv_obj_t *s_status_label = NULL;
-static lv_obj_t *s_entry_ta = NULL;
+
+static char s_committed_words[UI_MNEMONIC_WORDS][UI_BIP39_WORD_MAX];
+static size_t s_word_count = 0;
+static char s_prefix[UI_BIP39_WORD_MAX];
+static size_t s_prefix_len = 0;
+static bool s_checksum_override = false;
+
+static lv_obj_t *s_entry_words_label = NULL;
+static lv_obj_t *s_entry_prefix_label = NULL;
+static lv_obj_t *s_suggestion_row = NULL;
+static lv_obj_t *s_key_matrix = NULL;
+static lv_obj_t *s_checksum_panel = NULL;
+
+static uint16_t s_match_indices[UI_SUGGESTION_STORE_MAX];
+static size_t s_match_total = 0;
 
 static ui_approval_decision_t s_approval_decision = UI_APPROVAL_TIMEOUT;
 static lv_obj_t *s_approval_countdown = NULL;
@@ -41,6 +60,18 @@ static int64_t s_approval_deadline_us = 0;
 static char s_event_lines[UI_EVENT_LOG_MAX][UI_EVENT_LINE_MAX];
 static int s_event_count = 0;
 
+static void reset_screen_widget_refs(void)
+{
+    s_status_label = NULL;
+    s_entry_words_label = NULL;
+    s_entry_prefix_label = NULL;
+    s_suggestion_row = NULL;
+    s_key_matrix = NULL;
+    s_checksum_panel = NULL;
+    s_approval_countdown = NULL;
+    s_match_total = 0;
+}
+
 static void style_screen(lv_obj_t *scr)
 {
     lv_obj_set_style_bg_opa(scr, LV_OPA_COVER, 0);
@@ -62,31 +93,24 @@ static void style_button(lv_obj_t *btn)
     lv_obj_set_style_text_color(btn, lv_color_hex(0xFF0000), LV_STATE_FOCUSED);
 }
 
-static void style_text_area(lv_obj_t *ta)
+static void style_key_matrix(lv_obj_t *km)
 {
-    lv_obj_set_style_bg_opa(ta, LV_OPA_COVER, 0);
-    lv_obj_set_style_bg_color(ta, lv_color_hex(0x000000), 0);
-    lv_obj_set_style_border_width(ta, 2, 0);
-    lv_obj_set_style_border_color(ta, lv_color_hex(0xFFFFFF), 0);
-    lv_obj_set_style_text_color(ta, lv_color_hex(0xFFFFFF), 0);
-    lv_obj_set_style_text_color(ta, lv_color_hex(0xFF0000), LV_PART_CURSOR);
-}
+    lv_obj_set_style_bg_opa(km, LV_OPA_COVER, 0);
+    lv_obj_set_style_bg_color(km, lv_color_hex(0x000000), 0);
+    lv_obj_set_style_border_width(km, 1, 0);
+    lv_obj_set_style_border_color(km, lv_color_hex(0xFFFFFF), 0);
 
-static void style_keyboard(lv_obj_t *kb)
-{
-    lv_obj_set_style_bg_opa(kb, LV_OPA_COVER, 0);
-    lv_obj_set_style_bg_color(kb, lv_color_hex(0x000000), 0);
-    lv_obj_set_style_border_width(kb, 1, 0);
-    lv_obj_set_style_border_color(kb, lv_color_hex(0xFFFFFF), 0);
+    lv_obj_set_style_bg_opa(km, LV_OPA_COVER, LV_PART_ITEMS);
+    lv_obj_set_style_bg_color(km, lv_color_hex(0x000000), LV_PART_ITEMS);
+    lv_obj_set_style_border_color(km, lv_color_hex(0xFFFFFF), LV_PART_ITEMS);
+    lv_obj_set_style_border_width(km, 1, LV_PART_ITEMS);
+    lv_obj_set_style_text_color(km, lv_color_hex(0xFFFFFF), LV_PART_ITEMS);
 
-    lv_obj_set_style_bg_opa(kb, LV_OPA_COVER, LV_PART_ITEMS);
-    lv_obj_set_style_bg_color(kb, lv_color_hex(0x000000), LV_PART_ITEMS);
-    lv_obj_set_style_border_color(kb, lv_color_hex(0xFFFFFF), LV_PART_ITEMS);
-    lv_obj_set_style_border_width(kb, 1, LV_PART_ITEMS);
-    lv_obj_set_style_text_color(kb, lv_color_hex(0xFFFFFF), LV_PART_ITEMS);
+    lv_obj_set_style_border_color(km, lv_color_hex(0xFF0000), LV_PART_ITEMS | LV_STATE_PRESSED);
+    lv_obj_set_style_text_color(km, lv_color_hex(0xFF0000), LV_PART_ITEMS | LV_STATE_PRESSED);
 
-    lv_obj_set_style_border_color(kb, lv_color_hex(0xFF0000), LV_PART_ITEMS | LV_STATE_PRESSED);
-    lv_obj_set_style_text_color(kb, lv_color_hex(0xFF0000), LV_PART_ITEMS | LV_STATE_PRESSED);
+    lv_obj_set_style_text_color(km, lv_color_hex(0x505050), LV_PART_ITEMS | LV_STATE_DISABLED);
+    lv_obj_set_style_border_color(km, lv_color_hex(0x303030), LV_PART_ITEMS | LV_STATE_DISABLED);
 }
 
 static void lvgl_tick_cb(void *arg)
@@ -198,85 +222,443 @@ static void on_generate(lv_event_t *e)
 }
 
 static void build_main_menu(void);
+static void refresh_entry_ui(void);
+static bool verify_or_prompt_checksum(void);
 
-static void on_back_to_menu(lv_event_t *e)
+static const char *s_key_map[] = {
+    "q", "w", "e", "r", "t", "y", "u", "i", "o", "p", "\n",
+    "a", "s", "d", "f", "g", "h", "j", "k", "l", "\n",
+    "z", "x", "c", "v", "b", "n", "m", "<", "",
+};
+
+static void clear_entry_state(void)
 {
-    (void)e;
-    build_main_menu();
+    secure_memzero(s_committed_words, sizeof(s_committed_words));
+    secure_memzero(s_prefix, sizeof(s_prefix));
+    s_word_count = 0;
+    s_prefix_len = 0;
+    s_checksum_override = false;
+    s_match_total = 0;
 }
 
-static void on_use_entry(lv_event_t *e)
+static bool join_committed_words(char *out, size_t out_len)
+{
+    size_t cursor = 0;
+
+    if (out == NULL || out_len == 0) {
+        return false;
+    }
+
+    out[0] = '\0';
+
+    for (size_t i = 0; i < s_word_count; ++i) {
+        size_t wl = strlen(s_committed_words[i]);
+
+        if (cursor != 0) {
+            if (cursor + 1 >= out_len) {
+                out[0] = '\0';
+                return false;
+            }
+            out[cursor++] = ' ';
+        }
+
+        if (cursor + wl >= out_len) {
+            out[0] = '\0';
+            return false;
+        }
+
+        memcpy(out + cursor, s_committed_words[i], wl);
+        cursor += wl;
+        out[cursor] = '\0';
+    }
+
+    return true;
+}
+
+static void commit_word(const char *word)
+{
+    if (word == NULL || s_word_count >= UI_MNEMONIC_WORDS) {
+        return;
+    }
+
+    memset(s_committed_words[s_word_count], 0, UI_BIP39_WORD_MAX);
+    strncpy(s_committed_words[s_word_count], word, UI_BIP39_WORD_MAX - 1);
+    s_word_count++;
+
+    secure_memzero(s_prefix, sizeof(s_prefix));
+    s_prefix_len = 0;
+    s_checksum_override = false;
+}
+
+static void on_checksum_use_anyway(lv_event_t *e)
 {
     (void)e;
 
-    if (s_entry_ta == NULL) {
-        return;
-    }
-
-    const char *txt = lv_textarea_get_text(s_entry_ta);
-    if (txt == NULL || txt[0] == '\0') {
-        set_status("Mnemonic is empty");
-        return;
-    }
-
-    if (mnemonic_validate(txt) != 0) {
-        set_status("Invalid mnemonic");
+    char joined[256];
+    memset(joined, 0, sizeof(joined));
+    if (!join_committed_words(joined, sizeof(joined))) {
+        set_status("Mnemonic buffer error");
+        secure_memzero(joined, sizeof(joined));
         return;
     }
 
     memset(s_selected_mnemonic, 0, sizeof(s_selected_mnemonic));
-    strncpy(s_selected_mnemonic, txt, sizeof(s_selected_mnemonic) - 1);
+    strncpy(s_selected_mnemonic, joined, sizeof(s_selected_mnemonic) - 1);
     s_have_mnemonic = true;
     s_done = true;
+    s_checksum_override = true;
+    secure_memzero(joined, sizeof(joined));
+}
+
+static void on_checksum_edit_words(lv_event_t *e)
+{
+    (void)e;
+
+    if (s_checksum_panel != NULL) {
+        lv_obj_del(s_checksum_panel);
+        s_checksum_panel = NULL;
+    }
+    set_status("Checksum mismatch: edit or use anyway");
+    refresh_entry_ui();
+}
+
+static bool verify_or_prompt_checksum(void)
+{
+    char joined[256];
+
+    if (s_key_matrix == NULL || s_entry_words_label == NULL || s_entry_prefix_label == NULL) {
+        return false;
+    }
+
+    if (s_word_count != UI_MNEMONIC_WORDS || s_prefix_len != 0) {
+        set_status("Need exactly 12 complete words");
+        return false;
+    }
+
+    memset(joined, 0, sizeof(joined));
+    if (!join_committed_words(joined, sizeof(joined))) {
+        set_status("Mnemonic buffer error");
+        secure_memzero(joined, sizeof(joined));
+        return false;
+    }
+
+    if (mnemonic_validate(joined) == 0) {
+        if (s_checksum_panel != NULL) {
+            lv_obj_del(s_checksum_panel);
+            s_checksum_panel = NULL;
+        }
+        set_status("Checksum valid");
+        memset(s_selected_mnemonic, 0, sizeof(s_selected_mnemonic));
+        strncpy(s_selected_mnemonic, joined, sizeof(s_selected_mnemonic) - 1);
+        s_have_mnemonic = true;
+        s_done = true;
+        secure_memzero(joined, sizeof(joined));
+        return true;
+    }
+
+    if (s_checksum_panel != NULL) {
+        lv_obj_del(s_checksum_panel);
+        s_checksum_panel = NULL;
+    }
+
+    s_checksum_panel = lv_obj_create(lv_scr_act());
+    lv_obj_set_size(s_checksum_panel, DISPLAY_WIDTH - 20, 82);
+    lv_obj_align(s_checksum_panel, LV_ALIGN_TOP_MID, 0, 78);
+    lv_obj_set_style_bg_color(s_checksum_panel, lv_color_hex(0x000000), 0);
+    lv_obj_set_style_border_color(s_checksum_panel, lv_color_hex(0xFFFFFF), 0);
+    lv_obj_set_style_border_width(s_checksum_panel, 2, 0);
+    lv_obj_set_style_radius(s_checksum_panel, 6, 0);
+    lv_obj_set_style_pad_all(s_checksum_panel, 6, 0);
+
+    lv_obj_t *txt = lv_label_create(s_checksum_panel);
+    lv_label_set_text(txt, "Checksum invalid. Use anyway?");
+    lv_obj_set_style_text_color(txt, lv_color_hex(0xFF0000), 0);
+    lv_obj_align(txt, LV_ALIGN_TOP_MID, 0, 0);
+
+    lv_obj_t *use_btn = lv_btn_create(s_checksum_panel);
+    lv_obj_set_size(use_btn, 128, 30);
+    lv_obj_align(use_btn, LV_ALIGN_BOTTOM_LEFT, 4, -2);
+    style_button(use_btn);
+    lv_obj_set_style_border_color(use_btn, lv_color_hex(0xFF0000), 0);
+    lv_obj_add_event_cb(use_btn, on_checksum_use_anyway, LV_EVENT_RELEASED, NULL);
+    lv_obj_t *use_lbl = lv_label_create(use_btn);
+    lv_label_set_text(use_lbl, "Use Anyway");
+    lv_obj_center(use_lbl);
+
+    lv_obj_t *edit_btn = lv_btn_create(s_checksum_panel);
+    lv_obj_set_size(edit_btn, 128, 30);
+    lv_obj_align(edit_btn, LV_ALIGN_BOTTOM_RIGHT, -4, -2);
+    style_button(edit_btn);
+    lv_obj_add_event_cb(edit_btn, on_checksum_edit_words, LV_EVENT_RELEASED, NULL);
+    lv_obj_t *edit_lbl = lv_label_create(edit_btn);
+    lv_label_set_text(edit_lbl, "Edit Words");
+    lv_obj_center(edit_lbl);
+
+    set_status("Checksum invalid");
+    secure_memzero(joined, sizeof(joined));
+    return false;
+}
+
+static void on_back_to_menu(lv_event_t *e)
+{
+    (void)e;
+    if (s_checksum_panel != NULL) {
+        lv_obj_del(s_checksum_panel);
+        s_checksum_panel = NULL;
+    }
+    clear_entry_state();
+    build_main_menu();
+}
+
+static void on_suggestion_tap(lv_event_t *e)
+{
+    const char *word = (const char *)lv_event_get_user_data(e);
+
+    if (s_suggestion_row == NULL || word == NULL || s_word_count >= UI_MNEMONIC_WORDS) {
+        return;
+    }
+
+    commit_word(word);
+    refresh_entry_ui();
+
+    if (s_word_count == UI_MNEMONIC_WORDS) {
+        (void)verify_or_prompt_checksum();
+    }
+}
+
+static void entry_backspace_step(void)
+{
+    if (s_prefix_len > 0) {
+        s_prefix_len--;
+        s_prefix[s_prefix_len] = '\0';
+    } else if (s_word_count > 0) {
+        s_word_count--;
+        memset(s_prefix, 0, sizeof(s_prefix));
+        strncpy(s_prefix, s_committed_words[s_word_count], sizeof(s_prefix) - 1);
+        s_prefix_len = strlen(s_prefix);
+        secure_memzero(s_committed_words[s_word_count], sizeof(s_committed_words[s_word_count]));
+    }
+
+    s_checksum_override = false;
+    if (s_checksum_panel != NULL) {
+        lv_obj_del(s_checksum_panel);
+        s_checksum_panel = NULL;
+    }
+    refresh_entry_ui();
+}
+
+static void on_key_matrix(lv_event_t *e)
+{
+    lv_obj_t *obj = lv_event_get_target(e);
+    if (s_key_matrix == NULL || obj != s_key_matrix) {
+        return;
+    }
+
+    uint16_t idx = lv_btnmatrix_get_selected_btn(obj);
+    const char *txt = lv_btnmatrix_get_btn_text(obj, idx);
+
+    if (txt == NULL || txt[0] == '\0' || txt[1] != '\0') {
+        return;
+    }
+
+    if (txt[0] == '<') {
+        entry_backspace_step();
+        return;
+    }
+
+    if (s_word_count >= UI_MNEMONIC_WORDS) {
+        set_status("Already have 12 words");
+        return;
+    }
+
+    if (s_prefix_len + 1 >= sizeof(s_prefix)) {
+        set_status("Word too long");
+        return;
+    }
+
+    s_prefix[s_prefix_len++] = txt[0];
+    s_prefix[s_prefix_len] = '\0';
+    s_checksum_override = false;
+
+    refresh_entry_ui();
+
+    if (s_match_total == 1) {
+        const char *word = mnemonic_word_at(s_match_indices[0]);
+        if (word != NULL) {
+            commit_word(word);
+            refresh_entry_ui();
+            if (s_word_count == UI_MNEMONIC_WORDS) {
+                (void)verify_or_prompt_checksum();
+            }
+        }
+    }
+}
+
+static void refresh_entry_ui(void)
+{
+    size_t shown = 0;
+    char words_line[256];
+    char prefix_line[64];
+
+    if (s_checksum_panel != NULL) {
+        lv_obj_del(s_checksum_panel);
+        s_checksum_panel = NULL;
+    }
+
+    memset(words_line, 0, sizeof(words_line));
+    (void)join_committed_words(words_line, sizeof(words_line));
+
+    if (s_entry_words_label != NULL) {
+        if (s_word_count == 0) {
+            lv_label_set_text(s_entry_words_label, "(no words selected)");
+        } else {
+            lv_label_set_text(s_entry_words_label, words_line);
+        }
+    }
+
+    snprintf(prefix_line, sizeof(prefix_line), "Word %u/12 prefix: %s",
+             (unsigned)(s_word_count + 1),
+             (s_prefix_len > 0) ? s_prefix : "-");
+    if (s_entry_prefix_label != NULL) {
+        lv_label_set_text(s_entry_prefix_label, prefix_line);
+    }
+
+    if (s_suggestion_row != NULL) {
+        lv_obj_clean(s_suggestion_row);
+
+        if (s_prefix_len > 0 && s_word_count < UI_MNEMONIC_WORDS) {
+            s_match_total = mnemonic_words_with_prefix(s_prefix, s_match_indices, UI_SUGGESTION_STORE_MAX);
+            shown = (s_match_total > UI_SUGGESTION_VISIBLE_MAX) ? UI_SUGGESTION_VISIBLE_MAX : s_match_total;
+
+            for (size_t i = 0; i < shown; ++i) {
+                const char *word = mnemonic_word_at(s_match_indices[i]);
+                lv_obj_t *btn;
+                lv_obj_t *lbl;
+                if (word == NULL) {
+                    continue;
+                }
+                btn = lv_btn_create(s_suggestion_row);
+                lv_obj_set_size(btn, 84, 26);
+                style_button(btn);
+                lv_obj_add_event_cb(btn, on_suggestion_tap, LV_EVENT_RELEASED, (void *)word);
+                lbl = lv_label_create(btn);
+                lv_label_set_text(lbl, word);
+                lv_obj_center(lbl);
+            }
+
+            if (s_match_total > shown) {
+                char more[24];
+                lv_obj_t *m = lv_label_create(s_suggestion_row);
+                snprintf(more, sizeof(more), "+%u more", (unsigned)(s_match_total - shown));
+                lv_label_set_text(m, more);
+                lv_obj_set_style_text_color(m, lv_color_hex(0xFFFFFF), 0);
+            }
+
+            if (s_match_total == 0) {
+                set_status("No matches");
+            } else {
+                set_status("");
+            }
+        } else {
+            s_match_total = 0;
+        }
+    }
+
+    if (s_key_matrix != NULL) {
+        const uint16_t matrix_btn_count = 27;
+        for (uint16_t i = 0; i < matrix_btn_count; ++i) {
+            const char *txt = lv_btnmatrix_get_btn_text(s_key_matrix, i);
+            bool enabled = false;
+            if (txt == NULL || txt[0] == '\0' || txt[1] != '\0') {
+                continue;
+            }
+
+            if (txt[0] == '<') {
+                enabled = (s_prefix_len > 0 || s_word_count > 0);
+            } else if (s_word_count >= UI_MNEMONIC_WORDS) {
+                enabled = false;
+            } else if (s_prefix_len == 0) {
+                size_t start = 0;
+                enabled = (mnemonic_words_for_letter(txt[0], &start) > 0);
+            } else {
+                enabled = mnemonic_letter_extends_prefix(s_prefix, s_prefix_len, txt[0]);
+            }
+
+            if (enabled) {
+                lv_btnmatrix_clear_btn_ctrl(s_key_matrix, i, LV_BTNMATRIX_CTRL_DISABLED);
+            } else {
+                lv_btnmatrix_set_btn_ctrl(s_key_matrix, i, LV_BTNMATRIX_CTRL_DISABLED);
+            }
+        }
+    }
 }
 
 static void build_entry_screen(void)
 {
     lv_obj_t *scr = lv_scr_act();
+    lv_obj_t *title;
+    lv_obj_t *close_btn;
+    lv_obj_t *close_lbl;
+
+    reset_screen_widget_refs();
     lv_obj_clean(scr);
     style_screen(scr);
+    clear_entry_state();
 
-    lv_obj_t *title = lv_label_create(scr);
+    title = lv_label_create(scr);
     lv_label_set_text(title, "Enter Mnemonic");
     lv_obj_set_style_text_font(title, &lv_font_montserrat_14, 0);
     lv_obj_set_style_text_color(title, lv_color_hex(0xFFFFFF), 0);
-    lv_obj_align(title, LV_ALIGN_TOP_MID, 0, 6);
+    lv_obj_align(title, LV_ALIGN_TOP_MID, 0, 4);
 
-    s_entry_ta = lv_textarea_create(scr);
-    lv_obj_set_size(s_entry_ta, DISPLAY_WIDTH - 16, 70);
-    lv_obj_align(s_entry_ta, LV_ALIGN_TOP_MID, 0, 32);
-    lv_textarea_set_placeholder_text(s_entry_ta, "12 words separated by spaces");
-    lv_textarea_set_one_line(s_entry_ta, false);
-    style_text_area(s_entry_ta);
+    s_entry_words_label = lv_label_create(scr);
+    lv_obj_set_width(s_entry_words_label, DISPLAY_WIDTH - 16);
+    lv_label_set_long_mode(s_entry_words_label, LV_LABEL_LONG_WRAP);
+    lv_label_set_text(s_entry_words_label, "(no words selected)");
+    lv_obj_set_style_text_color(s_entry_words_label, lv_color_hex(0xFFFFFF), 0);
+    lv_obj_align(s_entry_words_label, LV_ALIGN_TOP_LEFT, 8, 26);
 
-    lv_obj_t *kb = lv_keyboard_create(scr);
-    lv_obj_set_size(kb, DISPLAY_WIDTH, 110);
-    lv_obj_align(kb, LV_ALIGN_BOTTOM_MID, 0, 0);
-    lv_keyboard_set_textarea(kb, s_entry_ta);
-    style_keyboard(kb);
-
-    lv_obj_t *use_btn = lv_btn_create(scr);
-    lv_obj_set_size(use_btn, 150, 30);
-    lv_obj_align(use_btn, LV_ALIGN_TOP_LEFT, 8, 110);
-    lv_obj_add_event_cb(use_btn, on_use_entry, LV_EVENT_RELEASED, NULL);
-    style_button(use_btn);
-    lv_obj_t *use_lbl = lv_label_create(use_btn);
-    lv_label_set_text(use_lbl, "Use Mnemonic");
-    lv_obj_center(use_lbl);
-
-    lv_obj_t *back_btn = lv_btn_create(scr);
-    lv_obj_set_size(back_btn, 150, 30);
-    lv_obj_align(back_btn, LV_ALIGN_TOP_RIGHT, -8, 110);
-    lv_obj_add_event_cb(back_btn, on_back_to_menu, LV_EVENT_RELEASED, NULL);
-    style_button(back_btn);
-    lv_obj_t *back_lbl = lv_label_create(back_btn);
-    lv_label_set_text(back_lbl, "Back");
-    lv_obj_center(back_lbl);
+    s_entry_prefix_label = lv_label_create(scr);
+    lv_label_set_text(s_entry_prefix_label, "Word 1/12 prefix: -");
+    lv_obj_set_style_text_color(s_entry_prefix_label, lv_color_hex(0xFFFFFF), 0);
+    lv_obj_align(s_entry_prefix_label, LV_ALIGN_TOP_LEFT, 8, 66);
 
     s_status_label = lv_label_create(scr);
     lv_label_set_text(s_status_label, "");
     lv_obj_set_style_text_color(s_status_label, lv_color_hex(0xFF0000), 0);
-    lv_obj_align(s_status_label, LV_ALIGN_TOP_LEFT, 8, 144);
+    lv_obj_align(s_status_label, LV_ALIGN_TOP_LEFT, 8, 82);
+
+    s_suggestion_row = lv_obj_create(scr);
+    lv_obj_set_size(s_suggestion_row, DISPLAY_WIDTH - 12, 30);
+    lv_obj_align(s_suggestion_row, LV_ALIGN_TOP_MID, 0, 96);
+    lv_obj_set_style_bg_color(s_suggestion_row, lv_color_hex(0x000000), 0);
+    lv_obj_set_style_border_color(s_suggestion_row, lv_color_hex(0xFFFFFF), 0);
+    lv_obj_set_style_border_width(s_suggestion_row, 1, 0);
+    lv_obj_set_style_pad_all(s_suggestion_row, 2, 0);
+    lv_obj_set_scroll_dir(s_suggestion_row, LV_DIR_HOR);
+    lv_obj_set_flex_flow(s_suggestion_row, LV_FLEX_FLOW_ROW);
+    lv_obj_set_flex_align(s_suggestion_row, LV_FLEX_ALIGN_START, LV_FLEX_ALIGN_CENTER, LV_FLEX_ALIGN_CENTER);
+
+    close_btn = lv_btn_create(scr);
+    lv_obj_set_size(close_btn, 42, 30);
+    lv_obj_align(close_btn, LV_ALIGN_TOP_RIGHT, -4, 2);
+    style_button(close_btn);
+    lv_obj_add_event_cb(close_btn, on_back_to_menu, LV_EVENT_CLICKED, NULL);
+    close_lbl = lv_label_create(close_btn);
+    lv_label_set_text(close_lbl, "X");
+    lv_obj_center(close_lbl);
+
+    s_key_matrix = lv_btnmatrix_create(scr);
+    lv_obj_set_size(s_key_matrix, DISPLAY_WIDTH - 16, 100);
+    lv_obj_align(s_key_matrix, LV_ALIGN_TOP_MID, 0, 132);
+    lv_btnmatrix_set_map(s_key_matrix, s_key_map);
+    lv_obj_add_event_cb(s_key_matrix, on_key_matrix, LV_EVENT_VALUE_CHANGED, NULL);
+    style_key_matrix(s_key_matrix);
+    lv_obj_set_style_pad_all(s_key_matrix, 0, 0);
+    lv_obj_set_style_pad_gap(s_key_matrix, 0, LV_PART_ITEMS);
+    lv_obj_set_style_border_width(s_key_matrix, 1, LV_PART_ITEMS);
+
+    refresh_entry_ui();
 }
 
 static void on_enter(lv_event_t *e)
@@ -316,6 +698,7 @@ static void on_use_viewed(lv_event_t *e)
 static void build_view_screen(void)
 {
     lv_obj_t *scr = lv_scr_act();
+    reset_screen_widget_refs();
     lv_obj_clean(scr);
     style_screen(scr);
 
@@ -370,6 +753,7 @@ static void on_view(lv_event_t *e)
 static void build_main_menu(void)
 {
     lv_obj_t *scr = lv_scr_act();
+    reset_screen_widget_refs();
     lv_obj_clean(scr);
     style_screen(scr);
 
@@ -424,6 +808,7 @@ void ui_show_approval_prompt(const char *caller_pubkey_hex, int kind, const char
     }
 
     lv_obj_t *scr = lv_scr_act();
+    reset_screen_widget_refs();
     lv_obj_clean(scr);
     style_screen(scr);
 
@@ -535,6 +920,7 @@ ui_approval_decision_t ui_wait_for_approval(uint32_t timeout_ms)
 static void show_event_log_screen(void)
 {
     lv_obj_t *scr = lv_scr_act();
+    reset_screen_widget_refs();
     lv_obj_clean(scr);
     style_screen(scr);
 
@@ -579,6 +965,7 @@ void ui_show_idle(const char *npub_full, const char *mnemonic_full, const char *
     }
 
     lv_obj_t *scr = lv_scr_act();
+    reset_screen_widget_refs();
     lv_obj_clean(scr);
     style_screen(scr);
 

firmware/kb2040_dual_test/kb2040_dual_test.ino

@@ -0,0 +1,77 @@
+// Proof-of-concept: KB2040 as composite HID + WebUSB using Adafruit TinyUSB
+//
+// Board/IDE requirements:
+// - Board: Adafruit KB2040 (RP2040)
+// - Tools -> USB Stack: Adafruit TinyUSB
+// - Library: Adafruit TinyUSB Library
+
+#include <Adafruit_TinyUSB.h>
+
+// HID report descriptor: Consumer Control for media keys
+static const uint8_t desc_hid_report[] = {
+    TUD_HID_REPORT_DESC_CONSUMER(HID_REPORT_ID(1))
+};
+
+Adafruit_USBD_HID usb_hid;
+Adafruit_USBD_WebUSB usb_web;
+WEBUSB_URL_DEF(landing_url, 1 /* https */, "example.com/nsigner/kb2040");
+
+static uint32_t last_hid_ms = 0;
+static uint8_t rx_buf[64];
+
+void setup() {
+  // WebUSB vendor interface
+  usb_web.setLandingPage(&landing_url);
+  usb_web.setStringDescriptor("n_signer WebUSB");
+  usb_web.begin();
+
+  // HID interface (media keys)
+  usb_hid.setPollInterval(2);
+  usb_hid.setReportDescriptor(desc_hid_report, sizeof(desc_hid_report));
+  usb_hid.setStringDescriptor("KB2040 Media");
+  usb_hid.begin();
+
+  pinMode(LED_BUILTIN, OUTPUT);
+  digitalWrite(LED_BUILTIN, LOW);
+
+  // Wait for host enumeration
+  while (!TinyUSBDevice.mounted()) {
+    delay(1);
+  }
+
+  digitalWrite(LED_BUILTIN, HIGH);
+}
+
+void loop() {
+  // Demonstrate HID activity: send volume-up every 5 seconds
+  if (millis() - last_hid_ms >= 5000) {
+    last_hid_ms = millis();
+    if (usb_hid.ready()) {
+      uint16_t key = HID_USAGE_CONSUMER_VOLUME_INCREMENT;
+      usb_hid.sendReport16(1, key);
+      delay(30);
+      usb_hid.sendReport16(1, 0);
+
+      digitalWrite(LED_BUILTIN, LOW);
+      delay(80);
+      digitalWrite(LED_BUILTIN, HIGH);
+    }
+  }
+
+  // Demonstrate WebUSB activity: echo back received bytes with prefix
+  if (usb_web.available()) {
+    uint32_t n = usb_web.read(rx_buf, sizeof(rx_buf));
+    if (n > 0) {
+      usb_web.write((const uint8_t *)"KB2040:", 7);
+      usb_web.write(rx_buf, n);
+      usb_web.flush();
+
+      for (int i = 0; i < 2; i++) {
+        digitalWrite(LED_BUILTIN, LOW);
+        delay(50);
+        digitalWrite(LED_BUILTIN, HIGH);
+        delay(50);
+      }
+    }
+  }
+}

firmware/kb2040_hidden_signer/DISPLAY_SCREENS.md

@@ -0,0 +1,340 @@
+# KB2040 Hidden Signer — Display Screens
+
+Reference for the on-device UI so we can iterate on screen designs.
+
+- Panel: **SSD1327 128x128 grayscale OLED** (I2C, STEMMA QT, addr `0x3D`).
+- Rendering source: [`display.cpp`](./display.cpp), driven by call sites in [`kb2040_hidden_signer.ino`](./kb2040_hidden_signer.ino).
+- Grayscale levels in use:
+  - dim (headers / outlines): `0x04`
+  - bar fill: `0x08`
+  - bright text: `0x0F`
+- Each screen historically ended with a bottom **status line** at `y=118`, drawn by `drawStatusLine()`. The status-line writes are currently commented out in the sketch (they were being overwritten by debug/diagnostic prints), so that line now stays effectively empty unless re-enabled.
+
+The boxes below are schematic (the panel is 128x128 px, not character-aligned). They show layout intent, relative position, and the text/labels actually printed.
+
+---
+
+## 1. Volume View
+Source: `drawVolumeView()` in [`display.cpp`](./display.cpp:60).
+Top-level "media mode" screen. Header switches between `MODE: MEDIA` / `MODE: SIGNER`.
+
+```
++--------------------------------+
+| MODE: MEDIA                    |  <- tiny, dim (size 1)
+|                                |
+|             VOL                |  <- size 2, dim
+|                                |
+|                                |
+|           ####  ####           |
+|          ##  ## #  ##          |  <- "50" centered, size 6
+|          ##  ## #  ##          |     (huge digits)
+|          ##  ## #  ##          |
+|           ####  ####           |
+|                                |
+|   +------------------------+   |  <- volume bar outline
+|   |##########              |   |     fill = volume %
+|   +------------------------+   |
+|                                |
+| [status line]                  |  <- currently disabled
++--------------------------------+
+```
+
+---
+
+## 2. Signer Menu
+Source: `drawSignerMenu()` in [`display.cpp`](./display.cpp:102).
+Two items; `>` marks the current selection (shown here on index 0).
+
+```
++--------------------------------+
+| SIGNER MENU                    |  <- size 1, dim
+|                                |
+|                                |
+|  >  Generate new               |  <- size 2, selected
+|                                |
+|                                |
+|     Enter mnemonic             |  <- size 2
+|                                |
+|                                |
+|                                |
+|                                |
+| [status line]                  |  <- currently disabled
++--------------------------------+
+```
+
+---
+
+## 3. Enter Mnemonic (in-place 2-column grid)
+Source (planned): `drawEnterMnemonic()` in [`display.cpp`](./display.cpp).
+Replaces the old separate `PICK FIRST LETTER` modal + `WORD PICK` modal with a
+single grid that looks like the Generated Phrase screen but is filled in by the
+user. Header reads `ENTER MNEMONIC`.
+
+Layout: 2 columns x 6 rows (slots 1-6 left, 7-12 right), same geometry as the
+Generated Phrase screen. All 12 numbers are shown; words are blank until entered.
+A cursor marks the active slot (starts at slot 1).
+
+```
++--------------------------------+
+| ENTER MNEMONIC                 |  <- size 1, dim
+|> 1 m         7                 |  <- cursor '>' on active slot
+|  2           8                 |     slot 1 building: "m"
+|  3           9                 |
+|  4          10                 |
+|  5          11                 |
+|  6          12                 |
+|                                |
+| back     letter                |  <- footer legend (stage-dependent)
++--------------------------------+
+```
+
+### Per-word 3-stage entry (in the active slot)
+
+Only the letters chosen so far are shown; a full word appears only at stage 3.
+
+| Stage | Scroll wheel cycles                | Active slot shows | PLAY does                  |
+| ----- | ---------------------------------- | ----------------- | -------------------------- |
+| 1     | first letter `a`..`z`              | `m`               | lock letter 1 -> stage 2   |
+| 2     | valid 2nd letters for letter 1     | `mo`              | lock letter 2 -> stage 3   |
+| 3     | words matching first two letters   | `mosaic`          | select word -> next slot   |
+
+- After slot 12's word is selected: build phrase, run
+  `mnemonic_validate_basic()`, then go to Signer Ready (or INVALID modal).
+
+### BACK behavior (context-sensitive erase)
+
+`BACK` = the NEXT button (PREV stays unused here), consistent with other entry
+screens.
+
+| Position                         | BACK action                                   |
+| -------------------------------- | --------------------------------------------- |
+| Stage 3 (choosing word)          | erase 2nd letter -> return to stage 2         |
+| Stage 2 (choosing 2nd letter)    | erase 1st letter -> return to stage 1         |
+| Stage 1, slot N > 1              | clear previous slot's word, move cursor back to slot N-1 at stage 1 |
+| Stage 1, slot 1                  | exit to Signer Menu                           |
+
+### Footer legend (stage-dependent)
+
+| Stage   | PREV (left) | PLAY (center) | NEXT (right) |
+| ------- | ----------- | ------------- | ------------ |
+| Stage 1 | `-`         | `letter`      | `back`       |
+| Stage 2 | `-`         | `letter`      | `back`       |
+| Stage 3 | `-`         | `select`      | `back`       |
+
+### New wordlist helpers required (in `mnemonic_kb.cpp` / `.h`)
+
+- `mnemonic_second_letters(char first, char *out, uint8_t *count)`
+  -> set of valid 2nd letters given the 1st letter.
+- `mnemonic_prefix_range(char first, char second, uint16_t *start, uint16_t *count)`
+  -> wordlist index range for all words starting with those two letters.
+
+(`mnemonic_letter_range()` already provides the first-letter range and can back
+the stage-1 -> stage-2 transition.)
+
+---
+
+## 4. Mnemonic Page (Generated Phrase)
+Source: `drawMnemonicPage()` in [`display.cpp`](./display.cpp:152).
+Shows generated phrase in one screen: 2 columns × 6 rows (all 12 words, no spacer rows).
+
+```
++--------------------------------+
+| GENERATED PHRASE               |  <- size 1, dim
+|  1 abandon   7 issue           |  <- size 1, tight rows
+|  2 ability   8 jungle          |
+|  3 able      9 kitchen         |
+|  4 about    10 lemon           |
+|  5 above    11 mosquito        |
+|  6 absent   12 napkin          |
+|                                |
+| PLAY confirm  NEXT cancel      |  <- size 1
+|                                |
+| [status line]                  |  <- currently disabled
++--------------------------------+
+```
+
+---
+
+## 5. Message (generic 2-line modal)
+Source: `drawMessage()` in [`display.cpp`](./display.cpp:193).
+Generic title + 2 lines. Reused for several prompts.
+
+Example — **Approval prompt** (title `APPROVAL`):
+
+```
++--------------------------------+
+| APPROVAL                       |  <- size 1, dim
+|                                |
+|                                |
+|  PLAY=Allow                    |  <- size 2
+|                                |
+|  PREV=Deny                     |  <- size 2
+|                                |
+|                                |
+|                                |
+|                                |
+|                                |
+| [status line]                  |  <- currently disabled
++--------------------------------+
+```
+
+Other current uses of this same screen:
+- `PICK FIRST LETTER` with lines `First letter` / `Letter: a`
+- `INVALID` with `Bad mnemonic` / `NEXT to return`
+- `ERROR` with `Generate failed` / `Try again`
+
+---
+
+## 6. Signer Ready
+Source: `drawSignerReady()` in [`display.cpp`](./display.cpp:210).
+Shown while waiting for the host to request signing.
+
+```
++--------------------------------+
+| SIGNER READY                   |  <- size 1, dim
+|                                |
+|   +------------------------+   |
+|   |    Awaiting            |   |  <- size 2
+|   |                        |   |
+|   |       host             |   |  <- size 2
+|   +------------------------+   |
+|                                |
+|  NEXT/PLAY: menu               |  <- size 1
+|                                |
+| [status line]                  |  <- currently disabled
++--------------------------------+
+```
+
+---
+
+## Notes / observations for redesign
+
+- The bottom status line frequently **duplicated** the in-body hint text (e.g. Word Pick showed `ENC scroll PLAY select` both in the body and in the status line). With status writes disabled, that redundancy is gone.
+- `PICK FIRST LETTER` reuses the generic Message screen rather than having a dedicated layout — a candidate for a purpose-built screen.
+- All hint text (`ENC` / `PLAY` / `NEXT` / `PREV`) refers to the physical controls: rotary encoder + the PLAY/NEXT/PREV buttons.
+```
+
+---
+
+## Screen ↔ render-function map
+
+| Screen          | Render function       | display.cpp |
+| --------------- | --------------------- | ----------- |
+| Volume View     | `drawVolumeView()`    | [60](./display.cpp:60) |
+| Signer Menu     | `drawSignerMenu()`    | [102](./display.cpp:102) |
+| Word Pick       | `drawWordPick()`      | [123](./display.cpp:123) |
+| Mnemonic Page   | `drawMnemonicPage()`  | [152](./display.cpp:152) |
+| Message (modal) | `drawMessage()`       | [193](./display.cpp:193) |
+| Signer Ready    | `drawSignerReady()`   | [210](./display.cpp:210) |
+| Status line     | `drawStatusLine()`    | [53](./display.cpp:53) |
+
+---
+
+# PROPOSAL: three-zone button legend footer
+
+The three physical buttons sit directly below the screen in this order:
+
+```
+  PREV    PLAY/PAUSE    NEXT
+   ^           ^          ^
+ (left)    (center)    (right)
+```
+
+Idea: replace the free-text status line with a fixed **3-zone legend** along the
+bottom of every screen. Each zone shows a single short verb for what that button
+does on the current screen — left-aligned, center-aligned, right-aligned so each
+label sits over its physical button. No need to print the button name; position
+implies it. An empty zone means that button does nothing on that screen.
+
+### Layout math (size 1 font, 6 px/char on a 128 px panel)
+
+- Left zone: left-aligned at `x = 2`.
+- Center zone: centered around `x = 64` (use `getTextBounds` to center).
+- Right zone: right-aligned to `x = 126` (compute `x = 126 - width`).
+- Budget ~7 chars per zone worst case (7 x 6 = 42 px x 3 = 126 px). Keep verbs
+  <= 7 chars (`select`, `confirm`, `cancel`, `back`, `deny`, `allow`, `next`,
+  `prev`) to guarantee no overlap.
+- Optional: a thin divider line above the legend at `y ~= 112`, and 1 px vertical
+  ticks between zones to reinforce the 3-button mapping.
+
+```
++--------------------------------+
+| ...screen body...              |
+|                                |
+| -------------------------------|  <- optional divider (y~112)
+| prev      confirm        next  |  <- 3 zones (left/center/right)
++--------------------------------+
+   ^PREV       ^PLAY        ^NEXT     (physical buttons below glass)
+```
+
+### Per-screen legend mapping (derived from `signer_mode_tick()`)
+
+Encoder still scrolls/selects on every screen; the legend only describes the 3
+buttons. `-` = button does nothing on that screen.
+
+| Screen / state                         | PREV (left) | PLAY (center) | NEXT (right) |
+| -------------------------------------- | ----------- | ------------- | ------------ |
+| Volume / Media view                    | `prev`      | `play`        | `next`       |
+| Signer Menu (`SIGNER_UI_MENU`)         | `-`         | `select`      | `-`          |
+| Generated Phrase (`GENERATE_REVIEW`)   | `cancel`    | `confirm`     | `new`        |
+| Signer Ready (`READY`)                 | `-`         | `-`           | `menu`       |
+| Letter Pick (`ENTER_LETTER`)           | `-`         | `confirm`     | `back`       |
+| Word Pick (`ENTER_PICK`)               | `-`         | `select`      | `back`       |
+| Approval prompt (Message modal)        | `deny`      | `allow`       | `-`          |
+
+Notes:
+- `PREV` is currently unused in most signer entry screens; it is meaningful in
+  Media view (`prev` track), the Approval prompt (`deny`), and now the Generated
+  Phrase screen (`cancel`).
+
+### Behavior change required: Generated Phrase (`SIGNER_UI_GENERATE_REVIEW`)
+
+The legend wording above implies a **functional change** in
+[`signer_mode_tick()`](./kb2040_hidden_signer.ino:657), not just labels:
+
+| Button | Current behavior            | Proposed behavior                          |
+| ------ | --------------------------- | ------------------------------------------ |
+| PREV   | (unused)                    | `cancel` -> return to Signer Menu          |
+| PLAY   | confirm -> save seed        | `confirm` -> save seed (unchanged)         |
+| NEXT   | cancel -> Signer Menu       | `new` -> regenerate a fresh 12-word phrase and refresh this screen |
+
+Implementation detail for `new`:
+- On `s_evt_next_pressed`, call `generate_mnemonic_12(s_generated_mnemonic, ...)`
+  again, then `signer_enter_review_screen()` to redraw with the new words.
+- On `s_evt_prev_pressed`, call `signer_enter_menu_screen()` (the old NEXT path).
+
+> Dependency check (resolved): `s_evt_prev_pressed` already exists and is wired
+> the same way as PLAY/NEXT — declared at [line 112](./kb2040_hidden_signer.ino:112),
+> reset in [`update_button_events()`](./kb2040_hidden_signer.ino:560), set on PREV
+> press at [line 581](./kb2040_hidden_signer.ino:581). No new plumbing needed.
+
+### What this replaces on each screen
+
+- Word Pick body lines `ENC scroll  PLAY select` / `NEXT back` -> removed; the
+  encoder action stays implicit, and PLAY/NEXT move to the footer legend.
+- Mnemonic Page body line `PLAY confirm  NEXT cancel` -> moves to the footer
+  legend (frees a body row).
+- Signer Ready body line `NEXT/PLAY: menu` -> becomes a single `menu` in the
+  NEXT zone.
+- Approval modal `PLAY=Allow` / `PREV=Deny` body lines -> footer legend
+  (`deny` left / `allow` center).
+
+### Implementation sketch
+
+1. Add a helper `drawButtonLegend(const char *left, const char *center, const char *right)`
+   in [`display.cpp`](./display.cpp) that renders the 3 aligned zones (plus the
+   optional divider/ticks) at the bottom.
+2. Give each screen a small static legend (or pass it in) and call
+   `drawButtonLegend(...)` instead of `drawStatusLine()`.
+3. Remove the now-redundant in-body hint rows listed above.
+4. Keep `drawStatusLine()` available (commented/disabled) for transient debug.
+
+### Open design decisions (need your call)
+
+1. **NEXT "back" wording**: use the word `back` vs a glyph like `<` / `<<`.
+2. **Divider/ticks**: include the thin divider line + inter-zone ticks, or keep
+   it text-only for a cleaner look.
+3. **Empty zones**: render nothing, or a subtle `·` placeholder so the user can
+   tell the button is intentionally inactive.
+4. **Media view**: apply the same legend (`prev` / `play` / `next`), or leave the
+   Volume view visually as-is since its meaning is already obvious.

firmware/kb2040_hidden_signer/README.md

@@ -0,0 +1,100 @@
+# KB2040 Hidden Signer (HID + WebUSB)
+
+This directory contains an Arduino firmware scaffold that implements the `kb2040_hidden_signer` plan on top of a TinyUSB composite device.
+
+- Firmware: [`kb2040_hidden_signer.ino`](./kb2040_hidden_signer.ino)
+- Host client: [`examples/kb2040_hidden_signer_client.py`](../../examples/kb2040_hidden_signer_client.py)
+
+## What is implemented
+
+1. Composite USB device with two active interfaces:
+   - HID Consumer Control (media keys)
+   - Vendor/WebUSB transport (framed JSON)
+2. Default media mode:
+   - Play/Pause, Next, Previous buttons emit HID consumer usages
+   - Rotary encoder emits volume up/down
+3. Hidden mode toggle:
+   - Hold PLAY + NEXT for 3 seconds to toggle media/signer mode
+4. WebUSB framed transport:
+   - 4-byte big-endian length + JSON payload
+5. Signer RPC scaffold methods:
+   - `ping`
+   - `get_status`
+   - `set_mnemonic`
+   - `set_auto_approve`
+   - `get_public_key` (deterministic placeholder pubkey)
+   - `sign_event` (approval gate + placeholder signature)
+
+## What remains to reach production n_signer parity
+
+1. Replace placeholder crypto with real `n_signer` core integration:
+   - mnemonic -> seed -> key derivation
+   - secp256k1 schnorr signing
+   - full auth envelope verification
+2. Replace naive JSON parsing with robust parsing (e.g. `ArduinoJson` or cJSON port).
+3. Wire exact `keyboard_modules` pin mapping and display abstraction.
+4. Add secure memory wiping and persistent policy storage if required.
+
+## Arduino setup (IDE)
+
+1. Install Adafruit board index in Arduino IDE.
+2. Install **Adafruit RP2040** boards package.
+3. Select board **Adafruit KB2040**.
+4. Set **Tools -> USB Stack -> Adafruit TinyUSB**.
+5. Install library **Adafruit TinyUSB Library**.
+6. Open and flash [`kb2040_hidden_signer.ino`](./kb2040_hidden_signer.ino).
+
+## Arduino CLI flashing (recommended repeatable command)
+
+Use this exact command when flashing from CLI:
+
+```bash
+arduino-cli compile --upload -p /dev/ttyACM0 \
+  --fqbn rp2040:rp2040:adafruit_kb2040:usbstack=tinyusb \
+  firmware/kb2040_hidden_signer
+```
+
+Notes:
+- `usbstack=tinyusb` is **required** for this firmware (TinyUSB composite device).
+- If you omit that option, build fails with `TinyUSB is not selected`.
+- If `/dev/ttyACM0` changes, find the current port with:
+
+```bash
+arduino-cli board list
+```
+
+## Host validation
+
+Install dependency:
+
+```bash
+pip install pyusb
+```
+
+Basic dual-interface verification:
+
+```bash
+python3 tests/test_kb2040_dual.py
+```
+
+Signer RPC flow (WebUSB/vendor interface):
+
+```bash
+python3 examples/kb2040_hidden_signer_client.py status
+python3 examples/kb2040_hidden_signer_client.py set-mnemonic --mnemonic "abandon abandon abandon abandon abandon abandon abandon abandon abandon abandon abandon about"
+python3 examples/kb2040_hidden_signer_client.py get-public-key
+python3 examples/kb2040_hidden_signer_client.py sign-event --event '{"kind":1,"content":"hello"}'
+```
+
+## Pin mapping
+
+Current defaults in [`kb2040_hidden_signer.ino`](./kb2040_hidden_signer.ino):
+
+- `PIN_BTN_PLAY = 2`
+- `PIN_BTN_NEXT = 3`
+- `PIN_BTN_PREV = 4`
+- `PIN_ENC_A = 5`
+- `PIN_ENC_B = 6`
+- `PIN_ENC_SW = 7`
+
+Update these constants to match your physical `keyboard_modules` build.

firmware/kb2040_hidden_signer/display.cpp

@@ -0,0 +1,467 @@
+#include "display.h"
+
+#include <Arduino.h>
+#include <Wire.h>
+
+#include <Adafruit_GFX.h>
+#include <Adafruit_SSD1327.h>
+
+namespace {
+
+static constexpr uint8_t kDisplayWidth = 128;
+static constexpr uint8_t kDisplayHeight = 128;
+static constexpr uint8_t kDefaultI2cAddr = 0x3D;
+
+static constexpr uint8_t kGrayDim = 0x04;
+static constexpr uint8_t kGrayBar = 0x08;
+static constexpr uint8_t kGrayText = 0x0F;
+
+Adafruit_SSD1327 g_display(kDisplayWidth, kDisplayHeight, &Wire, -1, 400000, 100000);
+
+bool g_displayPresent = false;
+bool g_dirty = true;
+display_view_t g_view = DISPLAY_VIEW_VOLUME;
+uint8_t g_volume = 50;
+bool g_signerMode = false;
+char g_status[24] = "BOOT";
+
+uint8_t g_menuSelected = 0;
+uint8_t g_mnemonicPage = 0;
+char g_mnemonic[256] = "";
+char g_msgTitle[18] = "";
+char g_msgLine1[22] = "";
+char g_msgLine2[22] = "";
+char g_enterSlots[12][16] = {{0}};
+uint8_t g_enterActiveSlot = 0;
+uint8_t g_enterStage = 1;
+char g_enterBuilding[16] = "";
+uint8_t g_enterCursorPos = 0;
+
+enum signer_screen_t {
+  SIGNER_SCREEN_MENU = 0,
+  SIGNER_SCREEN_ENTER_GRID = 1,
+  SIGNER_SCREEN_MNEMONIC_PAGE = 2,
+  SIGNER_SCREEN_MESSAGE = 3,
+  SIGNER_SCREEN_READY = 4,
+};
+
+signer_screen_t g_signerScreen = SIGNER_SCREEN_MENU;
+
+uint8_t clampVolume(uint8_t v) {
+  return (v > 100) ? 100 : v;
+}
+
+void drawStatusLine() {
+  g_display.setTextSize(1);
+  g_display.setTextColor(kGrayText);
+  g_display.setCursor(2, 118);
+  g_display.print(g_status);
+}
+
+void drawButtonLegend(const char *left, const char *center, const char *right) {
+  g_display.setTextSize(1);
+  g_display.setTextColor(kGrayText);
+  g_display.setTextWrap(false);
+
+  if (left && left[0] != '\0') {
+    g_display.setCursor(2, 118);
+    g_display.print(left);
+  }
+
+  int16_t x1 = 0;
+  int16_t y1 = 0;
+  uint16_t w = 0;
+  uint16_t h = 0;
+
+  if (center && center[0] != '\0') {
+    g_display.getTextBounds(center, 0, 0, &x1, &y1, &w, &h);
+    const int16_t x = static_cast<int16_t>((kDisplayWidth - w) / 2);
+    g_display.setCursor(x, 118);
+    g_display.print(center);
+  }
+
+  if (right && right[0] != '\0') {
+    g_display.getTextBounds(right, 0, 0, &x1, &y1, &w, &h);
+    const int16_t x = static_cast<int16_t>(126 - w);
+    g_display.setCursor(x, 118);
+    g_display.print(right);
+  }
+}
+
+void drawVolumeView() {
+  g_display.setTextWrap(false);
+
+  g_display.setTextColor(kGrayDim);
+  g_display.setTextSize(2);
+  g_display.setCursor(40, 18);
+  g_display.print("VOL");
+
+  char volBuf[4];
+  snprintf(volBuf, sizeof(volBuf), "%u", g_volume);
+
+  int16_t x1 = 0;
+  int16_t y1 = 0;
+  uint16_t w = 0;
+  uint16_t h = 0;
+  g_display.setTextSize(6);
+  g_display.getTextBounds(volBuf, 0, 0, &x1, &y1, &w, &h);
+
+  const int16_t x = static_cast<int16_t>((kDisplayWidth - w) / 2);
+  const int16_t y = 42;
+  g_display.setTextColor(kGrayText);
+  g_display.setCursor(x, y);
+  g_display.print(volBuf);
+
+  const int16_t barX = 8;
+  const int16_t barY = 102;
+  const int16_t barW = kDisplayWidth - 16;
+  const int16_t barH = 8;
+  g_display.drawRect(barX, barY, barW, barH, kGrayDim);
+
+  const int16_t fillW = static_cast<int16_t>((static_cast<uint32_t>(barW - 2) * g_volume) / 100U);
+  if (fillW > 0) {
+    g_display.fillRect(barX + 1, barY + 1, fillW, barH - 2, kGrayBar);
+  }
+
+  drawButtonLegend("prev", "play", "next");
+}
+
+void drawSignerMenu() {
+  g_display.setTextWrap(false);
+  g_display.setTextSize(1);
+  g_display.setTextColor(kGrayDim);
+  g_display.setCursor(2, 2);
+  g_display.print("SIGNER MENU");
+
+  const char *items[2] = {"Generate new", "Enter mnemonic"};
+
+  g_display.setTextColor(kGrayText);
+  g_display.setTextSize(2);
+  for (uint8_t i = 0; i < 2; ++i) {
+    g_display.setCursor(6, 28 + i * 24);
+    g_display.print((i == g_menuSelected) ? ">" : " ");
+    g_display.setCursor(20, 28 + i * 24);
+    g_display.print(items[i]);
+  }
+
+  drawButtonLegend("", "select", "");
+}
+
+void drawEnterMnemonic() {
+  g_display.setTextWrap(false);
+  g_display.setTextSize(1);
+  g_display.setTextColor(kGrayDim);
+  g_display.setCursor(2, 2);
+  g_display.print("ENTER MNEMONIC");
+
+  g_display.setTextColor(kGrayText);
+  for (uint8_t i = 0; i < 12; ++i) {
+    const uint8_t row = (i < 6) ? i : (i - 6);
+    const int16_t x = (i < 6) ? 0 : 64;
+    const int16_t y = static_cast<int16_t>(18 + row * 9);
+
+    const bool isActive = (i == g_enterActiveSlot);
+    const char cursor = isActive ? '>' : ' ';
+
+    const char *slotWord = g_enterSlots[i];
+    if (!slotWord) {
+      slotWord = "";
+    }
+
+    char activeBuf[16];
+    const char *shownWord = slotWord;
+    if (isActive) {
+      const char *src = g_enterBuilding;
+      if (!src) {
+        src = "";
+      }
+
+      if (g_enterStage < 3) {
+        size_t srcLen = strlen(src);
+        if (srcLen > 14) {
+          srcLen = 14;
+        }
+        size_t pos = g_enterCursorPos;
+        if (pos > srcLen) {
+          pos = srcLen;
+        }
+
+        size_t out = 0;
+        for (size_t j = 0; j < pos && out < sizeof(activeBuf) - 1; ++j) {
+          activeBuf[out++] = src[j];
+        }
+        if (out < sizeof(activeBuf) - 1) {
+          activeBuf[out++] = '_';
+        }
+        for (size_t j = pos; j < srcLen && out < sizeof(activeBuf) - 1; ++j) {
+          activeBuf[out++] = src[j];
+        }
+        activeBuf[out] = '\0';
+        shownWord = activeBuf;
+      } else if (src[0] != '\0') {
+        shownWord = src;
+      }
+    }
+
+    char lineBuf[22];
+    snprintf(lineBuf, sizeof(lineBuf), "%c%2u %s", cursor, (unsigned)(i + 1), shownWord);
+    g_display.setCursor(x, y);
+    g_display.print(lineBuf);
+  }
+
+  if (g_enterStage == 3) {
+    drawButtonLegend("", "select", "back");
+  } else {
+    drawButtonLegend("", "letter", "back");
+  }
+}
+
+void drawMnemonicPage() {
+  g_display.setTextWrap(false);
+  g_display.setTextSize(1);
+  g_display.setTextColor(kGrayDim);
+  g_display.setCursor(2, 2);
+  g_display.print("GENERATED PHRASE");
+
+  char copy[256];
+  strncpy(copy, g_mnemonic, sizeof(copy) - 1);
+  copy[sizeof(copy) - 1] = '\0';
+
+  char *words[12] = {nullptr};
+  uint8_t count = 0;
+  char *saveptr = nullptr;
+  char *tok = strtok_r(copy, " ", &saveptr);
+  while (tok && count < 12) {
+    words[count++] = tok;
+    tok = strtok_r(nullptr, " ", &saveptr);
+  }
+
+  g_display.setTextColor(kGrayText);
+  for (uint8_t i = 0; i < count; ++i) {
+    const uint8_t row = (i < 6) ? i : (i - 6);
+    const int16_t x = (i < 6) ? 0 : 64;
+    const int16_t y = static_cast<int16_t>(18 + row * 9);
+
+    char lineBuf[20];
+    snprintf(lineBuf, sizeof(lineBuf), "%2u %s", (unsigned)(i + 1), words[i]);
+    g_display.setCursor(x, y);
+    g_display.print(lineBuf);
+  }
+
+  drawButtonLegend("cancel", "confirm", "new");
+}
+
+void drawMessage() {
+  g_display.setTextWrap(false);
+  g_display.setTextSize(1);
+  g_display.setTextColor(kGrayDim);
+  g_display.setCursor(2, 2);
+  g_display.print(g_msgTitle);
+
+  g_display.setTextSize(2);
+  g_display.setTextColor(kGrayText);
+  g_display.setCursor(6, 34);
+  g_display.print(g_msgLine1);
+  g_display.setCursor(6, 62);
+  g_display.print(g_msgLine2);
+
+  const char *left = "";
+  const char *center = "";
+  const char *right = "";
+
+  if (strcmp(g_msgTitle, "APPROVAL") == 0) {
+    left = "deny";
+    center = "allow";
+  } else if (strcmp(g_msgTitle, "INVALID") == 0) {
+    center = "select";
+    right = "back";
+  } else if (strcmp(g_msgTitle, "ERROR") == 0) {
+    center = "select";
+  }
+
+  drawButtonLegend(left, center, right);
+}
+
+void drawSignerReady() {
+  g_display.setTextWrap(false);
+  g_display.setTextSize(1);
+  g_display.setTextColor(kGrayDim);
+  g_display.setCursor(2, 2);
+  g_display.print("SIGNER READY");
+
+  g_display.drawRect(4, 22, 120, 62, kGrayDim);
+
+  g_display.setTextSize(2);
+  g_display.setTextColor(kGrayText);
+  g_display.setCursor(16, 36);
+  g_display.print("Awaiting");
+  g_display.setCursor(30, 58);
+  g_display.print("host");
+
+  drawButtonLegend("", "", "menu");
+}
+
+void renderFrame() {
+  if (!g_displayPresent) {
+    return;
+  }
+
+  g_display.clearDisplay();
+
+  if (g_view == DISPLAY_VIEW_VOLUME) {
+    drawVolumeView();
+  } else {
+    switch (g_signerScreen) {
+      case SIGNER_SCREEN_MENU:
+        drawSignerMenu();
+        break;
+      case SIGNER_SCREEN_ENTER_GRID:
+        drawEnterMnemonic();
+        break;
+      case SIGNER_SCREEN_MNEMONIC_PAGE:
+        drawMnemonicPage();
+        break;
+      case SIGNER_SCREEN_MESSAGE:
+        drawMessage();
+        break;
+      case SIGNER_SCREEN_READY:
+        drawSignerReady();
+        break;
+      default:
+        drawMessage();
+        break;
+    }
+  }
+
+  g_display.display();
+}
+
+void copy_text(char *dst, size_t dst_sz, const char *src) {
+  if (!dst || dst_sz == 0) {
+    return;
+  }
+  if (!src) {
+    dst[0] = '\0';
+    return;
+  }
+  strncpy(dst, src, dst_sz - 1);
+  dst[dst_sz - 1] = '\0';
+}
+
+}  // namespace
+
+void display_init() {
+  Wire.setClock(400000);
+  Wire.begin();
+
+  Wire.beginTransmission(kDefaultI2cAddr);
+  const uint8_t probeErr = Wire.endTransmission();
+  if (probeErr != 0) {
+    g_displayPresent = false;
+    return;
+  }
+
+  g_displayPresent = g_display.begin(kDefaultI2cAddr, true);
+  if (!g_displayPresent) {
+    return;
+  }
+
+  g_dirty = true;
+  renderFrame();
+}
+
+bool display_is_present() {
+  return g_displayPresent;
+}
+
+void display_set_view(display_view_t view) {
+  if (g_view == view) {
+    return;
+  }
+  g_view = view;
+  g_dirty = true;
+}
+
+void display_set_mode(bool signer_mode) {
+  if (g_signerMode == signer_mode) {
+    return;
+  }
+  g_signerMode = signer_mode;
+  g_dirty = true;
+}
+
+void display_set_volume(uint8_t volume) {
+  const uint8_t v = clampVolume(volume);
+  if (v == g_volume) {
+    return;
+  }
+
+  g_volume = v;
+  g_dirty = true;
+}
+
+void display_show_signer_menu(uint8_t selected_index) {
+  g_signerScreen = SIGNER_SCREEN_MENU;
+  g_menuSelected = selected_index > 1 ? 1 : selected_index;
+  g_dirty = true;
+}
+
+void display_show_enter_mnemonic(const char *const slots[12], uint8_t active_slot, uint8_t stage,
+                                 const char *building_text, uint8_t cursor_pos) {
+  g_signerScreen = SIGNER_SCREEN_ENTER_GRID;
+  g_enterActiveSlot = (active_slot > 11) ? 11 : active_slot;
+  g_enterStage = stage;
+  g_enterCursorPos = cursor_pos;
+  copy_text(g_enterBuilding, sizeof(g_enterBuilding), building_text);
+
+  for (uint8_t i = 0; i < 12; ++i) {
+    const char *src = "";
+    if (slots && slots[i]) {
+      src = slots[i];
+    }
+    copy_text(g_enterSlots[i], sizeof(g_enterSlots[i]), src);
+  }
+
+  g_dirty = true;
+}
+
+void display_show_mnemonic_page(const char *mnemonic, uint8_t page_index) {
+  g_signerScreen = SIGNER_SCREEN_MNEMONIC_PAGE;
+  g_mnemonicPage = page_index;
+  copy_text(g_mnemonic, sizeof(g_mnemonic), mnemonic);
+  g_dirty = true;
+}
+
+void display_show_message(const char *title, const char *line1, const char *line2) {
+  g_signerScreen = SIGNER_SCREEN_MESSAGE;
+  copy_text(g_msgTitle, sizeof(g_msgTitle), title);
+  copy_text(g_msgLine1, sizeof(g_msgLine1), line1);
+  copy_text(g_msgLine2, sizeof(g_msgLine2), line2);
+  g_dirty = true;
+}
+
+void display_show_signer_ready() {
+  g_signerScreen = SIGNER_SCREEN_READY;
+  g_dirty = true;
+}
+
+// Note: status-line updates are currently disabled at call sites in
+// kb2040_hidden_signer.ino by commenting out display_set_status(...)
+// invocations to keep the bottom status line from being overwritten.
+void display_set_status(const char *status) {
+  if (!status) {
+    return;
+  }
+
+  copy_text(g_status, sizeof(g_status), status);
+  g_dirty = true;
+}
+
+void display_tick() {
+  if (!g_displayPresent || !g_dirty) {
+    return;
+  }
+
+  renderFrame();
+  g_dirty = false;
+}

firmware/kb2040_hidden_signer/display.h

@@ -0,0 +1,38 @@
+#pragma once
+
+#include <stdbool.h>
+#include <stdint.h>
+
+enum display_view_t {
+  DISPLAY_VIEW_VOLUME = 0,
+  DISPLAY_VIEW_SIGNER = 1,
+};
+
+// Initialize the SSD1327 OLED on KB2040 STEMMA QT (Wire = Wire0, GPIO12/13).
+void display_init();
+
+// Returns true when the display was detected and initialized successfully.
+bool display_is_present();
+
+// Select top-level display view.
+void display_set_view(display_view_t view);
+
+// Set current mode text for volume view header.
+void display_set_mode(bool signer_mode);
+
+// Set local volume value shown on-screen. Input is clamped to 0..100.
+void display_set_volume(uint8_t volume);
+
+// Signer UI rendering helpers.
+void display_show_signer_menu(uint8_t selected_index);
+void display_show_enter_mnemonic(const char *const slots[12], uint8_t active_slot, uint8_t stage,
+                                 const char *building_text, uint8_t cursor_pos);
+void display_show_mnemonic_page(const char *mnemonic, uint8_t page_index);
+void display_show_message(const char *title, const char *line1, const char *line2);
+void display_show_signer_ready();
+
+// Set short status text line (truncated to fit).
+void display_set_status(const char *status);
+
+// Non-blocking tick; renders only when state changed.
+void display_tick();

firmware/kb2040_hidden_signer/mnemonic_kb.cpp

@@ -0,0 +1,246 @@
+#include "mnemonic_kb.h"
+
+#include <Arduino.h>
+#include <string.h>
+
+#include "mnemonic_wordlist.h"
+
+namespace {
+
+static bool s_rng_seeded = false;
+
+void ensure_rng_seeded() {
+  if (s_rng_seeded) {
+    return;
+  }
+
+  uint32_t seed = micros() ^ (millis() << 16);
+  for (int i = 0; i < 16; ++i) {
+    seed ^= ((uint32_t)analogRead(A0) & 0x3FFu) << (i % 22);
+    delayMicroseconds(50);
+  }
+
+  randomSeed(seed);
+  s_rng_seeded = true;
+}
+
+bool append_word(char* out, size_t out_len, size_t* cursor, const char* word) {
+  const size_t wlen = strlen(word);
+
+  if (*cursor >= out_len) {
+    return false;
+  }
+
+  if (*cursor != 0) {
+    if (*cursor + 1 >= out_len) {
+      return false;
+    }
+    out[*cursor] = ' ';
+    (*cursor)++;
+  }
+
+  if (*cursor + wlen >= out_len) {
+    return false;
+  }
+
+  memcpy(out + *cursor, word, wlen);
+  *cursor += wlen;
+  out[*cursor] = '\0';
+  return true;
+}
+
+}  // namespace
+
+bool mnemonic_letter_range(char letter, uint16_t *out_start, uint16_t *out_count) {
+  if (!out_start || !out_count) {
+    return false;
+  }
+
+  if (letter >= 'A' && letter <= 'Z') {
+    letter = (char)(letter - 'A' + 'a');
+  }
+  if (letter < 'a' || letter > 'z') {
+    return false;
+  }
+
+  int first = -1;
+  int last = -1;
+  for (int i = 0; i < 2048; ++i) {
+    const char c = BIP39_WORDLIST[i][0];
+    if (c == letter) {
+      if (first < 0) first = i;
+      last = i;
+    } else if (first >= 0) {
+      break;
+    }
+  }
+
+  if (first < 0 || last < first) {
+    return false;
+  }
+
+  *out_start = (uint16_t)first;
+  *out_count = (uint16_t)(last - first + 1);
+  return true;
+}
+
+bool mnemonic_second_letters(char first, char *out, uint8_t *count) {
+  if (!out || !count) {
+    return false;
+  }
+
+  *count = 0;
+
+  if (first >= 'A' && first <= 'Z') {
+    first = (char)(first - 'A' + 'a');
+  }
+  if (first < 'a' || first > 'z') {
+    return false;
+  }
+
+  uint16_t start = 0;
+  uint16_t range_count = 0;
+  if (!mnemonic_letter_range(first, &start, &range_count) || range_count == 0) {
+    return false;
+  }
+
+  bool seen[26] = {false};
+  uint8_t found = 0;
+  for (uint16_t i = 0; i < range_count; ++i) {
+    const char* w = BIP39_WORDLIST[start + i];
+    char c = w[1];
+    if (c >= 'A' && c <= 'Z') {
+      c = (char)(c - 'A' + 'a');
+    }
+    if (c < 'a' || c > 'z') {
+      continue;
+    }
+
+    const uint8_t idx = (uint8_t)(c - 'a');
+    if (!seen[idx]) {
+      seen[idx] = true;
+      out[found++] = c;
+    }
+  }
+
+  *count = found;
+  return found > 0;
+}
+
+bool mnemonic_prefix_range(char first, char second, uint16_t *out_start, uint16_t *out_count) {
+  if (!out_start || !out_count) {
+    return false;
+  }
+
+  if (first >= 'A' && first <= 'Z') {
+    first = (char)(first - 'A' + 'a');
+  }
+  if (second >= 'A' && second <= 'Z') {
+    second = (char)(second - 'A' + 'a');
+  }
+  if (first < 'a' || first > 'z' || second < 'a' || second > 'z') {
+    return false;
+  }
+
+  uint16_t start = 0;
+  uint16_t range_count = 0;
+  if (!mnemonic_letter_range(first, &start, &range_count) || range_count == 0) {
+    return false;
+  }
+
+  int first_match = -1;
+  int last_match = -1;
+  for (uint16_t i = 0; i < range_count; ++i) {
+    const char* w = BIP39_WORDLIST[start + i];
+    char c = w[1];
+    if (c >= 'A' && c <= 'Z') {
+      c = (char)(c - 'A' + 'a');
+    }
+
+    if (c == second) {
+      if (first_match < 0) {
+        first_match = (int)(start + i);
+      }
+      last_match = (int)(start + i);
+    } else if (first_match >= 0) {
+      break;
+    }
+  }
+
+  if (first_match < 0 || last_match < first_match) {
+    return false;
+  }
+
+  *out_start = (uint16_t)first_match;
+  *out_count = (uint16_t)(last_match - first_match + 1);
+  return true;
+}
+
+const char* mnemonic_word_at(uint16_t index) {
+  if (index >= 2048) {
+    return nullptr;
+  }
+  return BIP39_WORDLIST[index];
+}
+
+int mnemonic_word_index(const char* word) {
+  if (!word || !word[0]) {
+    return -1;
+  }
+
+  for (int i = 0; i < 2048; ++i) {
+    if (strcmp(word, BIP39_WORDLIST[i]) == 0) {
+      return i;
+    }
+  }
+
+  return -1;
+}
+
+int generate_mnemonic_12(char* out, size_t out_len) {
+  if (!out || out_len == 0) {
+    return -1;
+  }
+
+  out[0] = '\0';
+  ensure_rng_seeded();
+
+  size_t cursor = 0;
+  for (int i = 0; i < 12; ++i) {
+    const uint16_t idx = (uint16_t)random(0, 2048);
+    const char* word = mnemonic_word_at(idx);
+    if (!word) {
+      return -1;
+    }
+
+    if (!append_word(out, out_len, &cursor, word)) {
+      return -1;
+    }
+  }
+
+  return 0;
+}
+
+bool mnemonic_validate_basic(const char* mnemonic) {
+  if (!mnemonic || !mnemonic[0]) {
+    return false;
+  }
+
+  char buf[256];
+  strncpy(buf, mnemonic, sizeof(buf) - 1);
+  buf[sizeof(buf) - 1] = '\0';
+
+  int count = 0;
+  char* saveptr = nullptr;
+  char* tok = strtok_r(buf, " ", &saveptr);
+  while (tok) {
+    if (mnemonic_word_index(tok) < 0) {
+      return false;
+    }
+
+    ++count;
+    tok = strtok_r(nullptr, " ", &saveptr);
+  }
+
+  return count == 12;
+}

firmware/kb2040_hidden_signer/mnemonic_kb.h

@@ -0,0 +1,13 @@
+#pragma once
+
+#include <stdbool.h>
+#include <stddef.h>
+#include <stdint.h>
+
+const char* mnemonic_word_at(uint16_t index);
+int mnemonic_word_index(const char* word);
+bool mnemonic_letter_range(char letter, uint16_t *out_start, uint16_t *out_count);
+bool mnemonic_second_letters(char first, char *out, uint8_t *count);
+bool mnemonic_prefix_range(char first, char second, uint16_t *out_start, uint16_t *out_count);
+int generate_mnemonic_12(char* out, size_t out_len);
+bool mnemonic_validate_basic(const char* mnemonic);

firmware/kb2040_hidden_signer/mnemonic_wordlist.h

@@ -0,0 +1,261 @@
+#pragma once
+
+/* BIP-39 English wordlist (2048 words) */
+static const char *BIP39_WORDLIST[2048] = {
+    "abandon", "ability", "able", "about", "above", "absent", "absorb", "abstract",
+    "absurd", "abuse", "access", "accident", "account", "accuse", "achieve", "acid",
+    "acoustic", "acquire", "across", "act", "action", "actor", "actress", "actual",
+    "adapt", "add", "addict", "address", "adjust", "admit", "adult", "advance",
+    "advice", "aerobic", "affair", "afford", "afraid", "again", "age", "agent",
+    "agree", "ahead", "aim", "air", "airport", "aisle", "alarm", "album",
+    "alcohol", "alert", "alien", "all", "alley", "allow", "almost", "alone",
+    "alpha", "already", "also", "alter", "always", "amateur", "amazing", "among",
+    "amount", "amused", "analyst", "anchor", "ancient", "anger", "angle", "angry",
+    "animal", "ankle", "announce", "annual", "another", "answer", "antenna", "antique",
+    "anxiety", "any", "apart", "apology", "appear", "apple", "approve", "april",
+    "arch", "arctic", "area", "arena", "argue", "arm", "armed", "armor",
+    "army", "around", "arrange", "arrest", "arrive", "arrow", "art", "artefact",
+    "artist", "artwork", "ask", "aspect", "assault", "asset", "assist", "assume",
+    "asthma", "athlete", "atom", "attack", "attend", "attitude", "attract", "auction",
+    "audit", "august", "aunt", "author", "auto", "autumn", "average", "avocado",
+    "avoid", "awake", "aware", "away", "awesome", "awful", "awkward", "axis",
+    "baby", "bachelor", "bacon", "badge", "bag", "balance", "balcony", "ball",
+    "bamboo", "banana", "banner", "bar", "barely", "bargain", "barrel", "base",
+    "basic", "basket", "battle", "beach", "bean", "beauty", "because", "become",
+    "beef", "before", "begin", "behave", "behind", "believe", "below", "belt",
+    "bench", "benefit", "best", "betray", "better", "between", "beyond", "bicycle",
+    "bid", "bike", "bind", "biology", "bird", "birth", "bitter", "black",
+    "blade", "blame", "blanket", "blast", "bleak", "bless", "blind", "blood",
+    "blossom", "blouse", "blue", "blur", "blush", "board", "boat", "body",
+    "boil", "bomb", "bone", "bonus", "book", "boost", "border", "boring",
+    "borrow", "boss", "bottom", "bounce", "box", "boy", "bracket", "brain",
+    "brand", "brass", "brave", "bread", "breeze", "brick", "bridge", "brief",
+    "bright", "bring", "brisk", "broccoli", "broken", "bronze", "broom", "brother",
+    "brown", "brush", "bubble", "buddy", "budget", "buffalo", "build", "bulb",
+    "bulk", "bullet", "bundle", "bunker", "burden", "burger", "burst", "bus",
+    "business", "busy", "butter", "buyer", "buzz", "cabbage", "cabin", "cable",
+    "cactus", "cage", "cake", "call", "calm", "camera", "camp", "can",
+    "canal", "cancel", "candy", "cannon", "canoe", "canvas", "canyon", "capable",
+    "capital", "captain", "car", "carbon", "card", "cargo", "carpet", "carry",
+    "cart", "case", "cash", "casino", "castle", "casual", "cat", "catalog",
+    "catch", "category", "cattle", "caught", "cause", "caution", "cave", "ceiling",
+    "celery", "cement", "census", "century", "cereal", "certain", "chair", "chalk",
+    "champion", "change", "chaos", "chapter", "charge", "chase", "chat", "cheap",
+    "check", "cheese", "chef", "cherry", "chest", "chicken", "chief", "child",
+    "chimney", "choice", "choose", "chronic", "chuckle", "chunk", "churn", "cigar",
+    "cinnamon", "circle", "citizen", "city", "civil", "claim", "clap", "clarify",
+    "claw", "clay", "clean", "clerk", "clever", "click", "client", "cliff",
+    "climb", "clinic", "clip", "clock", "clog", "close", "cloth", "cloud",
+    "clown", "club", "clump", "cluster", "clutch", "coach", "coast", "coconut",
+    "code", "coffee", "coil", "coin", "collect", "color", "column", "combine",
+    "come", "comfort", "comic", "common", "company", "concert", "conduct", "confirm",
+    "congress", "connect", "consider", "control", "convince", "cook", "cool", "copper",
+    "copy", "coral", "core", "corn", "correct", "cost", "cotton", "couch",
+    "country", "couple", "course", "cousin", "cover", "coyote", "crack", "cradle",
+    "craft", "cram", "crane", "crash", "crater", "crawl", "crazy", "cream",
+    "credit", "creek", "crew", "cricket", "crime", "crisp", "critic", "crop",
+    "cross", "crouch", "crowd", "crucial", "cruel", "cruise", "crumble", "crunch",
+    "crush", "cry", "crystal", "cube", "culture", "cup", "cupboard", "curious",
+    "current", "curtain", "curve", "cushion", "custom", "cute", "cycle", "dad",
+    "damage", "damp", "dance", "danger", "daring", "dash", "daughter", "dawn",
+    "day", "deal", "debate", "debris", "decade", "december", "decide", "decline",
+    "decorate", "decrease", "deer", "defense", "define", "defy", "degree", "delay",
+    "deliver", "demand", "demise", "denial", "dentist", "deny", "depart", "depend",
+    "deposit", "depth", "deputy", "derive", "describe", "desert", "design", "desk",
+    "despair", "destroy", "detail", "detect", "develop", "device", "devote", "diagram",
+    "dial", "diamond", "diary", "dice", "diesel", "diet", "differ", "digital",
+    "dignity", "dilemma", "dinner", "dinosaur", "direct", "dirt", "disagree", "discover",
+    "disease", "dish", "dismiss", "disorder", "display", "distance", "divert", "divide",
+    "divorce", "dizzy", "doctor", "document", "dog", "doll", "dolphin", "domain",
+    "donate", "donkey", "donor", "door", "dose", "double", "dove", "draft",
+    "dragon", "drama", "drastic", "draw", "dream", "dress", "drift", "drill",
+    "drink", "drip", "drive", "drop", "drum", "dry", "duck", "dumb",
+    "dune", "during", "dust", "dutch", "duty", "dwarf", "dynamic", "eager",
+    "eagle", "early", "earn", "earth", "easily", "east", "easy", "echo",
+    "ecology", "economy", "edge", "edit", "educate", "effort", "egg", "eight",
+    "either", "elbow", "elder", "electric", "elegant", "element", "elephant", "elevator",
+    "elite", "else", "embark", "embody", "embrace", "emerge", "emotion", "employ",
+    "empower", "empty", "enable", "enact", "end", "endless", "endorse", "enemy",
+    "energy", "enforce", "engage", "engine", "enhance", "enjoy", "enlist", "enough",
+    "enrich", "enroll", "ensure", "enter", "entire", "entry", "envelope", "episode",
+    "equal", "equip", "era", "erase", "erode", "erosion", "error", "erupt",
+    "escape", "essay", "essence", "estate", "eternal", "ethics", "evidence", "evil",
+    "evoke", "evolve", "exact", "example", "excess", "exchange", "excite", "exclude",
+    "excuse", "execute", "exercise", "exhaust", "exhibit", "exile", "exist", "exit",
+    "exotic", "expand", "expect", "expire", "explain", "expose", "express", "extend",
+    "extra", "eye", "eyebrow", "fabric", "face", "faculty", "fade", "faint",
+    "faith", "fall", "false", "fame", "family", "famous", "fan", "fancy",
+    "fantasy", "farm", "fashion", "fat", "fatal", "father", "fatigue", "fault",
+    "favorite", "feature", "february", "federal", "fee", "feed", "feel", "female",
+    "fence", "festival", "fetch", "fever", "few", "fiber", "fiction", "field",
+    "figure", "file", "film", "filter", "final", "find", "fine", "finger",
+    "finish", "fire", "firm", "first", "fiscal", "fish", "fit", "fitness",
+    "fix", "flag", "flame", "flash", "flat", "flavor", "flee", "flight",
+    "flip", "float", "flock", "floor", "flower", "fluid", "flush", "fly",
+    "foam", "focus", "fog", "foil", "fold", "follow", "food", "foot",
+    "force", "forest", "forget", "fork", "fortune", "forum", "forward", "fossil",
+    "foster", "found", "fox", "fragile", "frame", "frequent", "fresh", "friend",
+    "fringe", "frog", "front", "frost", "frown", "frozen", "fruit", "fuel",
+    "fun", "funny", "furnace", "fury", "future", "gadget", "gain", "galaxy",
+    "gallery", "game", "gap", "garage", "garbage", "garden", "garlic", "garment",
+    "gas", "gasp", "gate", "gather", "gauge", "gaze", "general", "genius",
+    "genre", "gentle", "genuine", "gesture", "ghost", "giant", "gift", "giggle",
+    "ginger", "giraffe", "girl", "give", "glad", "glance", "glare", "glass",
+    "glide", "glimpse", "globe", "gloom", "glory", "glove", "glow", "glue",
+    "goat", "goddess", "gold", "good", "goose", "gorilla", "gospel", "gossip",
+    "govern", "gown", "grab", "grace", "grain", "grant", "grape", "grass",
+    "gravity", "great", "green", "grid", "grief", "grit", "grocery", "group",
+    "grow", "grunt", "guard", "guess", "guide", "guilt", "guitar", "gun",
+    "gym", "habit", "hair", "half", "hammer", "hamster", "hand", "happy",
+    "harbor", "hard", "harsh", "harvest", "hat", "have", "hawk", "hazard",
+    "head", "health", "heart", "heavy", "hedgehog", "height", "hello", "helmet",
+    "help", "hen", "hero", "hidden", "high", "hill", "hint", "hip",
+    "hire", "history", "hobby", "hockey", "hold", "hole", "holiday", "hollow",
+    "home", "honey", "hood", "hope", "horn", "horror", "horse", "hospital",
+    "host", "hotel", "hour", "hover", "hub", "huge", "human", "humble",
+    "humor", "hundred", "hungry", "hunt", "hurdle", "hurry", "hurt", "husband",
+    "hybrid", "ice", "icon", "idea", "identify", "idle", "ignore", "ill",
+    "illegal", "illness", "image", "imitate", "immense", "immune", "impact", "impose",
+    "improve", "impulse", "inch", "include", "income", "increase", "index", "indicate",
+    "indoor", "industry", "infant", "inflict", "inform", "inhale", "inherit", "initial",
+    "inject", "injury", "inmate", "inner", "innocent", "input", "inquiry", "insane",
+    "insect", "inside", "inspire", "install", "intact", "interest", "into", "invest",
+    "invite", "involve", "iron", "island", "isolate", "issue", "item", "ivory",
+    "jacket", "jaguar", "jar", "jazz", "jealous", "jeans", "jelly", "jewel",
+    "job", "join", "joke", "journey", "joy", "judge", "juice", "jump",
+    "jungle", "junior", "junk", "just", "kangaroo", "keen", "keep", "ketchup",
+    "key", "kick", "kid", "kidney", "kind", "kingdom", "kiss", "kit",
+    "kitchen", "kite", "kitten", "kiwi", "knee", "knife", "knock", "know",
+    "lab", "label", "labor", "ladder", "lady", "lake", "lamp", "language",
+    "laptop", "large", "later", "latin", "laugh", "laundry", "lava", "law",
+    "lawn", "lawsuit", "layer", "lazy", "leader", "leaf", "learn", "leave",
+    "lecture", "left", "leg", "legal", "legend", "leisure", "lemon", "lend",
+    "length", "lens", "leopard", "lesson", "letter", "level", "liar", "liberty",
+    "library", "license", "life", "lift", "light", "like", "limb", "limit",
+    "link", "lion", "liquid", "list", "little", "live", "lizard", "load",
+    "loan", "lobster", "local", "lock", "logic", "lonely", "long", "loop",
+    "lottery", "loud", "lounge", "love", "loyal", "lucky", "luggage", "lumber",
+    "lunar", "lunch", "luxury", "lyrics", "machine", "mad", "magic", "magnet",
+    "maid", "mail", "main", "major", "make", "mammal", "man", "manage",
+    "mandate", "mango", "mansion", "manual", "maple", "marble", "march", "margin",
+    "marine", "market", "marriage", "mask", "mass", "master", "match", "material",
+    "math", "matrix", "matter", "maximum", "maze", "meadow", "mean", "measure",
+    "meat", "mechanic", "medal", "media", "melody", "melt", "member", "memory",
+    "mention", "menu", "mercy", "merge", "merit", "merry", "mesh", "message",
+    "metal", "method", "middle", "midnight", "milk", "million", "mimic", "mind",
+    "minimum", "minor", "minute", "miracle", "mirror", "misery", "miss", "mistake",
+    "mix", "mixed", "mixture", "mobile", "model", "modify", "mom", "moment",
+    "monitor", "monkey", "monster", "month", "moon", "moral", "more", "morning",
+    "mosquito", "mother", "motion", "motor", "mountain", "mouse", "move", "movie",
+    "much", "muffin", "mule", "multiply", "muscle", "museum", "mushroom", "music",
+    "must", "mutual", "myself", "mystery", "myth", "naive", "name", "napkin",
+    "narrow", "nasty", "nation", "nature", "near", "neck", "need", "negative",
+    "neglect", "neither", "nephew", "nerve", "nest", "net", "network", "neutral",
+    "never", "news", "next", "nice", "night", "noble", "noise", "nominee",
+    "noodle", "normal", "north", "nose", "notable", "note", "nothing", "notice",
+    "novel", "now", "nuclear", "number", "nurse", "nut", "oak", "obey",
+    "object", "oblige", "obscure", "observe", "obtain", "obvious", "occur", "ocean",
+    "october", "odor", "off", "offer", "office", "often", "oil", "okay",
+    "old", "olive", "olympic", "omit", "once", "one", "onion", "online",
+    "only", "open", "opera", "opinion", "oppose", "option", "orange", "orbit",
+    "orchard", "order", "ordinary", "organ", "orient", "original", "orphan", "ostrich",
+    "other", "outdoor", "outer", "output", "outside", "oval", "oven", "over",
+    "own", "owner", "oxygen", "oyster", "ozone", "pact", "paddle", "page",
+    "pair", "palace", "palm", "panda", "panel", "panic", "panther", "paper",
+    "parade", "parent", "park", "parrot", "party", "pass", "patch", "path",
+    "patient", "patrol", "pattern", "pause", "pave", "payment", "peace", "peanut",
+    "pear", "peasant", "pelican", "pen", "penalty", "pencil", "people", "pepper",
+    "perfect", "permit", "person", "pet", "phone", "photo", "phrase", "physical",
+    "piano", "picnic", "picture", "piece", "pig", "pigeon", "pill", "pilot",
+    "pink", "pioneer", "pipe", "pistol", "pitch", "pizza", "place", "planet",
+    "plastic", "plate", "play", "please", "pledge", "pluck", "plug", "plunge",
+    "poem", "poet", "point", "polar", "pole", "police", "pond", "pony",
+    "pool", "popular", "portion", "position", "possible", "post", "potato", "pottery",
+    "poverty", "powder", "power", "practice", "praise", "predict", "prefer", "prepare",
+    "present", "pretty", "prevent", "price", "pride", "primary", "print", "priority",
+    "prison", "private", "prize", "problem", "process", "produce", "profit", "program",
+    "project", "promote", "proof", "property", "prosper", "protect", "proud", "provide",
+    "public", "pudding", "pull", "pulp", "pulse", "pumpkin", "punch", "pupil",
+    "puppy", "purchase", "purity", "purpose", "purse", "push", "put", "puzzle",
+    "pyramid", "quality", "quantum", "quarter", "question", "quick", "quit", "quiz",
+    "quote", "rabbit", "raccoon", "race", "rack", "radar", "radio", "rail",
+    "rain", "raise", "rally", "ramp", "ranch", "random", "range", "rapid",
+    "rare", "rate", "rather", "raven", "raw", "razor", "ready", "real",
+    "reason", "rebel", "rebuild", "recall", "receive", "recipe", "record", "recycle",
+    "reduce", "reflect", "reform", "refuse", "region", "regret", "regular", "reject",
+    "relax", "release", "relief", "rely", "remain", "remember", "remind", "remove",
+    "render", "renew", "rent", "reopen", "repair", "repeat", "replace", "report",
+    "require", "rescue", "resemble", "resist", "resource", "response", "result", "retire",
+    "retreat", "return", "reunion", "reveal", "review", "reward", "rhythm", "rib",
+    "ribbon", "rice", "rich", "ride", "ridge", "rifle", "right", "rigid",
+    "ring", "riot", "ripple", "risk", "ritual", "rival", "river", "road",
+    "roast", "robot", "robust", "rocket", "romance", "roof", "rookie", "room",
+    "rose", "rotate", "rough", "round", "route", "royal", "rubber", "rude",
+    "rug", "rule", "run", "runway", "rural", "sad", "saddle", "sadness",
+    "safe", "sail", "salad", "salmon", "salon", "salt", "salute", "same",
+    "sample", "sand", "satisfy", "satoshi", "sauce", "sausage", "save", "say",
+    "scale", "scan", "scare", "scatter", "scene", "scheme", "school", "science",
+    "scissors", "scorpion", "scout", "scrap", "screen", "script", "scrub", "sea",
+    "search", "season", "seat", "second", "secret", "section", "security", "seed",
+    "seek", "segment", "select", "sell", "seminar", "senior", "sense", "sentence",
+    "series", "service", "session", "settle", "setup", "seven", "shadow", "shaft",
+    "shallow", "share", "shed", "shell", "sheriff", "shield", "shift", "shine",
+    "ship", "shiver", "shock", "shoe", "shoot", "shop", "short", "shoulder",
+    "shove", "shrimp", "shrug", "shuffle", "shy", "sibling", "sick", "side",
+    "siege", "sight", "sign", "silent", "silk", "silly", "silver", "similar",
+    "simple", "since", "sing", "siren", "sister", "situate", "six", "size",
+    "skate", "sketch", "ski", "skill", "skin", "skirt", "skull", "slab",
+    "slam", "sleep", "slender", "slice", "slide", "slight", "slim", "slogan",
+    "slot", "slow", "slush", "small", "smart", "smile", "smoke", "smooth",
+    "snack", "snake", "snap", "sniff", "snow", "soap", "soccer", "social",
+    "sock", "soda", "soft", "solar", "soldier", "solid", "solution", "solve",
+    "someone", "song", "soon", "sorry", "sort", "soul", "sound", "soup",
+    "source", "south", "space", "spare", "spatial", "spawn", "speak", "special",
+    "speed", "spell", "spend", "sphere", "spice", "spider", "spike", "spin",
+    "spirit", "split", "spoil", "sponsor", "spoon", "sport", "spot", "spray",
+    "spread", "spring", "spy", "square", "squeeze", "squirrel", "stable", "stadium",
+    "staff", "stage", "stairs", "stamp", "stand", "start", "state", "stay",
+    "steak", "steel", "stem", "step", "stereo", "stick", "still", "sting",
+    "stock", "stomach", "stone", "stool", "story", "stove", "strategy", "street",
+    "strike", "strong", "struggle", "student", "stuff", "stumble", "style", "subject",
+    "submit", "subway", "success", "such", "sudden", "suffer", "sugar", "suggest",
+    "suit", "summer", "sun", "sunny", "sunset", "super", "supply", "supreme",
+    "sure", "surface", "surge", "surprise", "surround", "survey", "suspect", "sustain",
+    "swallow", "swamp", "swap", "swarm", "swear", "sweet", "swift", "swim",
+    "swing", "switch", "sword", "symbol", "symptom", "syrup", "system", "table",
+    "tackle", "tag", "tail", "talent", "talk", "tank", "tape", "target",
+    "task", "taste", "tattoo", "taxi", "teach", "team", "tell", "ten",
+    "tenant", "tennis", "tent", "term", "test", "text", "thank", "that",
+    "theme", "then", "theory", "there", "they", "thing", "this", "thought",
+    "three", "thrive", "throw", "thumb", "thunder", "ticket", "tide", "tiger",
+    "tilt", "timber", "time", "tiny", "tip", "tired", "tissue", "title",
+    "toast", "tobacco", "today", "toddler", "toe", "together", "toilet", "token",
+    "tomato", "tomorrow", "tone", "tongue", "tonight", "tool", "tooth", "top",
+    "topic", "topple", "torch", "tornado", "tortoise", "toss", "total", "tourist",
+    "toward", "tower", "town", "toy", "track", "trade", "traffic", "tragic",
+    "train", "transfer", "trap", "trash", "travel", "tray", "treat", "tree",
+    "trend", "trial", "tribe", "trick", "trigger", "trim", "trip", "trophy",
+    "trouble", "truck", "true", "truly", "trumpet", "trust", "truth", "try",
+    "tube", "tuition", "tumble", "tuna", "tunnel", "turkey", "turn", "turtle",
+    "twelve", "twenty", "twice", "twin", "twist", "two", "type", "typical",
+    "ugly", "umbrella", "unable", "unaware", "uncle", "uncover", "under", "undo",
+    "unfair", "unfold", "unhappy", "uniform", "unique", "unit", "universe", "unknown",
+    "unlock", "until", "unusual", "unveil", "update", "upgrade", "uphold", "upon",
+    "upper", "upset", "urban", "urge", "usage", "use", "used", "useful",
+    "useless", "usual", "utility", "vacant", "vacuum", "vague", "valid", "valley",
+    "valve", "van", "vanish", "vapor", "various", "vast", "vault", "vehicle",
+    "velvet", "vendor", "venture", "venue", "verb", "verify", "version", "very",
+    "vessel", "veteran", "viable", "vibrant", "vicious", "victory", "video", "view",
+    "village", "vintage", "violin", "virtual", "virus", "visa", "visit", "visual",
+    "vital", "vivid", "vocal", "voice", "void", "volcano", "volume", "vote",
+    "voyage", "wage", "wagon", "wait", "walk", "wall", "walnut", "want",
+    "warfare", "warm", "warrior", "wash", "wasp", "waste", "water", "wave",
+    "way", "wealth", "weapon", "wear", "weasel", "weather", "web", "wedding",
+    "weekend", "weird", "welcome", "west", "wet", "whale", "what", "wheat",
+    "wheel", "when", "where", "whip", "whisper", "wide", "width", "wife",
+    "wild", "will", "win", "window", "wine", "wing", "wink", "winner",
+    "winter", "wire", "wisdom", "wise", "wish", "witness", "wolf", "woman",
+    "wonder", "wood", "wool", "word", "work", "world", "worry", "worth",
+    "wrap", "wreck", "wrestle", "wrist", "write", "wrong", "yard", "year",
+    "yellow", "you", "young", "youth", "zebra", "zero", "zone", "zoo"
+};

firmware/kb2040_hidden_signer/src/cjson/cJSON.h

@@ -0,0 +1,306 @@
+/*
+  Copyright (c) 2009-2017 Dave Gamble and cJSON contributors
+
+  Permission is hereby granted, free of charge, to any person obtaining a copy
+  of this software and associated documentation files (the "Software"), to deal
+  in the Software without restriction, including without limitation the rights
+  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+  copies of the Software, and to permit persons to whom the Software is
+  furnished to do so, subject to the following conditions:
+
+  The above copyright notice and this permission notice shall be included in
+  all copies or substantial portions of the Software.
+
+  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+  THE SOFTWARE.
+*/
+
+#ifndef cJSON__h
+#define cJSON__h
+
+#ifdef __cplusplus
+extern "C"
+{
+#endif
+
+#if !defined(__WINDOWS__) && (defined(WIN32) || defined(WIN64) || defined(_MSC_VER) || defined(_WIN32))
+#define __WINDOWS__
+#endif
+
+#ifdef __WINDOWS__
+
+/* When compiling for windows, we specify a specific calling convention to avoid issues where we are being called from a project with a different default calling convention.  For windows you have 3 define options:
+
+CJSON_HIDE_SYMBOLS - Define this in the case where you don't want to ever dllexport symbols
+CJSON_EXPORT_SYMBOLS - Define this on library build when you want to dllexport symbols (default)
+CJSON_IMPORT_SYMBOLS - Define this if you want to dllimport symbol
+
+For *nix builds that support visibility attribute, you can define similar behavior by
+
+setting default visibility to hidden by adding
+-fvisibility=hidden (for gcc)
+or
+-xldscope=hidden (for sun cc)
+to CFLAGS
+
+then using the CJSON_API_VISIBILITY flag to "export" the same symbols the way CJSON_EXPORT_SYMBOLS does
+
+*/
+
+#define CJSON_CDECL __cdecl
+#define CJSON_STDCALL __stdcall
+
+/* export symbols by default, this is necessary for copy pasting the C and header file */
+#if !defined(CJSON_HIDE_SYMBOLS) && !defined(CJSON_IMPORT_SYMBOLS) && !defined(CJSON_EXPORT_SYMBOLS)
+#define CJSON_EXPORT_SYMBOLS
+#endif
+
+#if defined(CJSON_HIDE_SYMBOLS)
+#define CJSON_PUBLIC(type)   type CJSON_STDCALL
+#elif defined(CJSON_EXPORT_SYMBOLS)
+#define CJSON_PUBLIC(type)   __declspec(dllexport) type CJSON_STDCALL
+#elif defined(CJSON_IMPORT_SYMBOLS)
+#define CJSON_PUBLIC(type)   __declspec(dllimport) type CJSON_STDCALL
+#endif
+#else /* !__WINDOWS__ */
+#define CJSON_CDECL
+#define CJSON_STDCALL
+
+#if (defined(__GNUC__) || defined(__SUNPRO_CC) || defined (__SUNPRO_C)) && defined(CJSON_API_VISIBILITY)
+#define CJSON_PUBLIC(type)   __attribute__((visibility("default"))) type
+#else
+#define CJSON_PUBLIC(type) type
+#endif
+#endif
+
+/* project version */
+#define CJSON_VERSION_MAJOR 1
+#define CJSON_VERSION_MINOR 7
+#define CJSON_VERSION_PATCH 18
+
+#include <stddef.h>
+
+/* cJSON Types: */
+#define cJSON_Invalid (0)
+#define cJSON_False  (1 << 0)
+#define cJSON_True   (1 << 1)
+#define cJSON_NULL   (1 << 2)
+#define cJSON_Number (1 << 3)
+#define cJSON_String (1 << 4)
+#define cJSON_Array  (1 << 5)
+#define cJSON_Object (1 << 6)
+#define cJSON_Raw    (1 << 7) /* raw json */
+
+#define cJSON_IsReference 256
+#define cJSON_StringIsConst 512
+
+/* The cJSON structure: */
+typedef struct cJSON
+{
+    /* next/prev allow you to walk array/object chains. Alternatively, use GetArraySize/GetArrayItem/GetObjectItem */
+    struct cJSON *next;
+    struct cJSON *prev;
+    /* An array or object item will have a child pointer pointing to a chain of the items in the array/object. */
+    struct cJSON *child;
+
+    /* The type of the item, as above. */
+    int type;
+
+    /* The item's string, if type==cJSON_String  and type == cJSON_Raw */
+    char *valuestring;
+    /* writing to valueint is DEPRECATED, use cJSON_SetNumberValue instead */
+    int valueint;
+    /* The item's number, if type==cJSON_Number */
+    double valuedouble;
+
+    /* The item's name string, if this item is the child of, or is in the list of subitems of an object. */
+    char *string;
+} cJSON;
+
+typedef struct cJSON_Hooks
+{
+      /* malloc/free are CDECL on Windows regardless of the default calling convention of the compiler, so ensure the hooks allow passing those functions directly. */
+      void *(CJSON_CDECL *malloc_fn)(size_t sz);
+      void (CJSON_CDECL *free_fn)(void *ptr);
+} cJSON_Hooks;
+
+typedef int cJSON_bool;
+
+/* Limits how deeply nested arrays/objects can be before cJSON rejects to parse them.
+ * This is to prevent stack overflows. */
+#ifndef CJSON_NESTING_LIMIT
+#define CJSON_NESTING_LIMIT 1000
+#endif
+
+/* Limits the length of circular references can be before cJSON rejects to parse them.
+ * This is to prevent stack overflows. */
+#ifndef CJSON_CIRCULAR_LIMIT
+#define CJSON_CIRCULAR_LIMIT 10000
+#endif
+
+/* returns the version of cJSON as a string */
+CJSON_PUBLIC(const char*) cJSON_Version(void);
+
+/* Supply malloc, realloc and free functions to cJSON */
+CJSON_PUBLIC(void) cJSON_InitHooks(cJSON_Hooks* hooks);
+
+/* Memory Management: the caller is always responsible to free the results from all variants of cJSON_Parse (with cJSON_Delete) and cJSON_Print (with stdlib free, cJSON_Hooks.free_fn, or cJSON_free as appropriate). The exception is cJSON_PrintPreallocated, where the caller has full responsibility of the buffer. */
+/* Supply a block of JSON, and this returns a cJSON object you can interrogate. */
+CJSON_PUBLIC(cJSON *) cJSON_Parse(const char *value);
+CJSON_PUBLIC(cJSON *) cJSON_ParseWithLength(const char *value, size_t buffer_length);
+/* ParseWithOpts allows you to require (and check) that the JSON is null terminated, and to retrieve the pointer to the final byte parsed. */
+/* If you supply a ptr in return_parse_end and parsing fails, then return_parse_end will contain a pointer to the error so will match cJSON_GetErrorPtr(). */
+CJSON_PUBLIC(cJSON *) cJSON_ParseWithOpts(const char *value, const char **return_parse_end, cJSON_bool require_null_terminated);
+CJSON_PUBLIC(cJSON *) cJSON_ParseWithLengthOpts(const char *value, size_t buffer_length, const char **return_parse_end, cJSON_bool require_null_terminated);
+
+/* Render a cJSON entity to text for transfer/storage. */
+CJSON_PUBLIC(char *) cJSON_Print(const cJSON *item);
+/* Render a cJSON entity to text for transfer/storage without any formatting. */
+CJSON_PUBLIC(char *) cJSON_PrintUnformatted(const cJSON *item);
+/* Render a cJSON entity to text using a buffered strategy. prebuffer is a guess at the final size. guessing well reduces reallocation. fmt=0 gives unformatted, =1 gives formatted */
+CJSON_PUBLIC(char *) cJSON_PrintBuffered(const cJSON *item, int prebuffer, cJSON_bool fmt);
+/* Render a cJSON entity to text using a buffer already allocated in memory with given length. Returns 1 on success and 0 on failure. */
+/* NOTE: cJSON is not always 100% accurate in estimating how much memory it will use, so to be safe allocate 5 bytes more than you actually need */
+CJSON_PUBLIC(cJSON_bool) cJSON_PrintPreallocated(cJSON *item, char *buffer, const int length, const cJSON_bool format);
+/* Delete a cJSON entity and all subentities. */
+CJSON_PUBLIC(void) cJSON_Delete(cJSON *item);
+
+/* Returns the number of items in an array (or object). */
+CJSON_PUBLIC(int) cJSON_GetArraySize(const cJSON *array);
+/* Retrieve item number "index" from array "array". Returns NULL if unsuccessful. */
+CJSON_PUBLIC(cJSON *) cJSON_GetArrayItem(const cJSON *array, int index);
+/* Get item "string" from object. Case insensitive. */
+CJSON_PUBLIC(cJSON *) cJSON_GetObjectItem(const cJSON * const object, const char * const string);
+CJSON_PUBLIC(cJSON *) cJSON_GetObjectItemCaseSensitive(const cJSON * const object, const char * const string);
+CJSON_PUBLIC(cJSON_bool) cJSON_HasObjectItem(const cJSON *object, const char *string);
+/* For analysing failed parses. This returns a pointer to the parse error. You'll probably need to look a few chars back to make sense of it. Defined when cJSON_Parse() returns 0. 0 when cJSON_Parse() succeeds. */
+CJSON_PUBLIC(const char *) cJSON_GetErrorPtr(void);
+
+/* Check item type and return its value */
+CJSON_PUBLIC(char *) cJSON_GetStringValue(const cJSON * const item);
+CJSON_PUBLIC(double) cJSON_GetNumberValue(const cJSON * const item);
+
+/* These functions check the type of an item */
+CJSON_PUBLIC(cJSON_bool) cJSON_IsInvalid(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsFalse(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsTrue(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsBool(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsNull(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsNumber(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsString(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsArray(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsObject(const cJSON * const item);
+CJSON_PUBLIC(cJSON_bool) cJSON_IsRaw(const cJSON * const item);
+
+/* These calls create a cJSON item of the appropriate type. */
+CJSON_PUBLIC(cJSON *) cJSON_CreateNull(void);
+CJSON_PUBLIC(cJSON *) cJSON_CreateTrue(void);
+CJSON_PUBLIC(cJSON *) cJSON_CreateFalse(void);
+CJSON_PUBLIC(cJSON *) cJSON_CreateBool(cJSON_bool boolean);
+CJSON_PUBLIC(cJSON *) cJSON_CreateNumber(double num);
+CJSON_PUBLIC(cJSON *) cJSON_CreateString(const char *string);
+/* raw json */
+CJSON_PUBLIC(cJSON *) cJSON_CreateRaw(const char *raw);
+CJSON_PUBLIC(cJSON *) cJSON_CreateArray(void);
+CJSON_PUBLIC(cJSON *) cJSON_CreateObject(void);
+
+/* Create a string where valuestring references a string so
+ * it will not be freed by cJSON_Delete */
+CJSON_PUBLIC(cJSON *) cJSON_CreateStringReference(const char *string);
+/* Create an object/array that only references it's elements so
+ * they will not be freed by cJSON_Delete */
+CJSON_PUBLIC(cJSON *) cJSON_CreateObjectReference(const cJSON *child);
+CJSON_PUBLIC(cJSON *) cJSON_CreateArrayReference(const cJSON *child);
+
+/* These utilities create an Array of count items.
+ * The parameter count cannot be greater than the number of elements in the number array, otherwise array access will be out of bounds.*/
+CJSON_PUBLIC(cJSON *) cJSON_CreateIntArray(const int *numbers, int count);
+CJSON_PUBLIC(cJSON *) cJSON_CreateFloatArray(const float *numbers, int count);
+CJSON_PUBLIC(cJSON *) cJSON_CreateDoubleArray(const double *numbers, int count);
+CJSON_PUBLIC(cJSON *) cJSON_CreateStringArray(const char *const *strings, int count);
+
+/* Append item to the specified array/object. */
+CJSON_PUBLIC(cJSON_bool) cJSON_AddItemToArray(cJSON *array, cJSON *item);
+CJSON_PUBLIC(cJSON_bool) cJSON_AddItemToObject(cJSON *object, const char *string, cJSON *item);
+/* Use this when string is definitely const (i.e. a literal, or as good as), and will definitely survive the cJSON object.
+ * WARNING: When this function was used, make sure to always check that (item->type & cJSON_StringIsConst) is zero before
+ * writing to `item->string` */
+CJSON_PUBLIC(cJSON_bool) cJSON_AddItemToObjectCS(cJSON *object, const char *string, cJSON *item);
+/* Append reference to item to the specified array/object. Use this when you want to add an existing cJSON to a new cJSON, but don't want to corrupt your existing cJSON. */
+CJSON_PUBLIC(cJSON_bool) cJSON_AddItemReferenceToArray(cJSON *array, cJSON *item);
+CJSON_PUBLIC(cJSON_bool) cJSON_AddItemReferenceToObject(cJSON *object, const char *string, cJSON *item);
+
+/* Remove/Detach items from Arrays/Objects. */
+CJSON_PUBLIC(cJSON *) cJSON_DetachItemViaPointer(cJSON *parent, cJSON * const item);
+CJSON_PUBLIC(cJSON *) cJSON_DetachItemFromArray(cJSON *array, int which);
+CJSON_PUBLIC(void) cJSON_DeleteItemFromArray(cJSON *array, int which);
+CJSON_PUBLIC(cJSON *) cJSON_DetachItemFromObject(cJSON *object, const char *string);
+CJSON_PUBLIC(cJSON *) cJSON_DetachItemFromObjectCaseSensitive(cJSON *object, const char *string);
+CJSON_PUBLIC(void) cJSON_DeleteItemFromObject(cJSON *object, const char *string);
+CJSON_PUBLIC(void) cJSON_DeleteItemFromObjectCaseSensitive(cJSON *object, const char *string);
+
+/* Update array items. */
+CJSON_PUBLIC(cJSON_bool) cJSON_InsertItemInArray(cJSON *array, int which, cJSON *newitem); /* Shifts pre-existing items to the right. */
+CJSON_PUBLIC(cJSON_bool) cJSON_ReplaceItemViaPointer(cJSON * const parent, cJSON * const item, cJSON * replacement);
+CJSON_PUBLIC(cJSON_bool) cJSON_ReplaceItemInArray(cJSON *array, int which, cJSON *newitem);
+CJSON_PUBLIC(cJSON_bool) cJSON_ReplaceItemInObject(cJSON *object,const char *string,cJSON *newitem);
+CJSON_PUBLIC(cJSON_bool) cJSON_ReplaceItemInObjectCaseSensitive(cJSON *object,const char *string,cJSON *newitem);
+
+/* Duplicate a cJSON item */
+CJSON_PUBLIC(cJSON *) cJSON_Duplicate(const cJSON *item, cJSON_bool recurse);
+/* Duplicate will create a new, identical cJSON item to the one you pass, in new memory that will
+ * need to be released. With recurse!=0, it will duplicate any children connected to the item.
+ * The item->next and ->prev pointers are always zero on return from Duplicate. */
+/* Recursively compare two cJSON items for equality. If either a or b is NULL or invalid, they will be considered unequal.
+ * case_sensitive determines if object keys are treated case sensitive (1) or case insensitive (0) */
+CJSON_PUBLIC(cJSON_bool) cJSON_Compare(const cJSON * const a, const cJSON * const b, const cJSON_bool case_sensitive);
+
+/* Minify a strings, remove blank characters(such as ' ', '\t', '\r', '\n') from strings.
+ * The input pointer json cannot point to a read-only address area, such as a string constant, 
+ * but should point to a readable and writable address area. */
+CJSON_PUBLIC(void) cJSON_Minify(char *json);
+
+/* Helper functions for creating and adding items to an object at the same time.
+ * They return the added item or NULL on failure. */
+CJSON_PUBLIC(cJSON*) cJSON_AddNullToObject(cJSON * const object, const char * const name);
+CJSON_PUBLIC(cJSON*) cJSON_AddTrueToObject(cJSON * const object, const char * const name);
+CJSON_PUBLIC(cJSON*) cJSON_AddFalseToObject(cJSON * const object, const char * const name);
+CJSON_PUBLIC(cJSON*) cJSON_AddBoolToObject(cJSON * const object, const char * const name, const cJSON_bool boolean);
+CJSON_PUBLIC(cJSON*) cJSON_AddNumberToObject(cJSON * const object, const char * const name, const double number);
+CJSON_PUBLIC(cJSON*) cJSON_AddStringToObject(cJSON * const object, const char * const name, const char * const string);
+CJSON_PUBLIC(cJSON*) cJSON_AddRawToObject(cJSON * const object, const char * const name, const char * const raw);
+CJSON_PUBLIC(cJSON*) cJSON_AddObjectToObject(cJSON * const object, const char * const name);
+CJSON_PUBLIC(cJSON*) cJSON_AddArrayToObject(cJSON * const object, const char * const name);
+
+/* When assigning an integer value, it needs to be propagated to valuedouble too. */
+#define cJSON_SetIntValue(object, number) ((object) ? (object)->valueint = (object)->valuedouble = (number) : (number))
+/* helper for the cJSON_SetNumberValue macro */
+CJSON_PUBLIC(double) cJSON_SetNumberHelper(cJSON *object, double number);
+#define cJSON_SetNumberValue(object, number) ((object != NULL) ? cJSON_SetNumberHelper(object, (double)number) : (number))
+/* Change the valuestring of a cJSON_String object, only takes effect when type of object is cJSON_String */
+CJSON_PUBLIC(char*) cJSON_SetValuestring(cJSON *object, const char *valuestring);
+
+/* If the object is not a boolean type this does nothing and returns cJSON_Invalid else it returns the new type*/
+#define cJSON_SetBoolValue(object, boolValue) ( \
+    (object != NULL && ((object)->type & (cJSON_False|cJSON_True))) ? \
+    (object)->type=((object)->type &(~(cJSON_False|cJSON_True)))|((boolValue)?cJSON_True:cJSON_False) : \
+    cJSON_Invalid\
+)
+
+/* Macro for iterating over an array or object */
+#define cJSON_ArrayForEach(element, array) for(element = (array != NULL) ? (array)->child : NULL; element != NULL; element = element->next)
+
+/* malloc/free objects using the malloc/free functions that have been set with cJSON_InitHooks */
+CJSON_PUBLIC(void *) cJSON_malloc(size_t size);
+CJSON_PUBLIC(void) cJSON_free(void *object);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

firmware/kb2040_hidden_signer/src/nostr_core/crypto/nostr_secp256k1.c

@@ -0,0 +1,320 @@
+#include "../../secp256k1/include/secp256k1.h"
+#include "../../secp256k1/include/secp256k1_schnorrsig.h"
+#include "../../secp256k1/include/secp256k1_ecdh.h"
+#include <string.h>
+#include <stdlib.h>
+#include <stddef.h>
+#include "../nostr_platform.h"
+
+/*
+ * PRIVATE INTERNAL FUNCTIONS - NOT EXPORTED
+ * These functions are for internal library use only.
+ */
+
+/** Opaque data structure that holds a parsed and valid public key.
+ *  Guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ */
+typedef struct nostr_secp256k1_pubkey {
+    unsigned char data[64];
+} nostr_secp256k1_pubkey;
+
+/** Opaque data structure that holds a parsed keypair.
+ *  Guaranteed to be 96 bytes in size, and can be safely copied/moved.
+ */
+typedef struct nostr_secp256k1_keypair {
+    unsigned char data[96];
+} nostr_secp256k1_keypair;
+
+/** Opaque data structure that holds a parsed x-only public key.
+ *  Guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ */
+typedef struct nostr_secp256k1_xonly_pubkey {
+    unsigned char data[64];
+} nostr_secp256k1_xonly_pubkey;
+
+// Global context for secp256k1 operations
+static secp256k1_context* g_ctx = NULL;
+
+int nostr_secp256k1_context_create(void) {
+    if (g_ctx != NULL) {
+        return 1; // Already initialized
+    }
+    
+    g_ctx = secp256k1_context_create(SECP256K1_CONTEXT_SIGN | SECP256K1_CONTEXT_VERIFY);
+    if (g_ctx == NULL) {
+        return 0;
+    }
+    
+    // Add randomization to the context using platform entropy.
+    unsigned char randomize[32];
+    if (nostr_platform_random(randomize, sizeof(randomize)) != 0) {
+        secp256k1_context_destroy(g_ctx);
+        g_ctx = NULL;
+        return 0;
+    }
+
+    if (!secp256k1_context_randomize(g_ctx, randomize)) {
+        secp256k1_context_destroy(g_ctx);
+        g_ctx = NULL;
+        return 0;
+    }
+    
+    return 1;
+}
+
+void nostr_secp256k1_context_destroy(void) {
+    if (g_ctx != NULL) {
+        secp256k1_context_destroy(g_ctx);
+        g_ctx = NULL;
+    }
+}
+
+int nostr_secp256k1_ec_seckey_verify(const unsigned char *seckey) {
+    if (g_ctx == NULL || seckey == NULL) {
+        return 0;
+    }
+    
+    return secp256k1_ec_seckey_verify(g_ctx, seckey);
+}
+
+int nostr_secp256k1_ec_pubkey_create(nostr_secp256k1_pubkey *pubkey, const unsigned char *seckey) {
+    if (g_ctx == NULL || pubkey == NULL || seckey == NULL) {
+        return 0;
+    }
+    
+    secp256k1_pubkey internal_pubkey;
+    if (!secp256k1_ec_pubkey_create(g_ctx, &internal_pubkey, seckey)) {
+        return 0;
+    }
+    
+    // Copy the internal representation to our wrapper
+    memcpy(pubkey->data, &internal_pubkey, sizeof(secp256k1_pubkey));
+    
+    return 1;
+}
+
+int nostr_secp256k1_keypair_create(nostr_secp256k1_keypair *keypair, const unsigned char *seckey) {
+    if (g_ctx == NULL || keypair == NULL || seckey == NULL) {
+        return 0;
+    }
+    
+    secp256k1_keypair internal_keypair;
+    if (!secp256k1_keypair_create(g_ctx, &internal_keypair, seckey)) {
+        return 0;
+    }
+    
+    // Copy the internal representation to our wrapper
+    memcpy(keypair->data, &internal_keypair, sizeof(secp256k1_keypair));
+    
+    return 1;
+}
+
+int nostr_secp256k1_keypair_xonly_pub(nostr_secp256k1_xonly_pubkey *pubkey, const nostr_secp256k1_keypair *keypair) {
+    if (g_ctx == NULL || pubkey == NULL || keypair == NULL) {
+        return 0;
+    }
+    
+    secp256k1_keypair internal_keypair;
+    secp256k1_xonly_pubkey internal_xonly;
+    
+    // Copy from our wrapper to internal representation
+    memcpy(&internal_keypair, keypair->data, sizeof(secp256k1_keypair));
+    
+    if (!secp256k1_keypair_xonly_pub(g_ctx, &internal_xonly, NULL, &internal_keypair)) {
+        return 0;
+    }
+    
+    // Copy the internal representation to our wrapper
+    memcpy(pubkey->data, &internal_xonly, sizeof(secp256k1_xonly_pubkey));
+    
+    return 1;
+}
+
+int nostr_secp256k1_xonly_pubkey_parse(nostr_secp256k1_xonly_pubkey *pubkey, const unsigned char *input32) {
+    if (g_ctx == NULL || pubkey == NULL || input32 == NULL) {
+        return 0;
+    }
+    
+    secp256k1_xonly_pubkey internal_xonly;
+    if (!secp256k1_xonly_pubkey_parse(g_ctx, &internal_xonly, input32)) {
+        return 0;
+    }
+    
+    // Copy the internal representation to our wrapper
+    memcpy(pubkey->data, &internal_xonly, sizeof(secp256k1_xonly_pubkey));
+    
+    return 1;
+}
+
+int nostr_secp256k1_xonly_pubkey_serialize(unsigned char *output32, const nostr_secp256k1_xonly_pubkey *pubkey) {
+    if (g_ctx == NULL || output32 == NULL || pubkey == NULL) {
+        return 0;
+    }
+    
+    secp256k1_xonly_pubkey internal_xonly;
+    
+    // Copy from our wrapper to internal representation
+    memcpy(&internal_xonly, pubkey->data, sizeof(secp256k1_xonly_pubkey));
+    
+    return secp256k1_xonly_pubkey_serialize(g_ctx, output32, &internal_xonly);
+}
+
+int nostr_secp256k1_schnorrsig_sign32(unsigned char *sig64, const unsigned char *msghash32, const nostr_secp256k1_keypair *keypair, const unsigned char *aux_rand32) {
+    if (g_ctx == NULL || sig64 == NULL || msghash32 == NULL || keypair == NULL) {
+        return 0;
+    }
+    
+    secp256k1_keypair internal_keypair;
+    
+    // Copy from our wrapper to internal representation
+    memcpy(&internal_keypair, keypair->data, sizeof(secp256k1_keypair));
+    
+    return secp256k1_schnorrsig_sign32(g_ctx, sig64, msghash32, &internal_keypair, aux_rand32);
+}
+
+int nostr_secp256k1_schnorrsig_verify(const unsigned char *sig64, const unsigned char *msghash32, const nostr_secp256k1_xonly_pubkey *pubkey) {
+    if (g_ctx == NULL || sig64 == NULL || msghash32 == NULL || pubkey == NULL) {
+        return 0;
+    }
+    
+    secp256k1_xonly_pubkey internal_xonly;
+    
+    // Copy from our wrapper to internal representation
+    memcpy(&internal_xonly, pubkey->data, sizeof(secp256k1_xonly_pubkey));
+    
+    return secp256k1_schnorrsig_verify(g_ctx, sig64, msghash32, 32, &internal_xonly);
+}
+
+int nostr_secp256k1_ec_pubkey_serialize_compressed(unsigned char *output, const nostr_secp256k1_pubkey *pubkey) {
+    if (g_ctx == NULL || output == NULL || pubkey == NULL) {
+        return 0;
+    }
+    
+    secp256k1_pubkey internal_pubkey;
+    size_t outputlen = 33;
+    
+    // Copy from our wrapper to internal representation
+    memcpy(&internal_pubkey, pubkey->data, sizeof(secp256k1_pubkey));
+    
+    return secp256k1_ec_pubkey_serialize(g_ctx, output, &outputlen, &internal_pubkey, SECP256K1_EC_COMPRESSED);
+}
+
+int nostr_secp256k1_ec_seckey_tweak_add(unsigned char *seckey, const unsigned char *tweak) {
+    if (g_ctx == NULL || seckey == NULL || tweak == NULL) {
+        return 0;
+    }
+    
+    return secp256k1_ec_seckey_tweak_add(g_ctx, seckey, tweak);
+}
+
+int nostr_secp256k1_ec_pubkey_parse(nostr_secp256k1_pubkey *pubkey, const unsigned char *input, size_t inputlen) {
+    if (g_ctx == NULL || pubkey == NULL || input == NULL) {
+        return 0;
+    }
+    
+    secp256k1_pubkey internal_pubkey;
+    if (!secp256k1_ec_pubkey_parse(g_ctx, &internal_pubkey, input, inputlen)) {
+        return 0;
+    }
+    
+    // Copy the internal representation to our wrapper
+    memcpy(pubkey->data, &internal_pubkey, sizeof(secp256k1_pubkey));
+    
+    return 1;
+}
+
+int nostr_secp256k1_ecdh(unsigned char *result, const nostr_secp256k1_pubkey *pubkey, const unsigned char *seckey, void *hashfp, void *data) {
+    if (g_ctx == NULL || result == NULL || pubkey == NULL || seckey == NULL) {
+        return 0;
+    }
+    
+    secp256k1_pubkey internal_pubkey;
+    
+    // Copy from our wrapper to internal representation
+    memcpy(&internal_pubkey, pubkey->data, sizeof(secp256k1_pubkey));
+    
+    return secp256k1_ecdh(g_ctx, result, &internal_pubkey, seckey, hashfp, data);
+}
+
+int nostr_secp256k1_ec_pubkey_tweak_mul(nostr_secp256k1_pubkey* pubkey, const unsigned char* tweak32) {
+    if (g_ctx == NULL || pubkey == NULL || tweak32 == NULL) {
+        return 0;
+    }
+
+    secp256k1_pubkey internal_pubkey;
+    memcpy(&internal_pubkey, pubkey->data, sizeof(secp256k1_pubkey));
+
+    if (!secp256k1_ec_pubkey_tweak_mul(g_ctx, &internal_pubkey, tweak32)) {
+        return 0;
+    }
+
+    memcpy(pubkey->data, &internal_pubkey, sizeof(secp256k1_pubkey));
+    return 1;
+}
+
+int nostr_secp256k1_ec_pubkey_negate(nostr_secp256k1_pubkey* pubkey) {
+    if (g_ctx == NULL || pubkey == NULL) {
+        return 0;
+    }
+
+    secp256k1_pubkey internal_pubkey;
+    memcpy(&internal_pubkey, pubkey->data, sizeof(secp256k1_pubkey));
+
+    if (!secp256k1_ec_pubkey_negate(g_ctx, &internal_pubkey)) {
+        return 0;
+    }
+
+    memcpy(pubkey->data, &internal_pubkey, sizeof(secp256k1_pubkey));
+    return 1;
+}
+
+int nostr_secp256k1_ec_pubkey_combine(nostr_secp256k1_pubkey* out,
+                                      const nostr_secp256k1_pubkey* const* ins,
+                                      size_t n) {
+    if (g_ctx == NULL || out == NULL || ins == NULL || n == 0) {
+        return 0;
+    }
+
+    secp256k1_pubkey* parsed = (secp256k1_pubkey*)calloc(n, sizeof(secp256k1_pubkey));
+    const secp256k1_pubkey** ptrs = (const secp256k1_pubkey**)calloc(n, sizeof(secp256k1_pubkey*));
+    if (!parsed || !ptrs) {
+        free(parsed);
+        free(ptrs);
+        return 0;
+    }
+
+    for (size_t i = 0; i < n; i++) {
+        if (!ins[i]) {
+            free(parsed);
+            free(ptrs);
+            return 0;
+        }
+        memcpy(&parsed[i], ins[i]->data, sizeof(secp256k1_pubkey));
+        ptrs[i] = &parsed[i];
+    }
+
+    secp256k1_pubkey combined;
+    int ok = secp256k1_ec_pubkey_combine(g_ctx, &combined, ptrs, n);
+
+    free(parsed);
+    free(ptrs);
+
+    if (!ok) {
+        return 0;
+    }
+
+    memcpy(out->data, &combined, sizeof(secp256k1_pubkey));
+    return 1;
+}
+
+int nostr_secp256k1_get_random_bytes(unsigned char *buf, size_t len) {
+    if (buf == NULL || len == 0) {
+        return 0;
+    }
+    
+    if (nostr_platform_random(buf, len) != 0) {
+        return 0;
+    }
+
+    return 1;
+}

firmware/kb2040_hidden_signer/src/nostr_core/nip001.c

@@ -0,0 +1,345 @@
+/*
+ * NOSTR Core Library - NIP-001: Basic Protocol Flow
+ * 
+ * Event creation, signing, serialization and core protocol functions
+ */
+
+#include "nip001.h"
+#include "utils.h"
+#include "../cjson/cJSON.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <time.h>
+#include "../nostr_core/nostr_common.h"
+
+// Forward declarations for crypto functions (private API)
+// These functions are implemented in crypto/ but not exposed through public headers
+typedef struct {
+    unsigned char data[64];
+} nostr_secp256k1_xonly_pubkey;
+
+int nostr_secp256k1_xonly_pubkey_parse(nostr_secp256k1_xonly_pubkey* pubkey, const unsigned char* input32);
+int nostr_secp256k1_schnorrsig_verify(const unsigned char* sig64, const unsigned char* msg32, const nostr_secp256k1_xonly_pubkey* pubkey);
+
+// Declare utility functions
+void nostr_bytes_to_hex(const unsigned char* bytes, size_t len, char* hex);
+int nostr_hex_to_bytes(const char* hex, unsigned char* bytes, size_t len);
+int nostr_sha256(const unsigned char* data, size_t len, unsigned char* hash);
+int nostr_ec_public_key_from_private_key(const unsigned char* private_key, unsigned char* public_key);
+int nostr_ec_sign(const unsigned char* private_key, const unsigned char* hash, unsigned char* signature);
+
+/**
+ * Create and sign a NOSTR event
+ */
+cJSON* nostr_create_and_sign_event(int kind, const char* content, cJSON* tags, const unsigned char* private_key, time_t timestamp) {
+    if (!private_key) {
+        return NULL;
+    }
+    
+    if (!content) {
+        content = ""; // Default to empty content
+    }
+    
+    // Convert private key to public key
+    unsigned char public_key[32];
+    if (nostr_ec_public_key_from_private_key(private_key, public_key) != 0) {
+        return NULL;
+    }
+    
+    // Convert public key to hex
+    char pubkey_hex[65];
+    nostr_bytes_to_hex(public_key, 32, pubkey_hex);
+    
+    // Create event structure
+    cJSON* event = cJSON_CreateObject();
+    if (!event) {
+        return NULL;
+    }
+    
+    // Use provided timestamp or current time if timestamp is 0
+    time_t event_time = (timestamp == 0) ? time(NULL) : timestamp;
+    
+    cJSON_AddStringToObject(event, "pubkey", pubkey_hex);
+    cJSON_AddNumberToObject(event, "created_at", (double)event_time);
+    cJSON_AddNumberToObject(event, "kind", kind);
+    
+    // Add tags (copy provided tags or create empty array)
+    if (tags) {
+        cJSON_AddItemToObject(event, "tags", cJSON_Duplicate(tags, 1));
+    } else {
+        cJSON_AddItemToObject(event, "tags", cJSON_CreateArray());
+    }
+    
+    cJSON_AddStringToObject(event, "content", content);
+    
+    // ============================================================================
+    // INLINE SERIALIZATION AND SIGNING LOGIC 
+    // ============================================================================
+    
+    // Get event fields for serialization
+    cJSON* pubkey_item = cJSON_GetObjectItem(event, "pubkey");
+    cJSON* created_at_item = cJSON_GetObjectItem(event, "created_at");
+    cJSON* kind_item = cJSON_GetObjectItem(event, "kind");
+    cJSON* tags_item = cJSON_GetObjectItem(event, "tags");
+    cJSON* content_item = cJSON_GetObjectItem(event, "content");
+    
+    if (!pubkey_item || !created_at_item || !kind_item || !tags_item || !content_item) {
+        cJSON_Delete(event);
+        return NULL;
+    }
+    
+    // Create serialization array: [0, pubkey, created_at, kind, tags, content]
+    cJSON* serialize_array = cJSON_CreateArray();
+    if (!serialize_array) {
+        cJSON_Delete(event);
+        return NULL;
+    }
+    
+    cJSON_AddItemToArray(serialize_array, cJSON_CreateNumber(0));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(pubkey_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(created_at_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(kind_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(tags_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(content_item, 1));
+    
+    char* serialize_string = cJSON_PrintUnformatted(serialize_array);
+    cJSON_Delete(serialize_array);
+    
+    if (!serialize_string) {
+        cJSON_Delete(event);
+        return NULL;
+    }
+    
+    // Hash the serialized event
+    unsigned char event_hash[32];
+    if (nostr_sha256((const unsigned char*)serialize_string, strlen(serialize_string), event_hash) != 0) {
+        free(serialize_string);
+        cJSON_Delete(event);
+        return NULL;
+    }
+    
+    // Convert hash to hex for event ID
+    char event_id[65];
+    nostr_bytes_to_hex(event_hash, 32, event_id);
+    
+    // Sign the hash using ECDSA
+    unsigned char signature[64];
+    if (nostr_ec_sign(private_key, event_hash, signature) != 0) {
+        free(serialize_string);
+        cJSON_Delete(event);
+        return NULL;
+    }
+    
+    // Convert signature to hex
+    char sig_hex[129];
+    nostr_bytes_to_hex(signature, 64, sig_hex);
+    
+    // Add ID and signature to the event
+    cJSON_AddStringToObject(event, "id", event_id);
+    cJSON_AddStringToObject(event, "sig", sig_hex);
+    
+    free(serialize_string);
+    
+    return event;
+}
+
+/**
+ * Validate the structure of a NOSTR event
+ * Checks required fields, types, and basic format validation
+ */
+int nostr_validate_event_structure(cJSON* event) {
+    if (!event || !cJSON_IsObject(event)) {
+        return NOSTR_ERROR_EVENT_INVALID_STRUCTURE;
+    }
+    
+    // Check required fields exist
+    cJSON* id_item = cJSON_GetObjectItem(event, "id");
+    cJSON* pubkey_item = cJSON_GetObjectItem(event, "pubkey");
+    cJSON* created_at_item = cJSON_GetObjectItem(event, "created_at");
+    cJSON* kind_item = cJSON_GetObjectItem(event, "kind");
+    cJSON* tags_item = cJSON_GetObjectItem(event, "tags");
+    cJSON* content_item = cJSON_GetObjectItem(event, "content");
+    cJSON* sig_item = cJSON_GetObjectItem(event, "sig");
+    
+    if (!id_item || !pubkey_item || !created_at_item || !kind_item || 
+        !tags_item || !content_item || !sig_item) {
+        return NOSTR_ERROR_EVENT_INVALID_STRUCTURE;
+    }
+    
+    // Validate field types
+    if (!cJSON_IsString(id_item)) return NOSTR_ERROR_EVENT_INVALID_ID;
+    if (!cJSON_IsString(pubkey_item)) return NOSTR_ERROR_EVENT_INVALID_PUBKEY;
+    if (!cJSON_IsNumber(created_at_item)) return NOSTR_ERROR_EVENT_INVALID_CREATED_AT;
+    if (!cJSON_IsNumber(kind_item)) return NOSTR_ERROR_EVENT_INVALID_KIND;
+    if (!cJSON_IsArray(tags_item)) return NOSTR_ERROR_EVENT_INVALID_TAGS;
+    if (!cJSON_IsString(content_item)) return NOSTR_ERROR_EVENT_INVALID_CONTENT;
+    if (!cJSON_IsString(sig_item)) return NOSTR_ERROR_EVENT_INVALID_SIGNATURE;
+    
+    // Validate hex string lengths
+    const char* id_str = cJSON_GetStringValue(id_item);
+    const char* pubkey_str = cJSON_GetStringValue(pubkey_item);
+    const char* sig_str = cJSON_GetStringValue(sig_item);
+    
+    if (!id_str || strlen(id_str) != 64) return NOSTR_ERROR_EVENT_INVALID_ID;
+    if (!pubkey_str || strlen(pubkey_str) != 64) return NOSTR_ERROR_EVENT_INVALID_PUBKEY;
+    if (!sig_str || strlen(sig_str) != 128) return NOSTR_ERROR_EVENT_INVALID_SIGNATURE;
+    
+    // Validate hex characters (lowercase)
+    for (int i = 0; i < 64; i++) {
+        char c = id_str[i];
+        if (!((c >= '0' && c <= '9') || (c >= 'a' && c <= 'f'))) {
+            return NOSTR_ERROR_EVENT_INVALID_ID;
+        }
+        c = pubkey_str[i];
+        if (!((c >= '0' && c <= '9') || (c >= 'a' && c <= 'f'))) {
+            return NOSTR_ERROR_EVENT_INVALID_PUBKEY;
+        }
+    }
+    
+    // Validate signature hex characters (lowercase) - 128 characters
+    for (int i = 0; i < 128; i++) {
+        char c = sig_str[i];
+        if (!((c >= '0' && c <= '9') || (c >= 'a' && c <= 'f'))) {
+            return NOSTR_ERROR_EVENT_INVALID_SIGNATURE;
+        }
+    }
+    
+    // Validate created_at is a valid timestamp (positive number)
+    double created_at = cJSON_GetNumberValue(created_at_item);
+    if (created_at < 0) return NOSTR_ERROR_EVENT_INVALID_CREATED_AT;
+    
+    // Validate kind is valid (0-65535)
+    double kind = cJSON_GetNumberValue(kind_item);
+    if (kind < 0 || kind > 65535 || kind != (int)kind) {
+        return NOSTR_ERROR_EVENT_INVALID_KIND;
+    }
+    
+    // Validate tags array structure (array of arrays of strings)
+    cJSON* tag_item;
+    cJSON_ArrayForEach(tag_item, tags_item) {
+        if (!cJSON_IsArray(tag_item)) {
+            return NOSTR_ERROR_EVENT_INVALID_TAGS;
+        }
+        cJSON* tag_element;
+        cJSON_ArrayForEach(tag_element, tag_item) {
+            if (!cJSON_IsString(tag_element)) {
+                return NOSTR_ERROR_EVENT_INVALID_TAGS;
+            }
+        }
+    }
+    
+    return NOSTR_SUCCESS;
+}
+
+/**
+ * Verify the cryptographic signature of a NOSTR event
+ * Validates event ID and signature according to NIP-01
+ */
+int nostr_verify_event_signature(cJSON* event) {
+    if (!event) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    // Get event fields
+    cJSON* id_item = cJSON_GetObjectItem(event, "id");
+    cJSON* pubkey_item = cJSON_GetObjectItem(event, "pubkey");
+    cJSON* created_at_item = cJSON_GetObjectItem(event, "created_at");
+    cJSON* kind_item = cJSON_GetObjectItem(event, "kind");
+    cJSON* tags_item = cJSON_GetObjectItem(event, "tags");
+    cJSON* content_item = cJSON_GetObjectItem(event, "content");
+    cJSON* sig_item = cJSON_GetObjectItem(event, "sig");
+    
+    if (!id_item || !pubkey_item || !created_at_item || !kind_item || 
+        !tags_item || !content_item || !sig_item) {
+        return NOSTR_ERROR_EVENT_INVALID_STRUCTURE;
+    }
+    
+    // Create serialization array: [0, pubkey, created_at, kind, tags, content]
+    cJSON* serialize_array = cJSON_CreateArray();
+    if (!serialize_array) {
+        return NOSTR_ERROR_MEMORY_FAILED;
+    }
+    
+    cJSON_AddItemToArray(serialize_array, cJSON_CreateNumber(0));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(pubkey_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(created_at_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(kind_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(tags_item, 1));
+    cJSON_AddItemToArray(serialize_array, cJSON_Duplicate(content_item, 1));
+    
+    char* serialize_string = cJSON_PrintUnformatted(serialize_array);
+    cJSON_Delete(serialize_array);
+    
+    if (!serialize_string) {
+        return NOSTR_ERROR_MEMORY_FAILED;
+    }
+    
+    // Hash the serialized event
+    unsigned char event_hash[32];
+    if (nostr_sha256((const unsigned char*)serialize_string, strlen(serialize_string), event_hash) != 0) {
+        free(serialize_string);
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    // Convert hash to hex for event ID verification
+    char calculated_id[65];
+    nostr_bytes_to_hex(event_hash, 32, calculated_id);
+    
+    // Compare with provided event ID
+    const char* provided_id = cJSON_GetStringValue(id_item);
+    if (!provided_id || strcmp(calculated_id, provided_id) != 0) {
+        free(serialize_string);
+        return NOSTR_ERROR_EVENT_INVALID_ID;
+    }
+    
+    // Verify signature
+    const char* pubkey_str = cJSON_GetStringValue(pubkey_item);
+    const char* sig_str = cJSON_GetStringValue(sig_item);
+    
+    if (!pubkey_str || !sig_str) {
+        free(serialize_string);
+        return NOSTR_ERROR_EVENT_INVALID_STRUCTURE;
+    }
+    
+    // Convert hex strings to bytes
+    unsigned char pubkey_bytes[32];
+    unsigned char sig_bytes[64];
+    
+    if (nostr_hex_to_bytes(pubkey_str, pubkey_bytes, 32) != 0 ||
+        nostr_hex_to_bytes(sig_str, sig_bytes, 64) != 0) {
+        free(serialize_string);
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    // Parse the public key into secp256k1 format
+    nostr_secp256k1_xonly_pubkey xonly_pubkey;
+    if (!nostr_secp256k1_xonly_pubkey_parse(&xonly_pubkey, pubkey_bytes)) {
+        free(serialize_string);
+        return NOSTR_ERROR_EVENT_INVALID_PUBKEY;
+    }
+    
+    // Verify Schnorr signature
+    if (!nostr_secp256k1_schnorrsig_verify(sig_bytes, event_hash, &xonly_pubkey)) {
+        free(serialize_string);
+        return NOSTR_ERROR_EVENT_INVALID_SIGNATURE;
+    }
+    
+    free(serialize_string);
+    return NOSTR_SUCCESS;
+}
+
+/**
+ * Complete validation of a NOSTR event
+ * Performs both structure and cryptographic validation
+ */
+int nostr_validate_event(cJSON* event) {
+    // First validate structure (fast check)
+    int structure_result = nostr_validate_event_structure(event);
+    if (structure_result != NOSTR_SUCCESS) {
+        return structure_result;
+    }
+    
+    // Then verify signature (expensive check)
+    return nostr_verify_event_signature(event);
+}

firmware/kb2040_hidden_signer/src/nostr_core/nip001.h

@@ -0,0 +1,23 @@
+/*
+ * NOSTR Core Library - NIP-001: Basic Protocol Flow
+ * 
+ * Event creation, signing, serialization and core protocol functions
+ */
+
+#ifndef NIP001_H
+#define NIP001_H
+
+#include <stdint.h>
+#include <time.h>
+#include "../cjson/cJSON.h"
+
+
+// Function declarations
+cJSON* nostr_create_and_sign_event(int kind, const char* content, cJSON* tags, const unsigned char* private_key, time_t timestamp);
+
+// Event validation functions
+int nostr_validate_event_structure(cJSON* event);
+int nostr_verify_event_signature(cJSON* event);
+int nostr_validate_event(cJSON* event);
+
+#endif // NIP001_H

firmware/kb2040_hidden_signer/src/nostr_core/nip006.c

@@ -0,0 +1,104 @@
+/*
+ * NOSTR Core Library - NIP-006: Key Derivation from Mnemonic
+ */
+
+#include "nip006.h"
+#include "utils.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include <time.h>
+#include "../nostr_core/nostr_common.h"
+#include "nostr_platform.h"
+
+int nostr_generate_keypair(unsigned char* private_key, unsigned char* public_key) {
+    if (!private_key || !public_key) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    if (nostr_platform_random(private_key, 32) != 0) {
+        return NOSTR_ERROR_IO_FAILED;
+    }
+    
+    // Validate private key
+    if (nostr_ec_private_key_verify(private_key) != 0) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    // Generate public key from private key (already x-only for NOSTR)
+    if (nostr_ec_public_key_from_private_key(private_key, public_key) != 0) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    return NOSTR_SUCCESS;
+}
+
+int nostr_generate_mnemonic_and_keys(char* mnemonic, size_t mnemonic_size, 
+                                    int account, unsigned char* private_key, 
+                                    unsigned char* public_key) {
+    if (!mnemonic || mnemonic_size < 256 || !private_key || !public_key) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    // Generate entropy for 12-word mnemonic
+    unsigned char entropy[16];
+    if (nostr_platform_random(entropy, sizeof(entropy)) != 0) {
+        return NOSTR_ERROR_IO_FAILED;
+    }
+    
+    // Generate mnemonic from entropy
+    if (nostr_bip39_mnemonic_from_bytes(entropy, sizeof(entropy), mnemonic) != 0) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    // Derive keys from the generated mnemonic
+    return nostr_derive_keys_from_mnemonic(mnemonic, account, private_key, public_key);
+}
+
+int nostr_derive_keys_from_mnemonic(const char* mnemonic, int account,
+                                   unsigned char* private_key, unsigned char* public_key) {
+    if (!mnemonic || !private_key || !public_key) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    // Validate mnemonic
+    if (nostr_bip39_mnemonic_validate(mnemonic) != 0) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    // Convert mnemonic to seed
+    unsigned char seed[64];
+    if (nostr_bip39_mnemonic_to_seed(mnemonic, "", seed, sizeof(seed)) != 0) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    // Derive master key from seed
+    nostr_hd_key_t master_key;
+    if (nostr_bip32_key_from_seed(seed, sizeof(seed), &master_key) != 0) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    // NIP-06 path: m/44'/1237'/account'/0/0
+    nostr_hd_key_t derived_key;
+    uint32_t path[] = {
+        0x80000000 + 44,    // 44' (hardened)
+        0x80000000 + 1237,  // 1237' (hardened)
+        0x80000000 + account, // account' (hardened)
+        0,                   // 0 (not hardened)
+        0                    // 0 (not hardened)
+    };
+    
+    if (nostr_bip32_derive_path(&master_key, path, sizeof(path) / sizeof(path[0]), &derived_key) != 0) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    // Extract private key and public key
+    memcpy(private_key, derived_key.private_key, 32);
+    memcpy(public_key, derived_key.public_key + 1, 32); // Remove compression prefix for x-only
+    
+    return NOSTR_SUCCESS;
+}
+
+// Note: nostr_detect_input_type, nostr_decode_nsec, and nostr_decode_npub
+// are implemented in NIP-019 to avoid multiple definitions

firmware/kb2040_hidden_signer/src/nostr_core/nip006.h

@@ -0,0 +1,30 @@
+/*
+ * NOSTR Core Library - NIP-006: Key Derivation from Mnemonic
+ */
+
+#ifndef NIP006_H
+#define NIP006_H
+
+#include "nip001.h"
+#include <stdint.h>
+
+// Input type detection
+typedef enum {
+    NOSTR_INPUT_UNKNOWN = 0,
+    NOSTR_INPUT_NSEC_HEX,
+    NOSTR_INPUT_NSEC_BECH32,
+    NOSTR_INPUT_MNEMONIC
+} nostr_input_type_t;
+
+// Function declarations
+int nostr_generate_keypair(unsigned char* private_key, unsigned char* public_key);
+int nostr_generate_mnemonic_and_keys(char* mnemonic, size_t mnemonic_size, 
+                                    int account, unsigned char* private_key, 
+                                    unsigned char* public_key);
+int nostr_derive_keys_from_mnemonic(const char* mnemonic, int account,
+                                   unsigned char* private_key, unsigned char* public_key);
+nostr_input_type_t nostr_detect_input_type(const char* input);
+int nostr_decode_nsec(const char* input, unsigned char* private_key);
+int nostr_decode_npub(const char* input, unsigned char* public_key);
+
+#endif // NIP006_H

firmware/kb2040_hidden_signer/src/nostr_core/nip019.c

@@ -0,0 +1,265 @@
+/*
+ * NOSTR Core Library - NIP-019: Bech32-encoded Entities
+ */
+
+#include "nip019.h"
+#include "utils.h"
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+#include "../nostr_core/nostr_common.h"
+
+#define BECH32_CONST 1
+
+static const char bech32_charset[] = "qpzry9x8gf2tvdw0s3jn54khce6mua7l";
+
+static const int8_t bech32_charset_rev[128] = {
+    -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
+    -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
+    -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
+    15, -1, 10, 17, 21, 20, 26, 30,  7,  5, -1, -1, -1, -1, -1, -1,
+    -1, 29, -1, 24, 13, 25,  9,  8, 23, -1, 18, 22, 31, 27, 19, -1,
+    1,  0,  3, 16, 11, 28, 12, 14,  6,  4,  2, -1, -1, -1, -1, -1,
+    -1, 29, -1, 24, 13, 25,  9,  8, 23, -1, 18, 22, 31, 27, 19, -1,
+    1,  0,  3, 16, 11, 28, 12, 14,  6,  4,  2, -1, -1, -1, -1, -1
+};
+
+static uint32_t bech32_polymod_step(uint32_t pre) {
+    uint8_t b = pre >> 25;
+    return ((pre & 0x1FFFFFF) << 5) ^
+           (-((b >> 0) & 1) & 0x3b6a57b2UL) ^
+           (-((b >> 1) & 1) & 0x26508e6dUL) ^
+           (-((b >> 2) & 1) & 0x1ea119faUL) ^
+           (-((b >> 3) & 1) & 0x3d4233ddUL) ^
+           (-((b >> 4) & 1) & 0x2a1462b3UL);
+}
+
+static int convert_bits(uint8_t *out, size_t *outlen, int outbits, const uint8_t *in, size_t inlen, int inbits, int pad) {
+    uint32_t val = 0;
+    int bits = 0;
+    uint32_t maxv = (((uint32_t)1) << outbits) - 1;
+    *outlen = 0;
+    while (inlen--) {
+        val = (val << inbits) | *(in++);
+        bits += inbits;
+        while (bits >= outbits) {
+            bits -= outbits;
+            out[(*outlen)++] = (val >> bits) & maxv;
+        }
+    }
+    if (pad) {
+        if (bits) {
+            out[(*outlen)++] = (val << (outbits - bits)) & maxv;
+        }
+    } else if (((val << (outbits - bits)) & maxv) || bits >= inbits) {
+        return 0;
+    }
+    return 1;
+}
+
+static int bech32_encode(char *output, const char *hrp, const uint8_t *data, size_t data_len) {
+    uint32_t chk = 1;
+    size_t i, hrp_len = strlen(hrp);
+    
+    for (i = 0; i < hrp_len; ++i) {
+        int ch = hrp[i];
+        if (ch < 33 || ch > 126) return 0;
+        if (ch >= 'A' && ch <= 'Z') return 0;
+        chk = bech32_polymod_step(chk) ^ (ch >> 5);
+    }
+    
+    chk = bech32_polymod_step(chk);
+    for (i = 0; i < hrp_len; ++i) {
+        chk = bech32_polymod_step(chk) ^ (hrp[i] & 0x1f);
+        *(output++) = hrp[i];
+    }
+    
+    *(output++) = '1';
+    for (i = 0; i < data_len; ++i) {
+        if (*data >> 5) return 0;
+        chk = bech32_polymod_step(chk) ^ (*data);
+        *(output++) = bech32_charset[*(data++)];
+    }
+    
+    for (i = 0; i < 6; ++i) {
+        chk = bech32_polymod_step(chk);
+    }
+    
+    chk ^= BECH32_CONST;
+    for (i = 0; i < 6; ++i) {
+        *(output++) = bech32_charset[(chk >> ((5 - i) * 5)) & 0x1f];
+    }
+    
+    *output = 0;
+    return 1;
+}
+
+static int bech32_decode(const char* input, const char* hrp, unsigned char* data, size_t* data_len) {
+    if (!input || !hrp || !data || !data_len) {
+        return 0;
+    }
+    
+    size_t input_len = strlen(input);
+    size_t hrp_len = strlen(hrp);
+    
+    if (input_len < hrp_len + 7) return 0;
+    if (strncmp(input, hrp, hrp_len) != 0) return 0;
+    if (input[hrp_len] != '1') return 0;
+    
+    const char* data_part = input + hrp_len + 1;
+    size_t data_part_len = input_len - hrp_len - 1;
+    
+    uint8_t values[256];
+    for (size_t i = 0; i < data_part_len; i++) {
+        unsigned char c = (unsigned char)data_part[i];
+        if (c >= 128) return 0;
+        int8_t val = bech32_charset_rev[c];
+        if (val == -1) return 0;
+        values[i] = (uint8_t)val;
+    }
+    
+    if (data_part_len < 6) return 0;
+    
+    uint32_t chk = 1;
+    for (size_t i = 0; i < hrp_len; i++) {
+        chk = bech32_polymod_step(chk) ^ (hrp[i] >> 5);
+    }
+    chk = bech32_polymod_step(chk);
+    for (size_t i = 0; i < hrp_len; i++) {
+        chk = bech32_polymod_step(chk) ^ (hrp[i] & 0x1f);
+    }
+    for (size_t i = 0; i < data_part_len; i++) {
+        chk = bech32_polymod_step(chk) ^ values[i];
+    }
+    
+    if (chk != BECH32_CONST) return 0;
+    
+    size_t payload_len = data_part_len - 6;
+    size_t decoded_len;
+    if (!convert_bits(data, &decoded_len, 8, values, payload_len, 5, 0)) {
+        return 0;
+    }
+    
+    *data_len = decoded_len;
+    return 1;
+}
+
+int nostr_key_to_bech32(const unsigned char* key, const char* hrp, char* output) {
+    if (!key || !hrp || !output) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    uint8_t conv[64];
+    size_t conv_len;
+    
+    if (!convert_bits(conv, &conv_len, 5, key, 32, 8, 1)) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    if (!bech32_encode(output, hrp, conv, conv_len)) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    
+    return NOSTR_SUCCESS;
+}
+
+nostr_input_type_t nostr_detect_input_type(const char* input) {
+    if (!input || strlen(input) == 0) {
+        return NOSTR_INPUT_UNKNOWN;
+    }
+    
+    size_t len = strlen(input);
+    
+    // Check for bech32 nsec
+    if (len > 5 && strncmp(input, "nsec1", 5) == 0) {
+        return NOSTR_INPUT_NSEC_BECH32;
+    }
+    
+    // Check for hex nsec (64 characters, all hex)
+    if (len == 64) {
+        int is_hex = 1;
+        for (size_t i = 0; i < len; i++) {
+            if (!isxdigit((unsigned char)input[i])) {
+                is_hex = 0;
+                break;
+            }
+        }
+        if (is_hex) {
+            return NOSTR_INPUT_NSEC_HEX;
+        }
+    }
+    
+    // Check for mnemonic (space-separated words)
+    int word_count = 0;
+    char temp[1024];
+    strncpy(temp, input, sizeof(temp) - 1);
+    temp[sizeof(temp) - 1] = '\0';
+    
+    char* token = strtok(temp, " ");
+    while (token != NULL) {
+        word_count++;
+        token = strtok(NULL, " ");
+    }
+    
+    // BIP39 mnemonics are typically 12, 18, or 24 words
+    if (word_count >= 12 && word_count <= 24) {
+        return NOSTR_INPUT_MNEMONIC;
+    }
+    
+    return NOSTR_INPUT_UNKNOWN;
+}
+
+int nostr_decode_nsec(const char* input, unsigned char* private_key) {
+    if (!input || !private_key) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    nostr_input_type_t type = nostr_detect_input_type(input);
+    
+    if (type == NOSTR_INPUT_NSEC_HEX) {
+        if (nostr_hex_to_bytes(input, private_key, 32) != NOSTR_SUCCESS) {
+            return NOSTR_ERROR_INVALID_INPUT;
+        }
+    } else if (type == NOSTR_INPUT_NSEC_BECH32) {
+        size_t decoded_len;
+        if (!bech32_decode(input, "nsec", private_key, &decoded_len)) {
+            return NOSTR_ERROR_INVALID_INPUT;
+        }
+        if (decoded_len != 32) {
+            return NOSTR_ERROR_INVALID_INPUT;
+        }
+    } else {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    // TODO: Add private key validation if crypto functions are available
+    
+    return NOSTR_SUCCESS;
+}
+
+int nostr_decode_npub(const char* input, unsigned char* public_key) {
+    if (!input || !public_key) {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    nostr_input_type_t type = nostr_detect_input_type(input);
+    
+    if (type == NOSTR_INPUT_NSEC_HEX) {  // Actually public key hex
+        if (nostr_hex_to_bytes(input, public_key, 32) != NOSTR_SUCCESS) {
+            return NOSTR_ERROR_INVALID_INPUT;
+        }
+    } else if (strncmp(input, "npub1", 4) == 0) {  // Bech32 npub
+        size_t decoded_len;
+        if (!bech32_decode(input, "npub", public_key, &decoded_len)) {
+            return NOSTR_ERROR_INVALID_INPUT;
+        }
+        if (decoded_len != 32) {
+            return NOSTR_ERROR_INVALID_INPUT;
+        }
+    } else {
+        return NOSTR_ERROR_INVALID_INPUT;
+    }
+    
+    return NOSTR_SUCCESS;
+}

firmware/kb2040_hidden_signer/src/nostr_core/nip019.h

@@ -0,0 +1,17 @@
+/*
+ * NOSTR Core Library - NIP-019: Bech32-encoded Entities
+ */
+
+#ifndef NIP019_H
+#define NIP019_H
+
+#include "nip001.h"
+#include "nip006.h"  // For nostr_input_type_t enum
+
+// Function declarations
+int nostr_key_to_bech32(const unsigned char* key, const char* hrp, char* output);
+nostr_input_type_t nostr_detect_input_type(const char* input);
+int nostr_decode_nsec(const char* input, unsigned char* private_key);
+int nostr_decode_npub(const char* input, unsigned char* public_key);
+
+#endif // NIP019_H

firmware/kb2040_hidden_signer/src/nostr_core/nostr_common.c

@@ -0,0 +1,106 @@
+/*
+ * NOSTR Core Library - Common Utilities
+ * 
+ * Common functions and utilities shared across the library
+ */
+
+#include "nostr_common.h"
+#include "utils.h"
+
+/**
+ * Convert error code to human-readable string
+ * Handles all error codes defined in nostr_common.h
+ */
+const char* nostr_strerror(int error_code) {
+    switch (error_code) {
+        case NOSTR_SUCCESS: return "Success";
+        case NOSTR_ERROR_INVALID_INPUT: return "Invalid input";
+        case NOSTR_ERROR_CRYPTO_FAILED: return "Cryptographic operation failed";
+        case NOSTR_ERROR_MEMORY_FAILED: return "Memory allocation failed";
+        case NOSTR_ERROR_IO_FAILED: return "I/O operation failed";
+        case NOSTR_ERROR_NETWORK_FAILED: return "Network operation failed";
+        case NOSTR_ERROR_NIP04_INVALID_FORMAT: return "NIP-04 invalid format";
+        case NOSTR_ERROR_NIP04_DECRYPT_FAILED: return "NIP-04 decryption failed";
+        case NOSTR_ERROR_NIP04_BUFFER_TOO_SMALL: return "NIP-04 buffer too small";
+        case NOSTR_ERROR_NIP44_INVALID_FORMAT: return "NIP-44: Invalid format";
+        case NOSTR_ERROR_NIP44_DECRYPT_FAILED: return "NIP-44: Decryption failed";
+        case NOSTR_ERROR_NIP44_BUFFER_TOO_SMALL: return "NIP-44: Buffer too small";
+        case NOSTR_ERROR_NIP05_INVALID_IDENTIFIER: return "NIP-05: Invalid identifier format";
+        case NOSTR_ERROR_NIP05_HTTP_FAILED: return "NIP-05: HTTP request failed";
+        case NOSTR_ERROR_NIP05_JSON_PARSE_FAILED: return "NIP-05: JSON parsing failed";
+        case NOSTR_ERROR_NIP05_NAME_NOT_FOUND: return "NIP-05: Name not found in .well-known";
+        case NOSTR_ERROR_NIP05_PUBKEY_MISMATCH: return "NIP-05: Public key mismatch";
+        case NOSTR_ERROR_EVENT_INVALID_STRUCTURE: return "Event has invalid structure";
+        case NOSTR_ERROR_EVENT_INVALID_ID: return "Event has invalid ID";
+        case NOSTR_ERROR_EVENT_INVALID_PUBKEY: return "Event has invalid public key";
+        case NOSTR_ERROR_EVENT_INVALID_SIGNATURE: return "Event has invalid signature";
+        case NOSTR_ERROR_EVENT_INVALID_CREATED_AT: return "Event has invalid timestamp";
+        case NOSTR_ERROR_EVENT_INVALID_KIND: return "Event has invalid kind";
+        case NOSTR_ERROR_EVENT_INVALID_TAGS: return "Event has invalid tags";
+        case NOSTR_ERROR_EVENT_INVALID_CONTENT: return "Event has invalid content";
+        case NOSTR_ERROR_NIP13_INSUFFICIENT: return "NIP-13: Insufficient PoW difficulty";
+        case NOSTR_ERROR_NIP13_NO_NONCE_TAG: return "NIP-13: Missing nonce tag";
+        case NOSTR_ERROR_NIP13_INVALID_NONCE_TAG: return "NIP-13: Invalid nonce tag format";
+        case NOSTR_ERROR_NIP13_TARGET_MISMATCH: return "NIP-13: Target difficulty mismatch";
+        case NOSTR_ERROR_NIP13_CALCULATION: return "NIP-13: PoW calculation error";
+        case NOSTR_ERROR_NIP42_INVALID_CHALLENGE: return "NIP-42: Invalid challenge";
+        case NOSTR_ERROR_NIP42_CHALLENGE_EXPIRED: return "NIP-42: Challenge expired";
+        case NOSTR_ERROR_NIP42_AUTH_EVENT_INVALID: return "NIP-42: Authentication event invalid";
+        case NOSTR_ERROR_NIP42_URL_MISMATCH: return "NIP-42: Relay URL mismatch";
+        case NOSTR_ERROR_NIP42_TIME_TOLERANCE: return "NIP-42: Timestamp outside tolerance";
+        case NOSTR_ERROR_NIP42_NOT_AUTHENTICATED: return "NIP-42: Client not authenticated";
+        case NOSTR_ERROR_NIP42_INVALID_MESSAGE_FORMAT: return "NIP-42: Invalid message format";
+        case NOSTR_ERROR_NIP42_CHALLENGE_TOO_SHORT: return "NIP-42: Challenge too short";
+        case NOSTR_ERROR_NIP42_CHALLENGE_TOO_LONG: return "NIP-42: Challenge too long";
+        case NOSTR_ERROR_NIP46_INVALID_BUNKER_URL: return "NIP-46: Invalid bunker URL";
+        case NOSTR_ERROR_NIP46_INVALID_NOSTRCONNECT: return "NIP-46: Invalid nostrconnect URL";
+        case NOSTR_ERROR_NIP46_INVALID_REQUEST: return "NIP-46: Invalid request payload";
+        case NOSTR_ERROR_NIP46_INVALID_RESPONSE: return "NIP-46: Invalid response payload";
+        case NOSTR_ERROR_NIP46_ENCRYPTION_FAILED: return "NIP-46: Encryption failed";
+        case NOSTR_ERROR_NIP46_DECRYPTION_FAILED: return "NIP-46: Decryption failed";
+        case NOSTR_ERROR_NIP46_CONNECTION_FAILED: return "NIP-46: Connection failed";
+        case NOSTR_ERROR_NIP46_TIMEOUT: return "NIP-46: Timeout";
+        case NOSTR_ERROR_NIP46_SECRET_MISMATCH: return "NIP-46: Secret mismatch";
+        case NOSTR_ERROR_NIP46_UNKNOWN_METHOD: return "NIP-46: Unknown method";
+        case NOSTR_ERROR_NIP46_AUTH_CHALLENGE: return "NIP-46: Auth challenge required";
+        case NOSTR_ERROR_NIP46_NOT_CONNECTED: return "NIP-46: Not connected";
+        case NOSTR_ERROR_NIP60_INVALID_WALLET: return "NIP-60: Invalid wallet event";
+        case NOSTR_ERROR_NIP60_INVALID_TOKEN: return "NIP-60: Invalid token event";
+        case NOSTR_ERROR_NIP60_INVALID_HISTORY: return "NIP-60: Invalid history event";
+        case NOSTR_ERROR_NIP60_INVALID_QUOTE: return "NIP-60: Invalid quote event";
+        case NOSTR_ERROR_NIP60_DECRYPT_FAILED: return "NIP-60: Decryption failed";
+        case NOSTR_ERROR_NIP60_INVALID_PROOFS: return "NIP-60: Invalid proofs payload";
+        case NOSTR_ERROR_NIP60_INSUFFICIENT_FUNDS: return "NIP-60: Insufficient funds";
+        case NOSTR_ERROR_NIP61_INVALID_INFO: return "NIP-61: Invalid info event";
+        case NOSTR_ERROR_NIP61_INVALID_NUTZAP: return "NIP-61: Invalid nutzap event";
+        case NOSTR_ERROR_NIP61_MINT_MISMATCH: return "NIP-61: Mint mismatch";
+        case NOSTR_ERROR_NIP61_PUBKEY_MISMATCH: return "NIP-61: Pubkey mismatch";
+        case NOSTR_ERROR_NIP61_VERIFICATION_FAILED: return "NIP-61: Verification failed";
+        case NOSTR_ERROR_CASHU_HTTP_FAILED: return "Cashu: HTTP request failed";
+        case NOSTR_ERROR_CASHU_JSON_PARSE_FAILED: return "Cashu: JSON parsing failed";
+        case NOSTR_ERROR_CASHU_MINT_ERROR: return "Cashu: Mint returned an error";
+        case NOSTR_ERROR_CASHU_QUOTE_NOT_PAID: return "Cashu: Quote not paid";
+        case NOSTR_ERROR_CASHU_QUOTE_EXPIRED: return "Cashu: Quote expired";
+        case NOSTR_ERROR_CASHU_PROOFS_SPENT: return "Cashu: One or more proofs are already spent";
+        case NOSTR_ERROR_CASHU_CRYPTO_FAILED: return "Cashu: Cryptographic operation failed";
+        case NOSTR_ERROR_CASHU_INVALID_KEYSET: return "Cashu: Invalid keyset";
+        default: return "Unknown error";
+    }
+}
+
+/**
+ * Initialize the NOSTR library
+ */
+int nostr_init(void) {
+    if (nostr_crypto_init() != 0) {
+        return NOSTR_ERROR_CRYPTO_FAILED;
+    }
+    return NOSTR_SUCCESS;
+}
+
+/**
+ * Cleanup the NOSTR library
+ */
+void nostr_cleanup(void) {
+    nostr_crypto_cleanup();
+}

firmware/kb2040_hidden_signer/src/nostr_core/nostr_common.h

@@ -0,0 +1,131 @@
+/*
+ * NOSTR Core - Common Definitions
+ * Shared error constants and basic types for the modular NOSTR library
+ */
+
+#ifndef NOSTR_COMMON_H
+#define NOSTR_COMMON_H
+
+#include <stddef.h>
+#include <stdint.h>
+
+// Return codes
+#define NOSTR_SUCCESS 0
+#define NOSTR_ERROR_INVALID_INPUT -1
+#define NOSTR_ERROR_CRYPTO_FAILED -2
+#define NOSTR_ERROR_MEMORY_FAILED -3
+#define NOSTR_ERROR_IO_FAILED -4
+#define NOSTR_ERROR_NETWORK_FAILED -5
+#define NOSTR_ERROR_NIP04_INVALID_FORMAT -10
+#define NOSTR_ERROR_NIP04_DECRYPT_FAILED -11
+#define NOSTR_ERROR_NIP04_BUFFER_TOO_SMALL -12
+#define NOSTR_ERROR_NIP44_INVALID_FORMAT -13
+#define NOSTR_ERROR_NIP44_DECRYPT_FAILED -14
+#define NOSTR_ERROR_NIP44_BUFFER_TOO_SMALL -15
+#define NOSTR_ERROR_NIP05_INVALID_IDENTIFIER -16
+#define NOSTR_ERROR_NIP05_HTTP_FAILED -17
+#define NOSTR_ERROR_NIP05_JSON_PARSE_FAILED -18
+#define NOSTR_ERROR_NIP05_NAME_NOT_FOUND -19
+#define NOSTR_ERROR_NIP05_PUBKEY_MISMATCH -20
+#define NOSTR_ERROR_EVENT_INVALID_STRUCTURE -30
+#define NOSTR_ERROR_EVENT_INVALID_ID -31
+#define NOSTR_ERROR_EVENT_INVALID_PUBKEY -32
+#define NOSTR_ERROR_EVENT_INVALID_SIGNATURE -33
+#define NOSTR_ERROR_EVENT_INVALID_CREATED_AT -34
+#define NOSTR_ERROR_EVENT_INVALID_KIND -35
+#define NOSTR_ERROR_EVENT_INVALID_TAGS -36
+#define NOSTR_ERROR_EVENT_INVALID_CONTENT -37
+
+// Authentication Rules System Error Codes
+#define NOSTR_ERROR_AUTH_RULES_DISABLED -50
+#define NOSTR_ERROR_AUTH_RULES_DENIED -51
+#define NOSTR_ERROR_AUTH_RULES_DB_FAILED -52
+#define NOSTR_ERROR_AUTH_RULES_INVALID_RULE -53
+#define NOSTR_ERROR_AUTH_RULES_CACHE_FAILED -54
+#define NOSTR_ERROR_AUTH_RULES_BACKEND_NOT_FOUND -55
+
+// NIP-13 PoW-specific error codes
+#define NOSTR_ERROR_NIP13_INSUFFICIENT -100
+#define NOSTR_ERROR_NIP13_NO_NONCE_TAG -101
+#define NOSTR_ERROR_NIP13_INVALID_NONCE_TAG -102
+#define NOSTR_ERROR_NIP13_TARGET_MISMATCH -103
+#define NOSTR_ERROR_NIP13_CALCULATION -104
+
+// NIP-42 Authentication-specific error codes
+#define NOSTR_ERROR_NIP42_INVALID_CHALLENGE -200
+#define NOSTR_ERROR_NIP42_CHALLENGE_EXPIRED -201
+#define NOSTR_ERROR_NIP42_AUTH_EVENT_INVALID -202
+#define NOSTR_ERROR_NIP42_URL_MISMATCH -203
+#define NOSTR_ERROR_NIP42_TIME_TOLERANCE -204
+#define NOSTR_ERROR_NIP42_NOT_AUTHENTICATED -205
+#define NOSTR_ERROR_NIP42_INVALID_MESSAGE_FORMAT -206
+#define NOSTR_ERROR_NIP42_CHALLENGE_TOO_SHORT -207
+#define NOSTR_ERROR_NIP42_CHALLENGE_TOO_LONG -208
+
+// NIP-46 Remote Signing error codes
+#define NOSTR_ERROR_NIP46_INVALID_BUNKER_URL -300
+#define NOSTR_ERROR_NIP46_INVALID_NOSTRCONNECT -301
+#define NOSTR_ERROR_NIP46_INVALID_REQUEST -302
+#define NOSTR_ERROR_NIP46_INVALID_RESPONSE -303
+#define NOSTR_ERROR_NIP46_ENCRYPTION_FAILED -304
+#define NOSTR_ERROR_NIP46_DECRYPTION_FAILED -305
+#define NOSTR_ERROR_NIP46_CONNECTION_FAILED -306
+#define NOSTR_ERROR_NIP46_TIMEOUT -307
+#define NOSTR_ERROR_NIP46_SECRET_MISMATCH -308
+#define NOSTR_ERROR_NIP46_UNKNOWN_METHOD -309
+#define NOSTR_ERROR_NIP46_AUTH_CHALLENGE -310
+#define NOSTR_ERROR_NIP46_NOT_CONNECTED -311
+
+// NIP-60 Cashu Wallet error codes
+#define NOSTR_ERROR_NIP60_INVALID_WALLET -400
+#define NOSTR_ERROR_NIP60_INVALID_TOKEN -401
+#define NOSTR_ERROR_NIP60_INVALID_HISTORY -402
+#define NOSTR_ERROR_NIP60_INVALID_QUOTE -403
+#define NOSTR_ERROR_NIP60_DECRYPT_FAILED -404
+#define NOSTR_ERROR_NIP60_INVALID_PROOFS -405
+#define NOSTR_ERROR_NIP60_INSUFFICIENT_FUNDS -406
+
+// NIP-61 Nutzap error codes
+#define NOSTR_ERROR_NIP61_INVALID_INFO -410
+#define NOSTR_ERROR_NIP61_INVALID_NUTZAP -411
+#define NOSTR_ERROR_NIP61_MINT_MISMATCH -412
+#define NOSTR_ERROR_NIP61_PUBKEY_MISMATCH -413
+#define NOSTR_ERROR_NIP61_VERIFICATION_FAILED -414
+
+// Cashu Mint client error codes
+#define NOSTR_ERROR_CASHU_HTTP_FAILED -420
+#define NOSTR_ERROR_CASHU_JSON_PARSE_FAILED -421
+#define NOSTR_ERROR_CASHU_MINT_ERROR -422
+#define NOSTR_ERROR_CASHU_QUOTE_NOT_PAID -423
+#define NOSTR_ERROR_CASHU_QUOTE_EXPIRED -424
+#define NOSTR_ERROR_CASHU_PROOFS_SPENT -425
+#define NOSTR_ERROR_CASHU_CRYPTO_FAILED -426
+#define NOSTR_ERROR_CASHU_INVALID_KEYSET -427
+
+// Constants
+#define NOSTR_PRIVATE_KEY_SIZE 32
+#define NOSTR_PUBLIC_KEY_SIZE 32
+#define NOSTR_HEX_KEY_SIZE 65  // 64 + null terminator
+#define NOSTR_BECH32_KEY_SIZE 100
+#define NOSTR_MAX_CONTENT_SIZE 2048
+#define NOSTR_MAX_URL_SIZE 256
+#define NIP05_DEFAULT_TIMEOUT 10
+
+// NIP-04 Constants
+#define NOSTR_NIP04_MAX_PLAINTEXT_SIZE 1048576    // 1MB
+#define NOSTR_NIP04_MAX_ENCRYPTED_SIZE 22369621    // ~21.3MB (accounts for base64 overhead + IV)
+
+// NIP-44 Constants
+#define NOSTR_NIP44_MAX_PLAINTEXT_SIZE 65535         // 64KB - 1 (NIP-44 spec compliant)
+
+// Forward declaration for cJSON (to avoid requiring cJSON.h in header)
+struct cJSON;
+
+// Function declarations
+const char* nostr_strerror(int error_code);
+
+// Library initialization functions
+int nostr_init(void);
+void nostr_cleanup(void);
+
+#endif // NOSTR_COMMON_H

firmware/kb2040_hidden_signer/src/nostr_core/nostr_platform.h

@@ -0,0 +1,20 @@
+#ifndef NOSTR_PLATFORM_H
+#define NOSTR_PLATFORM_H
+
+#include <stddef.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/*
+ * Fill buffer with cryptographically secure random bytes.
+ * Returns 0 on success, -1 on failure.
+ */
+int nostr_platform_random(unsigned char *buf, size_t len);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* NOSTR_PLATFORM_H */

firmware/kb2040_hidden_signer/src/nostr_core/utils.h

@@ -0,0 +1,189 @@
+/*
+ * NOSTR Core Library - Utilities
+ *
+ * General utility functions used across multiple NIPs
+ */
+
+#ifndef NOSTR_UTILS_H
+#define NOSTR_UTILS_H
+
+#include <stddef.h>
+#include <stdint.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+// =============================================================================
+// UTILITY FUNCTIONS
+// =============================================================================
+
+// Convert bytes to hexadecimal string
+void nostr_bytes_to_hex(const unsigned char *bytes, size_t len, char *hex);
+
+// Convert hexadecimal string to bytes
+int nostr_hex_to_bytes(const char *hex, unsigned char *bytes, size_t len);
+
+// Base64 encoding function 
+size_t base64_encode(const unsigned char *data, size_t len, char *output,
+                     size_t output_size);
+
+// Base64 decoding function
+size_t base64_decode(const char *input, unsigned char *output);
+
+
+// =============================================================================
+// CORE CRYPTO FUNCTIONS
+// =============================================================================
+
+// Initialize crypto subsystem
+int nostr_crypto_init(void);
+
+// Cleanup crypto subsystem
+void nostr_crypto_cleanup(void);
+
+// SHA-256 hash function
+int nostr_sha256(const unsigned char *data, size_t len, unsigned char *hash);
+
+// =============================================================================
+// STREAMING SHA-256 FUNCTIONS
+// =============================================================================
+
+// SHA-256 streaming context
+typedef struct {
+    uint32_t state[8];      // Current hash state
+    unsigned char buffer[64]; // Input buffer for incomplete blocks
+    uint64_t bitlen;        // Total bits processed
+    size_t buflen;          // Current buffer length
+} nostr_sha256_ctx_t;
+
+// Initialize SHA-256 streaming context
+int nostr_sha256_init(nostr_sha256_ctx_t* ctx);
+
+// Update SHA-256 context with new data
+int nostr_sha256_update(nostr_sha256_ctx_t* ctx, const unsigned char* data, size_t len);
+
+// Finalize SHA-256 and output hash
+int nostr_sha256_final(nostr_sha256_ctx_t* ctx, unsigned char* hash);
+
+// Stream SHA-256 hash of a file
+int nostr_sha256_file_stream(const char* filename, unsigned char* hash);
+
+// HMAC-SHA256
+int nostr_hmac_sha256(const unsigned char *key, size_t key_len,
+                      const unsigned char *data, size_t data_len,
+                      unsigned char *output);
+
+// HMAC-SHA512
+int nostr_hmac_sha512(const unsigned char *key, size_t key_len,
+                      const unsigned char *data, size_t data_len,
+                      unsigned char *output);
+
+// PBKDF2 with HMAC-SHA512
+int nostr_pbkdf2_hmac_sha512(const unsigned char *password, size_t password_len,
+                             const unsigned char *salt, size_t salt_len,
+                             int iterations, unsigned char *output,
+                             size_t output_len);
+
+// SHA-512 implementation (for testing)
+int nostr_sha512(const unsigned char *data, size_t len, unsigned char *hash);
+
+// =============================================================================
+// SECP256K1 ELLIPTIC CURVE FUNCTIONS
+// =============================================================================
+
+// Verify private key is valid
+int nostr_ec_private_key_verify(const unsigned char *private_key);
+
+// Generate public key from private key
+int nostr_ec_public_key_from_private_key(const unsigned char *private_key,
+                                         unsigned char *public_key);
+
+// Sign data with ECDSA
+int nostr_ec_sign(const unsigned char *private_key, const unsigned char *hash,
+                  unsigned char *signature);
+
+// RFC 6979 deterministic nonce generation
+int nostr_rfc6979_generate_k(const unsigned char *private_key,
+                             const unsigned char *message_hash,
+                             unsigned char *k_out);
+
+int nostr_schnorr_sign(const unsigned char* private_key,
+                       const unsigned char* hash,
+                       unsigned char* signature);
+
+
+// =============================================================================
+// HKDF KEY DERIVATION FUNCTIONS
+// =============================================================================
+
+// HKDF Extract step
+int nostr_hkdf_extract(const unsigned char *salt, size_t salt_len,
+                       const unsigned char *ikm, size_t ikm_len,
+                       unsigned char *prk);
+
+// HKDF Expand step
+int nostr_hkdf_expand(const unsigned char *prk, size_t prk_len,
+                      const unsigned char *info, size_t info_len,
+                      unsigned char *okm, size_t okm_len);
+
+// HKDF (Extract + Expand)
+int nostr_hkdf(const unsigned char *salt, size_t salt_len,
+               const unsigned char *ikm, size_t ikm_len,
+               const unsigned char *info, size_t info_len, unsigned char *okm,
+               size_t okm_len);
+
+// ECDH shared secret computation (for debugging)
+int ecdh_shared_secret(const unsigned char *private_key,
+                       const unsigned char *public_key_x,
+                       unsigned char *shared_secret);
+
+
+
+
+// =============================================================================
+// BIP39 MNEMONIC FUNCTIONS
+// =============================================================================
+
+// Generate mnemonic from entropy
+int nostr_bip39_mnemonic_from_bytes(const unsigned char *entropy,
+                                    size_t entropy_len, char *mnemonic);
+
+// Validate mnemonic
+int nostr_bip39_mnemonic_validate(const char *mnemonic);
+
+// Convert mnemonic to seed
+int nostr_bip39_mnemonic_to_seed(const char *mnemonic, const char *passphrase,
+                                 unsigned char *seed, size_t seed_len);
+
+// =============================================================================
+// BIP32 HD WALLET FUNCTIONS
+// =============================================================================
+
+typedef struct {
+  unsigned char private_key[32];
+  unsigned char public_key[33];
+  unsigned char chain_code[32];
+  uint32_t depth;
+  uint32_t parent_fingerprint;
+  uint32_t child_number;
+} nostr_hd_key_t;
+
+// Create master key from seed
+int nostr_bip32_key_from_seed(const unsigned char *seed, size_t seed_len,
+                              nostr_hd_key_t *master_key);
+
+// Derive child key from parent
+int nostr_bip32_derive_child(const nostr_hd_key_t *parent_key,
+                             uint32_t child_number, nostr_hd_key_t *child_key);
+
+// Derive key from path
+int nostr_bip32_derive_path(const nostr_hd_key_t *master_key,
+                            const uint32_t *path, size_t path_len,
+                            nostr_hd_key_t *derived_key);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif // NOSTR_UTILS_H

firmware/kb2040_hidden_signer/src/platform/rp2040.c

@@ -0,0 +1,79 @@
+#include <stdint.h>
+#include <stddef.h>
+#include <string.h>
+
+#include "../nostr_core/nostr_platform.h"
+
+#if defined(ARDUINO)
+#include <Arduino.h>
+#endif
+
+#if defined(__has_include)
+#  if __has_include("pico/rand.h")
+#    include "pico/rand.h"
+#    define NOSTR_HAVE_PICO_RAND 1
+#  endif
+#  if __has_include("hardware/adc.h")
+#    include "hardware/adc.h"
+#    define NOSTR_HAVE_PICO_ADC 1
+#  endif
+#endif
+
+static uint32_t xorshift32(uint32_t *state) {
+    uint32_t x = *state ? *state : 0xA5A5A5A5u;
+    x ^= x << 13;
+    x ^= x >> 17;
+    x ^= x << 5;
+    *state = x;
+    return x;
+}
+
+int nostr_platform_random(unsigned char *buf, size_t len) {
+    if (!buf) {
+        return -1;
+    }
+
+    size_t i = 0;
+
+#if defined(NOSTR_HAVE_PICO_RAND)
+    while (i + 4 <= len) {
+        uint32_t r = get_rand_32();
+        memcpy(buf + i, &r, 4);
+        i += 4;
+    }
+    if (i < len) {
+        uint32_t r = get_rand_32();
+        memcpy(buf + i, &r, len - i);
+    }
+    return 0;
+#else
+    uint32_t seed = 0x13579BDFu;
+
+#if defined(ARDUINO)
+    seed ^= (uint32_t)micros();
+    seed ^= ((uint32_t)millis() << 16);
+    seed ^= (uint32_t)(uintptr_t)&seed;
+#endif
+
+#if defined(NOSTR_HAVE_PICO_ADC)
+    adc_init();
+    adc_set_temp_sensor_enabled(true);
+    adc_select_input(4);
+    for (int k = 0; k < 16; ++k) {
+        seed ^= ((uint32_t)adc_read() << ((k & 3) * 8));
+    }
+#endif
+
+    while (i < len) {
+        uint32_t r = xorshift32(&seed);
+#if defined(ARDUINO)
+        r ^= (uint32_t)micros();
+#endif
+        size_t take = (len - i >= 4) ? 4 : (len - i);
+        memcpy(buf + i, &r, take);
+        i += take;
+    }
+
+    return 0;
+#endif
+}

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1.h

@@ -0,0 +1,929 @@
+#ifndef SECP256K1_H
+#define SECP256K1_H
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <stddef.h>
+#include <stdint.h>
+
+/** Unless explicitly stated all pointer arguments must not be NULL.
+ *
+ * The following rules specify the order of arguments in API calls:
+ *
+ * 1. Context pointers go first, followed by output arguments, combined
+ *    output/input arguments, and finally input-only arguments.
+ * 2. Array lengths always immediately follow the argument whose length
+ *    they describe, even if this violates rule 1.
+ * 3. Within the OUT/OUTIN/IN groups, pointers to data that is typically generated
+ *    later go first. This means: signatures, public nonces, secret nonces,
+ *    messages, public keys, secret keys, tweaks.
+ * 4. Arguments that are not data pointers go last, from more complex to less
+ *    complex: function pointers, algorithm names, messages, void pointers,
+ *    counts, flags, booleans.
+ * 5. Opaque data pointers follow the function pointer they are to be passed to.
+ */
+
+/** Opaque data structure that holds context information
+ *
+ *  The primary purpose of context objects is to store randomization data for
+ *  enhanced protection against side-channel leakage. This protection is only
+ *  effective if the context is randomized after its creation. See
+ *  secp256k1_context_create for creation of contexts and
+ *  secp256k1_context_randomize for randomization.
+ *
+ *  A secondary purpose of context objects is to store pointers to callback
+ *  functions that the library will call when certain error states arise. See
+ *  secp256k1_context_set_error_callback as well as
+ *  secp256k1_context_set_illegal_callback for details. Future library versions
+ *  may use context objects for additional purposes.
+ *
+ *  A constructed context can safely be used from multiple threads
+ *  simultaneously, but API calls that take a non-const pointer to a context
+ *  need exclusive access to it. In particular this is the case for
+ *  secp256k1_context_destroy, secp256k1_context_preallocated_destroy,
+ *  and secp256k1_context_randomize.
+ *
+ *  Regarding randomization, either do it once at creation time (in which case
+ *  you do not need any locking for the other calls), or use a read-write lock.
+ */
+typedef struct secp256k1_context_struct secp256k1_context;
+
+/** Opaque data structure that holds a parsed and valid public key.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission,
+ *  use secp256k1_ec_pubkey_serialize and secp256k1_ec_pubkey_parse. To
+ *  compare keys, use secp256k1_ec_pubkey_cmp.
+ */
+typedef struct secp256k1_pubkey {
+    unsigned char data[64];
+} secp256k1_pubkey;
+
+/** Opaque data structure that holds a parsed ECDSA signature.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage, transmission, or
+ *  comparison, use the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_parse_* functions.
+ */
+typedef struct secp256k1_ecdsa_signature {
+    unsigned char data[64];
+} secp256k1_ecdsa_signature;
+
+/** A pointer to a function to deterministically generate a nonce.
+ *
+ * Returns: 1 if a nonce was successfully generated. 0 will cause signing to fail.
+ * Out:     nonce32:   pointer to a 32-byte array to be filled by the function.
+ * In:      msg32:     the 32-byte message hash being verified (will not be NULL)
+ *          key32:     pointer to a 32-byte secret key (will not be NULL)
+ *          algo16:    pointer to a 16-byte array describing the signature
+ *                     algorithm (will be NULL for ECDSA for compatibility).
+ *          data:      Arbitrary data pointer that is passed through.
+ *          attempt:   how many iterations we have tried to find a nonce.
+ *                     This will almost always be 0, but different attempt values
+ *                     are required to result in a different nonce.
+ *
+ * Except for test cases, this function should compute some cryptographic hash of
+ * the message, the algorithm, the key and the attempt.
+ */
+typedef int (*secp256k1_nonce_function)(
+    unsigned char *nonce32,
+    const unsigned char *msg32,
+    const unsigned char *key32,
+    const unsigned char *algo16,
+    void *data,
+    unsigned int attempt
+);
+
+# if !defined(SECP256K1_GNUC_PREREQ)
+#  if defined(__GNUC__)&&defined(__GNUC_MINOR__)
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) \
+ ((__GNUC__<<16)+__GNUC_MINOR__>=((_maj)<<16)+(_min))
+#  else
+#   define SECP256K1_GNUC_PREREQ(_maj,_min) 0
+#  endif
+# endif
+
+/*  When this header is used at build-time the SECP256K1_BUILD define needs to be set
+ *  to correctly setup export attributes and nullness checks.  This is normally done
+ *  by secp256k1.c but to guard against this header being included before secp256k1.c
+ *  has had a chance to set the define (e.g. via test harnesses that just includes
+ *  secp256k1.c) we set SECP256K1_NO_BUILD when this header is processed without the
+ *  BUILD define so this condition can be caught.
+ */
+#ifndef SECP256K1_BUILD
+# define SECP256K1_NO_BUILD
+#endif
+
+/* Symbol visibility. */
+#if !defined(SECP256K1_API) && defined(SECP256K1_NO_API_VISIBILITY_ATTRIBUTES)
+     /* The user has requested that we don't specify visibility attributes in
+      * the public API.
+      *
+      * Since all our non-API declarations use the static qualifier, this means
+      * that the user can use -fvisibility=<value> to set the visibility of the
+      * API symbols. For instance, -fvisibility=hidden can be useful *even for
+      * the API symbols*, e.g., when building a static library which is linked
+      * into a shared library, and the latter should not re-export the
+      * libsecp256k1 API.
+      *
+      * While visibility is a concept that applies only to shared libraries,
+      * setting visibility will still make a difference when building a static
+      * library: the visibility settings will be stored in the static library,
+      * solely for the potential case that the static library will be linked into
+      * a shared library. In that case, the stored visibility settings will
+      * resurface and be honored for the shared library. */
+#    define SECP256K1_API extern
+#endif
+#if !defined(SECP256K1_API)
+#    if defined(SECP256K1_BUILD)
+         /* On Windows, assume a shared library only if explicitly requested.
+          *   1. If using Libtool, it defines DLL_EXPORT automatically.
+          *   2. In other cases, SECP256K1_DLL_EXPORT must be defined. */
+#        if defined(_WIN32) && (defined(SECP256K1_DLL_EXPORT) || defined(DLL_EXPORT))
+             /* GCC for Windows (e.g., MinGW) accepts the __declspec syntax for
+              * MSVC compatibility. A __declspec declaration implies (but is not
+              * exactly equivalent to) __attribute__ ((visibility("default"))),
+              * and so we actually want __declspec even on GCC, see "Microsoft
+              * Windows Function Attributes" in the GCC manual and the
+              * recommendations in https://gcc.gnu.org/wiki/Visibility . */
+#            define SECP256K1_API extern __declspec(dllexport)
+         /* Avoid __attribute__ ((visibility("default"))) on Windows to get rid
+          * of warnings when compiling with -flto due to a bug in GCC, see
+          * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=116478 . */
+#        elif !defined(_WIN32) && defined (__GNUC__) && (__GNUC__ >= 4)
+#            define SECP256K1_API extern __attribute__ ((visibility("default")))
+#        else
+#            define SECP256K1_API extern
+#        endif
+#    else
+         /* On Windows, SECP256K1_STATIC must be defined when consuming
+          * libsecp256k1 as a static library. Note that SECP256K1_STATIC is a
+          * "consumer-only" macro, and it has no meaning when building
+          * libsecp256k1. */
+#        if defined(_WIN32) && !defined(SECP256K1_STATIC)
+#            define SECP256K1_API extern __declspec(dllimport)
+#        else
+#            define SECP256K1_API extern
+#        endif
+#    endif
+#endif
+
+/* Warning attributes
+ * NONNULL is not used if SECP256K1_BUILD is set to avoid the compiler optimizing out
+ * some paranoid null checks. */
+# if defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_WARN_UNUSED_RESULT __attribute__ ((__warn_unused_result__))
+# else
+#  define SECP256K1_WARN_UNUSED_RESULT
+# endif
+# if !defined(SECP256K1_BUILD) && defined(__GNUC__) && SECP256K1_GNUC_PREREQ(3, 4)
+#  define SECP256K1_ARG_NONNULL(_x)  __attribute__ ((__nonnull__(_x)))
+# else
+#  define SECP256K1_ARG_NONNULL(_x)
+# endif
+
+/* Attribute for marking functions, types, and variables as deprecated */
+#if !defined(SECP256K1_BUILD) && defined(__has_attribute)
+# if __has_attribute(__deprecated__)
+#  define SECP256K1_DEPRECATED(_msg) __attribute__ ((__deprecated__(_msg)))
+# else
+#  define SECP256K1_DEPRECATED(_msg)
+# endif
+#else
+# define SECP256K1_DEPRECATED(_msg)
+#endif
+
+/* All flags' lower 8 bits indicate what they're for. Do not use directly. */
+#define SECP256K1_FLAGS_TYPE_MASK ((1 << 8) - 1)
+#define SECP256K1_FLAGS_TYPE_CONTEXT (1 << 0)
+#define SECP256K1_FLAGS_TYPE_COMPRESSION (1 << 1)
+/* The higher bits contain the actual data. Do not use directly. */
+#define SECP256K1_FLAGS_BIT_CONTEXT_VERIFY (1 << 8)
+#define SECP256K1_FLAGS_BIT_CONTEXT_SIGN (1 << 9)
+#define SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY (1 << 10)
+#define SECP256K1_FLAGS_BIT_COMPRESSION (1 << 8)
+
+/** Context flags to pass to secp256k1_context_create, secp256k1_context_preallocated_size, and
+ *  secp256k1_context_preallocated_create. */
+#define SECP256K1_CONTEXT_NONE (SECP256K1_FLAGS_TYPE_CONTEXT)
+
+/** Deprecated context flags. These flags are treated equivalent to SECP256K1_CONTEXT_NONE. */
+#define SECP256K1_CONTEXT_VERIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_VERIFY)
+#define SECP256K1_CONTEXT_SIGN (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_SIGN)
+
+/* Testing flag. Do not use. */
+#define SECP256K1_CONTEXT_DECLASSIFY (SECP256K1_FLAGS_TYPE_CONTEXT | SECP256K1_FLAGS_BIT_CONTEXT_DECLASSIFY)
+
+/** Flag to pass to secp256k1_ec_pubkey_serialize. */
+#define SECP256K1_EC_COMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION | SECP256K1_FLAGS_BIT_COMPRESSION)
+#define SECP256K1_EC_UNCOMPRESSED (SECP256K1_FLAGS_TYPE_COMPRESSION)
+
+/** Prefix byte used to tag various encoded curvepoints for specific purposes */
+#define SECP256K1_TAG_PUBKEY_EVEN 0x02
+#define SECP256K1_TAG_PUBKEY_ODD 0x03
+#define SECP256K1_TAG_PUBKEY_UNCOMPRESSED 0x04
+#define SECP256K1_TAG_PUBKEY_HYBRID_EVEN 0x06
+#define SECP256K1_TAG_PUBKEY_HYBRID_ODD 0x07
+
+/** A built-in constant secp256k1 context object with static storage duration, to be
+ *  used in conjunction with secp256k1_selftest.
+ *
+ *  This context object offers *only limited functionality* , i.e., it cannot be used
+ *  for API functions that perform computations involving secret keys, e.g., signing
+ *  and public key generation. If this restriction applies to a specific API function,
+ *  it is mentioned in its documentation. See secp256k1_context_create if you need a
+ *  full context object that supports all functionality offered by the library.
+ *
+ *  It is highly recommended to call secp256k1_selftest before using this context.
+ */
+SECP256K1_API const secp256k1_context * const secp256k1_context_static;
+
+/** Deprecated alias for secp256k1_context_static. */
+SECP256K1_API const secp256k1_context * const secp256k1_context_no_precomp
+SECP256K1_DEPRECATED("Use secp256k1_context_static instead");
+
+/** Perform basic self tests (to be used in conjunction with secp256k1_context_static)
+ *
+ *  This function performs self tests that detect some serious usage errors and
+ *  similar conditions, e.g., when the library is compiled for the wrong endianness.
+ *  This is a last resort measure to be used in production. The performed tests are
+ *  very rudimentary and are not intended as a replacement for running the test
+ *  binaries.
+ *
+ *  It is highly recommended to call this before using secp256k1_context_static.
+ *  It is not necessary to call this function before using a context created with
+ *  secp256k1_context_create (or secp256k1_context_preallocated_create), which will
+ *  take care of performing the self tests.
+ *
+ *  If the tests fail, this function will call the default error callback to abort the
+ *  program (see secp256k1_context_set_error_callback).
+ */
+SECP256K1_API void secp256k1_selftest(void);
+
+
+/** Create a secp256k1 context object (in dynamically allocated memory).
+ *
+ *  This function uses malloc to allocate memory. It is guaranteed that malloc is
+ *  called at most once for every call of this function. If you need to avoid dynamic
+ *  memory allocation entirely, see secp256k1_context_static and the functions in
+ *  secp256k1_preallocated.h.
+ *
+ *  Returns: pointer to a newly created context object.
+ *  In:      flags: Always set to SECP256K1_CONTEXT_NONE (see below).
+ *
+ *  The only valid non-deprecated flag in recent library versions is
+ *  SECP256K1_CONTEXT_NONE, which will create a context sufficient for all functionality
+ *  offered by the library. All other (deprecated) flags will be treated as equivalent
+ *  to the SECP256K1_CONTEXT_NONE flag. Though the flags parameter primarily exists for
+ *  historical reasons, future versions of the library may introduce new flags.
+ *
+ *  If the context is intended to be used for API functions that perform computations
+ *  involving secret keys, e.g., signing and public key generation, then it is highly
+ *  recommended to call secp256k1_context_randomize on the context before calling
+ *  those API functions. This will provide enhanced protection against side-channel
+ *  leakage, see secp256k1_context_randomize for details.
+ *
+ *  Do not create a new context object for each operation, as construction and
+ *  randomization can take non-negligible time.
+ */
+SECP256K1_API secp256k1_context *secp256k1_context_create(
+    unsigned int flags
+) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Copy a secp256k1 context object (into dynamically allocated memory).
+ *
+ *  This function uses malloc to allocate memory. It is guaranteed that malloc is
+ *  called at most once for every call of this function. If you need to avoid dynamic
+ *  memory allocation entirely, see the functions in secp256k1_preallocated.h.
+ *
+ *  Cloning secp256k1_context_static is not possible, and should not be emulated by
+ *  the caller (e.g., using memcpy). Create a new context instead.
+ *
+ *  Returns: pointer to a newly created context object.
+ *  Args:    ctx: pointer to a context to copy (not secp256k1_context_static).
+ */
+SECP256K1_API secp256k1_context *secp256k1_context_clone(
+    const secp256k1_context *ctx
+) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Destroy a secp256k1 context object (created in dynamically allocated memory).
+ *
+ *  The context pointer may not be used afterwards.
+ *
+ *  The context to destroy must have been created using secp256k1_context_create
+ *  or secp256k1_context_clone. If the context has instead been created using
+ *  secp256k1_context_preallocated_create or secp256k1_context_preallocated_clone, the
+ *  behaviour is undefined. In that case, secp256k1_context_preallocated_destroy must
+ *  be used instead.
+ *
+ *  Args:   ctx: pointer to a context to destroy, constructed using
+ *               secp256k1_context_create or secp256k1_context_clone
+ *               (i.e., not secp256k1_context_static).
+ */
+SECP256K1_API void secp256k1_context_destroy(
+    secp256k1_context *ctx
+) SECP256K1_ARG_NONNULL(1);
+
+/** Set a callback function to be called when an illegal argument is passed to
+ *  an API call. It will only trigger for violations that are mentioned
+ *  explicitly in the header.
+ *
+ *  The philosophy is that these shouldn't be dealt with through a specific
+ *  return value, as calling code should not have branches to deal with the case
+ *  that this code itself is broken.
+ *
+ *  On the other hand, during debug stage, one would want to be informed about
+ *  such mistakes, and the default (crashing) may be inadvisable. Should this
+ *  callback return instead of crashing, the return value and output arguments
+ *  of the API function call are undefined. Moreover, the same API call may
+ *  trigger the callback again in this case.
+ *
+ *  When this function has not been called (or called with fun==NULL), then the
+ *  default callback will be used. The library provides a default callback which
+ *  writes the message to stderr and calls abort. This default callback can be
+ *  replaced at link time if the preprocessor macro
+ *  USE_EXTERNAL_DEFAULT_CALLBACKS is defined, which is the case if the build
+ *  has been configured with --enable-external-default-callbacks (GNU Autotools) or
+ *  -DSECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS=ON (CMake). Then the
+ *  following two symbols must be provided to link against:
+ *   - void secp256k1_default_illegal_callback_fn(const char *message, void *data);
+ *   - void secp256k1_default_error_callback_fn(const char *message, void *data);
+ *  The library may call a default callback even before a proper callback data
+ *  pointer could have been set using secp256k1_context_set_illegal_callback or
+ *  secp256k1_context_set_error_callback, e.g., when the creation of a context
+ *  fails. In this case, the corresponding default callback will be called with
+ *  the data pointer argument set to NULL.
+ *
+ *  Args: ctx:  pointer to a context object.
+ *  In:   fun:  pointer to a function to call when an illegal argument is
+ *              passed to the API, taking a message and an opaque pointer.
+ *              (NULL restores the default callback.)
+ *        data: the opaque pointer to pass to fun above, must be NULL for the
+ *              default callback.
+ *
+ *  See also secp256k1_context_set_error_callback.
+ */
+SECP256K1_API void secp256k1_context_set_illegal_callback(
+    secp256k1_context *ctx,
+    void (*fun)(const char *message, void *data),
+    const void *data
+) SECP256K1_ARG_NONNULL(1);
+
+/** Set a callback function to be called when an internal consistency check
+ *  fails.
+ *
+ *  The default callback writes an error message to stderr and calls abort
+ *  to abort the program.
+ *
+ *  This can only trigger in case of a hardware failure, miscompilation,
+ *  memory corruption, serious bug in the library, or other error that would
+ *  result in undefined behaviour. It will not trigger due to mere
+ *  incorrect usage of the API (see secp256k1_context_set_illegal_callback
+ *  for that). After this callback returns, anything may happen, including
+ *  crashing.
+ *
+ *  Args: ctx:  pointer to a context object.
+ *  In:   fun:  pointer to a function to call when an internal error occurs,
+ *              taking a message and an opaque pointer (NULL restores the
+ *              default callback, see secp256k1_context_set_illegal_callback
+ *              for details).
+ *        data: the opaque pointer to pass to fun above, must be NULL for the
+ *              default callback.
+ *
+ *  See also secp256k1_context_set_illegal_callback.
+ */
+SECP256K1_API void secp256k1_context_set_error_callback(
+    secp256k1_context *ctx,
+    void (*fun)(const char *message, void *data),
+    const void *data
+) SECP256K1_ARG_NONNULL(1);
+
+/** A pointer to a function implementing SHA256's internal compression function.
+ *
+ * This function processes one or more contiguous 64-byte message blocks and
+ * updates the internal SHA256 state accordingly. The function is not responsible
+ * for counting consumed blocks or bytes, nor for performing padding.
+ *
+ * In/Out:  state:     pointer to eight 32-bit words representing the current internal state;
+ *                     the state is updated in place.
+ * In:      blocks64:  pointer to concatenation of n_blocks blocks, of 64 bytes each.
+ *                     no alignment guarantees are made for this pointer.
+ *          n_blocks:  number of contiguous 64-byte blocks to process.
+ */
+typedef void (*secp256k1_sha256_compression_function)(
+    uint32_t *state,
+    const unsigned char *blocks64,
+    size_t n_blocks
+);
+
+/**
+ * Set a callback function to override the internal SHA256 compression function.
+ *
+ * This installs a function to replace the built-in block-compression
+ * step used by the library's internal SHA256 implementation.
+ * The provided callback must exactly implement the effect of n_blocks
+ * repeated applications of the SHA256 compression function.
+ *
+ * This API exists to support environments that wish to route the
+ * SHA256 compression step through a hardware-accelerated or otherwise
+ * specialized implementation. It is NOT meant for replacing SHA256
+ * with a different hash function.
+ *
+ * Args:    ctx:             pointer to a context object.
+ * In:      fn_compression:  pointer to a function implementing the compression function;
+ *                           passing NULL restores the default implementation.
+ */
+SECP256K1_API void secp256k1_context_set_sha256_compression(
+        secp256k1_context *ctx,
+        secp256k1_sha256_compression_function fn_compression
+) SECP256K1_ARG_NONNULL(1);
+
+/** Parse a variable-length public key into the pubkey object.
+ *
+ *  Returns: 1 if the public key was fully valid.
+ *           0 if the public key could not be parsed or is invalid.
+ *  Args: ctx:      pointer to a context object.
+ *  Out:  pubkey:   pointer to a pubkey object. If 1 is returned, it is set to a
+ *                  parsed version of input. If not, its value is undefined.
+ *  In:   input:    pointer to a serialized public key
+ *        inputlen: length of the array pointed to by input
+ *
+ *  This function supports parsing compressed (33 bytes, header byte 0x02 or
+ *  0x03), uncompressed (65 bytes, header byte 0x04), or hybrid (65 bytes, header
+ *  byte 0x06 or 0x07) format public keys.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_parse(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a pubkey object into a serialized byte sequence.
+ *
+ *  Returns: 1 always.
+ *  Args:   ctx:        pointer to a context object.
+ *  Out:    output:     pointer to a 65-byte (if compressed==0) or 33-byte (if
+ *                      compressed==1) byte array to place the serialized key
+ *                      in.
+ *  In/Out: outputlen:  pointer to an integer which is initially set to the
+ *                      size of output, and is overwritten with the written
+ *                      size.
+ *  In:     pubkey:     pointer to a secp256k1_pubkey containing an
+ *                      initialized public key.
+ *          flags:      SECP256K1_EC_COMPRESSED if serialization should be in
+ *                      compressed format, otherwise SECP256K1_EC_UNCOMPRESSED.
+ */
+SECP256K1_API int secp256k1_ec_pubkey_serialize(
+    const secp256k1_context *ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_pubkey *pubkey,
+    unsigned int flags
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Compare two public keys using lexicographic (of compressed serialization) order
+ *
+ *  Returns: <0 if the first public key is less than the second
+ *           >0 if the first public key is greater than the second
+ *           0 if the two public keys are equal
+ *  Args: ctx:      pointer to a context object
+ *  In:   pubkey1:  first public key to compare
+ *        pubkey2:  second public key to compare
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_cmp(
+    const secp256k1_context *ctx,
+    const secp256k1_pubkey *pubkey1,
+    const secp256k1_pubkey *pubkey2
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Sort public keys using lexicographic (of compressed serialization) order
+ *
+ *  Returns: 0 if the arguments are invalid. 1 otherwise.
+ *
+ *  Args:     ctx: pointer to a context object
+ *  In:   pubkeys: array of pointers to pubkeys to sort
+ *      n_pubkeys: number of elements in the pubkeys array
+ */
+SECP256K1_API int secp256k1_ec_pubkey_sort(
+    const secp256k1_context *ctx,
+    const secp256k1_pubkey **pubkeys,
+    size_t n_pubkeys
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Parse an ECDSA signature in compact (64 bytes) format.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      pointer to a context object
+ *  Out:  sig:      pointer to a signature object
+ *  In:   input64:  pointer to the 64-byte array to parse
+ *
+ *  The signature must consist of a 32-byte big endian R value, followed by a
+ *  32-byte big endian S value. If R or S fall outside of [0..order-1], the
+ *  encoding is invalid. R and S with value 0 are allowed in the encoding.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or R or
+ *  S are zero, the resulting sig value is guaranteed to fail verification for
+ *  any message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_compact(
+    const secp256k1_context *ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *input64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse a DER ECDSA signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args: ctx:      pointer to a context object
+ *  Out:  sig:      pointer to a signature object
+ *  In:   input:    pointer to the signature to be parsed
+ *        inputlen: the length of the array pointed to be input
+ *
+ *  This function will accept any valid DER encoded signature, even if the
+ *  encoded numbers are out of range.
+ *
+ *  After the call, sig will always be initialized. If parsing failed or the
+ *  encoded numbers are out of range, signature verification with it is
+ *  guaranteed to fail for every message and public key.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_parse_der(
+    const secp256k1_context *ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *input,
+    size_t inputlen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in DER format.
+ *
+ *  Returns: 1 if enough space was available to serialize, 0 otherwise
+ *  Args:   ctx:       pointer to a context object
+ *  Out:    output:    pointer to an array to store the DER serialization
+ *  In/Out: outputlen: pointer to a length integer. Initially, this integer
+ *                     should be set to the length of output. After the call
+ *                     it will be set to the length of the serialization (even
+ *                     if 0 was returned).
+ *  In:     sig:       pointer to an initialized signature object
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_der(
+    const secp256k1_context *ctx,
+    unsigned char *output,
+    size_t *outputlen,
+    const secp256k1_ecdsa_signature *sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Serialize an ECDSA signature in compact (64 byte) format.
+ *
+ *  Returns: 1
+ *  Args:   ctx:       pointer to a context object
+ *  Out:    output64:  pointer to a 64-byte array to store the compact serialization
+ *  In:     sig:       pointer to an initialized signature object
+ *
+ *  See secp256k1_ecdsa_signature_parse_compact for details about the encoding.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_serialize_compact(
+    const secp256k1_context *ctx,
+    unsigned char *output64,
+    const secp256k1_ecdsa_signature *sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Verify an ECDSA signature.
+ *
+ *  Returns: 1: correct signature
+ *           0: incorrect or unparseable signature
+ *  Args:    ctx:       pointer to a context object
+ *  In:      sig:       the signature being verified.
+ *           msghash32: the 32-byte message hash being verified.
+ *                      The verifier must make sure to apply a cryptographic
+ *                      hash function to the message by itself and not accept an
+ *                      msghash32 value directly. Otherwise, it would be easy to
+ *                      create a "valid" signature without knowledge of the
+ *                      secret key. See also
+ *                      https://bitcoin.stackexchange.com/a/81116/35586 for more
+ *                      background on this topic.
+ *           pubkey:    pointer to an initialized public key to verify with.
+ *
+ * To avoid accepting malleable signatures, only ECDSA signatures in lower-S
+ * form are accepted.
+ *
+ * If you need to accept ECDSA signatures from sources that do not obey this
+ * rule, apply secp256k1_ecdsa_signature_normalize to the signature prior to
+ * verification, but be aware that doing so results in malleable signatures.
+ *
+ * For details, see the comments for that function.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_verify(
+    const secp256k1_context *ctx,
+    const secp256k1_ecdsa_signature *sig,
+    const unsigned char *msghash32,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Convert a signature to a normalized lower-S form.
+ *
+ *  Returns: 1 if sigin was not normalized, 0 if it already was.
+ *  Args: ctx:    pointer to a context object
+ *  Out:  sigout: pointer to a signature to fill with the normalized form,
+ *                or copy if the input was already normalized. (can be NULL if
+ *                you're only interested in whether the input was already
+ *                normalized).
+ *  In:   sigin:  pointer to a signature to check/normalize (can be identical to sigout)
+ *
+ *  With ECDSA a third-party can forge a second distinct signature of the same
+ *  message, given a single initial signature, but without knowing the key. This
+ *  is done by negating the S value modulo the order of the curve, 'flipping'
+ *  the sign of the random point R which is not included in the signature.
+ *
+ *  Forgery of the same message isn't universally problematic, but in systems
+ *  where message malleability or uniqueness of signatures is important this can
+ *  cause issues. This forgery can be blocked by all verifiers forcing signers
+ *  to use a normalized form.
+ *
+ *  The lower-S form reduces the size of signatures slightly on average when
+ *  variable length encodings (such as DER) are used and is cheap to verify,
+ *  making it a good choice. Security of always using lower-S is assured because
+ *  anyone can trivially modify a signature after the fact to enforce this
+ *  property anyway.
+ *
+ *  The lower S value is always between 0x1 and
+ *  0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
+ *  inclusive.
+ *
+ *  No other forms of ECDSA malleability are known and none seem likely, but
+ *  there is no formal proof that ECDSA, even with this additional restriction,
+ *  is free of other malleability. Commonly used serialization schemes will also
+ *  accept various non-unique encodings, so care should be taken when this
+ *  property is required for an application.
+ *
+ *  The secp256k1_ecdsa_sign function will by default create signatures in the
+ *  lower-S form, and secp256k1_ecdsa_verify will not accept others. In case
+ *  signatures come from a system that cannot enforce this property,
+ *  secp256k1_ecdsa_signature_normalize must be called before verification.
+ */
+SECP256K1_API int secp256k1_ecdsa_signature_normalize(
+    const secp256k1_context *ctx,
+    secp256k1_ecdsa_signature *sigout,
+    const secp256k1_ecdsa_signature *sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3);
+
+/** An implementation of RFC6979 (using HMAC-SHA256) as nonce generation function.
+ * If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
+ * extra entropy.
+ */
+SECP256K1_API const secp256k1_nonce_function secp256k1_nonce_function_rfc6979;
+
+/** A default safe nonce generation function (currently equal to secp256k1_nonce_function_rfc6979). */
+SECP256K1_API const secp256k1_nonce_function secp256k1_nonce_function_default;
+
+/** Create an ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the secret key was invalid.
+ *  Args:    ctx:       pointer to a context object (not secp256k1_context_static).
+ *  Out:     sig:       pointer to an array where the signature will be placed.
+ *  In:      msghash32: the 32-byte message hash being signed.
+ *           seckey:    pointer to a 32-byte secret key.
+ *           noncefp:   pointer to a nonce generation function. If NULL,
+ *                      secp256k1_nonce_function_default is used.
+ *           ndata:     pointer to arbitrary data used by the nonce generation function
+ *                      (can be NULL). If it is non-NULL and
+ *                      secp256k1_nonce_function_default is used, then ndata must be a
+ *                      pointer to 32-bytes of additional data.
+ *
+ * The created signature is always in lower-S form. See
+ * secp256k1_ecdsa_signature_normalize for more details.
+ */
+SECP256K1_API int secp256k1_ecdsa_sign(
+    const secp256k1_context *ctx,
+    secp256k1_ecdsa_signature *sig,
+    const unsigned char *msghash32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Verify an elliptic curve secret key.
+ *
+ *  A secret key is valid if it is not 0 and less than the secp256k1 curve order
+ *  when interpreted as an integer (most significant byte first). The
+ *  probability of choosing a 32-byte string uniformly at random which is an
+ *  invalid secret key is negligible. However, if it does happen it should
+ *  be assumed that the randomness source is severely broken and there should
+ *  be no retry.
+ *
+ *  Returns: 1: secret key is valid
+ *           0: secret key is invalid
+ *  Args:    ctx: pointer to a context object.
+ *  In:      seckey: pointer to a 32-byte secret key.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_verify(
+    const secp256k1_context *ctx,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Compute the public key for a secret key.
+ *
+ *  Returns: 1: secret was valid, public key stores.
+ *           0: secret was invalid, try again.
+ *  Args:    ctx:    pointer to a context object (not secp256k1_context_static).
+ *  Out:     pubkey: pointer to the created public key.
+ *  In:      seckey: pointer to a 32-byte secret key.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_create(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Negates a secret key in place.
+ *
+ *  Returns: 0 if the given secret key is invalid according to
+ *           secp256k1_ec_seckey_verify. 1 otherwise
+ *  Args:   ctx:    pointer to a context object
+ *  In/Out: seckey: pointer to the 32-byte secret key to be negated. If the
+ *                  secret key is invalid according to
+ *                  secp256k1_ec_seckey_verify, this function returns 0 and
+ *                  seckey will be set to some unspecified value.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_negate(
+    const secp256k1_context *ctx,
+    unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Negates a public key in place.
+ *
+ *  Returns: 1 always
+ *  Args:   ctx:        pointer to a context object
+ *  In/Out: pubkey:     pointer to the public key to be negated.
+ */
+SECP256K1_API int secp256k1_ec_pubkey_negate(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2);
+
+/** Tweak a secret key by adding tweak to it.
+ *
+ *  Returns: 0 if the arguments are invalid or the resulting secret key would be
+ *           invalid (only when the tweak is the negation of the secret key). 1
+ *           otherwise.
+ *  Args:    ctx:   pointer to a context object.
+ *  In/Out: seckey: pointer to a 32-byte secret key. If the secret key is
+ *                  invalid according to secp256k1_ec_seckey_verify, this
+ *                  function returns 0. seckey will be set to some unspecified
+ *                  value if this function returns 0.
+ *  In:    tweak32: pointer to a 32-byte tweak, which must be valid according to
+ *                  secp256k1_ec_seckey_verify or 32 zero bytes. For uniformly
+ *                  random 32-byte tweaks, the chance of being invalid is
+ *                  negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_add(
+    const secp256k1_context *ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by adding tweak times the generator to it.
+ *
+ *  Returns: 0 if the arguments are invalid or the resulting public key would be
+ *           invalid (only when the tweak is the negation of the corresponding
+ *           secret key). 1 otherwise.
+ *  Args:    ctx:   pointer to a context object.
+ *  In/Out: pubkey: pointer to a public key object. pubkey will be set to an
+ *                  invalid value if this function returns 0.
+ *  In:    tweak32: pointer to a 32-byte tweak, which must be valid according to
+ *                  secp256k1_ec_seckey_verify or 32 zero bytes. For uniformly
+ *                  random 32-byte tweaks, the chance of being invalid is
+ *                  negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_add(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a secret key by multiplying it by a tweak.
+ *
+ *  Returns: 0 if the arguments are invalid. 1 otherwise.
+ *  Args:   ctx:    pointer to a context object.
+ *  In/Out: seckey: pointer to a 32-byte secret key. If the secret key is
+ *                  invalid according to secp256k1_ec_seckey_verify, this
+ *                  function returns 0. seckey will be set to some unspecified
+ *                  value if this function returns 0.
+ *  In:    tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to
+ *                  secp256k1_ec_seckey_verify, this function returns 0. For
+ *                  uniformly random 32-byte arrays the chance of being invalid
+ *                  is negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_seckey_tweak_mul(
+    const secp256k1_context *ctx,
+    unsigned char *seckey,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Tweak a public key by multiplying it by a tweak value.
+ *
+ *  Returns: 0 if the arguments are invalid. 1 otherwise.
+ *  Args:    ctx:   pointer to a context object.
+ *  In/Out: pubkey: pointer to a public key object. pubkey will be set to an
+ *                  invalid value if this function returns 0.
+ *  In:    tweak32: pointer to a 32-byte tweak. If the tweak is invalid according to
+ *                  secp256k1_ec_seckey_verify, this function returns 0. For
+ *                  uniformly random 32-byte arrays the chance of being invalid
+ *                  is negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_tweak_mul(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Randomizes the context to provide enhanced protection against side-channel leakage.
+ *
+ *  Returns: 1: randomization successful
+ *           0: error
+ *  Args:    ctx:       pointer to a context object (not secp256k1_context_static).
+ *  In:      seed32:    pointer to a 32-byte random seed (NULL resets to initial state).
+ *
+ * While secp256k1 code is written and tested to be constant-time no matter what
+ * secret values are, it is possible that a compiler may output code which is not,
+ * and also that the CPU may not emit the same radio frequencies or draw the same
+ * amount of power for all values. Randomization of the context shields against
+ * side-channel observations which aim to exploit secret-dependent behaviour in
+ * certain computations which involve secret keys.
+ *
+ * It is highly recommended to call this function on contexts returned from
+ * secp256k1_context_create or secp256k1_context_clone (or from the corresponding
+ * functions in secp256k1_preallocated.h) before using these contexts to call API
+ * functions that perform computations involving secret keys, e.g., signing and
+ * public key generation. It is possible to call this function more than once on
+ * the same context, and doing so before every few computations involving secret
+ * keys is recommended as a defense-in-depth measure. Randomization of the static
+ * context secp256k1_context_static is not supported.
+ *
+ * Currently, the random seed is mainly used for blinding multiplications of a
+ * secret scalar with the elliptic curve base point. Multiplications of this
+ * kind are performed by exactly those API functions which are documented to
+ * require a context that is not secp256k1_context_static. As a rule of thumb,
+ * these are all functions which take a secret key (or a keypair) as an input.
+ * A notable exception to that rule is the ECDH module, which relies on a different
+ * kind of elliptic curve point multiplication and thus does not benefit from
+ * enhanced protection against side-channel leakage currently.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_context_randomize(
+    secp256k1_context *ctx,
+    const unsigned char *seed32
+) SECP256K1_ARG_NONNULL(1);
+
+/** Add a number of public keys together.
+ *
+ *  Returns: 1: the sum of the public keys is valid.
+ *           0: the sum of the public keys is not valid.
+ *  Args:   ctx:        pointer to a context object.
+ *  Out:    out:        pointer to a public key object for placing the resulting public key.
+ *  In:     ins:        pointer to array of pointers to public keys.
+ *          n:          the number of public keys to add together (must be at least 1).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ec_pubkey_combine(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *out,
+    const secp256k1_pubkey * const *ins,
+    size_t n
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Compute a tagged hash as defined in BIP-340.
+ *
+ *  This is useful for creating a message hash and achieving domain separation
+ *  through an application-specific tag. This function returns
+ *  SHA256(SHA256(tag)||SHA256(tag)||msg). Therefore, tagged hash
+ *  implementations optimized for a specific tag can precompute the SHA256 state
+ *  after hashing the tag hashes.
+ *
+ *  Returns: 1 always.
+ *  Args:    ctx: pointer to a context object
+ *  Out:  hash32: pointer to a 32-byte array to store the resulting hash
+ *  In:      tag: pointer to an array containing the tag
+ *        taglen: length of the tag array
+ *           msg: pointer to an array containing the message
+ *        msglen: length of the message array
+ */
+SECP256K1_API int secp256k1_tagged_sha256(
+    const secp256k1_context *ctx,
+    unsigned char *hash32,
+    const unsigned char *tag,
+    size_t taglen,
+    const unsigned char *msg,
+    size_t msglen
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_H */

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1_ecdh.h

@@ -0,0 +1,63 @@
+#ifndef SECP256K1_ECDH_H
+#define SECP256K1_ECDH_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** A pointer to a function that hashes an EC point to obtain an ECDH secret
+ *
+ *  Returns: 1 if the point was successfully hashed.
+ *           0 will cause secp256k1_ecdh to fail and return 0.
+ *           Other return values are not allowed, and the behaviour of
+ *           secp256k1_ecdh is undefined for other return values.
+ *  Out:     output:     pointer to an array to be filled by the function
+ *  In:      x32:        pointer to a 32-byte x coordinate
+ *           y32:        pointer to a 32-byte y coordinate
+ *           data:       arbitrary data pointer that is passed through
+ */
+typedef int (*secp256k1_ecdh_hash_function)(
+  unsigned char *output,
+  const unsigned char *x32,
+  const unsigned char *y32,
+  void *data
+);
+
+/** An implementation of SHA256 hash function that applies to compressed public key.
+ * Populates the output parameter with 32 bytes. */
+SECP256K1_API const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256;
+
+/** A default ECDH hash function (currently equal to secp256k1_ecdh_hash_function_sha256).
+ * Populates the output parameter with 32 bytes. */
+SECP256K1_API const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default;
+
+/** Compute an EC Diffie-Hellman secret in constant time
+ *
+ *  Returns: 1: exponentiation was successful
+ *           0: scalar was invalid (zero or overflow) or hashfp returned 0
+ *  Args:    ctx:        pointer to a context object.
+ *  Out:     output:     pointer to an array to be filled by hashfp.
+ *  In:      pubkey:     pointer to a secp256k1_pubkey containing an initialized public key.
+ *           seckey:     a 32-byte scalar with which to multiply the point.
+ *           hashfp:     pointer to a hash function. If NULL,
+ *                       secp256k1_ecdh_hash_function_sha256 is used
+ *                       (in which case, 32 bytes will be written to output).
+ *           data:       arbitrary data pointer that is passed through to hashfp
+ *                       (can be NULL for secp256k1_ecdh_hash_function_sha256).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdh(
+  const secp256k1_context *ctx,
+  unsigned char *output,
+  const secp256k1_pubkey *pubkey,
+  const unsigned char *seckey,
+  secp256k1_ecdh_hash_function hashfp,
+  void *data
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_ECDH_H */

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1_ellswift.h

@@ -0,0 +1,200 @@
+#ifndef SECP256K1_ELLSWIFT_H
+#define SECP256K1_ELLSWIFT_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* This module provides an implementation of ElligatorSwift as well as a
+ * version of x-only ECDH using it (including compatibility with BIP324).
+ *
+ * ElligatorSwift is described in https://eprint.iacr.org/2022/759 by
+ * Chavez-Saab, Rodriguez-Henriquez, and Tibouchi. It permits encoding
+ * uniformly chosen public keys as 64-byte arrays which are indistinguishable
+ * from uniformly random arrays.
+ *
+ * Let f be the function from pairs of field elements to point X coordinates,
+ * defined as follows (all operations modulo p = 2^256 - 2^32 - 977)
+ * f(u,t):
+ * - Let C = 0xa2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f852,
+ *   a square root of -3.
+ * - If u=0, set u=1 instead.
+ * - If t=0, set t=1 instead.
+ * - If u^3 + t^2 + 7 = 0, multiply t by 2.
+ * - Let X = (u^3 + 7 - t^2) / (2 * t)
+ * - Let Y = (X + t) / (C * u)
+ * - Return the first in [u + 4 * Y^2, (-X/Y - u) / 2, (X/Y - u) / 2] that is an
+ *   X coordinate on the curve (at least one of them is, for any u and t).
+ *
+ * Then an ElligatorSwift encoding of x consists of the 32-byte big-endian
+ * encodings of field elements u and t concatenated, where f(u,t) = x.
+ * The encoding algorithm is described in the paper, and effectively picks a
+ * uniformly random pair (u,t) among those which encode x.
+ *
+ * If the Y coordinate is relevant, it is given the same parity as t.
+ *
+ * Changes w.r.t. the paper:
+ * - The u=0, t=0, and u^3+t^2+7=0 conditions result in decoding to the point
+ *   at infinity in the paper. Here they are remapped to finite points.
+ * - The paper uses an additional encoding bit for the parity of y. Here the
+ *   parity of t is used (negating t does not affect the decoded x coordinate,
+ *   so this is possible).
+ *
+ * For mathematical background about the scheme, see the doc/ellswift.md file.
+ */
+
+/** A pointer to a function used by secp256k1_ellswift_xdh to hash the shared X
+ *  coordinate along with the encoded public keys to a uniform shared secret.
+ *
+ *  Returns: 1 if a shared secret was successfully computed.
+ *           0 will cause secp256k1_ellswift_xdh to fail and return 0.
+ *           Other return values are not allowed, and the behaviour of
+ *           secp256k1_ellswift_xdh is undefined for other return values.
+ *  Out:     output:     pointer to an array to be filled by the function
+ *  In:      x32:        pointer to the 32-byte serialized X coordinate
+ *                       of the resulting shared point (will not be NULL)
+ *           ell_a64:    pointer to the 64-byte encoded public key of party A
+ *                       (will not be NULL)
+ *           ell_b64:    pointer to the 64-byte encoded public key of party B
+ *                       (will not be NULL)
+ *           data:       arbitrary data pointer that is passed through
+ */
+typedef int (*secp256k1_ellswift_xdh_hash_function)(
+    unsigned char *output,
+    const unsigned char *x32,
+    const unsigned char *ell_a64,
+    const unsigned char *ell_b64,
+    void *data
+);
+
+/** An implementation of an secp256k1_ellswift_xdh_hash_function which uses
+ *  SHA256(prefix64 || ell_a64 || ell_b64 || x32), where prefix64 is the 64-byte
+ *  array pointed to by data. */
+SECP256K1_API const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_prefix;
+
+/** An implementation of an secp256k1_ellswift_xdh_hash_function compatible with
+ *  BIP324. It returns H_tag(ell_a64 || ell_b64 || x32), where H_tag is the
+ *  BIP340 tagged hash function with tag "bip324_ellswift_xonly_ecdh". Equivalent
+ *  to secp256k1_ellswift_xdh_hash_function_prefix with prefix64 set to
+ *  SHA256("bip324_ellswift_xonly_ecdh")||SHA256("bip324_ellswift_xonly_ecdh").
+ *  The data argument is ignored. */
+SECP256K1_API const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_bip324;
+
+/** Construct a 64-byte ElligatorSwift encoding of a given pubkey.
+ *
+ *  Returns: 1 always.
+ *  Args:    ctx:        pointer to a context object
+ *  Out:     ell64:      pointer to a 64-byte array to be filled
+ *  In:      pubkey:     pointer to a secp256k1_pubkey containing an
+ *                       initialized public key
+ *           rnd32:      pointer to 32 bytes of randomness
+ *
+ * It is recommended that rnd32 consists of 32 uniformly random bytes, not
+ * known to any adversary trying to detect whether public keys are being
+ * encoded, though 16 bytes of randomness (padded to an array of 32 bytes,
+ * e.g., with zeros) suffice to make the result indistinguishable from
+ * uniform. The randomness in rnd32 must not be a deterministic function of
+ * the pubkey (it can be derived from the private key, though).
+ *
+ * It is not guaranteed that the computed encoding is stable across versions
+ * of the library, even if all arguments to this function (including rnd32)
+ * are the same.
+ *
+ * This function runs in variable time.
+ */
+SECP256K1_API int secp256k1_ellswift_encode(
+    const secp256k1_context *ctx,
+    unsigned char *ell64,
+    const secp256k1_pubkey *pubkey,
+    const unsigned char *rnd32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Decode a 64-bytes ElligatorSwift encoded public key.
+ *
+ *  Returns: always 1
+ *  Args:    ctx:        pointer to a context object
+ *  Out:     pubkey:     pointer to a secp256k1_pubkey that will be filled
+ *  In:      ell64:      pointer to a 64-byte array to decode
+ *
+ * This function runs in variable time.
+ */
+SECP256K1_API int secp256k1_ellswift_decode(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *ell64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Compute an ElligatorSwift public key for a secret key.
+ *
+ *  Returns: 1: secret was valid, public key was stored.
+ *           0: secret was invalid, try again.
+ *  Args:    ctx:        pointer to a context object (not secp256k1_context_static)
+ *  Out:     ell64:      pointer to a 64-byte array to receive the ElligatorSwift
+ *                       public key
+ *  In:      seckey32:   pointer to a 32-byte secret key
+ *           auxrnd32:   (optional) pointer to 32 bytes of randomness
+ *
+ * Constant time in seckey and auxrnd32, but not in the resulting public key.
+ *
+ * It is recommended that auxrnd32 contains 32 uniformly random bytes, though
+ * it is optional (and does result in encodings that are indistinguishable from
+ * uniform even without any auxrnd32). It differs from the (mandatory) rnd32
+ * argument to secp256k1_ellswift_encode in this regard.
+ *
+ * This function can be used instead of calling secp256k1_ec_pubkey_create
+ * followed by secp256k1_ellswift_encode. It is safer, as it uses the secret
+ * key as entropy for the encoding (supplemented with auxrnd32, if provided).
+ *
+ * Like secp256k1_ellswift_encode, this function does not guarantee that the
+ * computed encoding is stable across versions of the library, even if all
+ * arguments (including auxrnd32) are the same.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ellswift_create(
+    const secp256k1_context *ctx,
+    unsigned char *ell64,
+    const unsigned char *seckey32,
+    const unsigned char *auxrnd32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Given a private key, and ElligatorSwift public keys sent in both directions,
+ *  compute a shared secret using x-only Elliptic Curve Diffie-Hellman (ECDH).
+ *
+ *  Returns: 1: shared secret was successfully computed
+ *           0: secret was invalid or hashfp returned 0
+ *  Args:    ctx:       pointer to a context object.
+ *  Out:     output:    pointer to an array to be filled by hashfp.
+ *  In:      ell_a64:   pointer to the 64-byte encoded public key of party A
+ *                      (will not be NULL)
+ *           ell_b64:   pointer to the 64-byte encoded public key of party B
+ *                      (will not be NULL)
+ *           seckey32:  pointer to our 32-byte secret key
+ *           party:     boolean indicating which party we are: zero if we are
+ *                      party A, non-zero if we are party B. seckey32 must be
+ *                      the private key corresponding to that party's ell_?64.
+ *                      This correspondence is not checked.
+ *           hashfp:    pointer to a hash function.
+ *           data:      arbitrary data pointer passed through to hashfp.
+ *
+ * Constant time in seckey32.
+ *
+ * This function is more efficient than decoding the public keys, and performing
+ * ECDH on them.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ellswift_xdh(
+  const secp256k1_context *ctx,
+  unsigned char *output,
+  const unsigned char *ell_a64,
+  const unsigned char *ell_b64,
+  const unsigned char *seckey32,
+  int party,
+  secp256k1_ellswift_xdh_hash_function hashfp,
+  void *data
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(7);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_ELLSWIFT_H */

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1_extrakeys.h

@@ -0,0 +1,250 @@
+#ifndef SECP256K1_EXTRAKEYS_H
+#define SECP256K1_EXTRAKEYS_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** Opaque data structure that holds a parsed and valid "x-only" public key.
+ *  An x-only pubkey encodes a point whose Y coordinate is even. It is
+ *  serialized using only its X coordinate (32 bytes). See BIP-340 for more
+ *  information about x-only pubkeys.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 64 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage, transmission, use
+ *  use secp256k1_xonly_pubkey_serialize and secp256k1_xonly_pubkey_parse. To
+ *  compare keys, use secp256k1_xonly_pubkey_cmp.
+ */
+typedef struct secp256k1_xonly_pubkey {
+    unsigned char data[64];
+} secp256k1_xonly_pubkey;
+
+/** Opaque data structure that holds a keypair consisting of a secret and a
+ *  public key.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 96 bytes in size, and can be safely copied/moved.
+ */
+typedef struct secp256k1_keypair {
+    unsigned char data[96];
+} secp256k1_keypair;
+
+/** Parse a 32-byte sequence into a xonly_pubkey object.
+ *
+ *  Returns: 1 if the public key was fully valid.
+ *           0 if the public key could not be parsed or is invalid.
+ *
+ *  Args:   ctx: pointer to a context object.
+ *  Out: pubkey: pointer to a pubkey object. If 1 is returned, it is set to a
+ *               parsed version of input. If not, it's set to an invalid value.
+ *  In: input32: pointer to a serialized xonly_pubkey.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_parse(
+    const secp256k1_context *ctx,
+    secp256k1_xonly_pubkey *pubkey,
+    const unsigned char *input32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an xonly_pubkey object into a 32-byte sequence.
+ *
+ *  Returns: 1 always.
+ *
+ *  Args:     ctx: pointer to a context object.
+ *  Out: output32: pointer to a 32-byte array to place the serialized key in.
+ *  In:    pubkey: pointer to a secp256k1_xonly_pubkey containing an initialized public key.
+ */
+SECP256K1_API int secp256k1_xonly_pubkey_serialize(
+    const secp256k1_context *ctx,
+    unsigned char *output32,
+    const secp256k1_xonly_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Compare two x-only public keys using lexicographic order
+ *
+ *  Returns: <0 if the first public key is less than the second
+ *           >0 if the first public key is greater than the second
+ *           0 if the two public keys are equal
+ *  Args: ctx:      pointer to a context object.
+ *  In:   pubkey1:  first public key to compare
+ *        pubkey2:  second public key to compare
+ */
+SECP256K1_API int secp256k1_xonly_pubkey_cmp(
+    const secp256k1_context *ctx,
+    const secp256k1_xonly_pubkey *pk1,
+    const secp256k1_xonly_pubkey *pk2
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Converts a secp256k1_pubkey into a secp256k1_xonly_pubkey.
+ *
+ *  Returns: 1 always.
+ *
+ *  Args:         ctx: pointer to a context object.
+ *  Out: xonly_pubkey: pointer to an x-only public key object for placing the converted public key.
+ *          pk_parity: Ignored if NULL. Otherwise, pointer to an integer that
+ *                     will be set to 1 if the point encoded by xonly_pubkey is
+ *                     the negation of the pubkey and set to 0 otherwise.
+ *  In:        pubkey: pointer to a public key that is converted.
+ */
+SECP256K1_API int secp256k1_xonly_pubkey_from_pubkey(
+    const secp256k1_context *ctx,
+    secp256k1_xonly_pubkey *xonly_pubkey,
+    int *pk_parity,
+    const secp256k1_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
+
+/** Tweak an x-only public key by adding the generator multiplied with tweak32
+ *  to it.
+ *
+ *  Note that the resulting point can not in general be represented by an x-only
+ *  pubkey because it may have an odd Y coordinate. Instead, the output_pubkey
+ *  is a normal secp256k1_pubkey.
+ *
+ *  Returns: 0 if the arguments are invalid or the resulting public key would be
+ *           invalid (only when the tweak is the negation of the corresponding
+ *           secret key). 1 otherwise.
+ *
+ *  Args:           ctx: pointer to a context object.
+ *  Out:  output_pubkey: pointer to a public key to store the result. Will be set
+ *                       to an invalid value if this function returns 0.
+ *  In: internal_pubkey: pointer to an x-only pubkey to apply the tweak to.
+ *              tweak32: pointer to a 32-byte tweak, which must be valid
+ *                       according to secp256k1_ec_seckey_verify or 32 zero
+ *                       bytes. For uniformly random 32-byte tweaks, the chance of
+ *                       being invalid is negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *output_pubkey,
+    const secp256k1_xonly_pubkey *internal_pubkey,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Checks that a tweaked pubkey is the result of calling
+ *  secp256k1_xonly_pubkey_tweak_add with internal_pubkey and tweak32.
+ *
+ *  The tweaked pubkey is represented by its 32-byte x-only serialization and
+ *  its pk_parity, which can both be obtained by converting the result of
+ *  tweak_add to a secp256k1_xonly_pubkey.
+ *
+ *  Note that this alone does _not_ verify that the tweaked pubkey is a
+ *  commitment. If the tweak is not chosen in a specific way, the tweaked pubkey
+ *  can easily be the result of a different internal_pubkey and tweak.
+ *
+ *  Returns: 0 if the arguments are invalid or the tweaked pubkey is not the
+ *           result of tweaking the internal_pubkey with tweak32. 1 otherwise.
+ *  Args:            ctx: pointer to a context object.
+ *  In: tweaked_pubkey32: pointer to a serialized xonly_pubkey.
+ *     tweaked_pk_parity: the parity of the tweaked pubkey (whose serialization
+ *                        is passed in as tweaked_pubkey32). This must match the
+ *                        pk_parity value that is returned when calling
+ *                        secp256k1_xonly_pubkey with the tweaked pubkey, or
+ *                        this function will fail.
+ *       internal_pubkey: pointer to an x-only public key object to apply the tweak to.
+ *               tweak32: pointer to a 32-byte tweak.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_xonly_pubkey_tweak_add_check(
+    const secp256k1_context *ctx,
+    const unsigned char *tweaked_pubkey32,
+    int tweaked_pk_parity,
+    const secp256k1_xonly_pubkey *internal_pubkey,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Compute the keypair for a valid secret key.
+ *
+ *  See the documentation of `secp256k1_ec_seckey_verify` for more information
+ *  about the validity of secret keys.
+ *
+ *  Returns: 1: secret key is valid
+ *           0: secret key is invalid
+ *  Args:    ctx: pointer to a context object (not secp256k1_context_static).
+ *  Out: keypair: pointer to the created keypair.
+ *  In:   seckey: pointer to a 32-byte secret key.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_create(
+    const secp256k1_context *ctx,
+    secp256k1_keypair *keypair,
+    const unsigned char *seckey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Get the secret key from a keypair.
+ *
+ *  Returns: 1 always.
+ *  Args:   ctx: pointer to a context object.
+ *  Out: seckey: pointer to a 32-byte buffer for the secret key.
+ *  In: keypair: pointer to a keypair.
+ */
+SECP256K1_API int secp256k1_keypair_sec(
+    const secp256k1_context *ctx,
+    unsigned char *seckey,
+    const secp256k1_keypair *keypair
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Get the public key from a keypair.
+ *
+ *  Returns: 1 always.
+ *  Args:   ctx: pointer to a context object.
+ *  Out: pubkey: pointer to a pubkey object, set to the keypair public key.
+ *  In: keypair: pointer to a keypair.
+ */
+SECP256K1_API int secp256k1_keypair_pub(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const secp256k1_keypair *keypair
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Get the x-only public key from a keypair.
+ *
+ *  This is the same as calling secp256k1_keypair_pub and then
+ *  secp256k1_xonly_pubkey_from_pubkey.
+ *
+ *  Returns: 1 always.
+ *  Args:   ctx: pointer to a context object.
+ *  Out: pubkey: pointer to an xonly_pubkey object, set to the keypair
+ *               public key after converting it to an xonly_pubkey.
+ *    pk_parity: Ignored if NULL. Otherwise, pointer to an integer that will be set to the
+ *               pk_parity argument of secp256k1_xonly_pubkey_from_pubkey.
+ *  In: keypair: pointer to a keypair.
+ */
+SECP256K1_API int secp256k1_keypair_xonly_pub(
+    const secp256k1_context *ctx,
+    secp256k1_xonly_pubkey *pubkey,
+    int *pk_parity,
+    const secp256k1_keypair *keypair
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(4);
+
+/** Tweak a keypair by adding tweak32 to the secret key and updating the public
+ *  key accordingly.
+ *
+ *  Calling this function and then secp256k1_keypair_pub results in the same
+ *  public key as calling secp256k1_keypair_xonly_pub and then
+ *  secp256k1_xonly_pubkey_tweak_add.
+ *
+ *  Returns: 0 if the arguments are invalid or the resulting keypair would be
+ *           invalid (only when the tweak is the negation of the keypair's
+ *           secret key). 1 otherwise.
+ *
+ *  Args:       ctx: pointer to a context object.
+ *  In/Out: keypair: pointer to a keypair to apply the tweak to. Will be set to
+ *                   an invalid value if this function returns 0.
+ *  In:     tweak32: pointer to a 32-byte tweak, which must be valid according to
+ *                   secp256k1_ec_seckey_verify or 32 zero bytes. For uniformly
+ *                   random 32-byte tweaks, the chance of being invalid is
+ *                   negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_keypair_xonly_tweak_add(
+    const secp256k1_context *ctx,
+    secp256k1_keypair *keypair,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_EXTRAKEYS_H */

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1_musig.h

@@ -0,0 +1,588 @@
+#ifndef SECP256K1_MUSIG_H
+#define SECP256K1_MUSIG_H
+
+#include "secp256k1_extrakeys.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+#include <stddef.h>
+#include <stdint.h>
+
+/** This module implements BIP 327 "MuSig2 for BIP340-compatible
+ *  Multi-Signatures"
+ *  (https://github.com/bitcoin/bips/blob/master/bip-0327.mediawiki)
+ *  v1.0.0. You can find an example demonstrating the musig module in
+ *  examples/musig.c.
+ *
+ *  The module also supports BIP 341 ("Taproot") public key tweaking.
+ *
+ *  It is recommended to read the documentation in this include file carefully.
+ *  Further notes on API usage can be found in doc/musig.md
+ *
+ *  Since the first version of MuSig is essentially replaced by MuSig2, we use
+ *  MuSig, musig and MuSig2 synonymously unless noted otherwise.
+ */
+
+/** Opaque data structures
+ *
+ *  The exact representation of data inside the opaque data structures is
+ *  implementation defined and not guaranteed to be portable between different
+ *  platforms or versions. With the exception of `secp256k1_musig_secnonce`, the
+ *  data structures can be safely copied/moved. If you need to convert to a
+ *  format suitable for storage, transmission, or comparison, use the
+ *  corresponding serialization and parsing functions.
+ */
+
+/** Opaque data structure that caches information about public key aggregation.
+ *
+ *  Guaranteed to be 197 bytes in size. No serialization and parsing functions
+ *  (yet).
+ */
+typedef struct secp256k1_musig_keyagg_cache {
+    unsigned char data[197];
+} secp256k1_musig_keyagg_cache;
+
+/** Opaque data structure that holds a signer's _secret_ nonce.
+ *
+ *  Guaranteed to be 132 bytes in size.
+ *
+ *  WARNING: This structure MUST NOT be copied or read or written to directly. A
+ *  signer who is online throughout the whole process and can keep this
+ *  structure in memory can use the provided API functions for a safe standard
+ *  workflow.
+ *
+ *  Copying this data structure can result in nonce reuse which will leak the
+ *  secret signing key.
+ */
+typedef struct secp256k1_musig_secnonce {
+    unsigned char data[132];
+} secp256k1_musig_secnonce;
+
+/** Opaque data structure that holds a signer's public nonce.
+ *
+ *  Guaranteed to be 132 bytes in size. Serialized and parsed with
+ *  `musig_pubnonce_serialize` and `musig_pubnonce_parse`.
+ */
+typedef struct secp256k1_musig_pubnonce {
+    unsigned char data[132];
+} secp256k1_musig_pubnonce;
+
+/** Opaque data structure that holds an aggregate public nonce.
+ *
+ *  Guaranteed to be 132 bytes in size. Serialized and parsed with
+ *  `musig_aggnonce_serialize` and `musig_aggnonce_parse`.
+ */
+typedef struct secp256k1_musig_aggnonce {
+    unsigned char data[132];
+} secp256k1_musig_aggnonce;
+
+/** Opaque data structure that holds a MuSig session.
+ *
+ *  This structure is not required to be kept secret for the signing protocol to
+ *  be secure. Guaranteed to be 133 bytes in size. No serialization and parsing
+ *  functions (yet).
+ */
+typedef struct secp256k1_musig_session {
+    unsigned char data[133];
+} secp256k1_musig_session;
+
+/** Opaque data structure that holds a partial MuSig signature.
+ *
+ *  Guaranteed to be 36 bytes in size. Serialized and parsed with
+ *  `musig_partial_sig_serialize` and `musig_partial_sig_parse`.
+ */
+typedef struct secp256k1_musig_partial_sig {
+    unsigned char data[36];
+} secp256k1_musig_partial_sig;
+
+/** Parse a signer's public nonce.
+ *
+ *  Returns: 1 when the nonce could be parsed, 0 otherwise.
+ *  Args:    ctx: pointer to a context object
+ *  Out:   nonce: pointer to a nonce object
+ *  In:     in66: pointer to the 66-byte nonce to be parsed
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_pubnonce_parse(
+    const secp256k1_context *ctx,
+    secp256k1_musig_pubnonce *nonce,
+    const unsigned char *in66
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a signer's public nonce
+ *
+ *  Returns: 1 always
+ *  Args:    ctx: pointer to a context object
+ *  Out:   out66: pointer to a 66-byte array to store the serialized nonce
+ *  In:    nonce: pointer to the nonce
+ */
+SECP256K1_API int secp256k1_musig_pubnonce_serialize(
+    const secp256k1_context *ctx,
+    unsigned char *out66,
+    const secp256k1_musig_pubnonce *nonce
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse an aggregate public nonce.
+ *
+ *  Returns: 1 when the nonce could be parsed, 0 otherwise.
+ *  Args:    ctx: pointer to a context object
+ *  Out:   nonce: pointer to a nonce object
+ *  In:     in66: pointer to the 66-byte nonce to be parsed
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_aggnonce_parse(
+    const secp256k1_context *ctx,
+    secp256k1_musig_aggnonce *nonce,
+    const unsigned char *in66
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an aggregate public nonce
+ *
+ *  Returns: 1 always
+ *  Args:    ctx: pointer to a context object
+ *  Out:   out66: pointer to a 66-byte array to store the serialized nonce
+ *  In:    nonce: pointer to the nonce
+ */
+SECP256K1_API int secp256k1_musig_aggnonce_serialize(
+    const secp256k1_context *ctx,
+    unsigned char *out66,
+    const secp256k1_musig_aggnonce *nonce
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Parse a MuSig partial signature.
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise.
+ *  Args:    ctx: pointer to a context object
+ *  Out:     sig: pointer to a signature object
+ *  In:     in32: pointer to the 32-byte signature to be parsed
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_partial_sig_parse(
+    const secp256k1_context *ctx,
+    secp256k1_musig_partial_sig *sig,
+    const unsigned char *in32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize a MuSig partial signature
+ *
+ *  Returns: 1 always
+ *  Args:    ctx: pointer to a context object
+ *  Out:   out32: pointer to a 32-byte array to store the serialized signature
+ *  In:      sig: pointer to the signature
+ */
+SECP256K1_API int secp256k1_musig_partial_sig_serialize(
+    const secp256k1_context *ctx,
+    unsigned char *out32,
+    const secp256k1_musig_partial_sig *sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Computes an aggregate public key and uses it to initialize a keyagg_cache
+ *
+ *  Different orders of `pubkeys` result in different `agg_pk`s.
+ *
+ *  Before aggregating, the pubkeys can be sorted with `secp256k1_ec_pubkey_sort`
+ *  which ensures the same `agg_pk` result for the same multiset of pubkeys.
+ *  This is useful to do before `pubkey_agg`, such that the order of pubkeys
+ *  does not affect the aggregate public key.
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:        ctx: pointer to a context object
+ *  Out:      agg_pk: the MuSig-aggregated x-only public key. If you do not need it,
+ *                    this arg can be NULL.
+ *      keyagg_cache: if non-NULL, pointer to a musig_keyagg_cache struct that
+ *                    is required for signing (or observing the signing session
+ *                    and verifying partial signatures).
+ *   In:     pubkeys: input array of pointers to public keys to aggregate. The order
+ *                    is important; a different order will result in a different
+ *                    aggregate public key.
+ *         n_pubkeys: length of pubkeys array. Must be greater than 0.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_pubkey_agg(
+    const secp256k1_context *ctx,
+    secp256k1_xonly_pubkey *agg_pk,
+    secp256k1_musig_keyagg_cache *keyagg_cache,
+    const secp256k1_pubkey * const *pubkeys,
+    size_t n_pubkeys
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(4);
+
+/** Obtain the aggregate public key from a keyagg_cache.
+ *
+ *  This is only useful if you need the non-xonly public key, in particular for
+ *  plain (non-xonly) tweaking or batch-verifying multiple key aggregations
+ *  (not implemented).
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:        ctx: pointer to a context object
+ *  Out:      agg_pk: the MuSig-aggregated public key.
+ *  In: keyagg_cache: pointer to a `musig_keyagg_cache` struct initialized by
+ *                    `musig_pubkey_agg`
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_pubkey_get(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *agg_pk,
+    const secp256k1_musig_keyagg_cache *keyagg_cache
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Apply plain "EC" tweaking to a public key in a given keyagg_cache by adding
+ *  the generator multiplied with `tweak32` to it. This is useful for deriving
+ *  child keys from an aggregate public key via BIP 32 where `tweak32` is set to
+ *  a hash as defined in BIP 32.
+ *
+ *  Callers are responsible for deriving `tweak32` in a way that does not reduce
+ *  the security of MuSig (for example, by following BIP 32).
+ *
+ *  The tweaking method is the same as `secp256k1_ec_pubkey_tweak_add`. So after
+ *  the following pseudocode buf and buf2 have identical contents (absent
+ *  earlier failures).
+ *
+ *  secp256k1_musig_pubkey_agg(..., keyagg_cache, pubkeys, ...)
+ *  secp256k1_musig_pubkey_get(..., agg_pk, keyagg_cache)
+ *  secp256k1_musig_pubkey_ec_tweak_add(..., output_pk, tweak32, keyagg_cache)
+ *  secp256k1_ec_pubkey_serialize(..., buf, ..., output_pk, ...)
+ *  secp256k1_ec_pubkey_tweak_add(..., agg_pk, tweak32)
+ *  secp256k1_ec_pubkey_serialize(..., buf2, ..., agg_pk, ...)
+ *
+ *  This function is required if you want to _sign_ for a tweaked aggregate key.
+ *  If you are only computing a public key but not intending to create a
+ *  signature for it, use `secp256k1_ec_pubkey_tweak_add` instead.
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:            ctx: pointer to a context object
+ *  Out:   output_pubkey: pointer to a public key to store the result. Will be set
+ *                        to an invalid value if this function returns 0. If you
+ *                        do not need it, this arg can be NULL.
+ *  In/Out: keyagg_cache: pointer to a `musig_keyagg_cache` struct initialized by
+ *                       `musig_pubkey_agg`
+ *  In:          tweak32: pointer to a 32-byte tweak. The tweak is valid if it passes
+ *                        `secp256k1_ec_seckey_verify` and is not equal to the
+ *                        secret key corresponding to the public key represented
+ *                        by keyagg_cache or its negation. For uniformly random
+ *                        32-byte arrays the chance of being invalid is
+ *                        negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_pubkey_ec_tweak_add(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *output_pubkey,
+    secp256k1_musig_keyagg_cache *keyagg_cache,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Apply x-only tweaking to a public key in a given keyagg_cache by adding the
+ *  generator multiplied with `tweak32` to it. This is useful for creating
+ *  Taproot outputs where `tweak32` is set to a TapTweak hash as defined in BIP
+ *  341.
+ *
+ *  Callers are responsible for deriving `tweak32` in a way that does not reduce
+ *  the security of MuSig (for example, by following Taproot BIP 341).
+ *
+ *  The tweaking method is the same as `secp256k1_xonly_pubkey_tweak_add`. So in
+ *  the following pseudocode xonly_pubkey_tweak_add_check (absent earlier
+ *  failures) returns 1.
+ *
+ *  secp256k1_musig_pubkey_agg(..., agg_pk, keyagg_cache, pubkeys, ...)
+ *  secp256k1_musig_pubkey_xonly_tweak_add(..., output_pk, keyagg_cache, tweak32)
+ *  secp256k1_xonly_pubkey_serialize(..., buf, output_pk)
+ *  secp256k1_xonly_pubkey_tweak_add_check(..., buf, ..., agg_pk, tweak32)
+ *
+ *  This function is required if you want to _sign_ for a tweaked aggregate key.
+ *  If you are only computing a public key but not intending to create a
+ *  signature for it, use `secp256k1_xonly_pubkey_tweak_add` instead.
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:            ctx: pointer to a context object
+ *  Out:   output_pubkey: pointer to a public key to store the result. Will be set
+ *                        to an invalid value if this function returns 0. If you
+ *                        do not need it, this arg can be NULL.
+ *  In/Out: keyagg_cache: pointer to a `musig_keyagg_cache` struct initialized by
+ *                       `musig_pubkey_agg`
+ *  In:          tweak32: pointer to a 32-byte tweak. The tweak is valid if it passes
+ *                        `secp256k1_ec_seckey_verify` and is not equal to the
+ *                        secret key corresponding to the public key represented
+ *                        by keyagg_cache or its negation. For uniformly random
+ *                        32-byte arrays the chance of being invalid is
+ *                        negligible (around 1 in 2^128).
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_pubkey_xonly_tweak_add(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *output_pubkey,
+    secp256k1_musig_keyagg_cache *keyagg_cache,
+    const unsigned char *tweak32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Starts a signing session by generating a nonce
+ *
+ *  This function outputs a secret nonce that will be required for signing and a
+ *  corresponding public nonce that is intended to be sent to other signers.
+ *
+ *  MuSig differs from regular Schnorr signing in that implementers _must_ take
+ *  special care to not reuse a nonce. This can be ensured by following these rules:
+ *
+ *  1. Each call to this function must have a UNIQUE session_secrand32 that must
+ *     NOT BE REUSED in subsequent calls to this function and must be KEPT
+ *     SECRET (even from other signers).
+ *  2. If you already know the seckey, message or aggregate public key
+ *     cache, they can be optionally provided to derive the nonce and increase
+ *     misuse-resistance. The extra_input32 argument can be used to provide
+ *     additional data that does not repeat in normal scenarios, such as the
+ *     current time.
+ *  3. Avoid copying (or serializing) the secnonce. This reduces the possibility
+ *     that it is used more than once for signing.
+ *
+ *  If you don't have access to good randomness for session_secrand32, but you
+ *  have access to a non-repeating counter, then see
+ *  secp256k1_musig_nonce_gen_counter.
+ *
+ *  Remember that nonce reuse will leak the secret key!
+ *  Note that using the same seckey for multiple MuSig sessions is fine.
+ *
+ *  Returns: 0 if the arguments are invalid and 1 otherwise
+ *  Args:         ctx: pointer to a context object (not secp256k1_context_static)
+ *  Out:     secnonce: pointer to a structure to store the secret nonce
+ *           pubnonce: pointer to a structure to store the public nonce
+ *  In/Out:
+ *  session_secrand32: a 32-byte session_secrand32 as explained above. Must be unique to this
+ *                     call to secp256k1_musig_nonce_gen and must be uniformly
+ *                     random. If the function call is successful, the
+ *                     session_secrand32 buffer is invalidated to prevent reuse.
+ *  In:
+ *             seckey: the 32-byte secret key that will later be used for signing, if
+ *                     already known (can be NULL)
+ *             pubkey: public key of the signer creating the nonce. The secnonce
+ *                     output of this function cannot be used to sign for any
+ *                     other public key. While the public key should correspond
+ *                     to the provided seckey, a mismatch will not cause the
+ *                     function to return 0.
+ *              msg32: the 32-byte message that will later be signed, if already known
+ *                     (can be NULL)
+ *       keyagg_cache: pointer to the keyagg_cache that was used to create the aggregate
+ *                     (and potentially tweaked) public key if already known
+ *                     (can be NULL)
+ *      extra_input32: an optional 32-byte array that is input to the nonce
+ *                     derivation function (can be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_nonce_gen(
+    const secp256k1_context *ctx,
+    secp256k1_musig_secnonce *secnonce,
+    secp256k1_musig_pubnonce *pubnonce,
+    unsigned char *session_secrand32,
+    const unsigned char *seckey,
+    const secp256k1_pubkey *pubkey,
+    const unsigned char *msg32,
+    const secp256k1_musig_keyagg_cache *keyagg_cache,
+    const unsigned char *extra_input32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(6);
+
+
+/** Alternative way to generate a nonce and start a signing session
+ *
+ *  This function outputs a secret nonce that will be required for signing and a
+ *  corresponding public nonce that is intended to be sent to other signers.
+ *
+ *  This function differs from `secp256k1_musig_nonce_gen` by accepting a
+ *  non-repeating counter value instead of a secret random value. This requires
+ *  that a secret key is provided to `secp256k1_musig_nonce_gen_counter`
+ *  (through the keypair argument), as opposed to `secp256k1_musig_nonce_gen`
+ *  where the seckey argument is optional.
+ *
+ *  MuSig differs from regular Schnorr signing in that implementers _must_ take
+ *  special care to not reuse a nonce. This can be ensured by following these rules:
+ *
+ *  1. The nonrepeating_cnt argument must be a counter value that never repeats,
+ *     i.e., you must never call `secp256k1_musig_nonce_gen_counter` twice with
+ *     the same keypair and nonrepeating_cnt value. For example, this implies
+ *     that if the same keypair is used with `secp256k1_musig_nonce_gen_counter`
+ *     on multiple devices, none of the devices should have the same counter
+ *     value as any other device.
+ *  2. If the seckey, message or aggregate public key cache is already available
+ *     at this stage, any of these can be optionally provided, in which case
+ *     they will be used in the derivation of the nonce and increase
+ *     misuse-resistance. The extra_input32 argument can be used to provide
+ *     additional data that does not repeat in normal scenarios, such as the
+ *     current time.
+ *  3. Avoid copying (or serializing) the secnonce. This reduces the possibility
+ *     that it is used more than once for signing.
+ *
+ *  Remember that nonce reuse will leak the secret key!
+ *  Note that using the same keypair for multiple MuSig sessions is fine.
+ *
+ *  Returns: 0 if the arguments are invalid and 1 otherwise
+ *  Args:         ctx: pointer to a context object (not secp256k1_context_static)
+ *  Out:     secnonce: pointer to a structure to store the secret nonce
+ *           pubnonce: pointer to a structure to store the public nonce
+ *  In:
+ *   nonrepeating_cnt: the value of a counter as explained above. Must be
+ *                     unique to this call to secp256k1_musig_nonce_gen.
+ *            keypair: keypair of the signer creating the nonce. The secnonce
+ *                     output of this function cannot be used to sign for any
+ *                     other keypair.
+ *              msg32: the 32-byte message that will later be signed, if already known
+ *                     (can be NULL)
+ *       keyagg_cache: pointer to the keyagg_cache that was used to create the aggregate
+ *                     (and potentially tweaked) public key if already known
+ *                     (can be NULL)
+ *      extra_input32: an optional 32-byte array that is input to the nonce
+ *                     derivation function (can be NULL)
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_nonce_gen_counter(
+    const secp256k1_context *ctx,
+    secp256k1_musig_secnonce *secnonce,
+    secp256k1_musig_pubnonce *pubnonce,
+    uint64_t nonrepeating_cnt,
+    const secp256k1_keypair *keypair,
+    const unsigned char *msg32,
+    const secp256k1_musig_keyagg_cache *keyagg_cache,
+    const unsigned char *extra_input32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(5);
+
+/** Aggregates the nonces of all signers into a single nonce
+ *
+ *  This can be done by an untrusted party to reduce the communication
+ *  between signers. Instead of everyone sending nonces to everyone else, there
+ *  can be one party receiving all nonces, aggregating the nonces with this
+ *  function and then sending only the aggregate nonce back to the signers.
+ *
+ *  If the aggregator does not compute the aggregate nonce correctly, the final
+ *  signature will be invalid.
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:           ctx: pointer to a context object
+ *  Out:       aggnonce: pointer to an aggregate public nonce object for
+ *                       musig_nonce_process
+ *  In:       pubnonces: array of pointers to public nonces sent by the
+ *                       signers
+ *          n_pubnonces: number of elements in the pubnonces array. Must be
+ *                       greater than 0.
+ */
+SECP256K1_API int secp256k1_musig_nonce_agg(
+    const secp256k1_context *ctx,
+    secp256k1_musig_aggnonce *aggnonce,
+    const secp256k1_musig_pubnonce * const *pubnonces,
+    size_t n_pubnonces
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Takes the aggregate nonce and creates a session that is required for signing
+ *  and verification of partial signatures.
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise
+ *  Args:          ctx: pointer to a context object
+ *  Out:       session: pointer to a struct to store the session
+ *  In:       aggnonce: pointer to an aggregate public nonce object that is the
+ *                      output of musig_nonce_agg
+ *              msg32:  the 32-byte message to sign
+ *       keyagg_cache:  pointer to the keyagg_cache that was used to create the
+ *                      aggregate (and potentially tweaked) pubkey
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_nonce_process(
+    const secp256k1_context *ctx,
+    secp256k1_musig_session *session,
+    const secp256k1_musig_aggnonce *aggnonce,
+    const unsigned char *msg32,
+    const secp256k1_musig_keyagg_cache *keyagg_cache
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5);
+
+/** Produces a partial signature
+ *
+ *  This function overwrites the given secnonce with zeros and will abort if given a
+ *  secnonce that is all zeros. This is a best effort attempt to protect against nonce
+ *  reuse. However, this is of course easily defeated if the secnonce has been
+ *  copied (or serialized). Remember that nonce reuse will leak the secret key!
+ *
+ *  For signing to succeed, the secnonce provided to this function must have
+ *  been generated for the provided keypair. This means that when signing for a
+ *  keypair consisting of a seckey and pubkey, the secnonce must have been
+ *  created by calling musig_nonce_gen with that pubkey. Otherwise, the
+ *  illegal_callback is called.
+ *
+ *  This function does not verify the output partial signature, deviating from
+ *  the BIP 327 specification. It is recommended to verify the output partial
+ *  signature with `secp256k1_musig_partial_sig_verify` to prevent random or
+ *  adversarially provoked computation errors.
+ *
+ *  Returns: 0 if the arguments are invalid or the provided secnonce has already
+ *           been used for signing, 1 otherwise
+ *  Args:         ctx: pointer to a context object
+ *  Out:  partial_sig: pointer to struct to store the partial signature
+ *  In/Out:  secnonce: pointer to the secnonce struct created in
+ *                     musig_nonce_gen that has been never used in a
+ *                     partial_sign call before and has been created for the
+ *                     keypair
+ *  In:       keypair: pointer to keypair to sign the message with
+ *       keyagg_cache: pointer to the keyagg_cache that was output when the
+ *                     aggregate public key for this session
+ *            session: pointer to the session that was created with
+ *                     musig_nonce_process
+ */
+SECP256K1_API int secp256k1_musig_partial_sign(
+    const secp256k1_context *ctx,
+    secp256k1_musig_partial_sig *partial_sig,
+    secp256k1_musig_secnonce *secnonce,
+    const secp256k1_keypair *keypair,
+    const secp256k1_musig_keyagg_cache *keyagg_cache,
+    const secp256k1_musig_session *session
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6);
+
+/** Verifies an individual signer's partial signature
+ *
+ *  The signature is verified for a specific signing session. In order to avoid
+ *  accidentally verifying a signature from a different or non-existing signing
+ *  session, you must ensure the following:
+ *    1. The `keyagg_cache` argument is identical to the one used to create the
+ *       `session` with `musig_nonce_process`.
+ *    2. The `pubkey` argument must be identical to the one sent by the signer
+ *       before aggregating it with `musig_pubkey_agg` to create the
+ *       `keyagg_cache`.
+ *    3. The `pubnonce` argument must be identical to the one sent by the signer
+ *       before aggregating it with `musig_nonce_agg` and using the result to
+ *       create the `session` with `musig_nonce_process`.
+ *
+ *  It is not required to call this function in regular MuSig sessions, because
+ *  if any partial signature does not verify, the final signature will not
+ *  verify either, so the problem will be caught. However, this function
+ *  provides the ability to identify which specific partial signature fails
+ *  verification.
+ *
+ *  Returns: 0 if the arguments are invalid or the partial signature does not
+ *           verify, 1 otherwise
+ *  Args         ctx: pointer to a context object
+ *  In:  partial_sig: pointer to partial signature to verify, sent by
+ *                    the signer associated with `pubnonce` and `pubkey`
+ *          pubnonce: public nonce of the signer in the signing session
+ *            pubkey: public key of the signer in the signing session
+ *      keyagg_cache: pointer to the keyagg_cache that was output when the
+ *                    aggregate public key for this signing session
+ *           session: pointer to the session that was created with
+ *                    `musig_nonce_process`
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_musig_partial_sig_verify(
+    const secp256k1_context *ctx,
+    const secp256k1_musig_partial_sig *partial_sig,
+    const secp256k1_musig_pubnonce *pubnonce,
+    const secp256k1_pubkey *pubkey,
+    const secp256k1_musig_keyagg_cache *keyagg_cache,
+    const secp256k1_musig_session *session
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(6);
+
+/** Aggregates partial signatures
+ *
+ *  Returns: 0 if the arguments are invalid, 1 otherwise (which does NOT mean
+ *           the resulting signature verifies).
+ *  Args:         ctx: pointer to a context object
+ *  Out:        sig64: complete (but possibly invalid) Schnorr signature
+ *  In:       session: pointer to the session that was created with
+ *                     musig_nonce_process
+ *       partial_sigs: array of pointers to partial signatures to aggregate
+ *             n_sigs: number of elements in the partial_sigs array. Must be
+ *                     greater than 0.
+ */
+SECP256K1_API int secp256k1_musig_partial_sig_agg(
+    const secp256k1_context *ctx,
+    unsigned char *sig64,
+    const secp256k1_musig_session *session,
+    const secp256k1_musig_partial_sig * const *partial_sigs,
+    size_t n_sigs
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1_preallocated.h

@@ -0,0 +1,134 @@
+#ifndef SECP256K1_PREALLOCATED_H
+#define SECP256K1_PREALLOCATED_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* The module provided by this header file is intended for settings in which it
+ * is not possible or desirable to rely on dynamic memory allocation. It provides
+ * functions for creating, cloning, and destroying secp256k1 context objects in a
+ * contiguous fixed-size block of memory provided by the caller.
+ *
+ * Context objects created by functions in this module can be used like contexts
+ * objects created by functions in secp256k1.h, i.e., they can be passed to any
+ * API function that expects a context object (see secp256k1.h for details). The
+ * only exception is that context objects created by functions in this module
+ * must be destroyed using secp256k1_context_preallocated_destroy (in this
+ * module) instead of secp256k1_context_destroy (in secp256k1.h).
+ *
+ * It is guaranteed that functions in this module will not call malloc or its
+ * friends realloc, calloc, and free.
+ */
+
+/** Determine the memory size of a secp256k1 context object to be created in
+ *  caller-provided memory.
+ *
+ *  The purpose of this function is to determine how much memory must be provided
+ *  to secp256k1_context_preallocated_create.
+ *
+ *  Returns: the required size of the caller-provided memory block
+ *  In:      flags:    which parts of the context to initialize.
+ */
+SECP256K1_API size_t secp256k1_context_preallocated_size(
+    unsigned int flags
+) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Create a secp256k1 context object in caller-provided memory.
+ *
+ *  The caller must provide a pointer to a rewritable contiguous block of memory
+ *  of size at least secp256k1_context_preallocated_size(flags) bytes, suitably
+ *  aligned to hold an object of any type.
+ *
+ *  The block of memory is exclusively owned by the created context object during
+ *  the lifetime of this context object, which begins with the call to this
+ *  function and ends when a call to secp256k1_context_preallocated_destroy
+ *  (which destroys the context object again) returns. During the lifetime of the
+ *  context object, the caller is obligated not to access this block of memory,
+ *  i.e., the caller may not read or write the memory, e.g., by copying the memory
+ *  contents to a different location or trying to create a second context object
+ *  in the memory. In simpler words, the prealloc pointer (or any pointer derived
+ *  from it) should not be used during the lifetime of the context object.
+ *
+ *  Returns: pointer to newly created context object.
+ *  In:      prealloc: pointer to a rewritable contiguous block of memory of
+ *                     size at least secp256k1_context_preallocated_size(flags)
+ *                     bytes, as detailed above.
+ *           flags:    which parts of the context to initialize.
+ *
+ *  See secp256k1_context_create (in secp256k1.h) for further details.
+ *
+ *  See also secp256k1_context_randomize (in secp256k1.h)
+ *  and secp256k1_context_preallocated_destroy.
+ */
+SECP256K1_API secp256k1_context *secp256k1_context_preallocated_create(
+    void *prealloc,
+    unsigned int flags
+) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Determine the memory size of a secp256k1 context object to be copied into
+ *  caller-provided memory.
+ *
+ *  Returns: the required size of the caller-provided memory block.
+ *  In:      ctx: pointer to a context to copy.
+ */
+SECP256K1_API size_t secp256k1_context_preallocated_clone_size(
+    const secp256k1_context *ctx
+) SECP256K1_ARG_NONNULL(1) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Copy a secp256k1 context object into caller-provided memory.
+ *
+ *  The caller must provide a pointer to a rewritable contiguous block of memory
+ *  of size at least secp256k1_context_preallocated_size(flags) bytes, suitably
+ *  aligned to hold an object of any type.
+ *
+ *  The block of memory is exclusively owned by the created context object during
+ *  the lifetime of this context object, see the description of
+ *  secp256k1_context_preallocated_create for details.
+ *
+ *  Cloning secp256k1_context_static is not possible, and should not be emulated by
+ *  the caller (e.g., using memcpy). Create a new context instead.
+ *
+ *  Returns: pointer to a newly created context object.
+ *  Args:    ctx:      pointer to a context to copy (not secp256k1_context_static).
+ *  In:      prealloc: pointer to a rewritable contiguous block of memory of
+ *                     size at least secp256k1_context_preallocated_size(flags)
+ *                     bytes, as detailed above.
+ */
+SECP256K1_API secp256k1_context *secp256k1_context_preallocated_clone(
+    const secp256k1_context *ctx,
+    void *prealloc
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_WARN_UNUSED_RESULT;
+
+/** Destroy a secp256k1 context object that has been created in
+ *  caller-provided memory.
+ *
+ *  The context pointer may not be used afterwards.
+ *
+ *  The context to destroy must have been created using
+ *  secp256k1_context_preallocated_create or secp256k1_context_preallocated_clone.
+ *  If the context has instead been created using secp256k1_context_create or
+ *  secp256k1_context_clone, the behaviour is undefined. In that case,
+ *  secp256k1_context_destroy must be used instead.
+ *
+ *  If required, it is the responsibility of the caller to deallocate the block
+ *  of memory properly after this function returns, e.g., by calling free on the
+ *  preallocated pointer given to secp256k1_context_preallocated_create or
+ *  secp256k1_context_preallocated_clone.
+ *
+ *  Args:   ctx: pointer to a context to destroy, constructed using
+ *               secp256k1_context_preallocated_create or
+ *               secp256k1_context_preallocated_clone
+ *               (i.e., not secp256k1_context_static).
+ */
+SECP256K1_API void secp256k1_context_preallocated_destroy(
+    secp256k1_context *ctx
+) SECP256K1_ARG_NONNULL(1);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_PREALLOCATED_H */

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1_recovery.h

@@ -0,0 +1,123 @@
+#ifndef SECP256K1_RECOVERY_H
+#define SECP256K1_RECOVERY_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** Opaque data structure that holds a parsed ECDSA signature,
+ *  supporting pubkey recovery.
+ *
+ *  The exact representation of data inside is implementation defined and not
+ *  guaranteed to be portable between different platforms or versions. It is
+ *  however guaranteed to be 65 bytes in size, and can be safely copied/moved.
+ *  If you need to convert to a format suitable for storage or transmission, use
+ *  the secp256k1_ecdsa_signature_serialize_* and
+ *  secp256k1_ecdsa_signature_parse_* functions.
+ *
+ *  Furthermore, it is guaranteed that identical signatures (including their
+ *  recoverability) will have identical representation, so they can be
+ *  memcmp'ed.
+ */
+typedef struct secp256k1_ecdsa_recoverable_signature {
+    unsigned char data[65];
+} secp256k1_ecdsa_recoverable_signature;
+
+/** Parse a compact ECDSA signature (64 bytes + recovery id).
+ *
+ *  Returns: 1 when the signature could be parsed, 0 otherwise
+ *  Args: ctx:     pointer to a context object
+ *  Out:  sig:     pointer to a signature object
+ *  In:   input64: pointer to a 64-byte compact signature
+ *        recid:   the recovery id (0, 1, 2 or 3)
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_parse_compact(
+    const secp256k1_context *ctx,
+    secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *input64,
+    int recid
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Convert a recoverable signature into a normal signature.
+ *
+ *  Returns: 1
+ *  Args: ctx:    pointer to a context object.
+ *  Out:  sig:    pointer to a normal signature.
+ *  In:   sigin:  pointer to a recoverable signature.
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_convert(
+    const secp256k1_context *ctx,
+    secp256k1_ecdsa_signature *sig,
+    const secp256k1_ecdsa_recoverable_signature *sigin
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Serialize an ECDSA signature in compact format (64 bytes + recovery id).
+ *
+ *  Returns: 1
+ *  Args: ctx:      pointer to a context object.
+ *  Out:  output64: pointer to a 64-byte array of the compact signature.
+ *        recid:    pointer to an integer to hold the recovery id.
+ *  In:   sig:      pointer to an initialized signature object.
+ */
+SECP256K1_API int secp256k1_ecdsa_recoverable_signature_serialize_compact(
+    const secp256k1_context *ctx,
+    unsigned char *output64,
+    int *recid,
+    const secp256k1_ecdsa_recoverable_signature *sig
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Create a recoverable ECDSA signature.
+ *
+ *  Returns: 1: signature created
+ *           0: the nonce generation function failed, or the secret key was invalid.
+ *  Args:    ctx:       pointer to a context object (not secp256k1_context_static).
+ *  Out:     sig:       pointer to an array where the signature will be placed.
+ *  In:      msghash32: the 32-byte message hash being signed.
+ *           seckey:    pointer to a 32-byte secret key.
+ *           noncefp:   pointer to a nonce generation function. If NULL,
+ *                      secp256k1_nonce_function_default is used.
+ *           ndata:     pointer to arbitrary data used by the nonce generation function
+ *                      (can be NULL for secp256k1_nonce_function_default).
+ */
+SECP256K1_API int secp256k1_ecdsa_sign_recoverable(
+    const secp256k1_context *ctx,
+    secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msghash32,
+    const unsigned char *seckey,
+    secp256k1_nonce_function noncefp,
+    const void *ndata
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Recover an ECDSA public key from a signature.
+ *
+ *  Successful public key recovery guarantees that the signature, after normalization,
+ *  passes `secp256k1_ecdsa_verify`. Thus, explicit verification is not necessary.
+ *
+ *  However, a recoverable signature that successfully passes `secp256k1_ecdsa_recover`,
+ *  when converted to a non-recoverable signature (using
+ *  `secp256k1_ecdsa_recoverable_signature_convert`), is not guaranteed to be
+ *  normalized and thus not guaranteed to pass `secp256k1_ecdsa_verify`. If a
+ *  normalized signature is required, call `secp256k1_ecdsa_signature_normalize`
+ *  after `secp256k1_ecdsa_recoverable_signature_convert`.
+ *
+ *  Returns: 1: public key successfully recovered
+ *           0: otherwise.
+ *  Args:    ctx:       pointer to a context object.
+ *  Out:     pubkey:    pointer to the recovered public key.
+ *  In:      sig:       pointer to initialized signature that supports pubkey recovery.
+ *           msghash32: the 32-byte message hash assumed to be signed.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ecdsa_recover(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const secp256k1_ecdsa_recoverable_signature *sig,
+    const unsigned char *msghash32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_RECOVERY_H */

firmware/kb2040_hidden_signer/src/secp256k1/include/secp256k1_schnorrsig.h

@@ -0,0 +1,190 @@
+#ifndef SECP256K1_SCHNORRSIG_H
+#define SECP256K1_SCHNORRSIG_H
+
+#include "secp256k1.h"
+#include "secp256k1_extrakeys.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/** This module implements a variant of Schnorr signatures compliant with
+ *  Bitcoin Improvement Proposal 340 "Schnorr Signatures for secp256k1"
+ *  (https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki).
+ */
+
+/** A pointer to a function to deterministically generate a nonce.
+ *
+ *  Same as secp256k1_nonce function with the exception of accepting an
+ *  additional pubkey argument and not requiring an attempt argument. The pubkey
+ *  argument can protect signature schemes with key-prefixed challenge hash
+ *  inputs against reusing the nonce when signing with the wrong precomputed
+ *  pubkey.
+ *
+ *  Returns: 1 if a nonce was successfully generated. 0 will cause signing to
+ *           return an error.
+ *  Out:  nonce32: pointer to a 32-byte array to be filled by the function
+ *  In:       msg: the message being verified. Is NULL if and only if msglen
+ *                 is 0.
+ *         msglen: the length of the message
+ *          key32: pointer to a 32-byte secret key (will not be NULL)
+ *     xonly_pk32: the 32-byte serialized xonly pubkey corresponding to key32
+ *                 (will not be NULL)
+ *           algo: pointer to an array describing the signature
+ *                 algorithm (will not be NULL)
+ *        algolen: the length of the algo array
+ *           data: arbitrary data pointer that is passed through
+ *
+ *  Except for test cases, this function should compute some cryptographic hash of
+ *  the message, the key, the pubkey, the algorithm description, and data.
+ */
+typedef int (*secp256k1_nonce_function_hardened)(
+    unsigned char *nonce32,
+    const unsigned char *msg,
+    size_t msglen,
+    const unsigned char *key32,
+    const unsigned char *xonly_pk32,
+    const unsigned char *algo,
+    size_t algolen,
+    void *data
+);
+
+/** An implementation of the nonce generation function as defined in Bitcoin
+ *  Improvement Proposal 340 "Schnorr Signatures for secp256k1"
+ *  (https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki).
+ *
+ *  If a data pointer is passed, it is assumed to be a pointer to 32 bytes of
+ *  auxiliary random data as defined in BIP-340. If the data pointer is NULL,
+ *  the nonce derivation procedure follows BIP-340 by setting the auxiliary
+ *  random data to zero. The algo argument must be non-NULL, otherwise the
+ *  function will fail and return 0. The hash will be tagged with algo.
+ *  Therefore, to create BIP-340 compliant signatures, algo must be set to
+ *  "BIP0340/nonce" and algolen to 13.
+ */
+SECP256K1_API const secp256k1_nonce_function_hardened secp256k1_nonce_function_bip340;
+
+/** Data structure that contains additional arguments for schnorrsig_sign_custom.
+ *
+ *  A schnorrsig_extraparams structure object can be initialized correctly by
+ *  setting it to SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT.
+ *
+ *  Members:
+ *      magic: set to SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC at initialization
+ *             and has no other function than making sure the object is
+ *             initialized.
+ *    noncefp: pointer to a nonce generation function. If NULL,
+ *             secp256k1_nonce_function_bip340 is used
+ *      ndata: pointer to arbitrary data used by the nonce generation function
+ *             (can be NULL). If it is non-NULL and
+ *             secp256k1_nonce_function_bip340 is used, then ndata must be a
+ *             pointer to 32-byte auxiliary randomness as per BIP-340.
+ */
+typedef struct secp256k1_schnorrsig_extraparams {
+    unsigned char magic[4];
+    secp256k1_nonce_function_hardened noncefp;
+    void *ndata;
+} secp256k1_schnorrsig_extraparams;
+
+#define SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC { 0xda, 0x6f, 0xb3, 0x8c }
+#define SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT {\
+    SECP256K1_SCHNORRSIG_EXTRAPARAMS_MAGIC,\
+    NULL,\
+    NULL\
+}
+
+/** Create a Schnorr signature.
+ *
+ *  Does _not_ strictly follow BIP-340 because it does not verify the resulting
+ *  signature. Instead, you can manually use secp256k1_schnorrsig_verify and
+ *  abort if it fails.
+ *
+ *  This function only signs 32-byte messages. If you have messages of a
+ *  different size (or the same size but without a context-specific tag
+ *  prefix), it is recommended to create a 32-byte message hash with
+ *  secp256k1_tagged_sha256 and then sign the hash. Tagged hashing allows
+ *  providing an context-specific tag for domain separation. This prevents
+ *  signatures from being valid in multiple contexts by accident.
+ *
+ *  Returns 1 on success, 0 on failure.
+ *  Args:    ctx: pointer to a context object (not secp256k1_context_static).
+ *  Out:   sig64: pointer to a 64-byte array to store the serialized signature.
+ *  In:    msg32: the 32-byte message being signed.
+ *       keypair: pointer to an initialized keypair.
+ *    aux_rand32: 32 bytes of fresh randomness. While recommended to provide
+ *                this, it is only supplemental to security and can be NULL. A
+ *                NULL argument is treated the same as an all-zero one. See
+ *                BIP-340 "Default Signing" for a full explanation of this
+ *                argument and for guidance if randomness is expensive.
+ */
+SECP256K1_API int secp256k1_schnorrsig_sign32(
+    const secp256k1_context *ctx,
+    unsigned char *sig64,
+    const unsigned char *msg32,
+    const secp256k1_keypair *keypair,
+    const unsigned char *aux_rand32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Same as secp256k1_schnorrsig_sign32, but DEPRECATED. Will be removed in
+ *  future versions. */
+SECP256K1_API int secp256k1_schnorrsig_sign(
+    const secp256k1_context *ctx,
+    unsigned char *sig64,
+    const unsigned char *msg32,
+    const secp256k1_keypair *keypair,
+    const unsigned char *aux_rand32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4)
+  SECP256K1_DEPRECATED("Use secp256k1_schnorrsig_sign32 instead");
+
+/** Create a Schnorr signature with a more flexible API.
+ *
+ *  Same arguments as secp256k1_schnorrsig_sign except that it allows signing
+ *  variable length messages and accepts a pointer to an extraparams object that
+ *  allows customizing signing by passing additional arguments.
+ *
+ *  Equivalent to secp256k1_schnorrsig_sign32(..., aux_rand32) if msglen is 32
+ *  and extraparams is initialized as follows:
+ *  ```
+ *  secp256k1_schnorrsig_extraparams extraparams = SECP256K1_SCHNORRSIG_EXTRAPARAMS_INIT;
+ *  extraparams.ndata = (unsigned char*)aux_rand32;
+ *  ```
+ *
+ *  Returns 1 on success, 0 on failure.
+ *  Args:   ctx: pointer to a context object (not secp256k1_context_static).
+ *  Out:  sig64: pointer to a 64-byte array to store the serialized signature.
+ *  In:     msg: the message being signed. Can only be NULL if msglen is 0.
+ *       msglen: length of the message.
+ *      keypair: pointer to an initialized keypair.
+ *  extraparams: pointer to an extraparams object (can be NULL).
+ */
+SECP256K1_API int secp256k1_schnorrsig_sign_custom(
+    const secp256k1_context *ctx,
+    unsigned char *sig64,
+    const unsigned char *msg,
+    size_t msglen,
+    const secp256k1_keypair *keypair,
+    secp256k1_schnorrsig_extraparams *extraparams
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(5);
+
+/** Verify a Schnorr signature.
+ *
+ *  Returns: 1: correct signature
+ *           0: incorrect signature
+ *  Args:    ctx: pointer to a context object.
+ *  In:    sig64: pointer to the 64-byte signature to verify.
+ *           msg: the message being verified. Can only be NULL if msglen is 0.
+ *        msglen: length of the message
+ *        pubkey: pointer to an x-only public key to verify with
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_schnorrsig_verify(
+    const secp256k1_context *ctx,
+    const unsigned char *sig64,
+    const unsigned char *msg,
+    size_t msglen,
+    const secp256k1_xonly_pubkey *pubkey
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(5);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_SCHNORRSIG_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/CMakeLists.txt

@@ -0,0 +1,229 @@
+add_library(secp256k1)
+
+set_property(TARGET secp256k1 PROPERTY PUBLIC_HEADER
+  ${PROJECT_SOURCE_DIR}/include/secp256k1.h
+  ${PROJECT_SOURCE_DIR}/include/secp256k1_preallocated.h
+)
+
+# Processing must be done in a topological sorting of the dependency graph
+# (dependent module first).
+if(SECP256K1_ENABLE_MODULE_ELLSWIFT)
+  add_compile_definitions(ENABLE_MODULE_ELLSWIFT=1)
+  set_property(TARGET secp256k1 APPEND PROPERTY PUBLIC_HEADER ${PROJECT_SOURCE_DIR}/include/secp256k1_ellswift.h)
+endif()
+
+if(SECP256K1_ENABLE_MODULE_MUSIG)
+  if(DEFINED SECP256K1_ENABLE_MODULE_SCHNORRSIG AND NOT SECP256K1_ENABLE_MODULE_SCHNORRSIG)
+    message(FATAL_ERROR "Module dependency error: You have disabled the schnorrsig module explicitly, but it is required by the musig module.")
+  endif()
+  set(SECP256K1_ENABLE_MODULE_SCHNORRSIG ON)
+  add_compile_definitions(ENABLE_MODULE_MUSIG=1)
+  set_property(TARGET secp256k1 APPEND PROPERTY PUBLIC_HEADER ${PROJECT_SOURCE_DIR}/include/secp256k1_musig.h)
+endif()
+
+if(SECP256K1_ENABLE_MODULE_SCHNORRSIG)
+  if(DEFINED SECP256K1_ENABLE_MODULE_EXTRAKEYS AND NOT SECP256K1_ENABLE_MODULE_EXTRAKEYS)
+    message(FATAL_ERROR "Module dependency error: You have disabled the extrakeys module explicitly, but it is required by the schnorrsig module.")
+  endif()
+  set(SECP256K1_ENABLE_MODULE_EXTRAKEYS ON)
+  add_compile_definitions(ENABLE_MODULE_SCHNORRSIG=1)
+  set_property(TARGET secp256k1 APPEND PROPERTY PUBLIC_HEADER ${PROJECT_SOURCE_DIR}/include/secp256k1_schnorrsig.h)
+endif()
+
+if(SECP256K1_ENABLE_MODULE_EXTRAKEYS)
+  add_compile_definitions(ENABLE_MODULE_EXTRAKEYS=1)
+  set_property(TARGET secp256k1 APPEND PROPERTY PUBLIC_HEADER ${PROJECT_SOURCE_DIR}/include/secp256k1_extrakeys.h)
+endif()
+
+if(SECP256K1_ENABLE_MODULE_RECOVERY)
+  add_compile_definitions(ENABLE_MODULE_RECOVERY=1)
+  set_property(TARGET secp256k1 APPEND PROPERTY PUBLIC_HEADER ${PROJECT_SOURCE_DIR}/include/secp256k1_recovery.h)
+endif()
+
+if(SECP256K1_ENABLE_MODULE_ECDH)
+  add_compile_definitions(ENABLE_MODULE_ECDH=1)
+  set_property(TARGET secp256k1 APPEND PROPERTY PUBLIC_HEADER ${PROJECT_SOURCE_DIR}/include/secp256k1_ecdh.h)
+endif()
+
+add_library(secp256k1_precomputed OBJECT EXCLUDE_FROM_ALL
+  precomputed_ecmult.c
+  precomputed_ecmult_gen.c
+)
+
+# Add objects explicitly rather than linking to the object libs to keep them
+# from being exported.
+target_sources(secp256k1 PRIVATE secp256k1.c $<TARGET_OBJECTS:secp256k1_precomputed>)
+
+if(NOT SECP256K1_ENABLE_API_VISIBILITY_ATTRIBUTES)
+  target_compile_definitions(secp256k1 PRIVATE SECP256K1_NO_API_VISIBILITY_ATTRIBUTES)
+endif()
+
+# Create a helper lib that parent projects can use to link secp256k1 into a
+# static lib.
+add_library(secp256k1_objs INTERFACE)
+target_sources(secp256k1_objs INTERFACE $<TARGET_OBJECTS:secp256k1> $<TARGET_OBJECTS:secp256k1_precomputed>)
+
+add_library(secp256k1_asm INTERFACE)
+if(SECP256K1_ASM STREQUAL "arm32")
+  add_library(secp256k1_asm_arm OBJECT EXCLUDE_FROM_ALL)
+  target_sources(secp256k1_asm_arm PUBLIC
+    asm/field_10x26_arm.s
+  )
+  target_sources(secp256k1 PRIVATE $<TARGET_OBJECTS:secp256k1_asm_arm>)
+  target_sources(secp256k1_objs INTERFACE $<TARGET_OBJECTS:secp256k1_asm_arm>)
+  target_link_libraries(secp256k1_asm INTERFACE secp256k1_asm_arm)
+endif()
+
+if(WIN32)
+  # Define our export symbol only for shared libs.
+  set_target_properties(secp256k1 PROPERTIES DEFINE_SYMBOL SECP256K1_DLL_EXPORT)
+  target_compile_definitions(secp256k1 INTERFACE $<$<NOT:$<BOOL:${BUILD_SHARED_LIBS}>>:SECP256K1_STATIC>)
+endif()
+
+# Object libs don't know if they're being built for a shared or static lib.
+# Grab the PIC property from secp256k1 which knows.
+get_target_property(use_pic secp256k1 POSITION_INDEPENDENT_CODE)
+set_target_properties(secp256k1_precomputed PROPERTIES POSITION_INDEPENDENT_CODE ${use_pic})
+
+# Add the include path for parent projects so that they don't have to manually add it.
+target_include_directories(secp256k1 INTERFACE
+  $<BUILD_INTERFACE:$<$<NOT:$<BOOL:${PROJECT_IS_TOP_LEVEL}>>:${PROJECT_SOURCE_DIR}/include>>
+)
+set_target_properties(secp256k1_objs PROPERTIES
+  INTERFACE_COMPILE_DEFINITIONS "$<TARGET_PROPERTY:secp256k1,INTERFACE_COMPILE_DEFINITIONS>"
+  INTERFACE_INCLUDE_DIRECTORIES "$<TARGET_PROPERTY:secp256k1,INTERFACE_INCLUDE_DIRECTORIES>"
+)
+
+# This emulates Libtool to make sure Libtool and CMake agree on the ABI version,
+# see below "Calculate the version variables" in autotools-aux/ltmain.sh.
+math(EXPR ${PROJECT_NAME}_soversion "${${PROJECT_NAME}_LIB_VERSION_CURRENT} - ${${PROJECT_NAME}_LIB_VERSION_AGE}")
+set_target_properties(secp256k1 PROPERTIES
+  SOVERSION ${${PROJECT_NAME}_soversion}
+)
+if(CMAKE_SYSTEM_NAME MATCHES "^(Linux|FreeBSD)$")
+  set_target_properties(secp256k1 PROPERTIES
+    VERSION ${${PROJECT_NAME}_soversion}.${${PROJECT_NAME}_LIB_VERSION_AGE}.${${PROJECT_NAME}_LIB_VERSION_REVISION}
+  )
+elseif(APPLE)
+  math(EXPR ${PROJECT_NAME}_compatibility_version "${${PROJECT_NAME}_LIB_VERSION_CURRENT} + 1")
+  set_target_properties(secp256k1 PROPERTIES
+    MACHO_COMPATIBILITY_VERSION ${${PROJECT_NAME}_compatibility_version}
+    MACHO_CURRENT_VERSION ${${PROJECT_NAME}_compatibility_version}.${${PROJECT_NAME}_LIB_VERSION_REVISION}
+  )
+  unset(${PROJECT_NAME}_compatibility_version)
+elseif(CMAKE_SYSTEM_NAME STREQUAL "Windows")
+  set(${PROJECT_NAME}_windows "secp256k1")
+  if(MSVC)
+    set(${PROJECT_NAME}_windows "${PROJECT_NAME}")
+  endif()
+  set_target_properties(secp256k1 PROPERTIES
+    ARCHIVE_OUTPUT_NAME "${${PROJECT_NAME}_windows}"
+    RUNTIME_OUTPUT_NAME "${${PROJECT_NAME}_windows}-${${PROJECT_NAME}_soversion}"
+  )
+  unset(${PROJECT_NAME}_windows)
+endif()
+unset(${PROJECT_NAME}_soversion)
+
+if(SECP256K1_BUILD_BENCHMARK)
+  add_executable(bench bench.c)
+  target_link_libraries(bench secp256k1)
+  add_executable(bench_internal bench_internal.c)
+  target_link_libraries(bench_internal secp256k1_precomputed secp256k1_asm)
+  add_executable(bench_ecmult bench_ecmult.c)
+  target_link_libraries(bench_ecmult secp256k1_precomputed secp256k1_asm)
+endif()
+
+if(SECP256K1_BUILD_TESTS)
+  include(CheckIncludeFile)
+  check_include_file(sys/types.h HAVE_SYS_TYPES_H)
+  check_include_file(sys/wait.h HAVE_SYS_WAIT_H)
+  check_include_file(unistd.h HAVE_UNISTD_H)
+
+  set(TEST_DEFINITIONS "")
+  if(HAVE_SYS_TYPES_H AND HAVE_SYS_WAIT_H AND HAVE_UNISTD_H)
+    list(APPEND TEST_DEFINITIONS SUPPORTS_CONCURRENCY=1)
+  endif()
+
+  function(add_executable_and_tests exe_name verify_definition)
+    add_executable(${exe_name} tests.c)
+    target_link_libraries(${exe_name} secp256k1_precomputed secp256k1_asm)
+    target_compile_definitions(${exe_name} PRIVATE ${verify_definition} ${TEST_DEFINITIONS})
+    include(DiscoverTests)
+    discover_tests(${exe_name}
+      DISCOVERY_ARGS        "--list_tests"
+      DISCOVERY_MATCH       "^\\t\\\\[ *[0-9]+\\\\] ([^ ].*)$"
+      TEST_NAME_REPLACEMENT "secp256k1.${exe_name}.\\\\1"
+      TEST_ARGS_REPLACEMENT "--target=\\\\1 --log=1"
+      PROPERTIES
+        LABELS "secp256k1_${exe_name}"
+    )
+  endfunction()
+
+  add_executable_and_tests(noverify_tests "")
+  if(NOT CMAKE_BUILD_TYPE STREQUAL "Coverage")
+    add_executable_and_tests(tests VERIFY)
+  endif()
+  unset(TEST_DEFINITIONS)
+endif()
+
+if(SECP256K1_BUILD_EXHAUSTIVE_TESTS)
+  # Note: do not include secp256k1_precomputed in exhaustive_tests (it uses runtime-generated tables).
+  add_executable(exhaustive_tests tests_exhaustive.c)
+  target_link_libraries(exhaustive_tests secp256k1_asm)
+  target_compile_definitions(exhaustive_tests PRIVATE $<$<NOT:$<CONFIG:Coverage>>:VERIFY>)
+  add_test(NAME secp256k1.exhaustive_tests COMMAND exhaustive_tests)
+  set_tests_properties(secp256k1.exhaustive_tests PROPERTIES
+    LABELS secp256k1_exhaustive
+  )
+endif()
+
+if(SECP256K1_BUILD_CTIME_TESTS)
+  add_executable(ctime_tests ctime_tests.c)
+  target_link_libraries(ctime_tests secp256k1)
+endif()
+
+if(SECP256K1_INSTALL)
+  include(GNUInstallDirs)
+  target_include_directories(secp256k1 INTERFACE
+    $<INSTALL_INTERFACE:${CMAKE_INSTALL_INCLUDEDIR}>
+  )
+  install(TARGETS secp256k1
+    EXPORT ${PROJECT_NAME}-targets
+    RUNTIME DESTINATION ${CMAKE_INSTALL_BINDIR}
+    LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR}
+    ARCHIVE DESTINATION ${CMAKE_INSTALL_LIBDIR}
+    PUBLIC_HEADER DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}
+  )
+
+  install(EXPORT ${PROJECT_NAME}-targets
+    FILE ${PROJECT_NAME}-targets.cmake
+    NAMESPACE ${PROJECT_NAME}::
+    DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
+  )
+
+  include(CMakePackageConfigHelpers)
+  configure_package_config_file(
+    ${PROJECT_SOURCE_DIR}/cmake/config.cmake.in
+    ${PROJECT_NAME}-config.cmake
+    INSTALL_DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
+    NO_SET_AND_CHECK_MACRO
+  )
+  write_basic_package_version_file(${PROJECT_NAME}-config-version.cmake
+    COMPATIBILITY SameMinorVersion
+  )
+
+  install(
+    FILES
+      ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config.cmake
+      ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}-config-version.cmake
+    DESTINATION ${CMAKE_INSTALL_LIBDIR}/cmake/${PROJECT_NAME}
+  )
+
+  include(GeneratePkgConfigFile)
+  generate_pkg_config_file(${PROJECT_SOURCE_DIR}/libsecp256k1.pc.in)
+  install(
+    FILES
+      ${CMAKE_CURRENT_BINARY_DIR}/${PROJECT_NAME}.pc
+    DESTINATION ${CMAKE_INSTALL_LIBDIR}/pkgconfig
+  )
+endif()

firmware/kb2040_hidden_signer/src/secp256k1/src/asm/field_10x26_arm.s

@@ -0,0 +1,916 @@
+@ vim: set tabstop=8 softtabstop=8 shiftwidth=8 noexpandtab syntax=armasm:
+/***********************************************************************
+ * Copyright (c) 2014 Wladimir J. van der Laan                         *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+/*
+ARM implementation of field_10x26 inner loops.
+
+Note:
+
+- To avoid unnecessary loads and make use of available registers, two
+  'passes' have every time been interleaved, with the odd passes accumulating c' and d' 
+  which will be added to c and d respectively in the even passes
+
+*/
+
+	.syntax unified
+	@ eabi attributes - see readelf -A
+	.eabi_attribute 24, 1 @ Tag_ABI_align_needed = 8-byte
+	.eabi_attribute 25, 1 @ Tag_ABI_align_preserved = 8-byte, except leaf SP
+	.text
+
+	@ Field constants
+	.set field_R0, 0x3d10
+	.set field_R1, 0x400
+	.set field_not_M, 0xfc000000	@ ~M = ~0x3ffffff
+
+	.align	2
+	.global secp256k1_fe_mul_inner
+	.type	secp256k1_fe_mul_inner, %function
+	.hidden secp256k1_fe_mul_inner
+	@ Arguments:
+	@  r0  r      Restrict: can overlap with a, not with b
+	@  r1  a
+	@  r2  b
+	@ Stack (total 4+10*4 = 44)
+	@  sp + #0        saved 'r' pointer
+	@  sp + #4 + 4*X  t0,t1,t2,t3,t4,t5,t6,t7,u8,t9
+secp256k1_fe_mul_inner:
+	stmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14}
+	sub	sp, sp, #48			@ frame=44 + alignment
+	str     r0, [sp, #0]			@ save result address, we need it only at the end
+
+	/******************************************
+	 * Main computation code.
+	 ******************************************
+
+	Allocation:
+	    r0,r14,r7,r8   scratch
+	    r1       a (pointer)
+	    r2       b (pointer)
+	    r3:r4    c
+	    r5:r6    d
+	    r11:r12  c'
+	    r9:r10   d'
+
+	Note: do not write to r[] here, it may overlap with a[]
+	*/
+
+	/* A - interleaved with B */
+	ldr	r7, [r1, #0*4]			@ a[0]
+	ldr	r8, [r2, #9*4]			@ b[9]
+	ldr	r0, [r1, #1*4]			@ a[1]
+	umull	r5, r6, r7, r8			@ d = a[0] * b[9]
+	ldr	r14, [r2, #8*4]			@ b[8]
+	umull	r9, r10, r0, r8			@ d' = a[1] * b[9]
+	ldr	r7, [r1, #2*4]			@ a[2]
+	umlal	r5, r6, r0, r14			@ d += a[1] * b[8]
+	ldr	r8, [r2, #7*4] 			@ b[7]
+	umlal	r9, r10, r7, r14		@ d' += a[2] * b[8]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal	r5, r6, r7, r8   		@ d += a[2] * b[7]
+	ldr	r14, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r8  		@ d' += a[3] * b[7]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal	r5, r6, r0, r14   		@ d += a[3] * b[6]
+	ldr	r8, [r2, #5*4]   		@ b[5]
+	umlal	r9, r10, r7, r14  		@ d' += a[4] * b[6]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal	r5, r6, r7, r8   		@ d += a[4] * b[5]
+	ldr	r14, [r2, #4*4]   		@ b[4]
+	umlal	r9, r10, r0, r8  		@ d' += a[5] * b[5]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r5, r6, r0, r14   		@ d += a[5] * b[4]
+	ldr	r8, [r2, #3*4]   		@ b[3]
+	umlal	r9, r10, r7, r14  		@ d' += a[6] * b[4]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r8   		@ d += a[6] * b[3]
+	ldr	r14, [r2, #2*4]   		@ b[2]
+	umlal	r9, r10, r0, r8  		@ d' += a[7] * b[3]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r14   		@ d += a[7] * b[2]
+	ldr	r8, [r2, #1*4]   		@ b[1]
+	umlal	r9, r10, r7, r14  		@ d' += a[8] * b[2]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r8   		@ d += a[8] * b[1]
+	ldr	r14, [r2, #0*4]   		@ b[0]
+	umlal	r9, r10, r0, r8  		@ d' += a[9] * b[1]
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	umlal	r5, r6, r0, r14   		@ d += a[9] * b[0]
+	@ r7,r14 used in B
+
+	bic	r0, r5, field_not_M 		@ t9 = d & M
+	str     r0, [sp, #4 + 4*9]
+	mov	r5, r5, lsr #26     		@ d >>= 26 
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+
+	/* B */
+	umull	r3, r4, r7, r14   		@ c = a[0] * b[0]
+	adds	r5, r5, r9       		@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u0 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u0 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t0 = c & M
+	str	r14, [sp, #4 + 0*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u0 * R1
+	umlal   r3, r4, r0, r14
+
+	/* C - interleaved with D */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[2]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[1]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[0]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal	r5, r6, r7, r14   		@ d += a[2] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14   		@ d' = a[3] * b[9]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal	r5, r6, r0, r8   		@ d += a[3] * b[8]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[4] * b[8]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal	r5, r6, r7, r14   		@ d += a[4] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r14   		@ d' += a[5] * b[7]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r5, r6, r0, r8   		@ d += a[5] * b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umlal	r9, r10, r7, r8   		@ d' += a[6] * b[6]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r14   		@ d += a[6] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal	r9, r10, r0, r14   		@ d' += a[7] * b[5]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r8   		@ d += a[7] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[4]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal	r9, r10, r0, r14   		@ d' += a[9] * b[3]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[2]
+
+	bic	r0, r5, field_not_M 		@ u1 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u1 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t1 = c & M
+	str	r14, [sp, #4 + 1*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u1 * R1
+	umlal   r3, r4, r0, r14
+
+	/* D */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u2 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u2 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t2 = c & M
+	str	r14, [sp, #4 + 2*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u2 * R1
+	umlal   r3, r4, r0, r14
+
+	/* E - interleaved with F */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[4]
+	ldr	r8, [r2, #3*4]   		@ b[3]
+	umlal   r3, r4, r7, r8   		@ c += a[0] * b[3]
+	ldr	r7, [r1, #1*4]   		@ a[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[1] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r3, r4, r7, r8   		@ c += a[1] * b[2]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[2]
+	ldr	r8, [r2, #1*4]   		@ b[1]
+	umlal   r3, r4, r7, r8   		@ c += a[2] * b[1]
+	ldr	r7, [r1, #3*4]   		@ a[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[3] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r3, r4, r7, r8   		@ c += a[3] * b[0]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[0]
+	ldr	r8, [r2, #9*4]   		@ b[9]
+	umlal	r5, r6, r7, r8   		@ d += a[4] * b[9]
+	ldr	r7, [r1, #5*4]   		@ a[5]
+	umull	r9, r10, r7, r8   		@ d' = a[5] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umlal	r5, r6, r7, r8   		@ d += a[5] * b[8]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal	r9, r10, r7, r8   		@ d' += a[6] * b[8]
+	ldr	r8, [r2, #7*4]   		@ b[7]
+	umlal	r5, r6, r7, r8   		@ d += a[6] * b[7]
+	ldr	r7, [r1, #7*4]   		@ a[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[7] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r5, r6, r7, r8   		@ d += a[7] * b[6]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[6]
+	ldr	r8, [r2, #5*4]   		@ b[5]
+	umlal	r5, r6, r7, r8   		@ d += a[8] * b[5]
+	ldr	r7, [r1, #9*4]   		@ a[9]
+	umlal	r9, r10, r7, r8   		@ d' += a[9] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal	r5, r6, r7, r8   		@ d += a[9] * b[4]
+
+	bic	r0, r5, field_not_M 		@ u3 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u3 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t3 = c & M
+	str	r14, [sp, #4 + 3*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u3 * R1
+	umlal   r3, r4, r0, r14
+
+	/* F */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u4 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u4 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t4 = c & M
+	str	r14, [sp, #4 + 4*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u4 * R1
+	umlal   r3, r4, r0, r14
+
+	/* G - interleaved with H */
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umull	r11, r12, r7, r8   		@ c' = a[0] * b[6]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[5]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[4]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal   r3, r4, r7, r14   		@ c += a[2] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r11, r12, r0, r14   		@ c' += a[3] * b[3]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r3, r4, r0, r8   		@ c += a[3] * b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[2]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal   r3, r4, r7, r14   		@ c += a[4] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[5] * b[1]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal   r3, r4, r0, r8   		@ c += a[5] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[6] * b[0]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal	r5, r6, r7, r14   		@ d += a[6] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14   		@ d' = a[7] * b[9]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal	r5, r6, r0, r8   		@ d += a[7] * b[8]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umlal	r9, r10, r7, r8   		@ d' += a[8] * b[8]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal	r9, r10, r0, r14   		@ d' += a[9] * b[7]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[6]
+
+	bic	r0, r5, field_not_M 		@ u5 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u5 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t5 = c & M
+	str	r14, [sp, #4 + 5*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u5 * R1
+	umlal   r3, r4, r0, r14
+
+	/* H */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u6 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u6 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t6 = c & M
+	str	r14, [sp, #4 + 6*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u6 * R1
+	umlal   r3, r4, r0, r14
+
+	/* I - interleaved with J */
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	ldr	r7, [r1, #0*4]   		@ a[0]
+	ldr	r14, [r2, #7*4]   		@ b[7]
+	umull   r11, r12, r7, r8   		@ c' = a[0] * b[8]
+	ldr	r0, [r1, #1*4]   		@ a[1]
+	umlal   r3, r4, r7, r14   		@ c += a[0] * b[7]
+	ldr	r8, [r2, #6*4]   		@ b[6]
+	umlal   r11, r12, r0, r14   		@ c' += a[1] * b[7]
+	ldr	r7, [r1, #2*4]   		@ a[2]
+	umlal   r3, r4, r0, r8   		@ c += a[1] * b[6]
+	ldr	r14, [r2, #5*4]   		@ b[5]
+	umlal   r11, r12, r7, r8   		@ c' += a[2] * b[6]
+	ldr	r0, [r1, #3*4]   		@ a[3]
+	umlal   r3, r4, r7, r14   		@ c += a[2] * b[5]
+	ldr	r8, [r2, #4*4]   		@ b[4]
+	umlal   r11, r12, r0, r14   		@ c' += a[3] * b[5]
+	ldr	r7, [r1, #4*4]   		@ a[4]
+	umlal   r3, r4, r0, r8   		@ c += a[3] * b[4]
+	ldr	r14, [r2, #3*4]   		@ b[3]
+	umlal   r11, r12, r7, r8   		@ c' += a[4] * b[4]
+	ldr	r0, [r1, #5*4]   		@ a[5]
+	umlal   r3, r4, r7, r14   		@ c += a[4] * b[3]
+	ldr	r8, [r2, #2*4]   		@ b[2]
+	umlal   r11, r12, r0, r14   		@ c' += a[5] * b[3]
+	ldr	r7, [r1, #6*4]   		@ a[6]
+	umlal   r3, r4, r0, r8   		@ c += a[5] * b[2]
+	ldr	r14, [r2, #1*4]   		@ b[1]
+	umlal   r11, r12, r7, r8   		@ c' += a[6] * b[2]
+	ldr	r0, [r1, #7*4]   		@ a[7]
+	umlal   r3, r4, r7, r14   		@ c += a[6] * b[1]
+	ldr	r8, [r2, #0*4]   		@ b[0]
+	umlal   r11, r12, r0, r14   		@ c' += a[7] * b[1]
+	ldr	r7, [r1, #8*4]   		@ a[8]
+	umlal   r3, r4, r0, r8   		@ c += a[7] * b[0]
+	ldr	r14, [r2, #9*4]   		@ b[9]
+	umlal   r11, r12, r7, r8   		@ c' += a[8] * b[0]
+	ldr	r0, [r1, #9*4]   		@ a[9]
+	umlal	r5, r6, r7, r14   		@ d += a[8] * b[9]
+	ldr	r8, [r2, #8*4]   		@ b[8]
+	umull	r9, r10, r0, r14  		@ d' = a[9] * b[9]
+	umlal	r5, r6, r0, r8   		@ d += a[9] * b[8]
+
+	bic	r0, r5, field_not_M 		@ u7 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u7 * R0
+	umlal   r3, r4, r0, r14
+
+	bic	r14, r3, field_not_M 		@ t7 = c & M
+	str	r14, [sp, #4 + 7*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u7 * R1
+	umlal   r3, r4, r0, r14
+
+	/* J */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u8 = d & M
+	str	r0, [sp, #4 + 8*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u8 * R0
+	umlal   r3, r4, r0, r14
+
+	/******************************************
+	 * compute and write back result
+	 ******************************************
+	Allocation:
+	    r0    r
+	    r3:r4 c
+	    r5:r6 d
+	    r7    t0
+	    r8    t1
+	    r9    t2
+	    r11   u8
+	    r12   t9
+	    r1,r2,r10,r14 scratch
+
+	Note: do not read from a[] after here, it may overlap with r[]
+	*/
+	ldr	r0, [sp, #0]
+	add	r1, sp, #4 + 3*4		@ r[3..7] = t3..7, r11=u8, r12=t9
+	ldmia	r1, {r2,r7,r8,r9,r10,r11,r12}
+	add	r1, r0, #3*4
+	stmia	r1, {r2,r7,r8,r9,r10}
+
+	bic	r2, r3, field_not_M 		@ r[8] = c & M
+	str	r2, [r0, #8*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u8 * R1
+	umlal   r3, r4, r11, r14
+	movw    r14, field_R0			@ c += d * R0
+	umlal   r3, r4, r5, r14
+	adds	r3, r3, r12			@ c += t9
+	adc	r4, r4, #0
+
+	add	r1, sp, #4 + 0*4		@ r7,r8,r9 = t0,t1,t2
+	ldmia	r1, {r7,r8,r9}
+
+	ubfx	r2, r3, #0, #22     		@ r[9] = c & (M >> 4)
+	str	r2, [r0, #9*4]
+	mov	r3, r3, lsr #22     		@ c >>= 22
+	orr	r3, r3, r4, asl #10
+	mov     r4, r4, lsr #22
+	movw    r14, field_R1 << 4   		@ c += d * (R1 << 4)
+	umlal   r3, r4, r5, r14
+
+	movw    r14, field_R0 >> 4   		@ d = c * (R0 >> 4) + t0 (64x64 multiply+add)
+	umull	r5, r6, r3, r14			@ d = c.lo * (R0 >> 4)
+	adds	r5, r5, r7	    		@ d.lo += t0
+	mla	r6, r14, r4, r6			@ d.hi += c.hi * (R0 >> 4)
+	adc	r6, r6, 0	     		@ d.hi += carry
+
+	bic	r2, r5, field_not_M 		@ r[0] = d & M
+	str	r2, [r0, #0*4]
+
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	
+	movw    r14, field_R1 >> 4   		@ d += c * (R1 >> 4) + t1 (64x64 multiply+add)
+	umull	r1, r2, r3, r14       		@ tmp = c.lo * (R1 >> 4)
+	adds	r5, r5, r8	    		@ d.lo += t1
+	adc	r6, r6, #0	    		@ d.hi += carry
+	adds	r5, r5, r1	    		@ d.lo += tmp.lo
+	mla	r2, r14, r4, r2      		@ tmp.hi += c.hi * (R1 >> 4)
+	adc	r6, r6, r2	   		@ d.hi += carry + tmp.hi
+
+	bic	r2, r5, field_not_M 		@ r[1] = d & M
+	str	r2, [r0, #1*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 (ignore hi)
+	orr	r5, r5, r6, asl #6
+
+	add	r5, r5, r9	  		@ d += t2
+	str	r5, [r0, #2*4]      		@ r[2] = d
+
+	add	sp, sp, #48
+	ldmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc}
+	.size	secp256k1_fe_mul_inner, .-secp256k1_fe_mul_inner
+
+	.align	2
+	.global secp256k1_fe_sqr_inner
+	.type	secp256k1_fe_sqr_inner, %function
+	.hidden secp256k1_fe_sqr_inner
+	@ Arguments:
+	@  r0  r	 Can overlap with a
+	@  r1  a
+	@ Stack (total 4+10*4 = 44)
+	@  sp + #0        saved 'r' pointer
+	@  sp + #4 + 4*X  t0,t1,t2,t3,t4,t5,t6,t7,u8,t9
+secp256k1_fe_sqr_inner:
+	stmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, r14}
+	sub	sp, sp, #48			@ frame=44 + alignment
+	str     r0, [sp, #0]			@ save result address, we need it only at the end
+	/******************************************
+	 * Main computation code.
+	 ******************************************
+
+	Allocation:
+	    r0,r14,r2,r7,r8   scratch
+	    r1       a (pointer)
+	    r3:r4    c
+	    r5:r6    d
+	    r11:r12  c'
+	    r9:r10   d'
+
+	Note: do not write to r[] here, it may overlap with a[]
+	*/
+	/* A interleaved with B */
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	ldr	r7, [r1, #0*4]			@ a[0]
+	mov	r0, r0, asl #1
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umull	r3, r4, r7, r7			@ c = a[0] * a[0]
+	ldr	r8, [r1, #8*4]			@ a[8]
+	mov	r7, r7, asl #1
+	umull	r5, r6, r7, r14			@ d = a[0]*2 * a[9]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umull	r9, r10, r0, r14		@ d' = a[1]*2 * a[9]
+	ldr	r14, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r8			@ d += a[1]*2 * a[8]
+	mov	r7, r7, asl #1
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	umlal	r9, r10, r7, r8			@ d' += a[2]*2 * a[8]
+	ldr	r8, [r1, #6*4]			@ a[6]
+	umlal	r5, r6, r7, r14			@ d += a[2]*2 * a[7]
+	mov	r0, r0, asl #1
+	ldr	r7, [r1, #4*4]			@ a[4]*2
+	umlal	r9, r10, r0, r14		@ d' += a[3]*2 * a[7]
+	ldr	r14, [r1, #5*4]			@ a[5]
+	mov	r7, r7, asl #1
+	umlal	r5, r6, r0, r8			@ d += a[3]*2 * a[6]
+	umlal	r9, r10, r7, r8			@ d' += a[4]*2 * a[6]
+	umlal	r5, r6, r7, r14			@ d += a[4]*2 * a[5]
+	umlal	r9, r10, r14, r14		@ d' += a[5] * a[5]
+
+	bic	r0, r5, field_not_M 		@ t9 = d & M
+	str     r0, [sp, #4 + 9*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+
+	/* B */
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u0 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u0 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t0 = c & M
+	str	r14, [sp, #4 + 0*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u0 * R1
+	umlal   r3, r4, r0, r14
+
+	/* C interleaved with D */
+	ldr	r0, [r1, #0*4]			@ a[0]*2
+	ldr	r14, [r1, #1*4]			@ a[1]
+	mov	r0, r0, asl #1
+	ldr	r8, [r1, #2*4]			@ a[2]
+	umlal	r3, r4, r0, r14			@ c += a[0]*2 * a[1]
+	mov	r7, r8, asl #1                  @ a[2]*2
+	umull	r11, r12, r14, r14		@ c' = a[1] * a[1]
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umlal	r11, r12, r0, r8		@ c' += a[0]*2 * a[2]
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	ldr	r8, [r1, #8*4]			@ a[8]
+	umlal	r5, r6, r7, r14			@ d += a[2]*2 * a[9]
+	mov	r0, r0, asl #1
+	ldr	r7, [r1, #4*4]			@ a[4]*2
+	umull	r9, r10, r0, r14		@ d' = a[3]*2 * a[9]
+	ldr	r14, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r8			@ d += a[3]*2 * a[8]
+	mov	r7, r7, asl #1
+	ldr	r0, [r1, #5*4]			@ a[5]*2
+	umlal	r9, r10, r7, r8			@ d' += a[4]*2 * a[8]
+	ldr	r8, [r1, #6*4]			@ a[6]
+	mov	r0, r0, asl #1
+	umlal	r5, r6, r7, r14			@ d += a[4]*2 * a[7]
+	umlal	r9, r10, r0, r14		@ d' += a[5]*2 * a[7]
+	umlal	r5, r6, r0, r8			@ d += a[5]*2 * a[6]
+	umlal	r9, r10, r8, r8			@ d' += a[6] * a[6]
+
+	bic	r0, r5, field_not_M 		@ u1 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u1 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t1 = c & M
+	str	r14, [sp, #4 + 1*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u1 * R1
+	umlal   r3, r4, r0, r14
+
+	/* D */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u2 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u2 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t2 = c & M
+	str	r14, [sp, #4 + 2*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u2 * R1
+	umlal   r3, r4, r0, r14
+
+	/* E interleaved with F */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	ldr	r14, [r1, #2*4]			@ a[2]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #3*4]			@ a[3]
+	ldr	r2, [r1, #4*4]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[3]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[4]
+	mov	r2, r2, asl #1			@ a[4]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[3]
+	ldr	r8, [r1, #9*4]			@ a[9]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[2]
+	ldr	r0, [r1, #5*4]			@ a[5]*2
+	umlal	r11, r12, r14, r14		@ c' += a[2] * a[2]
+	ldr	r14, [r1, #8*4]			@ a[8]
+	mov	r0, r0, asl #1
+	umlal	r5, r6, r2, r8			@ d += a[4]*2 * a[9]
+	ldr	r7, [r1, #6*4]			@ a[6]*2
+	umull	r9, r10, r0, r8			@ d' = a[5]*2 * a[9]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #7*4]			@ a[7]
+	umlal	r5, r6, r0, r14			@ d += a[5]*2 * a[8]
+	umlal	r9, r10, r7, r14		@ d' += a[6]*2 * a[8]
+	umlal	r5, r6, r7, r8			@ d += a[6]*2 * a[7]
+	umlal	r9, r10, r8, r8			@ d' += a[7] * a[7]
+
+	bic	r0, r5, field_not_M 		@ u3 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u3 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t3 = c & M
+	str	r14, [sp, #4 + 3*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u3 * R1
+	umlal   r3, r4, r0, r14
+
+	/* F */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u4 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u4 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t4 = c & M
+	str	r14, [sp, #4 + 4*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u4 * R1
+	umlal   r3, r4, r0, r14
+
+	/* G interleaved with H */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #5*4]			@ a[5]
+	ldr	r2, [r1, #6*4]			@ a[6]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[5]
+	ldr	r14, [r1, #4*4]			@ a[4]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[6]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[5]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #3*4]			@ a[3]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[4]
+	mov	r0, r2, asl #1			@ a[6]*2
+	umlal	r11, r12, r7, r14		@ c' += a[2]*2 * a[4]
+	ldr	r14, [r1, #9*4]			@ a[9]
+	umlal	r3, r4, r7, r8			@ c += a[2]*2 * a[3]
+	ldr	r7, [r1, #7*4]			@ a[7]*2
+	umlal	r11, r12, r8, r8		@ c' += a[3] * a[3]
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #8*4]			@ a[8]
+	umlal	r5, r6, r0, r14			@ d += a[6]*2 * a[9]
+	umull	r9, r10, r7, r14		@ d' = a[7]*2 * a[9]
+	umlal	r5, r6, r7, r8			@ d += a[7]*2 * a[8]
+	umlal	r9, r10, r8, r8			@ d' += a[8] * a[8]
+
+	bic	r0, r5, field_not_M 		@ u5 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u5 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t5 = c & M
+	str	r14, [sp, #4 + 5*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u5 * R1
+	umlal   r3, r4, r0, r14
+
+	/* H */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	adds	r5, r5, r9			@ d += d'
+	adc	r6, r6, r10
+
+	bic	r0, r5, field_not_M 		@ u6 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u6 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t6 = c & M
+	str	r14, [sp, #4 + 6*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u6 * R1
+	umlal   r3, r4, r0, r14
+
+	/* I interleaved with J */
+	ldr	r7, [r1, #0*4]			@ a[0]*2
+	ldr	r0, [r1, #1*4]			@ a[1]*2
+	mov	r7, r7, asl #1
+	ldr	r8, [r1, #7*4]			@ a[7]
+	ldr	r2, [r1, #8*4]			@ a[8]
+	umlal	r3, r4, r7, r8			@ c += a[0]*2 * a[7]
+	ldr	r14, [r1, #6*4]			@ a[6]
+	mov	r0, r0, asl #1
+	umull	r11, r12, r7, r2		@ c' = a[0]*2 * a[8]
+	ldr	r7, [r1, #2*4]			@ a[2]*2
+	umlal	r11, r12, r0, r8		@ c' += a[1]*2 * a[7]
+	ldr	r8, [r1, #5*4]			@ a[5]
+	umlal	r3, r4, r0, r14			@ c += a[1]*2 * a[6]
+	ldr	r0, [r1, #3*4]			@ a[3]*2
+	mov	r7, r7, asl #1
+	umlal	r11, r12, r7, r14		@ c' += a[2]*2 * a[6]
+	ldr	r14, [r1, #4*4]			@ a[4]
+	mov	r0, r0, asl #1
+	umlal	r3, r4, r7, r8			@ c += a[2]*2 * a[5]
+	mov	r2, r2, asl #1			@ a[8]*2
+	umlal	r11, r12, r0, r8		@ c' += a[3]*2 * a[5]
+	umlal	r3, r4, r0, r14			@ c += a[3]*2 * a[4]
+	umlal	r11, r12, r14, r14		@ c' += a[4] * a[4]
+	ldr	r8, [r1, #9*4]			@ a[9]
+	umlal	r5, r6, r2, r8			@ d += a[8]*2 * a[9]
+	@ r8 will be used in J
+
+	bic	r0, r5, field_not_M 		@ u7 = d & M
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u7 * R0
+	umlal   r3, r4, r0, r14
+	bic	r14, r3, field_not_M 		@ t7 = c & M
+	str	r14, [sp, #4 + 7*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u7 * R1
+	umlal   r3, r4, r0, r14
+
+	/* J */
+	adds	r3, r3, r11			@ c += c'
+	adc	r4, r4, r12
+	umlal	r5, r6, r8, r8			@ d += a[9] * a[9]
+
+	bic	r0, r5, field_not_M 		@ u8 = d & M
+	str	r0, [sp, #4 + 8*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	movw    r14, field_R0			@ c += u8 * R0
+	umlal   r3, r4, r0, r14
+
+	/******************************************
+	 * compute and write back result
+	 ******************************************
+	Allocation:
+	    r0    r
+	    r3:r4 c
+	    r5:r6 d
+	    r7    t0
+	    r8    t1
+	    r9    t2
+	    r11   u8
+	    r12   t9
+	    r1,r2,r10,r14 scratch
+
+	Note: do not read from a[] after here, it may overlap with r[]
+	*/
+	ldr	r0, [sp, #0]
+	add	r1, sp, #4 + 3*4		@ r[3..7] = t3..7, r11=u8, r12=t9
+	ldmia	r1, {r2,r7,r8,r9,r10,r11,r12}
+	add	r1, r0, #3*4
+	stmia	r1, {r2,r7,r8,r9,r10}
+
+	bic	r2, r3, field_not_M 		@ r[8] = c & M
+	str	r2, [r0, #8*4]
+	mov	r3, r3, lsr #26     		@ c >>= 26
+	orr	r3, r3, r4, asl #6
+	mov     r4, r4, lsr #26
+	mov     r14, field_R1			@ c += u8 * R1
+	umlal   r3, r4, r11, r14
+	movw    r14, field_R0			@ c += d * R0
+	umlal   r3, r4, r5, r14
+	adds	r3, r3, r12			@ c += t9
+	adc	r4, r4, #0
+
+	add	r1, sp, #4 + 0*4		@ r7,r8,r9 = t0,t1,t2
+	ldmia	r1, {r7,r8,r9}
+
+	ubfx	r2, r3, #0, #22     		@ r[9] = c & (M >> 4)
+	str	r2, [r0, #9*4]
+	mov	r3, r3, lsr #22     		@ c >>= 22
+	orr	r3, r3, r4, asl #10
+	mov     r4, r4, lsr #22
+	movw    r14, field_R1 << 4   		@ c += d * (R1 << 4)
+	umlal   r3, r4, r5, r14
+
+	movw    r14, field_R0 >> 4   		@ d = c * (R0 >> 4) + t0 (64x64 multiply+add)
+	umull	r5, r6, r3, r14			@ d = c.lo * (R0 >> 4)
+	adds	r5, r5, r7	    		@ d.lo += t0
+	mla	r6, r14, r4, r6			@ d.hi += c.hi * (R0 >> 4)
+	adc	r6, r6, 0	     		@ d.hi += carry
+
+	bic	r2, r5, field_not_M 		@ r[0] = d & M
+	str	r2, [r0, #0*4]
+
+	mov	r5, r5, lsr #26     		@ d >>= 26
+	orr	r5, r5, r6, asl #6
+	mov     r6, r6, lsr #26
+	
+	movw    r14, field_R1 >> 4   		@ d += c * (R1 >> 4) + t1 (64x64 multiply+add)
+	umull	r1, r2, r3, r14       		@ tmp = c.lo * (R1 >> 4)
+	adds	r5, r5, r8	    		@ d.lo += t1
+	adc	r6, r6, #0	    		@ d.hi += carry
+	adds	r5, r5, r1	    		@ d.lo += tmp.lo
+	mla	r2, r14, r4, r2      		@ tmp.hi += c.hi * (R1 >> 4)
+	adc	r6, r6, r2	   		@ d.hi += carry + tmp.hi
+
+	bic	r2, r5, field_not_M 		@ r[1] = d & M
+	str	r2, [r0, #1*4]
+	mov	r5, r5, lsr #26     		@ d >>= 26 (ignore hi)
+	orr	r5, r5, r6, asl #6
+
+	add	r5, r5, r9	  		@ d += t2
+	str	r5, [r0, #2*4]      		@ r[2] = d
+
+	add	sp, sp, #48
+	ldmfd	sp!, {r4, r5, r6, r7, r8, r9, r10, r11, pc}
+	.size	secp256k1_fe_sqr_inner, .-secp256k1_fe_sqr_inner
+
+	.section .note.GNU-stack,"",%progbits

firmware/kb2040_hidden_signer/src/secp256k1/src/assumptions.h

@@ -0,0 +1,87 @@
+/***********************************************************************
+ * Copyright (c) 2020 Pieter Wuille                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ASSUMPTIONS_H
+#define SECP256K1_ASSUMPTIONS_H
+
+#include <limits.h>
+
+#include "util.h"
+#if defined(SECP256K1_INT128_NATIVE)
+#include "int128_native.h"
+#endif
+
+/* This library, like most software, relies on a number of compiler implementation defined (but not undefined)
+   behaviours. Although the behaviours we require are essentially universal we test them specifically here to
+   reduce the odds of experiencing an unwelcome surprise.
+*/
+
+#if defined(__has_attribute)
+# if __has_attribute(__unavailable__)
+__attribute__((__unavailable__("Don't call this function. It only exists because STATIC_ASSERT cannot be used outside a function.")))
+# endif
+#endif
+static void secp256k1_assumption_checker(void) {
+    /* Bytes are 8 bits. */
+    STATIC_ASSERT(CHAR_BIT == 8);
+
+    /* No integer promotion for uint32_t. This ensures that we can multiply uintXX_t values where XX >= 32
+       without signed overflow, which would be undefined behaviour. */
+    STATIC_ASSERT(UINT_MAX <= UINT32_MAX);
+
+    /* Conversions from unsigned to signed outside of the bounds of the signed type are
+       implementation-defined. Verify that they function as reinterpreting the lower
+       bits of the input in two's complement notation. Do this for conversions:
+       - from uint(N)_t to int(N)_t with negative result
+       - from uint(2N)_t to int(N)_t with negative result
+       - from int(2N)_t to int(N)_t with negative result
+       - from int(2N)_t to int(N)_t with positive result */
+
+    /* To int8_t. */
+    STATIC_ASSERT(((int8_t)(uint8_t)0xAB == (int8_t)-(int8_t)0x55));
+    STATIC_ASSERT((int8_t)(uint16_t)0xABCD == (int8_t)-(int8_t)0x33);
+    STATIC_ASSERT((int8_t)(int16_t)(uint16_t)0xCDEF == (int8_t)(uint8_t)0xEF);
+    STATIC_ASSERT((int8_t)(int16_t)(uint16_t)0x9234 == (int8_t)(uint8_t)0x34);
+
+    /* To int16_t. */
+    STATIC_ASSERT((int16_t)(uint16_t)0xBCDE == (int16_t)-(int16_t)0x4322);
+    STATIC_ASSERT((int16_t)(uint32_t)0xA1B2C3D4 == (int16_t)-(int16_t)0x3C2C);
+    STATIC_ASSERT((int16_t)(int32_t)(uint32_t)0xC1D2E3F4 == (int16_t)(uint16_t)0xE3F4);
+    STATIC_ASSERT((int16_t)(int32_t)(uint32_t)0x92345678 == (int16_t)(uint16_t)0x5678);
+
+    /* To int32_t. */
+    STATIC_ASSERT((int32_t)(uint32_t)0xB2C3D4E5 == (int32_t)-(int32_t)0x4D3C2B1B);
+    STATIC_ASSERT((int32_t)(uint64_t)0xA123B456C789D012ULL == (int32_t)-(int32_t)0x38762FEE);
+    STATIC_ASSERT((int32_t)(int64_t)(uint64_t)0xC1D2E3F4A5B6C7D8ULL == (int32_t)(uint32_t)0xA5B6C7D8);
+    STATIC_ASSERT((int32_t)(int64_t)(uint64_t)0xABCDEF0123456789ULL == (int32_t)(uint32_t)0x23456789);
+
+    /* To int64_t. */
+    STATIC_ASSERT((int64_t)(uint64_t)0xB123C456D789E012ULL == (int64_t)-(int64_t)0x4EDC3BA928761FEEULL);
+#if defined(SECP256K1_INT128_NATIVE)
+    STATIC_ASSERT((int64_t)(((uint128_t)0xA1234567B8901234ULL << 64) + 0xC5678901D2345678ULL) == (int64_t)-(int64_t)0x3A9876FE2DCBA988ULL);
+    STATIC_ASSERT(((int64_t)(int128_t)(((uint128_t)0xB1C2D3E4F5A6B7C8ULL << 64) + 0xD9E0F1A2B3C4D5E6ULL)) == (int64_t)(uint64_t)0xD9E0F1A2B3C4D5E6ULL);
+    STATIC_ASSERT(((int64_t)(int128_t)(((uint128_t)0xABCDEF0123456789ULL << 64) + 0x0123456789ABCDEFULL)) == (int64_t)(uint64_t)0x0123456789ABCDEFULL);
+
+    /* To int128_t. */
+    STATIC_ASSERT((int128_t)(((uint128_t)0xB1234567C8901234ULL << 64) + 0xD5678901E2345678ULL) == (int128_t)(-(int128_t)0x8E1648B3F50E80DCULL * 0x8E1648B3F50E80DDULL + 0x5EA688D5482F9464ULL));
+#endif
+
+    /* Right shift on negative signed values is implementation defined. Verify that it
+       acts as a right shift in two's complement with sign extension (i.e duplicating
+       the top bit into newly added bits). */
+    STATIC_ASSERT((((int8_t)0xE8) >> 2) == (int8_t)(uint8_t)0xFA);
+    STATIC_ASSERT((((int16_t)0xE9AC) >> 4) == (int16_t)(uint16_t)0xFE9A);
+    STATIC_ASSERT((((int32_t)0x937C918A) >> 9) == (int32_t)(uint32_t)0xFFC9BE48);
+    STATIC_ASSERT((((int64_t)0xA8B72231DF9CF4B9ULL) >> 19) == (int64_t)(uint64_t)0xFFFFF516E4463BF3ULL);
+#if defined(SECP256K1_INT128_NATIVE)
+    STATIC_ASSERT((((int128_t)(((uint128_t)0xCD833A65684A0DBCULL << 64) + 0xB349312F71EA7637ULL)) >> 39) == (int128_t)(((uint128_t)0xFFFFFFFFFF9B0674ULL << 64) + 0xCAD0941B79669262ULL));
+#endif
+
+    /* This function is not supposed to be called. */
+    VERIFY_CHECK(0);
+}
+
+#endif /* SECP256K1_ASSUMPTIONS_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/bench.h

@@ -0,0 +1,174 @@
+/***********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_BENCH_H
+#define SECP256K1_BENCH_H
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <string.h>
+
+#include "tests_common.h"
+
+#define FP_EXP (6)
+#define FP_MULT (1000000LL)
+
+/* Format fixed point number. */
+static void print_number(const int64_t x) {
+    int64_t x_abs, y;
+    int c, i, rounding, g; /* g = integer part size, c = fractional part size */
+    size_t ptr;
+    char buffer[30];
+
+    if (x == INT64_MIN) {
+        /* Prevent UB. */
+        printf("ERR");
+        return;
+    }
+    x_abs = x < 0 ? -x : x;
+
+    /* Determine how many decimals we want to show (more than FP_EXP makes no
+     * sense). */
+    y = x_abs;
+    c = 0;
+    while (y > 0LL && y < 100LL * FP_MULT && c < FP_EXP) {
+        y *= 10LL;
+        c++;
+    }
+
+    /* Round to 'c' decimals. */
+    y = x_abs;
+    rounding = 0;
+    for (i = c; i < FP_EXP; ++i) {
+        rounding = (y % 10) >= 5;
+        y /= 10;
+    }
+    y += rounding;
+
+    /* Format and print the number. */
+    ptr = sizeof(buffer) - 1;
+    buffer[ptr] = 0;
+    g = 0;
+    if (c != 0) { /* non zero fractional part */
+        for (i = 0; i < c; ++i) {
+            buffer[--ptr] = '0' + (y % 10);
+            y /= 10;
+        }
+    } else if (c == 0) { /* fractional part is 0 */
+        buffer[--ptr] = '0';
+    }
+    buffer[--ptr] = '.';
+    do {
+        buffer[--ptr] = '0' + (y % 10);
+        y /= 10;
+        g++;
+    } while (y != 0);
+    if (x < 0) {
+        buffer[--ptr] = '-';
+        g++;
+    }
+    printf("%5.*s", g, &buffer[ptr]); /* Prints integer part */
+    printf("%-*s", FP_EXP, &buffer[ptr + g]); /* Prints fractional part */
+}
+
+static void run_benchmark(char *name, void (*benchmark)(void*, int), void (*setup)(void*), void (*teardown)(void*, int), void* data, int count, int iter) {
+    int i;
+    int64_t min = INT64_MAX;
+    int64_t sum = 0;
+    int64_t max = 0;
+    for (i = 0; i < count; i++) {
+        int64_t begin, total;
+        if (setup != NULL) {
+            setup(data);
+        }
+        begin = gettime_i64();
+        benchmark(data, iter);
+        total = gettime_i64() - begin;
+        if (teardown != NULL) {
+            teardown(data, iter);
+        }
+        if (total < min) {
+            min = total;
+        }
+        if (total > max) {
+            max = total;
+        }
+        sum += total;
+    }
+    /* ',' is used as a column delimiter */
+    printf("%-30s, ", name);
+    print_number(min * FP_MULT / iter);
+    printf("   , ");
+    print_number(((sum * FP_MULT) / count) / iter);
+    printf("   , ");
+    print_number(max * FP_MULT / iter);
+    printf("\n");
+}
+
+static int have_flag(int argc, char** argv, char *flag) {
+    char** argm = argv + argc;
+    argv++;
+    while (argv != argm) {
+        if (strcmp(*argv, flag) == 0) {
+            return 1;
+        }
+        argv++;
+    }
+    return 0;
+}
+
+/* takes an array containing the arguments that the user is allowed to enter on the command-line
+   returns:
+      - 1 if the user entered an invalid argument
+      - 0 if all the user entered arguments are valid */
+static int have_invalid_args(int argc, char** argv, char** valid_args, size_t n) {
+    size_t i;
+    int found_valid;
+    char** argm = argv + argc;
+    argv++;
+
+    while (argv != argm) {
+        found_valid = 0;
+        for (i = 0; i < n; i++) {
+            if (strcmp(*argv, valid_args[i]) == 0) {
+                found_valid = 1; /* user entered a valid arg from the list */
+                break;
+            }
+        }
+        if (found_valid == 0) {
+            return 1; /* invalid arg found */
+        }
+        argv++;
+    }
+    return 0;
+}
+
+static int get_iters(int default_iters) {
+    char* env = getenv("SECP256K1_BENCH_ITERS");
+    if (env) {
+        char* endptr;
+        long int iters = strtol(env, &endptr, 0);
+        if (*endptr != '\0' || iters <= 0) {
+            printf("Error: Value of SECP256K1_BENCH_ITERS is not a positive integer: %s\n\n", env);
+            return 0;
+        }
+        return iters;
+    } else {
+        return default_iters;
+    }
+}
+
+static void print_output_table_header_row(void) {
+    char* bench_str = "Benchmark";     /* left justified */
+    char* min_str = "    Min(us)    "; /* center alignment */
+    char* avg_str = "    Avg(us)    ";
+    char* max_str = "    Max(us)    ";
+    printf("%-30s,%-15s,%-15s,%-15s\n", bench_str, min_str, avg_str, max_str);
+    printf("\n");
+}
+
+#endif /* SECP256K1_BENCH_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/checkmem.h

@@ -0,0 +1,117 @@
+/***********************************************************************
+ * Copyright (c) 2022 Pieter Wuille                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+/* The code here is inspired by Kris Kwiatkowski's approach in
+ * https://github.com/kriskwiatkowski/pqc/blob/main/src/common/ct_check.h
+ * to provide a general interface for memory-checking mechanisms, primarily
+ * for constant-time checking.
+ */
+
+/* These macros are defined by this header file:
+ *
+ * - SECP256K1_CHECKMEM_ENABLED:
+ *   - 1 if memory-checking integration is available, 0 otherwise.
+ *     This is just a compile-time macro. Use the next macro to check it is actually
+ *     available at runtime.
+ * - SECP256K1_CHECKMEM_RUNNING():
+ *   - Acts like a function call, returning 1 if memory checking is available
+ *     at runtime.
+ * - SECP256K1_CHECKMEM_CHECK(p, len):
+ *   - Assert or otherwise fail in case the len-byte memory block pointed to by p is
+ *     not considered entirely defined.
+ * - SECP256K1_CHECKMEM_CHECK_VERIFY(p, len):
+ *   - Like SECP256K1_CHECKMEM_CHECK, but only works in VERIFY mode.
+ * - SECP256K1_CHECKMEM_UNDEFINE(p, len):
+ *   - marks the len-byte memory block pointed to by p as undefined data (secret data,
+ *     in the context of constant-time checking).
+ * - SECP256K1_CHECKMEM_DEFINE(p, len):
+ *   - marks the len-byte memory pointed to by p as defined data (public data, in the
+ *     context of constant-time checking).
+ * - SECP256K1_CHECKMEM_MSAN_DEFINE(p, len):
+ *   - Like SECP256K1_CHECKMEM_DEFINE, but applies only to memory_sanitizer.
+ *
+ */
+
+#ifndef SECP256K1_CHECKMEM_H
+#define SECP256K1_CHECKMEM_H
+
+/* Define a statement-like macro that ignores the arguments. */
+#define SECP256K1_CHECKMEM_NOOP(p, len) do { (void)(p); (void)(len); } while(0)
+
+/* If compiling under msan, map the SECP256K1_CHECKMEM_* functionality to msan.
+ * Choose this preferentially, even when VALGRIND is defined, as msan-compiled
+ * binaries can't be run under valgrind anyway. */
+#if defined(__has_feature)
+#  if __has_feature(memory_sanitizer)
+#    include <sanitizer/msan_interface.h>
+#    define SECP256K1_CHECKMEM_ENABLED 1
+#    if defined(__clang__) && ((__clang_major__ == 21 && __clang_minor__ >= 1) || __clang_major__ >= 22)
+#      define SECP256K1_CHECKMEM_UNDEFINE(p, len) do { \
+         /* Work around https://github.com/llvm/llvm-project/issues/160094 */ \
+         _Pragma("clang diagnostic push") \
+         _Pragma("clang diagnostic ignored \"-Wuninitialized-const-pointer\"") \
+         __msan_allocated_memory((p), (len)); \
+         _Pragma("clang diagnostic pop") \
+         } while(0)
+#    else
+#      define SECP256K1_CHECKMEM_UNDEFINE(p, len) __msan_allocated_memory((p), (len))
+#    endif
+#    define SECP256K1_CHECKMEM_DEFINE(p, len) __msan_unpoison((p), (len))
+#    define SECP256K1_CHECKMEM_MSAN_DEFINE(p, len) __msan_unpoison((p), (len))
+#    define SECP256K1_CHECKMEM_CHECK(p, len) __msan_check_mem_is_initialized((p), (len))
+#    define SECP256K1_CHECKMEM_RUNNING() (1)
+#  endif
+#endif
+
+#if !defined SECP256K1_CHECKMEM_MSAN_DEFINE
+#  define SECP256K1_CHECKMEM_MSAN_DEFINE(p, len) SECP256K1_CHECKMEM_NOOP((p), (len))
+#endif
+
+/* If valgrind integration is desired (through the VALGRIND define), implement the
+ * SECP256K1_CHECKMEM_* macros using valgrind. */
+#if !defined SECP256K1_CHECKMEM_ENABLED
+#  if defined VALGRIND
+#    include <stddef.h>
+#  if defined(__clang__) && defined(__APPLE__)
+#    pragma clang diagnostic push
+#    pragma clang diagnostic ignored "-Wreserved-identifier"
+#  elif defined(__GNUC__) && (__GNUC__ >= 15)
+#    pragma GCC diagnostic push
+#    pragma GCC diagnostic ignored "-Wtrailing-whitespace"
+#  endif
+#    include <valgrind/memcheck.h>
+#  if defined(__clang__) && defined(__APPLE__)
+#    pragma clang diagnostic pop
+#  elif defined(__GNUC__) && (__GNUC__ >= 15)
+#    pragma GCC diagnostic pop
+#  endif
+#    define SECP256K1_CHECKMEM_ENABLED 1
+#    define SECP256K1_CHECKMEM_UNDEFINE(p, len) VALGRIND_MAKE_MEM_UNDEFINED((p), (len))
+#    define SECP256K1_CHECKMEM_DEFINE(p, len) VALGRIND_MAKE_MEM_DEFINED((p), (len))
+#    define SECP256K1_CHECKMEM_CHECK(p, len) VALGRIND_CHECK_MEM_IS_DEFINED((p), (len))
+     /* VALGRIND_MAKE_MEM_DEFINED returns 0 iff not running on memcheck.
+      * This is more precise than the RUNNING_ON_VALGRIND macro, which
+      * checks for valgrind in general instead of memcheck specifically. */
+#    define SECP256K1_CHECKMEM_RUNNING() (VALGRIND_MAKE_MEM_DEFINED(NULL, 0) != 0)
+#  endif
+#endif
+
+/* As a fall-back, map these macros to dummy statements. */
+#if !defined SECP256K1_CHECKMEM_ENABLED
+#  define SECP256K1_CHECKMEM_ENABLED 0
+#  define SECP256K1_CHECKMEM_UNDEFINE(p, len) SECP256K1_CHECKMEM_NOOP((p), (len))
+#  define SECP256K1_CHECKMEM_DEFINE(p, len) SECP256K1_CHECKMEM_NOOP((p), (len))
+#  define SECP256K1_CHECKMEM_CHECK(p, len) SECP256K1_CHECKMEM_NOOP((p), (len))
+#  define SECP256K1_CHECKMEM_RUNNING() (0)
+#endif
+
+#if defined VERIFY
+#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len) SECP256K1_CHECKMEM_CHECK((p), (len))
+#else
+#define SECP256K1_CHECKMEM_CHECK_VERIFY(p, len) SECP256K1_CHECKMEM_NOOP((p), (len))
+#endif
+
+#endif /* SECP256K1_CHECKMEM_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecdsa.h

@@ -0,0 +1,21 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECDSA_H
+#define SECP256K1_ECDSA_H
+
+#include <stddef.h>
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult.h"
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *r, secp256k1_scalar *s, const unsigned char *sig, size_t size);
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar *r, const secp256k1_scalar *s);
+static int secp256k1_ecdsa_sig_verify(const secp256k1_scalar* r, const secp256k1_scalar* s, const secp256k1_ge *pubkey, const secp256k1_scalar *message);
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar* r, secp256k1_scalar* s, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid);
+
+#endif /* SECP256K1_ECDSA_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecdsa_impl.h

@@ -0,0 +1,312 @@
+/***********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille                               *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+
+#ifndef SECP256K1_ECDSA_IMPL_H
+#define SECP256K1_ECDSA_IMPL_H
+
+#include "scalar.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+#include "ecdsa.h"
+
+/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
+ *  $ sage -c 'load("secp256k1_params.sage"); print(hex(N))'
+ *  0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
+    0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
+    0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
+);
+
+/** Difference between field and order, values 'p' and 'n' values defined in
+ *  "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ *  $ sage -c 'load("secp256k1_params.sage"); print(hex(P-N))'
+ *  0x14551231950b75fc4402da1722fc9baee
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
+    0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
+);
+
+static int secp256k1_der_read_len(size_t *len, const unsigned char **sigp, const unsigned char *sigend) {
+    size_t lenleft;
+    unsigned char b1;
+    VERIFY_CHECK(len != NULL);
+    *len = 0;
+    if (*sigp >= sigend) {
+        return 0;
+    }
+    b1 = *((*sigp)++);
+    if (b1 == 0xFF) {
+        /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */
+        return 0;
+    }
+    if ((b1 & 0x80) == 0) {
+        /* X.690-0207 8.1.3.4 short form length octets */
+        *len = b1;
+        return 1;
+    }
+    if (b1 == 0x80) {
+        /* Indefinite length is not allowed in DER. */
+        return 0;
+    }
+    /* X.690-207 8.1.3.5 long form length octets */
+    lenleft = b1 & 0x7F; /* lenleft is at least 1 */
+    if (lenleft > (size_t)(sigend - *sigp)) {
+        return 0;
+    }
+    if (**sigp == 0) {
+        /* Not the shortest possible length encoding. */
+        return 0;
+    }
+    if (lenleft > sizeof(size_t)) {
+        /* The resulting length would exceed the range of a size_t, so
+         * it is certainly longer than the passed array size. */
+        return 0;
+    }
+    while (lenleft > 0) {
+        *len = (*len << 8) | **sigp;
+        (*sigp)++;
+        lenleft--;
+    }
+    if (*len > (size_t)(sigend - *sigp)) {
+        /* Result exceeds the length of the passed array.
+           (Checking this is the responsibility of the caller but it
+           can't hurt do it here, too.) */
+        return 0;
+    }
+    if (*len < 128) {
+        /* Not the shortest possible length encoding. */
+        return 0;
+    }
+    return 1;
+}
+
+static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) {
+    int overflow = 0;
+    unsigned char ra[32] = {0};
+    size_t rlen;
+
+    if (*sig == sigend || **sig != 0x02) {
+        /* Not a primitive integer (X.690-0207 8.3.1). */
+        return 0;
+    }
+    (*sig)++;
+    if (secp256k1_der_read_len(&rlen, sig, sigend) == 0) {
+        return 0;
+    }
+    if (rlen == 0 || rlen > (size_t)(sigend - *sig)) {
+        /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1).  */
+        return 0;
+    }
+    if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) {
+        /* Excessive 0x00 padding. */
+        return 0;
+    }
+    if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) {
+        /* Excessive 0xFF padding. */
+        return 0;
+    }
+    if ((**sig & 0x80) == 0x80) {
+        /* Negative. */
+        overflow = 1;
+    }
+    /* There is at most one leading zero byte:
+     * if there were two leading zero bytes, we would have failed and returned 0
+     * because of excessive 0x00 padding already. */
+    if (rlen > 0 && **sig == 0) {
+        /* Skip leading zero byte */
+        rlen--;
+        (*sig)++;
+    }
+    if (rlen > 32) {
+        overflow = 1;
+    }
+    if (!overflow) {
+        if (rlen) memcpy(ra + 32 - rlen, *sig, rlen);
+        secp256k1_scalar_set_b32(r, ra, &overflow);
+    }
+    if (overflow) {
+        secp256k1_scalar_set_int(r, 0);
+    }
+    (*sig) += rlen;
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) {
+    const unsigned char *sigend = sig + size;
+    size_t rlen;
+    if (sig == sigend || *(sig++) != 0x30) {
+        /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */
+        return 0;
+    }
+    if (secp256k1_der_read_len(&rlen, &sig, sigend) == 0) {
+        return 0;
+    }
+    if (rlen != (size_t)(sigend - sig)) {
+        /* Tuple exceeds bounds or garage after tuple. */
+        return 0;
+    }
+
+    if (!secp256k1_der_parse_integer(rr, &sig, sigend)) {
+        return 0;
+    }
+    if (!secp256k1_der_parse_integer(rs, &sig, sigend)) {
+        return 0;
+    }
+
+    if (sig != sigend) {
+        /* Trailing garbage inside tuple. */
+        return 0;
+    }
+
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) {
+    unsigned char r[33] = {0}, s[33] = {0};
+    unsigned char *rp = r, *sp = s;
+    size_t lenR = 33, lenS = 33;
+    secp256k1_scalar_get_b32(&r[1], ar);
+    secp256k1_scalar_get_b32(&s[1], as);
+    while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
+    while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
+    if (*size < 6+lenS+lenR) {
+        *size = 6 + lenS + lenR;
+        return 0;
+    }
+    *size = 6 + lenS + lenR;
+    sig[0] = 0x30;
+    sig[1] = 4 + lenS + lenR;
+    sig[2] = 0x02;
+    sig[3] = lenR;
+    memcpy(sig+4, rp, lenR);
+    sig[4+lenR] = 0x02;
+    sig[5+lenR] = lenS;
+    memcpy(sig+lenR+6, sp, lenS);
+    return 1;
+}
+
+static int secp256k1_ecdsa_sig_verify(const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
+    unsigned char c[32];
+    secp256k1_scalar sn, u1, u2;
+#if !defined(EXHAUSTIVE_TEST_ORDER)
+    int range;
+    secp256k1_fe xr;
+#endif
+    secp256k1_gej pubkeyj;
+    secp256k1_gej pr;
+
+    if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
+        return 0;
+    }
+
+    secp256k1_scalar_inverse_var(&sn, sigs);
+    secp256k1_scalar_mul(&u1, &sn, message);
+    secp256k1_scalar_mul(&u2, &sn, sigr);
+    secp256k1_gej_set_ge(&pubkeyj, pubkey);
+    secp256k1_ecmult(&pr, &pubkeyj, &u2, &u1);
+    if (secp256k1_gej_is_infinity(&pr)) {
+        return 0;
+    }
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+{
+    secp256k1_scalar computed_r;
+    secp256k1_ge pr_ge;
+    secp256k1_ge_set_gej(&pr_ge, &pr);
+    secp256k1_fe_normalize(&pr_ge.x);
+
+    secp256k1_fe_get_b32(c, &pr_ge.x);
+    secp256k1_scalar_set_b32(&computed_r, c, NULL);
+    return secp256k1_scalar_eq(sigr, &computed_r);
+}
+#else
+
+    /* Interpret sigr as a field element xr  */
+    secp256k1_scalar_get_b32(c, sigr);
+    range = secp256k1_fe_set_b32_limit(&xr, c);
+#ifdef VERIFY
+    /* We know that c is in range; it comes from a scalar. */
+    VERIFY_CHECK(range);
+#else
+    (void)range;
+#endif
+
+    /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
+     *  in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p),
+     *  compute the remainder modulo n, and compare it to xr. However:
+     *
+     *        xr == X(pr) mod n
+     *    <=> exists h. (xr + h * n < p && xr + h * n == X(pr))
+     *    [Since 2 * n > p, h can only be 0 or 1]
+     *    <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr))
+     *    [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p]
+     *    <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p)
+     *    [Multiplying both sides of the equations by pr.z^2 mod p]
+     *    <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x)
+     *
+     *  Thus, we can avoid the inversion, but we have to check both cases separately.
+     *  secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.
+     */
+    if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+        /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */
+        return 1;
+    }
+    if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
+        /* xr + n >= p, so we can skip testing the second case. */
+        return 0;
+    }
+    secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
+    if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+        /* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */
+        return 1;
+    }
+    return 0;
+#endif
+}
+
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
+    unsigned char b[32];
+    secp256k1_gej rp;
+    secp256k1_ge r;
+    secp256k1_scalar n;
+    int overflow = 0;
+    int high;
+
+    secp256k1_ecmult_gen(ctx, &rp, nonce);
+    secp256k1_ge_set_gej(&r, &rp);
+    secp256k1_fe_normalize(&r.x);
+    secp256k1_fe_normalize(&r.y);
+    secp256k1_fe_get_b32(b, &r.x);
+    secp256k1_scalar_set_b32(sigr, b, &overflow);
+    if (recid) {
+        /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log
+         * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria.
+         */
+        *recid = (overflow << 1) | secp256k1_fe_is_odd(&r.y);
+    }
+    secp256k1_scalar_mul(&n, sigr, seckey);
+    secp256k1_scalar_add(&n, &n, message);
+    secp256k1_scalar_inverse(sigs, nonce);
+    secp256k1_scalar_mul(sigs, sigs, &n);
+    secp256k1_scalar_clear(&n);
+    secp256k1_gej_clear(&rp);
+    secp256k1_ge_clear(&r);
+    high = secp256k1_scalar_is_high(sigs);
+    secp256k1_scalar_cond_negate(sigs, high);
+    if (recid) {
+        *recid ^= high;
+    }
+    /* P.x = order is on the curve, so technically sig->r could end up being zero, which would be an invalid signature.
+     * This is cryptographically unreachable as hitting it requires finding the discrete log of P.x = N.
+     */
+    return (int)(!secp256k1_scalar_is_zero(sigr)) & (int)(!secp256k1_scalar_is_zero(sigs));
+}
+
+#endif /* SECP256K1_ECDSA_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/eckey.h

@@ -0,0 +1,28 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECKEY_H
+#define SECP256K1_ECKEY_H
+
+#include <stddef.h>
+
+#include "group.h"
+#include "scalar.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size);
+/** Serialize a group element (that is not allowed to be infinity) to a compressed public key (33 bytes). */
+static void secp256k1_eckey_pubkey_serialize33(secp256k1_ge *elem, unsigned char *pub33);
+/** Serialize a group element (that is not allowed to be infinity) to an uncompressed public key (65 bytes). */
+static void secp256k1_eckey_pubkey_serialize65(secp256k1_ge *elem, unsigned char *pub65);
+
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak);
+static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak);
+
+#endif /* SECP256K1_ECKEY_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/eckey_impl.h

@@ -0,0 +1,94 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECKEY_IMPL_H
+#define SECP256K1_ECKEY_IMPL_H
+
+#include "eckey.h"
+
+#include "util.h"
+#include "scalar.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult_gen.h"
+
+static int secp256k1_eckey_pubkey_parse(secp256k1_ge *elem, const unsigned char *pub, size_t size) {
+    if (size == 33 && (pub[0] == SECP256K1_TAG_PUBKEY_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_ODD)) {
+        secp256k1_fe x;
+        return secp256k1_fe_set_b32_limit(&x, pub+1) && secp256k1_ge_set_xo_var(elem, &x, pub[0] == SECP256K1_TAG_PUBKEY_ODD);
+    } else if (size == 65 && (pub[0] == SECP256K1_TAG_PUBKEY_UNCOMPRESSED || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) {
+        secp256k1_fe x, y;
+        if (!secp256k1_fe_set_b32_limit(&x, pub+1) || !secp256k1_fe_set_b32_limit(&y, pub+33)) {
+            return 0;
+        }
+        secp256k1_ge_set_xy(elem, &x, &y);
+        if ((pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_EVEN || pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD) &&
+            secp256k1_fe_is_odd(&y) != (pub[0] == SECP256K1_TAG_PUBKEY_HYBRID_ODD)) {
+            return 0;
+        }
+        return secp256k1_ge_is_valid_var(elem);
+    } else {
+        return 0;
+    }
+}
+
+static void secp256k1_eckey_pubkey_serialize33(secp256k1_ge *elem, unsigned char *pub33) {
+    VERIFY_CHECK(!secp256k1_ge_is_infinity(elem));
+
+    secp256k1_fe_normalize_var(&elem->x);
+    secp256k1_fe_normalize_var(&elem->y);
+    pub33[0] = secp256k1_fe_is_odd(&elem->y) ? SECP256K1_TAG_PUBKEY_ODD : SECP256K1_TAG_PUBKEY_EVEN;
+    secp256k1_fe_get_b32(&pub33[1], &elem->x);
+}
+
+static void secp256k1_eckey_pubkey_serialize65(secp256k1_ge *elem, unsigned char *pub65) {
+    VERIFY_CHECK(!secp256k1_ge_is_infinity(elem));
+
+    secp256k1_fe_normalize_var(&elem->x);
+    secp256k1_fe_normalize_var(&elem->y);
+    pub65[0] = SECP256K1_TAG_PUBKEY_UNCOMPRESSED;
+    secp256k1_fe_get_b32(&pub65[1], &elem->x);
+    secp256k1_fe_get_b32(&pub65[33], &elem->y);
+}
+
+static int secp256k1_eckey_privkey_tweak_add(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
+    secp256k1_scalar_add(key, key, tweak);
+    return !secp256k1_scalar_is_zero(key);
+}
+
+static int secp256k1_eckey_pubkey_tweak_add(secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_gej pt;
+    secp256k1_gej_set_ge(&pt, key);
+    secp256k1_ecmult(&pt, &pt, &secp256k1_scalar_one, tweak);
+
+    if (secp256k1_gej_is_infinity(&pt)) {
+        return 0;
+    }
+    secp256k1_ge_set_gej(key, &pt);
+    return 1;
+}
+
+static int secp256k1_eckey_privkey_tweak_mul(secp256k1_scalar *key, const secp256k1_scalar *tweak) {
+    int ret;
+    ret = !secp256k1_scalar_is_zero(tweak);
+
+    secp256k1_scalar_mul(key, key, tweak);
+    return ret;
+}
+
+static int secp256k1_eckey_pubkey_tweak_mul(secp256k1_ge *key, const secp256k1_scalar *tweak) {
+    secp256k1_gej pt;
+    if (secp256k1_scalar_is_zero(tweak)) {
+        return 0;
+    }
+
+    secp256k1_gej_set_ge(&pt, key);
+    secp256k1_ecmult(&pt, &pt, tweak, NULL);
+    secp256k1_ge_set_gej(key, &pt);
+    return 1;
+}
+
+#endif /* SECP256K1_ECKEY_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult.h

@@ -0,0 +1,64 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra       *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_H
+#define SECP256K1_ECMULT_H
+
+#include "group.h"
+#include "scalar.h"
+#include "scratch.h"
+
+#ifndef ECMULT_WINDOW_SIZE
+#  define ECMULT_WINDOW_SIZE 15
+#  ifdef DEBUG_CONFIG
+#     pragma message DEBUG_CONFIG_MSG("ECMULT_WINDOW_SIZE undefined, assuming default value")
+#  endif
+#endif
+
+#ifdef DEBUG_CONFIG
+#  pragma message DEBUG_CONFIG_DEF(ECMULT_WINDOW_SIZE)
+#endif
+
+/* No one will ever need more than a window size of 24. The code might
+ * be correct for larger values of ECMULT_WINDOW_SIZE but this is not
+ * tested.
+ *
+ * The following limitations are known, and there are probably more:
+ * If WINDOW_G > 27 and size_t has 32 bits, then the code is incorrect
+ * because the size of the memory object that we allocate (in bytes)
+ * will not fit in a size_t.
+ * If WINDOW_G > 31 and int has 32 bits, then the code is incorrect
+ * because certain expressions will overflow.
+ */
+#if ECMULT_WINDOW_SIZE < 2 || ECMULT_WINDOW_SIZE > 24
+#  error Set ECMULT_WINDOW_SIZE to an integer in range [2..24].
+#endif
+
+/** The number of entries a table with precomputed multiples needs to have. */
+#define ECMULT_TABLE_SIZE(w) ((size_t)1 << ((w)-2))
+
+/** Double multiply: R = na*A + ng*G
+ *
+ * Passing NULL as ng is equivalent to the zero scalar but a tiny bit faster.
+ */
+static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng);
+
+typedef int (secp256k1_ecmult_multi_callback)(secp256k1_scalar *sc, secp256k1_ge *pt, size_t idx, void *data);
+
+/**
+ * Multi-multiply: R = inp_g_sc * G + sum_i ni * Ai.
+ * Chooses the right algorithm for a given number of points and scratch space
+ * size. Resets and overwrites the given scratch space. If the points do not
+ * fit in the scratch space the algorithm is repeatedly run with batches of
+ * points. If no scratch space is given then a simple algorithm is used that
+ * simply multiplies the points with the corresponding scalars and adds them up.
+ * Returns: 1 on success (including when inp_g_sc is NULL and n is 0)
+ *          0 if there is not enough scratch space for a single point or
+ *          callback returns 0
+ */
+static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n);
+
+#endif /* SECP256K1_ECMULT_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_compute_table.h

@@ -0,0 +1,16 @@
+/*****************************************************************************************************
+ * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor *
+ * Distributed under the MIT software license, see the accompanying                                  *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.                              *
+ *****************************************************************************************************/
+
+#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_H
+#define SECP256K1_ECMULT_COMPUTE_TABLE_H
+
+/* Construct table of all odd multiples of gen in range 1..(2**(window_g-1)-1). */
+static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen);
+
+/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */
+static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen);
+
+#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_compute_table_impl.h

@@ -0,0 +1,49 @@
+/*****************************************************************************************************
+ * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor *
+ * Distributed under the MIT software license, see the accompanying                                  *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.                              *
+ *****************************************************************************************************/
+
+#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H
+#define SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H
+
+#include "ecmult_compute_table.h"
+#include "group_impl.h"
+#include "field_impl.h"
+#include "ecmult.h"
+#include "util.h"
+
+static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen) {
+    secp256k1_gej gj;
+    secp256k1_ge ge, dgen;
+    size_t j;
+
+    gj = *gen;
+    secp256k1_ge_set_gej_var(&ge, &gj);
+    secp256k1_ge_to_storage(&table[0], &ge);
+
+    secp256k1_gej_double_var(&gj, gen, NULL);
+    secp256k1_ge_set_gej_var(&dgen, &gj);
+
+    for (j = 1; j < ECMULT_TABLE_SIZE(window_g); ++j) {
+        secp256k1_gej_set_ge(&gj, &ge);
+        secp256k1_gej_add_ge_var(&gj, &gj, &dgen, NULL);
+        secp256k1_ge_set_gej_var(&ge, &gj);
+        secp256k1_ge_to_storage(&table[j], &ge);
+    }
+}
+
+/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */
+static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen) {
+    secp256k1_gej gj;
+    int i;
+
+    secp256k1_gej_set_ge(&gj, gen);
+    secp256k1_ecmult_compute_table(table, window_g, &gj);
+    for (i = 0; i < 128; ++i) {
+        secp256k1_gej_double_var(&gj, &gj, NULL);
+    }
+    secp256k1_ecmult_compute_table(table_128, window_g, &gj);
+}
+
+#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_const.h

@@ -0,0 +1,38 @@
+/***********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                  *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_CONST_H
+#define SECP256K1_ECMULT_CONST_H
+
+#include "scalar.h"
+#include "group.h"
+
+/**
+ * Multiply: R = q*A (in constant-time for q)
+ */
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q);
+
+/**
+ * Same as secp256k1_ecmult_const, but takes in an x coordinate of the base point
+ * only, specified as fraction n/d (numerator/denominator). Only the x coordinate of the result is
+ * returned.
+ *
+ * If known_on_curve is 0, a verification is performed that n/d is a valid X
+ * coordinate, and 0 is returned if not. Otherwise, 1 is returned.
+ *
+ * d being NULL is interpreted as d=1. If non-NULL, d must not be zero. q must not be zero.
+ *
+ * Constant time in the value of q, but not any other inputs.
+ */
+static int secp256k1_ecmult_const_xonly(
+    secp256k1_fe *r,
+    const secp256k1_fe *n,
+    const secp256k1_fe *d,
+    const secp256k1_scalar *q,
+    int known_on_curve
+);
+
+#endif /* SECP256K1_ECMULT_CONST_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_const_impl.h

@@ -0,0 +1,402 @@
+/***********************************************************************
+ * Copyright (c) 2015, 2022 Pieter Wuille, Andrew Poelstra             *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_CONST_IMPL_H
+#define SECP256K1_ECMULT_CONST_IMPL_H
+
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_const.h"
+#include "ecmult_impl.h"
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/* We need 2^ECMULT_CONST_GROUP_SIZE - 1 to be less than EXHAUSTIVE_TEST_ORDER, because
+ * the tables cannot have infinities in them (this breaks the effective-affine technique's
+ * z-ratio tracking) */
+#  if EXHAUSTIVE_TEST_ORDER == 199
+#    define ECMULT_CONST_GROUP_SIZE 4
+#  elif EXHAUSTIVE_TEST_ORDER == 13
+#    define ECMULT_CONST_GROUP_SIZE 3
+#  elif EXHAUSTIVE_TEST_ORDER == 7
+#    define ECMULT_CONST_GROUP_SIZE 2
+#  else
+#    error "Unknown EXHAUSTIVE_TEST_ORDER"
+#  endif
+#else
+/* Group size 4 or 5 appears optimal. */
+#  define ECMULT_CONST_GROUP_SIZE 5
+#endif
+
+#define ECMULT_CONST_TABLE_SIZE (1L << (ECMULT_CONST_GROUP_SIZE - 1))
+#define ECMULT_CONST_GROUPS ((129 + ECMULT_CONST_GROUP_SIZE - 1) / ECMULT_CONST_GROUP_SIZE)
+#define ECMULT_CONST_BITS (ECMULT_CONST_GROUPS * ECMULT_CONST_GROUP_SIZE)
+
+/** Fill a table 'pre' with precomputed odd multiples of a.
+ *
+ *  The resulting point set is brought to a single constant Z denominator, stores the X and Y
+ *  coordinates as ge points in pre, and stores the global Z in globalz.
+ *
+ *  'pre' must be an array of size ECMULT_CONST_TABLE_SIZE.
+ */
+static void secp256k1_ecmult_const_odd_multiples_table_globalz(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
+    secp256k1_fe zr[ECMULT_CONST_TABLE_SIZE];
+
+    secp256k1_ecmult_odd_multiples_table(ECMULT_CONST_TABLE_SIZE, pre, zr, globalz, a);
+    secp256k1_ge_table_set_globalz(ECMULT_CONST_TABLE_SIZE, pre, zr);
+}
+
+/* Given a table 'pre' with odd multiples of a point, put in r the signed-bit multiplication of n with that point.
+ *
+ * For example, if ECMULT_CONST_GROUP_SIZE is 4, then pre is expected to contain 8 entries:
+ * [1*P, 3*P, 5*P, 7*P, 9*P, 11*P, 13*P, 15*P]. n is then expected to be a 4-bit integer (range 0-15), and its
+ * bits are interpreted as signs of powers of two to look up.
+ *
+ * For example, if n=4, which is 0100 in binary, which is interpreted as [- + - -], so the looked up value is
+ * [ -(2^3) + (2^2) - (2^1) - (2^0) ]*P = -7*P. Every valid n translates to an odd number in range [-15,15],
+ * which means we just need to look up one of the precomputed values, and optionally negate it.
+ */
+#define ECMULT_CONST_TABLE_GET_GE(r,pre,n) do { \
+    unsigned int m = 0; \
+    /* If the top bit of n is 0, we want the negation. */ \
+    volatile unsigned int negative = ((n) >> (ECMULT_CONST_GROUP_SIZE - 1)) ^ 1; \
+    /* Let n[i] be the i-th bit of n, then the index is
+     *     sum(cnot(n[i]) * 2^i, i=0..l-2)
+     * where cnot(b) = b if n[l-1] = 1 and 1 - b otherwise.
+     * For example, if n = 4, in binary 0100, the index is 3, in binary 011.
+     *
+     * Proof:
+     *     Let
+     *         x = sum((2*n[i] - 1)*2^i, i=0..l-1)
+     *           = 2*sum(n[i] * 2^i, i=0..l-1) - 2^l + 1
+     *     be the value represented by n.
+     *     The index is (x - 1)/2 if x > 0 and -(x + 1)/2 otherwise.
+     *     Case x > 0:
+     *         n[l-1] = 1
+     *         index = sum(n[i] * 2^i, i=0..l-1) - 2^(l-1)
+     *               = sum(n[i] * 2^i, i=0..l-2)
+     *     Case x <= 0:
+     *         n[l-1] = 0
+     *          index = -(2*sum(n[i] * 2^i, i=0..l-1) - 2^l + 2)/2
+     *                = 2^(l-1) - 1 - sum(n[i] * 2^i, i=0..l-1)
+     *                = sum((1 - n[i]) * 2^i, i=0..l-2)
+     */ \
+    unsigned int index = ((unsigned int)(-negative) ^ n) & ((1U << (ECMULT_CONST_GROUP_SIZE - 1)) - 1U); \
+    secp256k1_fe neg_y; \
+    VERIFY_CHECK((n) < (1U << ECMULT_CONST_GROUP_SIZE)); \
+    VERIFY_CHECK(index < (1U << (ECMULT_CONST_GROUP_SIZE - 1))); \
+    /* Unconditionally set r->x = (pre)[m].x and r->y = (pre)[m].y because it's either the correct one
+     * or will get replaced in the later iterations, this is needed to make sure `r` is initialized. */ \
+    secp256k1_ge_set_xy((r), &(pre)[m].x, &(pre)[m].y); \
+    for (m = 1; m < ECMULT_CONST_TABLE_SIZE; m++) { \
+        /* This loop is used to avoid secret data in array indices. See
+         * the comment in ecmult_gen_impl.h for rationale. */ \
+        secp256k1_fe_cmov(&(r)->x, &(pre)[m].x, m == index); \
+        secp256k1_fe_cmov(&(r)->y, &(pre)[m].y, m == index); \
+    } \
+    secp256k1_fe_negate(&neg_y, &(r)->y, 1); \
+    secp256k1_fe_cmov(&(r)->y, &neg_y, negative); \
+} while(0)
+
+/* For K as defined in the comment of secp256k1_ecmult_const, we have several precomputed
+ * formulas/constants.
+ * - in exhaustive test mode, we give an explicit expression to compute it at compile time: */
+#ifdef EXHAUSTIVE_TEST_ORDER
+static const secp256k1_scalar secp256k1_ecmult_const_K = ((SECP256K1_SCALAR_CONST(0, 0, 0, (1U << (ECMULT_CONST_BITS - 128)) - 2U, 0, 0, 0, 0) + EXHAUSTIVE_TEST_ORDER - 1U) * (1U + EXHAUSTIVE_TEST_LAMBDA)) % EXHAUSTIVE_TEST_ORDER;
+/* - for the real secp256k1 group we have constants for various ECMULT_CONST_BITS values. */
+#elif ECMULT_CONST_BITS == 129
+/* For GROUP_SIZE = 1,3. */
+static const secp256k1_scalar secp256k1_ecmult_const_K = SECP256K1_SCALAR_CONST(0xac9c52b3ul, 0x3fa3cf1ful, 0x5ad9e3fdul, 0x77ed9ba4ul, 0xa880b9fcul, 0x8ec739c2ul, 0xe0cfc810ul, 0xb51283ceul);
+#elif ECMULT_CONST_BITS == 130
+/* For GROUP_SIZE = 2,5. */
+static const secp256k1_scalar secp256k1_ecmult_const_K = SECP256K1_SCALAR_CONST(0xa4e88a7dul, 0xcb13034eul, 0xc2bdd6bful, 0x7c118d6bul, 0x589ae848ul, 0x26ba29e4ul, 0xb5c2c1dcul, 0xde9798d9ul);
+#elif ECMULT_CONST_BITS == 132
+/* For GROUP_SIZE = 4,6 */
+static const secp256k1_scalar secp256k1_ecmult_const_K = SECP256K1_SCALAR_CONST(0x76b1d93dul, 0x0fae3c6bul, 0x3215874bul, 0x94e93813ul, 0x7937fe0dul, 0xb66bcaaful, 0xb3749ca5ul, 0xd7b6171bul);
+#else
+#  error "Unknown ECMULT_CONST_BITS"
+#endif
+
+static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, const secp256k1_scalar *q) {
+    /* The approach below combines the signed-digit logic from Mike Hamburg's
+     * "Fast and compact elliptic-curve cryptography" (https://eprint.iacr.org/2012/309)
+     * Section 3.3, with the GLV endomorphism.
+     *
+     * The idea there is to interpret the bits of a scalar as signs (1 = +, 0 = -), and compute a
+     * point multiplication in that fashion. Let v be an n-bit non-negative integer (0 <= v < 2^n),
+     * and v[i] its i'th bit (so v = sum(v[i] * 2^i, i=0..n-1)). Then define:
+     *
+     *   C_l(v, A) = sum((2*v[i] - 1) * 2^i*A, i=0..l-1)
+     *
+     * Then it holds that C_l(v, A) = sum((2*v[i] - 1) * 2^i*A, i=0..l-1)
+     *                              = (2*sum(v[i] * 2^i, i=0..l-1) + 1 - 2^l) * A
+     *                              = (2*v + 1 - 2^l) * A
+     *
+     * Thus, one can compute q*A as C_256((q + 2^256 - 1) / 2, A). This is the basis for the
+     * paper's signed-digit multi-comb algorithm for multiplication using a precomputed table.
+     *
+     * It is appealing to try to combine this with the GLV optimization: the idea that a scalar
+     * s can be written as s1 + lambda*s2, where lambda is a curve-specific constant such that
+     * lambda*A is easy to compute, and where s1 and s2 are small. In particular we have the
+     * secp256k1_scalar_split_lambda function which performs such a split with the resulting s1
+     * and s2 in range (-2^128, 2^128) mod n. This does work, but is uninteresting:
+     *
+     *   To compute q*A:
+     *   - Let s1, s2 = split_lambda(q)
+     *   - Let R1 = C_256((s1 + 2^256 - 1) / 2, A)
+     *   - Let R2 = C_256((s2 + 2^256 - 1) / 2, lambda*A)
+     *   - Return R1 + R2
+     *
+     * The issue is that while s1 and s2 are small-range numbers, (s1 + 2^256 - 1) / 2 (mod n)
+     * and (s2 + 2^256 - 1) / 2 (mod n) are not, undoing the benefit of the splitting.
+     *
+     * To make it work, we want to modify the input scalar q first, before splitting, and then only
+     * add a 2^128 offset of the split results (so that they end up in the single 129-bit range
+     * [0,2^129]). A slightly smaller offset would work due to the bounds on the split, but we pick
+     * 2^128 for simplicity. Let s be the scalar fed to split_lambda, and f(q) the function to
+     * compute it from q:
+     *
+     *   To compute q*A:
+     *   - Compute s = f(q)
+     *   - Let s1, s2 = split_lambda(s)
+     *   - Let v1 = s1 + 2^128 (mod n)
+     *   - Let v2 = s2 + 2^128 (mod n)
+     *   - Let R1 = C_l(v1, A)
+     *   - Let R2 = C_l(v2, lambda*A)
+     *   - Return R1 + R2
+     *
+     * l will thus need to be at least 129, but we may overshoot by a few bits (see
+     * further), so keep it as a variable.
+     *
+     * To solve for s, we reason:
+     *     q*A  = R1 + R2
+     * <=> q*A  = C_l(s1 + 2^128, A) + C_l(s2 + 2^128, lambda*A)
+     * <=> q*A  = (2*(s1 + 2^128) + 1 - 2^l) * A + (2*(s2 + 2^128) + 1 - 2^l) * lambda*A
+     * <=> q*A  = (2*(s1 + s2*lambda) + (2^129 + 1 - 2^l) * (1 + lambda)) * A
+     * <=> q    = 2*(s1 + s2*lambda) + (2^129 + 1 - 2^l) * (1 + lambda) (mod n)
+     * <=> q    = 2*s + (2^129 + 1 - 2^l) * (1 + lambda) (mod n)
+     * <=> s    = (q + (2^l - 2^129 - 1) * (1 + lambda)) / 2 (mod n)
+     * <=> f(q) = (q + K) / 2 (mod n)
+     *            where K = (2^l - 2^129 - 1)*(1 + lambda) (mod n)
+     *
+     * We will process the computation of C_l(v1, A) and C_l(v2, lambda*A) in groups of
+     * ECMULT_CONST_GROUP_SIZE, so we set l to the smallest multiple of ECMULT_CONST_GROUP_SIZE
+     * that is not less than 129; this equals ECMULT_CONST_BITS.
+     */
+
+    /* The offset to add to s1 and s2 to make them non-negative. Equal to 2^128. */
+    static const secp256k1_scalar S_OFFSET = SECP256K1_SCALAR_CONST(0, 0, 0, 1, 0, 0, 0, 0);
+    secp256k1_scalar s, v1, v2;
+    secp256k1_ge pre_a[ECMULT_CONST_TABLE_SIZE];
+    secp256k1_ge pre_a_lam[ECMULT_CONST_TABLE_SIZE];
+    secp256k1_fe global_z;
+    int group, i;
+
+    /* We're allowed to be non-constant time in the point, and the code below (in particular,
+     * secp256k1_ecmult_const_odd_multiples_table_globalz) cannot deal with infinity in a
+     * constant-time manner anyway. */
+    if (secp256k1_ge_is_infinity(a)) {
+        secp256k1_gej_set_infinity(r);
+        return;
+    }
+
+    /* Compute v1 and v2. */
+    secp256k1_scalar_add(&s, q, &secp256k1_ecmult_const_K);
+    secp256k1_scalar_half(&s, &s);
+    secp256k1_scalar_split_lambda(&v1, &v2, &s);
+    secp256k1_scalar_add(&v1, &v1, &S_OFFSET);
+    secp256k1_scalar_add(&v2, &v2, &S_OFFSET);
+
+#ifdef VERIFY
+    /* Verify that v1 and v2 are in range [0, 2^129-1]. */
+    for (i = 129; i < 256; ++i) {
+        VERIFY_CHECK(secp256k1_scalar_get_bits_limb32(&v1, i, 1) == 0);
+        VERIFY_CHECK(secp256k1_scalar_get_bits_limb32(&v2, i, 1) == 0);
+    }
+#endif
+
+    /* Calculate odd multiples of A and A*lambda.
+     * All multiples are brought to the same Z 'denominator', which is stored
+     * in global_z. Due to secp256k1' isomorphism we can do all operations pretending
+     * that the Z coordinate was 1, use affine addition formulae, and correct
+     * the Z coordinate of the result once at the end.
+     */
+    secp256k1_gej_set_ge(r, a);
+    secp256k1_ecmult_const_odd_multiples_table_globalz(pre_a, &global_z, r);
+    for (i = 0; i < ECMULT_CONST_TABLE_SIZE; i++) {
+        secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
+    }
+
+    /* Next, we compute r = C_l(v1, A) + C_l(v2, lambda*A).
+     *
+     * We proceed in groups of ECMULT_CONST_GROUP_SIZE bits, operating on that many bits
+     * at a time, from high in v1, v2 to low. Call these bits1 (from v1) and bits2 (from v2).
+     *
+     * Now note that ECMULT_CONST_TABLE_GET_GE(&t, pre_a, bits1) loads into t a point equal
+     * to C_{ECMULT_CONST_GROUP_SIZE}(bits1, A), and analogously for pre_lam_a / bits2.
+     * This means that all we need to do is add these looked up values together, multiplied
+     * by 2^(ECMULT_GROUP_SIZE * group).
+     */
+    for (group = ECMULT_CONST_GROUPS - 1; group >= 0; --group) {
+        /* Using the _var get_bits function is ok here, since it's only variable in offset and count, not in the scalar. */
+        unsigned int bits1 = secp256k1_scalar_get_bits_var(&v1, group * ECMULT_CONST_GROUP_SIZE, ECMULT_CONST_GROUP_SIZE);
+        unsigned int bits2 = secp256k1_scalar_get_bits_var(&v2, group * ECMULT_CONST_GROUP_SIZE, ECMULT_CONST_GROUP_SIZE);
+        secp256k1_ge t;
+        int j;
+
+        ECMULT_CONST_TABLE_GET_GE(&t, pre_a, bits1);
+        if (group == ECMULT_CONST_GROUPS - 1) {
+            /* Directly set r in the first iteration. */
+            secp256k1_gej_set_ge(r, &t);
+        } else {
+            /* Shift the result so far up. */
+            for (j = 0; j < ECMULT_CONST_GROUP_SIZE; ++j) {
+                secp256k1_gej_double(r, r);
+            }
+            secp256k1_gej_add_ge(r, r, &t);
+        }
+        ECMULT_CONST_TABLE_GET_GE(&t, pre_a_lam, bits2);
+        secp256k1_gej_add_ge(r, r, &t);
+    }
+
+    /* Map the result back to the secp256k1 curve from the isomorphic curve. */
+    secp256k1_fe_mul(&r->z, &r->z, &global_z);
+}
+
+static int secp256k1_ecmult_const_xonly(secp256k1_fe* r, const secp256k1_fe *n, const secp256k1_fe *d, const secp256k1_scalar *q, int known_on_curve) {
+
+    /* This algorithm is a generalization of Peter Dettman's technique for
+     * avoiding the square root in a random-basepoint x-only multiplication
+     * on a Weierstrass curve:
+     * https://mailarchive.ietf.org/arch/msg/cfrg/7DyYY6gg32wDgHAhgSb6XxMDlJA/
+     *
+     *
+     * === Background: the effective affine technique ===
+     *
+     * Let phi_u be the isomorphism that maps (x, y) on secp256k1 curve y^2 = x^3 + 7 to
+     * x' = u^2*x, y' = u^3*y on curve y'^2 = x'^3 + u^6*7. This new curve has the same order as
+     * the original (it is isomorphic), but moreover, has the same addition/doubling formulas, as
+     * the curve b=7 coefficient does not appear in those formulas (or at least does not appear in
+     * the formulas implemented in this codebase, both affine and Jacobian). See also Example 9.5.2
+     * in https://www.math.auckland.ac.nz/~sgal018/crypto-book/ch9.pdf.
+     *
+     * This means any linear combination of secp256k1 points can be computed by applying phi_u
+     * (with non-zero u) on all input points (including the generator, if used), computing the
+     * linear combination on the isomorphic curve (using the same group laws), and then applying
+     * phi_u^{-1} to get back to secp256k1.
+     *
+     * Switching to Jacobian coordinates, note that phi_u applied to (X, Y, Z) is simply
+     * (X, Y, Z/u). Thus, if we want to compute (X1, Y1, Z) + (X2, Y2, Z), with identical Z
+     * coordinates, we can use phi_Z to transform it to (X1, Y1, 1) + (X2, Y2, 1) on an isomorphic
+     * curve where the affine addition formula can be used instead.
+     * If (X3, Y3, Z3) = (X1, Y1) + (X2, Y2) on that curve, then our answer on secp256k1 is
+     * (X3, Y3, Z3*Z).
+     *
+     * This is the effective affine technique: if we have a linear combination of group elements
+     * to compute, and all those group elements have the same Z coordinate, we can simply pretend
+     * that all those Z coordinates are 1, perform the computation that way, and then multiply the
+     * original Z coordinate back in.
+     *
+     * The technique works on any a=0 short Weierstrass curve. It is possible to generalize it to
+     * other curves too, but there the isomorphic curves will have different 'a' coefficients,
+     * which typically does affect the group laws.
+     *
+     *
+     * === Avoiding the square root for x-only point multiplication ===
+     *
+     * In this function, we want to compute the X coordinate of q*(n/d, y), for
+     * y = sqrt((n/d)^3 + 7). Its negation would also be a valid Y coordinate, but by convention
+     * we pick whatever sqrt returns (which we assume to be a deterministic function).
+     *
+     * Let g = y^2*d^3 = n^3 + 7*d^3. This also means y = sqrt(g/d^3).
+     * Further let v = sqrt(d*g), which must exist as d*g = y^2*d^4 = (y*d^2)^2.
+     *
+     * The input point (n/d, y) also has Jacobian coordinates:
+     *
+     *     (n/d, y, 1)
+     *   = (n/d * v^2, y * v^3, v)
+     *   = (n/d * d*g, y * sqrt(d^3*g^3), v)
+     *   = (n/d * d*g, sqrt(y^2 * d^3*g^3), v)
+     *   = (n*g, sqrt(g/d^3 * d^3*g^3), v)
+     *   = (n*g, sqrt(g^4), v)
+     *   = (n*g, g^2, v)
+     *
+     * It is easy to verify that both (n*g, g^2, v) and its negation (n*g, -g^2, v) have affine X
+     * coordinate n/d, and this holds even when the square root function doesn't have a
+     * deterministic sign. We choose the (n*g, g^2, v) version.
+     *
+     * Now switch to the effective affine curve using phi_v, where the input point has coordinates
+     * (n*g, g^2). Compute (X, Y, Z) = q * (n*g, g^2) there.
+     *
+     * Back on secp256k1, that means q * (n*g, g^2, v) = (X, Y, v*Z). This last point has affine X
+     * coordinate X / (v^2*Z^2) = X / (d*g*Z^2). Determining the affine Y coordinate would involve
+     * a square root, but as long as we only care about the resulting X coordinate, no square root
+     * is needed anywhere in this computation.
+     */
+
+    secp256k1_fe g, i;
+    secp256k1_ge p;
+    secp256k1_gej rj;
+
+    /* Compute g = (n^3 + B*d^3). */
+    secp256k1_fe_sqr(&g, n);
+    secp256k1_fe_mul(&g, &g, n);
+    if (d) {
+        secp256k1_fe b;
+        VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero(d));
+        secp256k1_fe_sqr(&b, d);
+        VERIFY_CHECK(SECP256K1_B <= 8); /* magnitude of b will be <= 8 after the next call */
+        secp256k1_fe_mul_int(&b, SECP256K1_B);
+        secp256k1_fe_mul(&b, &b, d);
+        secp256k1_fe_add(&g, &b);
+        if (!known_on_curve) {
+            /* We need to determine whether (n/d)^3 + 7 is square.
+             *
+             *     is_square((n/d)^3 + 7)
+             * <=> is_square(((n/d)^3 + 7) * d^4)
+             * <=> is_square((n^3 + 7*d^3) * d)
+             * <=> is_square(g * d)
+             */
+            secp256k1_fe c;
+            secp256k1_fe_mul(&c, &g, d);
+            if (!secp256k1_fe_is_square_var(&c)) return 0;
+        }
+    } else {
+        secp256k1_fe_add_int(&g, SECP256K1_B);
+        if (!known_on_curve) {
+            /* g at this point equals x^3 + 7. Test if it is square. */
+            if (!secp256k1_fe_is_square_var(&g)) return 0;
+        }
+    }
+
+    SECP256K1_FE_VERIFY_MAGNITUDE(&g, 2);
+
+    /* Compute base point P = (n*g, g^2), the effective affine version of
+     * (n*g, g^2, v), which has corresponding affine X coordinate n/d. */
+    {
+        secp256k1_fe x, y;
+        secp256k1_fe_mul(&x, &g, n);
+        secp256k1_fe_sqr(&y, &g);
+        secp256k1_ge_set_xy(&p, &x, &y);
+    }
+
+    /* Perform x-only EC multiplication of P with q. */
+    VERIFY_CHECK(!secp256k1_scalar_is_zero(q));
+    secp256k1_ecmult_const(&rj, &p, q);
+    VERIFY_CHECK(!secp256k1_gej_is_infinity(&rj));
+
+    /* The resulting (X, Y, Z) point on the effective-affine isomorphic curve corresponds to
+     * (X, Y, Z*v) on the secp256k1 curve. The affine version of that has X coordinate
+     * (X / (Z^2*d*g)). */
+    secp256k1_fe_sqr(&i, &rj.z);
+    secp256k1_fe_mul(&i, &i, &g);
+    if (d) secp256k1_fe_mul(&i, &i, d);
+    secp256k1_fe_inv(&i, &i);
+    secp256k1_fe_mul(r, &rj.x, &i);
+
+    return 1;
+}
+
+#endif /* SECP256K1_ECMULT_CONST_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_gen.h

@@ -0,0 +1,144 @@
+/***********************************************************************
+ * Copyright (c) Pieter Wuille, Peter Dettman                          *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_H
+#define SECP256K1_ECMULT_GEN_H
+
+#include "hash.h"
+#include "scalar.h"
+#include "group.h"
+
+
+/* Configuration parameters for the signed-digit multi-comb algorithm:
+ *
+ * - COMB_BLOCKS is the number of blocks the input is split into. Each
+ *   has a corresponding table.
+ * - COMB_TEETH is the number of bits simultaneously covered by one table.
+ * - COMB_RANGE is the number of bits in supported scalars. For production
+ *   purposes, only 256 is reasonable, but smaller numbers are supported for
+ *   exhaustive test mode.
+ *
+ * The comb's spacing (COMB_SPACING), or the distance between the teeth,
+ * is defined as ceil(COMB_RANGE / (COMB_BLOCKS * COMB_TEETH)). Each block covers
+ * COMB_SPACING * COMB_TEETH consecutive bits in the input.
+ *
+ * The size of the precomputed table is COMB_BLOCKS * (1 << (COMB_TEETH - 1))
+ * secp256k1_ge_storages.
+ *
+ * The number of point additions equals COMB_BLOCKS * COMB_SPACING. Each point
+ * addition involves a cmov from (1 << (COMB_TEETH - 1)) table entries and a
+ * conditional negation.
+ *
+ * The number of point doublings is COMB_SPACING - 1. */
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/* We need to control these values for exhaustive tests because
+ * the table cannot have infinities in them (secp256k1_ge_storage
+ * doesn't support infinities) */
+#  undef COMB_BLOCKS
+#  undef COMB_TEETH
+#  if EXHAUSTIVE_TEST_ORDER == 7
+#    define COMB_RANGE 3
+#    define COMB_BLOCKS 1
+#    define COMB_TEETH 2
+#  elif EXHAUSTIVE_TEST_ORDER == 13
+#    define COMB_RANGE 4
+#    define COMB_BLOCKS 1
+#    define COMB_TEETH 2
+#  elif EXHAUSTIVE_TEST_ORDER == 199
+#    define COMB_RANGE 8
+#    define COMB_BLOCKS 2
+#    define COMB_TEETH 3
+#  else
+#    error "Unknown exhaustive test order"
+#  endif
+#  if (COMB_RANGE >= 32) || ((EXHAUSTIVE_TEST_ORDER >> (COMB_RANGE - 1)) != 1)
+#    error "COMB_RANGE != ceil(log2(EXHAUSTIVE_TEST_ORDER+1))"
+#  endif
+#else /* !defined(EXHAUSTIVE_TEST_ORDER) */
+#  define COMB_RANGE 256
+#endif /* defined(EXHAUSTIVE_TEST_ORDER) */
+
+/* Use (11, 6) as default configuration, which results in a 22 kB table. */
+#ifndef COMB_BLOCKS
+#  define COMB_BLOCKS 11
+#  ifdef DEBUG_CONFIG
+#    pragma message DEBUG_CONFIG_MSG("COMB_BLOCKS undefined, assuming default value")
+#  endif
+#endif
+#ifndef COMB_TEETH
+#  define COMB_TEETH 6
+#  ifdef DEBUG_CONFIG
+#    pragma message DEBUG_CONFIG_MSG("COMB_TEETH undefined, assuming default value")
+#  endif
+#endif
+/* Use ceil(COMB_RANGE / (COMB_BLOCKS * COMB_TEETH)) as COMB_SPACING. */
+#define COMB_SPACING CEIL_DIV(COMB_RANGE, COMB_BLOCKS * COMB_TEETH)
+
+/* Range checks on the parameters. */
+
+/* The remaining COMB_* parameters are derived values, don't modify these. */
+/* - The number of bits covered by all the blocks; must be at least COMB_RANGE. */
+#define COMB_BITS (COMB_BLOCKS * COMB_TEETH * COMB_SPACING)
+/* - The number of entries per table. */
+#define COMB_POINTS (1 << (COMB_TEETH - 1))
+
+/* Sanity checks. */
+#if !(1 <= COMB_BLOCKS && COMB_BLOCKS <= 256)
+#  error "COMB_BLOCKS must be in the range [1, 256]"
+#endif
+#if !(1 <= COMB_TEETH && COMB_TEETH <= 8)
+#  error "COMB_TEETH must be in the range [1, 8]"
+#endif
+#if COMB_BITS < COMB_RANGE
+#  error "COMB_BLOCKS * COMB_TEETH * COMB_SPACING is too low"
+#endif
+
+/* These last 2 checks are not strictly required, but prevent gratuitously inefficient
+ * configurations. Note that they compare with 256 rather than COMB_RANGE, so they do
+ * permit somewhat excessive values for the exhaustive test case, where testing with
+ * suboptimal parameters may be desirable. */
+#if (COMB_BLOCKS - 1) * COMB_TEETH * COMB_SPACING >= 256
+#  error "COMB_BLOCKS can be reduced"
+#endif
+#if COMB_BLOCKS * (COMB_TEETH - 1) * COMB_SPACING >= 256
+#  error "COMB_TEETH can be reduced"
+#endif
+
+#ifdef DEBUG_CONFIG
+#  pragma message DEBUG_CONFIG_DEF(COMB_RANGE)
+#  pragma message DEBUG_CONFIG_DEF(COMB_BLOCKS)
+#  pragma message DEBUG_CONFIG_DEF(COMB_TEETH)
+#  pragma message DEBUG_CONFIG_DEF(COMB_SPACING)
+#endif
+
+typedef struct {
+    /* Whether the context has been built. */
+    int built;
+
+    /* Values chosen such that
+     *
+     *   n*G == comb(n + scalar_offset, G/2) + ge_offset.
+     *
+     * This expression lets us use scalar blinding and optimize the comb precomputation. See
+     * ecmult_gen_impl.h for more details. */
+    secp256k1_scalar scalar_offset;
+    secp256k1_ge ge_offset;
+
+    /* Factor used for projective blinding. This value is used to rescale the Z
+     * coordinate of the first table lookup. */
+    secp256k1_fe proj_blind;
+} secp256k1_ecmult_gen_context;
+
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context* ctx, const secp256k1_hash_ctx *hash_ctx);
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context* ctx);
+
+/** Multiply with the generator: R = a*G */
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context* ctx, secp256k1_gej *r, const secp256k1_scalar *a);
+
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const secp256k1_hash_ctx *hash_ctx, const unsigned char *seed32);
+
+#endif /* SECP256K1_ECMULT_GEN_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_gen_compute_table.h

@@ -0,0 +1,14 @@
+/***********************************************************************
+ * Copyright (c) Pieter Wuille, Gregory Maxwell                        *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H
+#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H
+
+#include "ecmult_gen.h"
+
+static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int blocks, int teeth, int spacing);
+
+#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_gen_compute_table_impl.h

@@ -0,0 +1,108 @@
+/***********************************************************************
+ * Copyright (c) Pieter Wuille, Gregory Maxwell, Peter Dettman         *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H
+#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H
+
+#include "ecmult_gen_compute_table.h"
+#include "group_impl.h"
+#include "field_impl.h"
+#include "scalar_impl.h"
+#include "ecmult_gen.h"
+#include "util.h"
+
+static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int blocks, int teeth, int spacing) {
+    size_t points = ((size_t)1) << (teeth - 1);
+    size_t points_total = points * blocks;
+    secp256k1_ge* prec = checked_malloc(&default_error_callback, points_total * sizeof(*prec));
+    secp256k1_gej* ds = checked_malloc(&default_error_callback, teeth * sizeof(*ds));
+    secp256k1_gej* vs = checked_malloc(&default_error_callback, points_total * sizeof(*vs));
+    secp256k1_gej u;
+    size_t vs_pos = 0;
+    secp256k1_scalar half;
+    int block, i;
+
+    VERIFY_CHECK(points_total > 0);
+
+    /* u is the running power of two times gen we're working with, initially gen/2. */
+    secp256k1_scalar_half(&half, &secp256k1_scalar_one);
+    secp256k1_gej_set_infinity(&u);
+    for (i = 255; i >= 0; --i) {
+        /* Use a very simple multiplication ladder to avoid dependency on ecmult. */
+        secp256k1_gej_double_var(&u, &u, NULL);
+        if (secp256k1_scalar_get_bits_limb32(&half, i, 1)) {
+            secp256k1_gej_add_ge_var(&u, &u, gen, NULL);
+        }
+    }
+#ifdef VERIFY
+    {
+        /* Verify that u*2 = gen. */
+        secp256k1_gej double_u;
+        secp256k1_gej_double_var(&double_u, &u, NULL);
+        VERIFY_CHECK(secp256k1_gej_eq_ge_var(&double_u, gen));
+    }
+#endif
+
+    for (block = 0; block < blocks; ++block) {
+        int tooth;
+        /* Here u = 2^(block*teeth*spacing) * gen/2. */
+        secp256k1_gej sum;
+        secp256k1_gej_set_infinity(&sum);
+        for (tooth = 0; tooth < teeth; ++tooth) {
+            /* Here u = 2^((block*teeth + tooth)*spacing) * gen/2. */
+            /* Make sum = sum(2^((block*teeth + t)*spacing), t=0..tooth) * gen/2. */
+            secp256k1_gej_add_var(&sum, &sum, &u, NULL);
+            /* Make u = 2^((block*teeth + tooth)*spacing + 1) * gen/2. */
+            secp256k1_gej_double_var(&u, &u, NULL);
+            /* Make ds[tooth] = u = 2^((block*teeth + tooth)*spacing + 1) * gen/2. */
+            ds[tooth] = u;
+            /* Make u = 2^((block*teeth + tooth + 1)*spacing) * gen/2, unless at the end. */
+            if (block + tooth != blocks + teeth - 2) {
+                int bit_off;
+                for (bit_off = 1; bit_off < spacing; ++bit_off) {
+                    secp256k1_gej_double_var(&u, &u, NULL);
+                }
+            }
+        }
+        /* Now u = 2^((block*teeth + teeth)*spacing) * gen/2
+         *       = 2^((block+1)*teeth*spacing) * gen/2       */
+
+        /* Next, compute the table entries for block number block in Jacobian coordinates.
+         * The entries will occupy vs[block*points + i] for i=0..points-1.
+         * We start by computing the first (i=0) value corresponding to all summed
+         * powers of two times G being negative. */
+        secp256k1_gej_neg(&vs[vs_pos++], &sum);
+        /* And then teeth-1 times "double" the range of i values for which the table
+         * is computed: in each iteration, double the table by taking an existing
+         * table entry and adding ds[tooth]. */
+        for (tooth = 0; tooth < teeth - 1; ++tooth) {
+            size_t stride = ((size_t)1) << tooth;
+            size_t index;
+            for (index = 0; index < stride; ++index, ++vs_pos) {
+                secp256k1_gej_add_var(&vs[vs_pos], &vs[vs_pos - stride], &ds[tooth], NULL);
+            }
+        }
+    }
+    VERIFY_CHECK(vs_pos == points_total);
+
+    /* Convert all points simultaneously from secp256k1_gej to secp256k1_ge. */
+    secp256k1_ge_set_all_gej_var(prec, vs, points_total);
+    /* Convert all points from secp256k1_ge to secp256k1_ge_storage output. */
+    for (block = 0; block < blocks; ++block) {
+        size_t index;
+        for (index = 0; index < points; ++index) {
+            VERIFY_CHECK(!secp256k1_ge_is_infinity(&prec[block * points + index]));
+            secp256k1_ge_to_storage(&table[block * points + index], &prec[block * points + index]);
+        }
+    }
+
+    /* Free memory. */
+    free(vs);
+    free(ds);
+    free(prec);
+}
+
+#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_gen_impl.h

@@ -0,0 +1,341 @@
+/***********************************************************************
+ * Copyright (c) Pieter Wuille, Gregory Maxwell, Peter Dettman         *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_ECMULT_GEN_IMPL_H
+#define SECP256K1_ECMULT_GEN_IMPL_H
+
+#include "util.h"
+#include "scalar.h"
+#include "group.h"
+#include "ecmult_gen.h"
+#include "hash_impl.h"
+#include "precomputed_ecmult_gen.h"
+
+static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx, const secp256k1_hash_ctx *hash_ctx) {
+    secp256k1_ecmult_gen_blind(ctx, hash_ctx, NULL);
+    ctx->built = 1;
+}
+
+static int secp256k1_ecmult_gen_context_is_built(const secp256k1_ecmult_gen_context* ctx) {
+    return ctx->built;
+}
+
+static void secp256k1_ecmult_gen_context_clear(secp256k1_ecmult_gen_context *ctx) {
+    ctx->built = 0;
+    secp256k1_scalar_clear(&ctx->scalar_offset);
+    secp256k1_ge_clear(&ctx->ge_offset);
+    secp256k1_fe_clear(&ctx->proj_blind);
+}
+
+/* Compute the scalar (2^COMB_BITS - 1) / 2, the difference between the gn argument to
+ * secp256k1_ecmult_gen, and the scalar whose encoding the table lookup bits are drawn
+ * from (before applying blinding). */
+static void secp256k1_ecmult_gen_scalar_diff(secp256k1_scalar* diff) {
+    int i;
+
+    /* Compute scalar -1/2. */
+    secp256k1_scalar neghalf;
+    secp256k1_scalar_half(&neghalf, &secp256k1_scalar_one);
+    secp256k1_scalar_negate(&neghalf, &neghalf);
+
+    /* Compute offset = 2^(COMB_BITS - 1). */
+    *diff = secp256k1_scalar_one;
+    for (i = 0; i < COMB_BITS - 1; ++i) {
+        secp256k1_scalar_add(diff, diff, diff);
+    }
+
+    /* The result is the sum 2^(COMB_BITS - 1) + (-1/2). */
+    secp256k1_scalar_add(diff, diff, &neghalf);
+}
+
+static void secp256k1_ecmult_gen(const secp256k1_ecmult_gen_context *ctx, secp256k1_gej *r, const secp256k1_scalar *gn) {
+    uint32_t comb_off;
+    secp256k1_ge add;
+    secp256k1_fe neg;
+    secp256k1_ge_storage adds;
+    secp256k1_scalar d;
+    /* Array of uint32_t values large enough to store COMB_BITS bits. Only the bottom
+     * 8 are ever nonzero, but having the zero padding at the end if COMB_BITS>256
+     * avoids the need to deal with out-of-bounds reads from a scalar. */
+    uint32_t recoded[(COMB_BITS + 31) >> 5] = {0};
+    int first = 1, i;
+
+    memset(&adds, 0, sizeof(adds));
+
+    /* We want to compute R = gn*G.
+     *
+     * To blind the scalar used in the computation, we rewrite this to be
+     * R = (gn - b)*G + b*G, with a blinding value b determined by the context.
+     *
+     * The multiplication (gn-b)*G will be performed using a signed-digit multi-comb (see Section
+     * 3.3 of "Fast and compact elliptic-curve cryptography" by Mike Hamburg,
+     * https://eprint.iacr.org/2012/309).
+     *
+     * Let comb(s, P) = sum((2*s[i]-1)*2^i*P for i=0..COMB_BITS-1), where s[i] is the i'th bit of
+     * the binary representation of scalar s. So the s[i] values determine whether -2^i*P (s[i]=0)
+     * or +2^i*P (s[i]=1) are added together. COMB_BITS is at least 256, so all bits of s are
+     * covered. By manipulating:
+     *
+     *     comb(s, P) = sum((2*s[i]-1)*2^i*P for i=0..COMB_BITS-1)
+     * <=> comb(s, P) = sum((2*s[i]-1)*2^i for i=0..COMB_BITS-1) * P
+     * <=> comb(s, P) = (2*sum(s[i]*2^i for i=0..COMB_BITS-1) - sum(2^i for i=0..COMB_BITS-1)) * P
+     * <=> comb(s, P) = (2*s - (2^COMB_BITS - 1)) * P
+     *
+     * If we wanted to compute (gn-b)*G as comb(s, G), it would need to hold that
+     *
+     *     (gn - b) * G = (2*s - (2^COMB_BITS - 1)) * G
+     * <=> s = (gn - b + (2^COMB_BITS - 1))/2 (mod order)
+     *
+     * We use an alternative here that avoids the modular division by two: instead we compute
+     * (gn-b)*G as comb(d, G/2). For that to hold it must be the case that
+     *
+     *     (gn - b) * G = (2*d - (2^COMB_BITS - 1)) * (G/2)
+     * <=> d = gn - b + (2^COMB_BITS - 1)/2 (mod order)
+     *
+     * Adding precomputation, our final equations become:
+     *
+     *     ctx->scalar_offset = (2^COMB_BITS - 1)/2 - b (mod order)
+     *     ctx->ge_offset = b*G
+     *     d = gn + ctx->scalar_offset (mod order)
+     *     R = comb(d, G/2) + ctx->ge_offset
+     *
+     * comb(d, G/2) function is then computed by summing + or - 2^(i-1)*G, for i=0..COMB_BITS-1,
+     * depending on the value of the bits d[i] of the binary representation of scalar d.
+     */
+
+    /* Compute the scalar d = (gn + ctx->scalar_offset). */
+    secp256k1_scalar_add(&d, &ctx->scalar_offset, gn);
+    /* Convert to recoded array. */
+    for (i = 0; i < 8 && i < ((COMB_BITS + 31) >> 5); ++i) {
+        recoded[i] = secp256k1_scalar_get_bits_limb32(&d, 32 * i, 32);
+    }
+    secp256k1_scalar_clear(&d);
+
+    /* In secp256k1_ecmult_gen_prec_table we have precomputed sums of the
+     * (2*d[i]-1) * 2^(i-1) * G points, for various combinations of i positions.
+     * We rewrite our equation in terms of these table entries.
+     *
+     * Let mask(b) = sum(2^((b*COMB_TEETH + t)*COMB_SPACING) for t=0..COMB_TEETH-1),
+     * with b ranging from 0 to COMB_BLOCKS-1. So for example with COMB_BLOCKS=11,
+     * COMB_TEETH=6, COMB_SPACING=4, we would have:
+     *   mask(0)  = 2^0   + 2^4   + 2^8   + 2^12  + 2^16  + 2^20,
+     *   mask(1)  = 2^24  + 2^28  + 2^32  + 2^36  + 2^40  + 2^44,
+     *   mask(2)  = 2^48  + 2^52  + 2^56  + 2^60  + 2^64  + 2^68,
+     *   ...
+     *   mask(10) = 2^240 + 2^244 + 2^248 + 2^252 + 2^256 + 2^260
+     *
+     * We will split up the bits d[i] using these masks. Specifically, each mask is
+     * used COMB_SPACING times, with different shifts:
+     *
+     * d = (d & mask(0)<<0) + (d & mask(1)<<0) + ... + (d & mask(COMB_BLOCKS-1)<<0) +
+     *     (d & mask(0)<<1) + (d & mask(1)<<1) + ... + (d & mask(COMB_BLOCKS-1)<<1) +
+     *     ...
+     *     (d & mask(0)<<(COMB_SPACING-1)) + ...
+     *
+     * Now define table(b, m) = (m - mask(b)/2) * G, and we will precompute these values for
+     * b=0..COMB_BLOCKS-1, and for all values m which (d & mask(b)) can take (so m can take on
+     * 2^COMB_TEETH distinct values).
+     *
+     * If m=(d & mask(b)), then table(b, m) is the sum of 2^i * (2*d[i]-1) * G/2, with i
+     * iterating over the set bits in mask(b). In our example, table(2, 2^48 + 2^56 + 2^68)
+     * would equal (2^48 - 2^52 + 2^56 - 2^60 - 2^64 + 2^68) * G/2.
+     *
+     * With that, we can rewrite comb(d, G/2) as:
+     *
+     *     2^0 * (table(0, d>>0 & mask(0)) + ... + table(COMB_BLOCKS-1, d>>0 & mask(COMP_BLOCKS-1)))
+     *   + 2^1 * (table(0, d>>1 & mask(0)) + ... + table(COMB_BLOCKS-1, d>>1 & mask(COMP_BLOCKS-1)))
+     *   + 2^2 * (table(0, d>>2 & mask(0)) + ... + table(COMB_BLOCKS-1, d>>2 & mask(COMP_BLOCKS-1)))
+     *   + ...
+     *   + 2^(COMB_SPACING-1) * (table(0, d>>(COMB_SPACING-1) & mask(0)) + ...)
+     *
+     * Or more generically as
+     *
+     *   sum(2^i * sum(table(b, d>>i & mask(b)), b=0..COMB_BLOCKS-1), i=0..COMB_SPACING-1)
+     *
+     * This is implemented using an outer loop that runs in reverse order over the lines of this
+     * equation, which in each iteration runs an inner loop that adds the terms of that line and
+     * then doubles the result before proceeding to the next line.
+     *
+     * In pseudocode:
+     *   c = infinity
+     *   for comb_off in range(COMB_SPACING - 1, -1, -1):
+     *     for block in range(COMB_BLOCKS):
+     *       c += table(block, (d >> comb_off) & mask(block))
+     *     if comb_off > 0:
+     *       c = 2*c
+     *   return c
+     *
+     * This computes c = comb(d, G/2), and thus finally R = c + ctx->ge_offset. Note that it would
+     * be possible to apply an initial offset instead of a final offset (moving ge_offset to take
+     * the place of infinity above), but the chosen approach allows using (in a future improvement)
+     * an incomplete addition formula for most of the multiplication.
+     *
+     * The last question is how to implement the table(b, m) function. For any value of b,
+     * m=(d & mask(b)) can only take on at most 2^COMB_TEETH possible values (the last one may have
+     * fewer as there mask(b) may exceed the curve order). So we could create COMB_BLOCK tables
+     * which contain a value for each such m value.
+     *
+     * Now note that if m=(d & mask(b)), then flipping the relevant bits of m results in negating
+     * the result of table(b, m). This is because table(b,m XOR mask(b)) = table(b, mask(b) - m) =
+     * (mask(b) - m - mask(b)/2)*G = (-m + mask(b)/2)*G = -(m - mask(b)/2)*G = -table(b, m).
+     * Because of this it suffices to only store the first half of the m values for every b. If an
+     * entry from the second half is needed, we look up its bit-flipped version instead, and negate
+     * it.
+     *
+     * secp256k1_ecmult_gen_prec_table[b][index] stores the table(b, m) entries. Index
+     * is the relevant mask(b) bits of m packed together without gaps. */
+
+    /* Outer loop: iterate over comb_off from COMB_SPACING - 1 down to 0. */
+    comb_off = COMB_SPACING - 1;
+    while (1) {
+        uint32_t block;
+        uint32_t bit_pos = comb_off;
+        /* Inner loop: for each block, add table entries to the result. */
+        for (block = 0; block < COMB_BLOCKS; ++block) {
+            /* Gather the mask(block)-selected bits of d into bits. They're packed:
+             * bits[tooth] = d[(block*COMB_TEETH + tooth)*COMB_SPACING + comb_off]. */
+            uint32_t bits = 0, sign, abs, index, tooth;
+            /* Instead of reading individual bits here to construct the bits variable,
+             * build up the result by xoring rotated reads together. In every iteration,
+             * one additional bit is made correct, starting at the bottom. The bits
+             * above that contain junk. This reduces leakage by avoiding computations
+             * on variables that can have only a low number of possible values (e.g.,
+             * just two values when reading a single bit into a variable.) See:
+             * https://www.usenix.org/system/files/conference/usenixsecurity18/sec18-alam.pdf
+             */
+            for (tooth = 0; tooth < COMB_TEETH; ++tooth) {
+                /* Construct bitdata s.t. the bottom bit is the bit we'd like to read.
+                 *
+                 * We could just set bitdata = recoded[bit_pos >> 5] >> (bit_pos & 0x1f)
+                 * but this would simply discard the bits that fall off at the bottom,
+                 * and thus, for example, bitdata could still have only two values if we
+                 * happen to shift by exactly 31 positions. We use a rotation instead,
+                 * which ensures that bitdata doesn't lose entropy. This relies on the
+                 * rotation being atomic, i.e., the compiler emitting an actual rot
+                 * instruction. */
+                uint32_t bitdata = secp256k1_rotr32(recoded[bit_pos >> 5], bit_pos & 0x1f);
+
+                /* Clear the bit at position tooth, but sssh, don't tell clang. */
+                uint32_t volatile vmask = ~(1 << tooth);
+                bits &= vmask;
+
+                /* Write the bit into position tooth (and junk into higher bits). */
+                bits ^= bitdata << tooth;
+                bit_pos += COMB_SPACING;
+            }
+
+            /* If the top bit of bits is 1, flip them all (corresponding to looking up
+             * the negated table value), and remember to negate the result in sign. */
+            sign = (bits >> (COMB_TEETH - 1)) & 1;
+            abs = (bits ^ -sign) & (COMB_POINTS - 1);
+            VERIFY_CHECK(sign == 0 || sign == 1);
+            VERIFY_CHECK(abs < COMB_POINTS);
+
+            /** This uses a conditional move to avoid any secret data in array indexes.
+             *   _Any_ use of secret indexes has been demonstrated to result in timing
+             *   sidechannels, even when the cache-line access patterns are uniform.
+             *  See also:
+             *   "A word of warning", CHES 2013 Rump Session, by Daniel J. Bernstein and Peter Schwabe
+             *    (https://cryptojedi.org/peter/data/chesrump-20130822.pdf) and
+             *   "Cache Attacks and Countermeasures: the Case of AES", RSA 2006,
+             *    by Dag Arne Osvik, Adi Shamir, and Eran Tromer
+             *    (https://eprint.iacr.org/2005/271.pdf)
+             */
+            for (index = 0; index < COMB_POINTS; ++index) {
+                secp256k1_ge_storage_cmov(&adds, &secp256k1_ecmult_gen_prec_table[block][index], index == abs);
+            }
+
+            /* Set add=adds or add=-adds, in constant time, based on sign. */
+            secp256k1_ge_from_storage(&add, &adds);
+            secp256k1_fe_negate(&neg, &add.y, 1);
+            secp256k1_fe_cmov(&add.y, &neg, sign);
+
+            /* Add the looked up and conditionally negated value to r. */
+            if (EXPECT(first, 0)) {
+                /* If this is the first table lookup, we can skip addition. */
+                secp256k1_gej_set_ge(r, &add);
+                /* Give the entry a random Z coordinate to blind intermediary results. */
+                secp256k1_gej_rescale(r, &ctx->proj_blind);
+                first = 0;
+            } else {
+                secp256k1_gej_add_ge(r, r, &add);
+            }
+        }
+
+        /* Double the result, except in the last iteration. */
+        if (comb_off-- == 0) break;
+        secp256k1_gej_double(r, r);
+    }
+
+    /* Correct for the scalar_offset added at the start (ge_offset = b*G, while b was
+     * subtracted from the input scalar gn). */
+    secp256k1_gej_add_ge(r, r, &ctx->ge_offset);
+
+    /* Cleanup. */
+    secp256k1_fe_clear(&neg);
+    secp256k1_ge_clear(&add);
+    secp256k1_memclear_explicit(&adds, sizeof(adds));
+    secp256k1_memclear_explicit(&recoded, sizeof(recoded));
+}
+
+/* Setup blinding values for secp256k1_ecmult_gen. */
+static void secp256k1_ecmult_gen_blind(secp256k1_ecmult_gen_context *ctx, const secp256k1_hash_ctx *hash_ctx, const unsigned char *seed32) {
+    secp256k1_scalar b;
+    secp256k1_scalar diff;
+    secp256k1_gej gb;
+    secp256k1_fe f;
+    unsigned char nonce32[32];
+    secp256k1_rfc6979_hmac_sha256 rng;
+    unsigned char keydata[64];
+
+    /* Compute the (2^COMB_BITS - 1)/2 term once. */
+    secp256k1_ecmult_gen_scalar_diff(&diff);
+
+    if (seed32 == NULL) {
+        /* When seed is NULL, reset the final point and blinding value. */
+        secp256k1_ge_neg(&ctx->ge_offset, &secp256k1_ge_const_g);
+        secp256k1_scalar_add(&ctx->scalar_offset, &secp256k1_scalar_one, &diff);
+        ctx->proj_blind = secp256k1_fe_one;
+        return;
+    }
+    /* The prior blinding value (if not reset) is chained forward by including it in the hash. */
+    secp256k1_scalar_get_b32(keydata, &ctx->scalar_offset);
+    /** Using a CSPRNG allows a failure free interface, avoids needing large amounts of random data,
+     *   and guards against weak or adversarial seeds.  This is a simpler and safer interface than
+     *   asking the caller for blinding values directly and expecting them to retry on failure.
+     */
+    VERIFY_CHECK(seed32 != NULL);
+    memcpy(keydata + 32, seed32, 32);
+    secp256k1_rfc6979_hmac_sha256_initialize(hash_ctx, &rng, keydata, 64);
+    secp256k1_memclear_explicit(keydata, sizeof(keydata));
+
+    /* Compute projective blinding factor (cannot be 0). */
+    secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, nonce32, 32);
+    secp256k1_fe_set_b32_mod(&f, nonce32);
+    secp256k1_fe_cmov(&f, &secp256k1_fe_one, secp256k1_fe_normalizes_to_zero(&f));
+    ctx->proj_blind = f;
+
+    /* For a random blinding value b, set scalar_offset=diff-b, ge_offset=bG */
+    secp256k1_rfc6979_hmac_sha256_generate(hash_ctx, &rng, nonce32, 32);
+    secp256k1_scalar_set_b32(&b, nonce32, NULL);
+    /* The blinding value cannot be zero, as that would mean ge_offset = infinity,
+     * which secp256k1_gej_add_ge cannot handle. */
+    secp256k1_scalar_cmov(&b, &secp256k1_scalar_one, secp256k1_scalar_is_zero(&b));
+    secp256k1_rfc6979_hmac_sha256_finalize(&rng);
+    secp256k1_ecmult_gen(ctx, &gb, &b);
+    secp256k1_scalar_negate(&b, &b);
+    secp256k1_scalar_add(&ctx->scalar_offset, &b, &diff);
+    secp256k1_ge_set_gej(&ctx->ge_offset, &gb);
+
+    /* Clean up. */
+    secp256k1_memclear_explicit(nonce32, sizeof(nonce32));
+    secp256k1_scalar_clear(&b);
+    secp256k1_gej_clear(&gb);
+    secp256k1_fe_clear(&f);
+    secp256k1_rfc6979_hmac_sha256_clear(&rng);
+}
+
+#endif /* SECP256K1_ECMULT_GEN_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/ecmult_impl.h

@@ -0,0 +1,869 @@
+/******************************************************************************
+ * Copyright (c) 2013, 2014, 2017 Pieter Wuille, Andrew Poelstra, Jonas Nick  *
+ * Distributed under the MIT software license, see the accompanying           *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.       *
+ ******************************************************************************/
+
+#ifndef SECP256K1_ECMULT_IMPL_H
+#define SECP256K1_ECMULT_IMPL_H
+
+#include <string.h>
+#include <stdint.h>
+
+#include "util.h"
+#include "group.h"
+#include "scalar.h"
+#include "ecmult.h"
+#include "precomputed_ecmult.h"
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+/* We need to lower these values for exhaustive tests because
+ * the tables cannot have infinities in them (this breaks the
+ * affine-isomorphism stuff which tracks z-ratios) */
+#  if EXHAUSTIVE_TEST_ORDER > 128
+#    define WINDOW_A 5
+#  elif EXHAUSTIVE_TEST_ORDER > 8
+#    define WINDOW_A 4
+#  else
+#    define WINDOW_A 2
+#  endif
+#else
+/* optimal for 128-bit and 256-bit exponents. */
+#  define WINDOW_A 5
+/** Larger values for ECMULT_WINDOW_SIZE result in possibly better
+ *  performance at the cost of an exponentially larger precomputed
+ *  table. The exact table size is
+ *      (1 << (WINDOW_G - 2)) * sizeof(secp256k1_ge_storage)  bytes,
+ *  where sizeof(secp256k1_ge_storage) is typically 64 bytes but can
+ *  be larger due to platform-specific padding and alignment.
+ *  Two tables of this size are used (due to the endomorphism
+ *  optimization).
+ */
+#endif
+
+#define WNAF_BITS 128
+#define WNAF_SIZE_BITS(bits, w) CEIL_DIV(bits, w)
+#define WNAF_SIZE(w) WNAF_SIZE_BITS(WNAF_BITS, w)
+
+/* The number of objects allocated on the scratch space for ecmult_multi algorithms */
+#define PIPPENGER_SCRATCH_OBJECTS 6
+#define STRAUSS_SCRATCH_OBJECTS 5
+
+#define PIPPENGER_MAX_BUCKET_WINDOW 12
+
+/* Minimum number of points for which pippenger_wnaf is faster than strauss wnaf */
+#define ECMULT_PIPPENGER_THRESHOLD 88
+
+#define ECMULT_MAX_POINTS_PER_BATCH 5000000
+
+/** Fill a table 'pre_a' with precomputed odd multiples of a.
+ *  pre_a will contain [1*a,3*a,...,(2*n-1)*a], so it needs space for n group elements.
+ *  zr needs space for n field elements.
+ *
+ *  Although pre_a is an array of _ge rather than _gej, it actually represents elements
+ *  in Jacobian coordinates with their z coordinates omitted. The omitted z-coordinates
+ *  can be recovered using z and zr. Using the notation z(b) to represent the omitted
+ *  z coordinate of b:
+ *  - z(pre_a[n-1]) = 'z'
+ *  - z(pre_a[i-1]) = z(pre_a[i]) / zr[i] for n > i > 0
+ *
+ *  Lastly the zr[0] value, which isn't used above, is set so that:
+ *  - a.z = z(pre_a[0]) / zr[0]
+ */
+static void secp256k1_ecmult_odd_multiples_table(size_t n, secp256k1_ge *pre_a, secp256k1_fe *zr, secp256k1_fe *z, const secp256k1_gej *a) {
+    secp256k1_gej d, ai;
+    secp256k1_ge d_ge;
+    size_t i;
+
+    VERIFY_CHECK(!secp256k1_gej_is_infinity(a));
+
+    secp256k1_gej_double_var(&d, a, NULL);
+
+    /*
+     * Perform the additions using an isomorphic curve Y^2 = X^3 + 7*C^6 where C := d.z.
+     * The isomorphism, phi, maps a secp256k1 point (x, y) to the point (x*C^2, y*C^3) on the other curve.
+     * In Jacobian coordinates phi maps (x, y, z) to (x*C^2, y*C^3, z) or, equivalently to (x, y, z/C).
+     *
+     *     phi(x, y, z) = (x*C^2, y*C^3, z) = (x, y, z/C)
+     *   d_ge := phi(d) = (d.x, d.y, 1)
+     *     ai := phi(a) = (a.x*C^2, a.y*C^3, a.z)
+     *
+     * The group addition functions work correctly on these isomorphic curves.
+     * In particular phi(d) is easy to represent in affine coordinates under this isomorphism.
+     * This lets us use the faster secp256k1_gej_add_ge_var group addition function that we wouldn't be able to use otherwise.
+     */
+    secp256k1_ge_set_xy(&d_ge, &d.x, &d.y);
+    secp256k1_ge_set_gej_zinv(&pre_a[0], a, &d.z);
+    secp256k1_gej_set_ge(&ai, &pre_a[0]);
+    ai.z = a->z;
+
+    /* pre_a[0] is the point (a.x*C^2, a.y*C^3, a.z*C) which is equivalent to a.
+     * Set zr[0] to C, which is the ratio between the omitted z(pre_a[0]) value and a.z.
+     */
+    zr[0] = d.z;
+
+    for (i = 1; i < n; i++) {
+        secp256k1_gej_add_ge_var(&ai, &ai, &d_ge, &zr[i]);
+        secp256k1_ge_set_xy(&pre_a[i], &ai.x, &ai.y);
+    }
+
+    /* Multiply the last z-coordinate by C to undo the isomorphism.
+     * Since the z-coordinates of the pre_a values are implied by the zr array of z-coordinate ratios,
+     * undoing the isomorphism here undoes the isomorphism for all pre_a values.
+     */
+    secp256k1_fe_mul(z, &ai.z, &d.z);
+}
+
+SECP256K1_INLINE static void secp256k1_ecmult_table_verify(int n, int w) {
+    (void)n;
+    (void)w;
+    VERIFY_CHECK(((n) & 1) == 1);
+    VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1));
+    VERIFY_CHECK((n) <=  ((1 << ((w)-1)) - 1));
+}
+
+SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge(secp256k1_ge *r, const secp256k1_ge *pre, int n, int w) {
+    secp256k1_ecmult_table_verify(n,w);
+    if (n > 0) {
+        *r = pre[(n-1)/2];
+    } else {
+        *r = pre[(-n-1)/2];
+        secp256k1_fe_negate(&(r->y), &(r->y), 1);
+    }
+}
+
+SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_lambda(secp256k1_ge *r, const secp256k1_ge *pre, const secp256k1_fe *x, int n, int w) {
+    secp256k1_ecmult_table_verify(n,w);
+    if (n > 0) {
+        secp256k1_ge_set_xy(r, &x[(n-1)/2], &pre[(n-1)/2].y);
+    } else {
+        secp256k1_ge_set_xy(r, &x[(-n-1)/2], &pre[(-n-1)/2].y);
+        secp256k1_fe_negate(&(r->y), &(r->y), 1);
+    }
+}
+
+SECP256K1_INLINE static void secp256k1_ecmult_table_get_ge_storage(secp256k1_ge *r, const secp256k1_ge_storage *pre, int n, int w) {
+    secp256k1_ecmult_table_verify(n,w);
+    if (n > 0) {
+        secp256k1_ge_from_storage(r, &pre[(n-1)/2]);
+    } else {
+        secp256k1_ge_from_storage(r, &pre[(-n-1)/2]);
+        secp256k1_fe_negate(&(r->y), &(r->y), 1);
+    }
+}
+
+/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
+ *  with the following guarantees:
+ *  - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
+ *  - two non-zero entries in wnaf are separated by at least w-1 zeroes.
+ *  - the number of set values in wnaf is returned. This number is at most 256, and at most one more
+ *    than the number of bits in the (absolute value) of the input.
+ */
+static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
+    secp256k1_scalar s;
+    int last_set_bit = -1;
+    int bit = 0;
+    int sign = 1;
+    int carry = 0;
+
+    VERIFY_CHECK(wnaf != NULL);
+    VERIFY_CHECK(0 <= len && len <= 256);
+    VERIFY_CHECK(a != NULL);
+    VERIFY_CHECK(2 <= w && w <= 31);
+
+    for (bit = 0; bit < len; bit++) {
+        wnaf[bit] = 0;
+    }
+
+    s = *a;
+    if (secp256k1_scalar_get_bits_limb32(&s, 255, 1)) {
+        secp256k1_scalar_negate(&s, &s);
+        sign = -1;
+    }
+
+    bit = 0;
+    while (bit < len) {
+        int now;
+        int word;
+        if (secp256k1_scalar_get_bits_limb32(&s, bit, 1) == (unsigned int)carry) {
+            bit++;
+            continue;
+        }
+
+        now = w;
+        if (now > len - bit) {
+            now = len - bit;
+        }
+
+        word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
+
+        carry = (word >> (w-1)) & 1;
+        word -= carry << w;
+
+        wnaf[bit] = sign * word;
+        last_set_bit = bit;
+
+        bit += now;
+    }
+#ifdef VERIFY
+    {
+        int verify_bit = bit;
+
+        VERIFY_CHECK(carry == 0);
+
+        while (verify_bit < 256) {
+            VERIFY_CHECK(secp256k1_scalar_get_bits_limb32(&s, verify_bit, 1) == 0);
+            verify_bit++;
+        }
+    }
+#endif
+    return last_set_bit + 1;
+}
+
+/* Same as secp256k1_ecmult_wnaf, but stores to int8_t array. Requires w <= 8. */
+static int secp256k1_ecmult_wnaf_small(int8_t *wnaf, int len, const secp256k1_scalar *a, int w) {
+    int wnaf_tmp[256];
+    int ret, i;
+
+    VERIFY_CHECK(2 <= w && w <= 8);
+    ret = secp256k1_ecmult_wnaf(wnaf_tmp, len, a, w);
+
+    for (i = 0; i < len; i++) {
+        wnaf[i] = (int8_t)wnaf_tmp[i];
+    }
+
+    return ret;
+}
+
+struct secp256k1_strauss_point_state {
+    int8_t wnaf_na_1[129];
+    int8_t wnaf_na_lam[129];
+    int bits_na_1;
+    int bits_na_lam;
+};
+
+struct secp256k1_strauss_state {
+    /* aux is used to hold z-ratios, and then used to hold pre_a[i].x * BETA values. */
+    secp256k1_fe* aux;
+    secp256k1_ge* pre_a;
+    struct secp256k1_strauss_point_state* ps;
+};
+
+static void secp256k1_ecmult_strauss_wnaf(const struct secp256k1_strauss_state *state, secp256k1_gej *r, size_t num, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+    secp256k1_ge tmpa;
+    secp256k1_fe Z;
+    /* Split G factors. */
+    secp256k1_scalar ng_1, ng_128;
+    int wnaf_ng_1[129];
+    int bits_ng_1 = 0;
+    int wnaf_ng_128[129];
+    int bits_ng_128 = 0;
+    int i;
+    int bits = 0;
+    size_t np;
+    size_t no = 0;
+
+    secp256k1_fe_set_int(&Z, 1);
+    for (np = 0; np < num; ++np) {
+        secp256k1_gej tmp;
+        secp256k1_scalar na_1, na_lam;
+        if (secp256k1_scalar_is_zero(&na[np]) || secp256k1_gej_is_infinity(&a[np])) {
+            continue;
+        }
+        /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */
+        secp256k1_scalar_split_lambda(&na_1, &na_lam, &na[np]);
+
+        /* build wnaf representation for na_1 and na_lam. */
+        state->ps[no].bits_na_1   = secp256k1_ecmult_wnaf_small(state->ps[no].wnaf_na_1,   129, &na_1,   WINDOW_A);
+        state->ps[no].bits_na_lam = secp256k1_ecmult_wnaf_small(state->ps[no].wnaf_na_lam, 129, &na_lam, WINDOW_A);
+        VERIFY_CHECK(state->ps[no].bits_na_1 <= 129);
+        VERIFY_CHECK(state->ps[no].bits_na_lam <= 129);
+        if (state->ps[no].bits_na_1 > bits) {
+            bits = state->ps[no].bits_na_1;
+        }
+        if (state->ps[no].bits_na_lam > bits) {
+            bits = state->ps[no].bits_na_lam;
+        }
+
+        /* Calculate odd multiples of a.
+         * All multiples are brought to the same Z 'denominator', which is stored
+         * in Z. Due to secp256k1' isomorphism we can do all operations pretending
+         * that the Z coordinate was 1, use affine addition formulae, and correct
+         * the Z coordinate of the result once at the end.
+         * The exception is the precomputed G table points, which are actually
+         * affine. Compared to the base used for other points, they have a Z ratio
+         * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
+         * isomorphism to efficiently add with a known Z inverse.
+         */
+        tmp = a[np];
+        if (no) {
+            secp256k1_gej_rescale(&tmp, &Z);
+        }
+        secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), state->pre_a + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &Z, &tmp);
+        if (no) secp256k1_fe_mul(state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + no * ECMULT_TABLE_SIZE(WINDOW_A), &(a[np].z));
+
+        ++no;
+    }
+
+    /* Bring them to the same Z denominator. */
+    if (no) {
+        secp256k1_ge_table_set_globalz(ECMULT_TABLE_SIZE(WINDOW_A) * no, state->pre_a, state->aux);
+    }
+
+    for (np = 0; np < no; ++np) {
+        size_t j;
+        for (j = 0; j < ECMULT_TABLE_SIZE(WINDOW_A); j++) {
+            secp256k1_fe_mul(&state->aux[np * ECMULT_TABLE_SIZE(WINDOW_A) + j], &state->pre_a[np * ECMULT_TABLE_SIZE(WINDOW_A) + j].x, &secp256k1_const_beta);
+        }
+    }
+
+    if (ng) {
+        /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */
+        secp256k1_scalar_split_128(&ng_1, &ng_128, ng);
+
+        /* Build wnaf representation for ng_1 and ng_128 */
+        bits_ng_1   = secp256k1_ecmult_wnaf(wnaf_ng_1,   129, &ng_1,   WINDOW_G);
+        bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
+        if (bits_ng_1 > bits) {
+            bits = bits_ng_1;
+        }
+        if (bits_ng_128 > bits) {
+            bits = bits_ng_128;
+        }
+    }
+
+    secp256k1_gej_set_infinity(r);
+
+    for (i = bits - 1; i >= 0; i--) {
+        int n;
+        secp256k1_gej_double_var(r, r, NULL);
+        for (np = 0; np < no; ++np) {
+            if (i < state->ps[np].bits_na_1 && (n = state->ps[np].wnaf_na_1[i])) {
+                secp256k1_ecmult_table_get_ge(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
+                secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+            }
+            if (i < state->ps[np].bits_na_lam && (n = state->ps[np].wnaf_na_lam[i])) {
+                secp256k1_ecmult_table_get_ge_lambda(&tmpa, state->pre_a + np * ECMULT_TABLE_SIZE(WINDOW_A), state->aux + np * ECMULT_TABLE_SIZE(WINDOW_A), n, WINDOW_A);
+                secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
+            }
+        }
+        if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
+            secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+        if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
+            secp256k1_ecmult_table_get_ge_storage(&tmpa, secp256k1_pre_g_128, n, WINDOW_G);
+            secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
+        }
+    }
+
+    if (!secp256k1_gej_is_infinity(r)) {
+        secp256k1_fe_mul(&r->z, &r->z, &Z);
+    }
+}
+
+static void secp256k1_ecmult(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
+    secp256k1_fe aux[ECMULT_TABLE_SIZE(WINDOW_A)];
+    secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
+    struct secp256k1_strauss_point_state ps[1];
+    struct secp256k1_strauss_state state;
+
+    state.aux = aux;
+    state.pre_a = pre_a;
+    state.ps = ps;
+    secp256k1_ecmult_strauss_wnaf(&state, r, 1, a, na, ng);
+}
+
+static size_t secp256k1_strauss_scratch_size(size_t n_points) {
+    static const size_t point_size = (sizeof(secp256k1_ge) + sizeof(secp256k1_fe)) * ECMULT_TABLE_SIZE(WINDOW_A) + sizeof(struct secp256k1_strauss_point_state) + sizeof(secp256k1_gej) + sizeof(secp256k1_scalar);
+    return n_points*point_size;
+}
+
+static int secp256k1_ecmult_strauss_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
+    secp256k1_gej* points;
+    secp256k1_scalar* scalars;
+    struct secp256k1_strauss_state state;
+    size_t i;
+    const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch);
+
+    secp256k1_gej_set_infinity(r);
+    if (inp_g_sc == NULL && n_points == 0) {
+        return 1;
+    }
+
+    /* We allocate STRAUSS_SCRATCH_OBJECTS objects on the scratch space. If these
+     * allocations change, make sure to update the STRAUSS_SCRATCH_OBJECTS
+     * constant and strauss_scratch_size accordingly. */
+    points = (secp256k1_gej*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_gej));
+    scalars = (secp256k1_scalar*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(secp256k1_scalar));
+    state.aux = (secp256k1_fe*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_fe));
+    state.pre_a = (secp256k1_ge*)secp256k1_scratch_alloc(error_callback, scratch, n_points * ECMULT_TABLE_SIZE(WINDOW_A) * sizeof(secp256k1_ge));
+    state.ps = (struct secp256k1_strauss_point_state*)secp256k1_scratch_alloc(error_callback, scratch, n_points * sizeof(struct secp256k1_strauss_point_state));
+
+    if (points == NULL || scalars == NULL || state.aux == NULL || state.pre_a == NULL || state.ps == NULL) {
+        secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
+        return 0;
+    }
+
+    for (i = 0; i < n_points; i++) {
+        secp256k1_ge point;
+        if (!cb(&scalars[i], &point, i+cb_offset, cbdata)) {
+            secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
+            return 0;
+        }
+        secp256k1_gej_set_ge(&points[i], &point);
+    }
+    secp256k1_ecmult_strauss_wnaf(&state, r, n_points, points, scalars, inp_g_sc);
+    secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
+    return 1;
+}
+
+/* Wrapper for secp256k1_ecmult_multi_func interface */
+static int secp256k1_ecmult_strauss_batch_single(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
+    return secp256k1_ecmult_strauss_batch(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0);
+}
+
+static size_t secp256k1_strauss_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) {
+    return secp256k1_scratch_max_allocation(error_callback, scratch, STRAUSS_SCRATCH_OBJECTS) / secp256k1_strauss_scratch_size(1);
+}
+
+/** Convert a number to WNAF notation.
+ *  The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
+ *  It has the following guarantees:
+ *  - each wnaf[i] is either 0 or an odd integer between -(1 << w) and (1 << w)
+ *  - the number of words set is always WNAF_SIZE(w)
+ *  - the returned skew is 0 or 1
+ */
+static int secp256k1_wnaf_fixed(int *wnaf, const secp256k1_scalar *s, int w) {
+    int skew = 0;
+    int pos;
+    int max_pos;
+    int last_w;
+    const secp256k1_scalar *work = s;
+
+    if (secp256k1_scalar_is_zero(s)) {
+        for (pos = 0; pos < WNAF_SIZE(w); pos++) {
+            wnaf[pos] = 0;
+        }
+        return 0;
+    }
+
+    if (secp256k1_scalar_is_even(s)) {
+        skew = 1;
+    }
+
+    wnaf[0] = secp256k1_scalar_get_bits_var(work, 0, w) + skew;
+    /* Compute last window size. Relevant when window size doesn't divide the
+     * number of bits in the scalar */
+    last_w = WNAF_BITS - (WNAF_SIZE(w) - 1) * w;
+
+    /* Store the position of the first nonzero word in max_pos to allow
+     * skipping leading zeros when calculating the wnaf. */
+    for (pos = WNAF_SIZE(w) - 1; pos > 0; pos--) {
+        int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
+        if(val != 0) {
+            break;
+        }
+        wnaf[pos] = 0;
+    }
+    max_pos = pos;
+    pos = 1;
+
+    while (pos <= max_pos) {
+        int val = secp256k1_scalar_get_bits_var(work, pos * w, pos == WNAF_SIZE(w)-1 ? last_w : w);
+        if ((val & 1) == 0) {
+            wnaf[pos - 1] -= (1 << w);
+            wnaf[pos] = (val + 1);
+        } else {
+            wnaf[pos] = val;
+        }
+        /* Set a coefficient to zero if it is 1 or -1 and the proceeding digit
+         * is strictly negative or strictly positive respectively. Only change
+         * coefficients at previous positions because above code assumes that
+         * wnaf[pos - 1] is odd.
+         */
+        if (pos >= 2 && ((wnaf[pos - 1] == 1 && wnaf[pos - 2] < 0) || (wnaf[pos - 1] == -1 && wnaf[pos - 2] > 0))) {
+            if (wnaf[pos - 1] == 1) {
+                wnaf[pos - 2] += 1 << w;
+            } else {
+                wnaf[pos - 2] -= 1 << w;
+            }
+            wnaf[pos - 1] = 0;
+        }
+        ++pos;
+    }
+
+    return skew;
+}
+
+struct secp256k1_pippenger_point_state {
+    int skew_na;
+    size_t input_pos;
+};
+
+struct secp256k1_pippenger_state {
+    int *wnaf_na;
+    struct secp256k1_pippenger_point_state* ps;
+};
+
+/*
+ * pippenger_wnaf computes the result of a multi-point multiplication as
+ * follows: The scalars are brought into wnaf with n_wnaf elements each. Then
+ * for every i < n_wnaf, first each point is added to a "bucket" corresponding
+ * to the point's wnaf[i]. Second, the buckets are added together such that
+ * r += 1*bucket[0] + 3*bucket[1] + 5*bucket[2] + ...
+ */
+static int secp256k1_ecmult_pippenger_wnaf(secp256k1_gej *buckets, int bucket_window, struct secp256k1_pippenger_state *state, secp256k1_gej *r, const secp256k1_scalar *sc, const secp256k1_ge *pt, size_t num) {
+    size_t n_wnaf = WNAF_SIZE(bucket_window+1);
+    size_t np;
+    size_t no = 0;
+    int i;
+
+    for (np = 0; np < num; ++np) {
+        if (secp256k1_scalar_is_zero(&sc[np]) || secp256k1_ge_is_infinity(&pt[np])) {
+            continue;
+        }
+        state->ps[no].input_pos = np;
+        state->ps[no].skew_na = secp256k1_wnaf_fixed(&state->wnaf_na[no*n_wnaf], &sc[np], bucket_window+1);
+        no++;
+    }
+    secp256k1_gej_set_infinity(r);
+
+    if (no == 0) {
+        return 1;
+    }
+
+    for (i = n_wnaf - 1; i >= 0; i--) {
+        secp256k1_gej running_sum;
+        int j;
+        size_t buc;
+
+        for (buc = 0; buc < ECMULT_TABLE_SIZE(bucket_window+2); buc++) {
+            secp256k1_gej_set_infinity(&buckets[buc]);
+        }
+
+        for (np = 0; np < no; ++np) {
+            int n = state->wnaf_na[np*n_wnaf + i];
+            struct secp256k1_pippenger_point_state point_state = state->ps[np];
+            secp256k1_ge tmp;
+
+            if (i == 0) {
+                /* correct for wnaf skew */
+                int skew = point_state.skew_na;
+                if (skew) {
+                    secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]);
+                    secp256k1_gej_add_ge_var(&buckets[0], &buckets[0], &tmp, NULL);
+                }
+            }
+            if (n > 0) {
+                buc = (n - 1)/2;
+                secp256k1_gej_add_ge_var(&buckets[buc], &buckets[buc], &pt[point_state.input_pos], NULL);
+            } else if (n < 0) {
+                buc = -(n + 1)/2;
+                secp256k1_ge_neg(&tmp, &pt[point_state.input_pos]);
+                secp256k1_gej_add_ge_var(&buckets[buc], &buckets[buc], &tmp, NULL);
+            }
+        }
+
+        for (j = 0; j < bucket_window; j++) {
+            secp256k1_gej_double_var(r, r, NULL);
+        }
+
+        secp256k1_gej_set_infinity(&running_sum);
+        /* Accumulate the sum: bucket[0] + 3*bucket[1] + 5*bucket[2] + 7*bucket[3] + ...
+         *                   = bucket[0] +   bucket[1] +   bucket[2] +   bucket[3] + ...
+         *                   +         2 *  (bucket[1] + 2*bucket[2] + 3*bucket[3] + ...)
+         * using an intermediate running sum:
+         * running_sum = bucket[0] +   bucket[1] +   bucket[2] + ...
+         *
+         * The doubling is done implicitly by deferring the final window doubling (of 'r').
+         */
+        for (buc = ECMULT_TABLE_SIZE(bucket_window+2) - 1; buc > 0; buc--) {
+            secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[buc], NULL);
+            secp256k1_gej_add_var(r, r, &running_sum, NULL);
+        }
+
+        secp256k1_gej_add_var(&running_sum, &running_sum, &buckets[0], NULL);
+        secp256k1_gej_double_var(r, r, NULL);
+        secp256k1_gej_add_var(r, r, &running_sum, NULL);
+    }
+    return 1;
+}
+
+/**
+ * Returns optimal bucket_window (number of bits of a scalar represented by a
+ * set of buckets) for a given number of points.
+ */
+static int secp256k1_pippenger_bucket_window(size_t n) {
+    if (n <= 1) {
+        return 1;
+    } else if (n <= 4) {
+        return 2;
+    } else if (n <= 20) {
+        return 3;
+    } else if (n <= 57) {
+        return 4;
+    } else if (n <= 136) {
+        return 5;
+    } else if (n <= 235) {
+        return 6;
+    } else if (n <= 1260) {
+        return 7;
+    } else if (n <= 4420) {
+        return 9;
+    } else if (n <= 7880) {
+        return 10;
+    } else if (n <= 16050) {
+        return 11;
+    } else {
+        return PIPPENGER_MAX_BUCKET_WINDOW;
+    }
+}
+
+/**
+ * Returns the maximum optimal number of points for a bucket_window.
+ */
+static size_t secp256k1_pippenger_bucket_window_inv(int bucket_window) {
+    switch(bucket_window) {
+        case 1: return 1;
+        case 2: return 4;
+        case 3: return 20;
+        case 4: return 57;
+        case 5: return 136;
+        case 6: return 235;
+        case 7: return 1260;
+        case 8: return 1260;
+        case 9: return 4420;
+        case 10: return 7880;
+        case 11: return 16050;
+        case PIPPENGER_MAX_BUCKET_WINDOW: return SIZE_MAX;
+    }
+    return 0;
+}
+
+
+SECP256K1_INLINE static void secp256k1_ecmult_endo_split(secp256k1_scalar *s1, secp256k1_scalar *s2, secp256k1_ge *p1, secp256k1_ge *p2) {
+    secp256k1_scalar tmp = *s1;
+    secp256k1_scalar_split_lambda(s1, s2, &tmp);
+    secp256k1_ge_mul_lambda(p2, p1);
+
+    if (secp256k1_scalar_is_high(s1)) {
+        secp256k1_scalar_negate(s1, s1);
+        secp256k1_ge_neg(p1, p1);
+    }
+    if (secp256k1_scalar_is_high(s2)) {
+        secp256k1_scalar_negate(s2, s2);
+        secp256k1_ge_neg(p2, p2);
+    }
+}
+
+/**
+ * Returns the scratch size required for a given number of points (excluding
+ * base point G) without considering alignment.
+ */
+static size_t secp256k1_pippenger_scratch_size(size_t n_points, int bucket_window) {
+    size_t entries = 2*n_points + 2;
+    size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
+    return (sizeof(secp256k1_gej) << bucket_window) + sizeof(struct secp256k1_pippenger_state) + entries * entry_size;
+}
+
+static int secp256k1_ecmult_pippenger_batch(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points, size_t cb_offset) {
+    const size_t scratch_checkpoint = secp256k1_scratch_checkpoint(error_callback, scratch);
+    /* Use 2(n+1) with the endomorphism, when calculating batch
+     * sizes. The reason for +1 is that we add the G scalar to the list of
+     * other scalars. */
+    size_t entries = 2*n_points + 2;
+    secp256k1_ge *points;
+    secp256k1_scalar *scalars;
+    secp256k1_gej *buckets;
+    struct secp256k1_pippenger_state *state_space;
+    size_t idx = 0;
+    size_t point_idx = 0;
+    int bucket_window;
+
+    secp256k1_gej_set_infinity(r);
+    if (inp_g_sc == NULL && n_points == 0) {
+        return 1;
+    }
+    bucket_window = secp256k1_pippenger_bucket_window(n_points);
+
+    /* We allocate PIPPENGER_SCRATCH_OBJECTS objects on the scratch space. If
+     * these allocations change, make sure to update the
+     * PIPPENGER_SCRATCH_OBJECTS constant and pippenger_scratch_size
+     * accordingly. */
+    points = (secp256k1_ge *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*points));
+    scalars = (secp256k1_scalar *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*scalars));
+    state_space = (struct secp256k1_pippenger_state *) secp256k1_scratch_alloc(error_callback, scratch, sizeof(*state_space));
+    if (points == NULL || scalars == NULL || state_space == NULL) {
+        secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
+        return 0;
+    }
+    state_space->ps = (struct secp256k1_pippenger_point_state *) secp256k1_scratch_alloc(error_callback, scratch, entries * sizeof(*state_space->ps));
+    state_space->wnaf_na = (int *) secp256k1_scratch_alloc(error_callback, scratch, entries*(WNAF_SIZE(bucket_window+1)) * sizeof(int));
+    buckets = (secp256k1_gej *) secp256k1_scratch_alloc(error_callback, scratch, ((size_t)1 << bucket_window) * sizeof(*buckets));
+    if (state_space->ps == NULL || state_space->wnaf_na == NULL || buckets == NULL) {
+        secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
+        return 0;
+    }
+
+    if (inp_g_sc != NULL) {
+        scalars[0] = *inp_g_sc;
+        points[0] = secp256k1_ge_const_g;
+        idx++;
+        secp256k1_ecmult_endo_split(&scalars[0], &scalars[1], &points[0], &points[1]);
+        idx++;
+    }
+
+    while (point_idx < n_points) {
+        if (!cb(&scalars[idx], &points[idx], point_idx + cb_offset, cbdata)) {
+            secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
+            return 0;
+        }
+        idx++;
+        secp256k1_ecmult_endo_split(&scalars[idx - 1], &scalars[idx], &points[idx - 1], &points[idx]);
+        idx++;
+        point_idx++;
+    }
+
+    secp256k1_ecmult_pippenger_wnaf(buckets, bucket_window, state_space, r, scalars, points, idx);
+    secp256k1_scratch_apply_checkpoint(error_callback, scratch, scratch_checkpoint);
+    return 1;
+}
+
+/* Wrapper for secp256k1_ecmult_multi_func interface */
+static int secp256k1_ecmult_pippenger_batch_single(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
+    return secp256k1_ecmult_pippenger_batch(error_callback, scratch, r, inp_g_sc, cb, cbdata, n, 0);
+}
+
+/**
+ * Returns the maximum number of points in addition to G that can be used with
+ * a given scratch space. The function ensures that fewer points may also be
+ * used.
+ */
+static size_t secp256k1_pippenger_max_points(const secp256k1_callback* error_callback, secp256k1_scratch *scratch) {
+    size_t max_alloc = secp256k1_scratch_max_allocation(error_callback, scratch, PIPPENGER_SCRATCH_OBJECTS);
+    int bucket_window;
+    size_t res = 0;
+
+    for (bucket_window = 1; bucket_window <= PIPPENGER_MAX_BUCKET_WINDOW; bucket_window++) {
+        size_t n_points;
+        size_t max_points = secp256k1_pippenger_bucket_window_inv(bucket_window);
+        size_t space_for_points;
+        size_t space_overhead;
+        size_t entry_size = sizeof(secp256k1_ge) + sizeof(secp256k1_scalar) + sizeof(struct secp256k1_pippenger_point_state) + (WNAF_SIZE(bucket_window+1)+1)*sizeof(int);
+
+        entry_size = 2*entry_size;
+        space_overhead = (sizeof(secp256k1_gej) << bucket_window) + entry_size + sizeof(struct secp256k1_pippenger_state);
+        if (space_overhead > max_alloc) {
+            break;
+        }
+        space_for_points = max_alloc - space_overhead;
+
+        n_points = space_for_points/entry_size;
+        n_points = n_points > max_points ? max_points : n_points;
+        if (n_points > res) {
+            res = n_points;
+        }
+        if (n_points < max_points) {
+            /* A larger bucket_window may support even more points. But if we
+             * would choose that then the caller couldn't safely use any number
+             * smaller than what this function returns */
+            break;
+        }
+    }
+    return res;
+}
+
+/* Computes ecmult_multi by simply multiplying and adding each point. Does not
+ * require a scratch space */
+static int secp256k1_ecmult_multi_simple_var(secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n_points) {
+    size_t point_idx;
+    secp256k1_gej tmpj;
+
+    secp256k1_gej_set_infinity(r);
+    secp256k1_gej_set_infinity(&tmpj);
+    /* r = inp_g_sc*G */
+    secp256k1_ecmult(r, &tmpj, &secp256k1_scalar_zero, inp_g_sc);
+    for (point_idx = 0; point_idx < n_points; point_idx++) {
+        secp256k1_ge point;
+        secp256k1_gej pointj;
+        secp256k1_scalar scalar;
+        if (!cb(&scalar, &point, point_idx, cbdata)) {
+            return 0;
+        }
+        /* r += scalar*point */
+        secp256k1_gej_set_ge(&pointj, &point);
+        secp256k1_ecmult(&tmpj, &pointj, &scalar, NULL);
+        secp256k1_gej_add_var(r, r, &tmpj, NULL);
+    }
+    return 1;
+}
+
+/* Compute the number of batches and the batch size given the maximum batch size and the
+ * total number of points */
+static int secp256k1_ecmult_multi_batch_size_helper(size_t *n_batches, size_t *n_batch_points, size_t max_n_batch_points, size_t n) {
+    if (max_n_batch_points == 0) {
+        return 0;
+    }
+    if (max_n_batch_points > ECMULT_MAX_POINTS_PER_BATCH) {
+        max_n_batch_points = ECMULT_MAX_POINTS_PER_BATCH;
+    }
+    if (n == 0) {
+        *n_batches = 0;
+        *n_batch_points = 0;
+        return 1;
+    }
+    /* Compute ceil(n/max_n_batch_points) and ceil(n/n_batches) */
+    *n_batches = CEIL_DIV(n, max_n_batch_points);
+    *n_batch_points = CEIL_DIV(n, *n_batches);
+    return 1;
+}
+
+typedef int (*secp256k1_ecmult_multi_func)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t);
+static int secp256k1_ecmult_multi_var(const secp256k1_callback* error_callback, secp256k1_scratch *scratch, secp256k1_gej *r, const secp256k1_scalar *inp_g_sc, secp256k1_ecmult_multi_callback cb, void *cbdata, size_t n) {
+    size_t i;
+
+    int (*f)(const secp256k1_callback* error_callback, secp256k1_scratch*, secp256k1_gej*, const secp256k1_scalar*, secp256k1_ecmult_multi_callback cb, void*, size_t, size_t);
+    size_t n_batches;
+    size_t n_batch_points;
+
+    secp256k1_gej_set_infinity(r);
+    if (inp_g_sc == NULL && n == 0) {
+        return 1;
+    } else if (n == 0) {
+        secp256k1_ecmult(r, r, &secp256k1_scalar_zero, inp_g_sc);
+        return 1;
+    }
+    if (scratch == NULL) {
+        return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n);
+    }
+
+    /* Compute the batch sizes for Pippenger's algorithm given a scratch space. If it's greater than
+     * a threshold use Pippenger's algorithm. Otherwise use Strauss' algorithm.
+     * As a first step check if there's enough space for Pippenger's algo (which requires less space
+     * than Strauss' algo) and if not, use the simple algorithm. */
+    if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_pippenger_max_points(error_callback, scratch), n)) {
+        return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n);
+    }
+    if (n_batch_points >= ECMULT_PIPPENGER_THRESHOLD) {
+        f = secp256k1_ecmult_pippenger_batch;
+    } else {
+        if (!secp256k1_ecmult_multi_batch_size_helper(&n_batches, &n_batch_points, secp256k1_strauss_max_points(error_callback, scratch), n)) {
+            return secp256k1_ecmult_multi_simple_var(r, inp_g_sc, cb, cbdata, n);
+        }
+        f = secp256k1_ecmult_strauss_batch;
+    }
+    for(i = 0; i < n_batches; i++) {
+        size_t nbp = n < n_batch_points ? n : n_batch_points;
+        size_t offset = n_batch_points*i;
+        secp256k1_gej tmp;
+        if (!f(error_callback, scratch, &tmp, i == 0 ? inp_g_sc : NULL, cb, cbdata, nbp, offset)) {
+            return 0;
+        }
+        secp256k1_gej_add_var(r, r, &tmp, NULL);
+        n -= nbp;
+    }
+    return 1;
+}
+
+#endif /* SECP256K1_ECMULT_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/field.h

@@ -0,0 +1,351 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_FIELD_H
+#define SECP256K1_FIELD_H
+
+#include "util.h"
+
+/* This file defines the generic interface for working with secp256k1_fe
+ * objects, which represent field elements (integers modulo 2^256 - 2^32 - 977).
+ *
+ * The actual definition of the secp256k1_fe type depends on the chosen field
+ * implementation; see the field_5x52.h and field_10x26.h files for details.
+ *
+ * All secp256k1_fe objects have implicit properties that determine what
+ * operations are permitted on it. These are purely a function of what
+ * secp256k1_fe_ operations are applied on it, generally (implicitly) fixed at
+ * compile time, and do not depend on the chosen field implementation. Despite
+ * that, what these properties actually entail for the field representation
+ * values depends on the chosen field implementation. These properties are:
+ * - magnitude: an integer in [0,32]
+ * - normalized: 0 or 1; normalized=1 implies magnitude <= 1.
+ *
+ * In VERIFY mode, they are materialized explicitly as fields in the struct,
+ * allowing run-time verification of these properties. In that case, the field
+ * implementation also provides a secp256k1_fe_verify routine to verify that
+ * these fields match the run-time value and perform internal consistency
+ * checks. */
+#ifdef VERIFY
+#  define SECP256K1_FE_VERIFY_FIELDS \
+    int magnitude; \
+    int normalized;
+#else
+#  define SECP256K1_FE_VERIFY_FIELDS
+#endif
+
+#if defined(SECP256K1_WIDEMUL_INT128)
+#include "field_5x52.h"
+#elif defined(SECP256K1_WIDEMUL_INT64)
+#include "field_10x26.h"
+#else
+#error "Please select wide multiplication implementation"
+#endif
+
+#ifdef VERIFY
+/* Magnitude and normalized value for constants. */
+#define SECP256K1_FE_VERIFY_CONST(d7, d6, d5, d4, d3, d2, d1, d0) \
+    /* Magnitude is 0 for constant 0; 1 otherwise. */ \
+    , (((d7) | (d6) | (d5) | (d4) | (d3) | (d2) | (d1) | (d0)) != 0) \
+    /* Normalized is 1 unless sum(d_i<<(32*i) for i=0..7) exceeds field modulus. */ \
+    , (!(((d7) & (d6) & (d5) & (d4) & (d3) & (d2)) == 0xfffffffful && ((d1) == 0xfffffffful || ((d1) == 0xfffffffe && (d0 >= 0xfffffc2f)))))
+#else
+#define SECP256K1_FE_VERIFY_CONST(d7, d6, d5, d4, d3, d2, d1, d0)
+#endif
+
+/** This expands to an initializer for a secp256k1_fe valued sum((i*32) * d_i, i=0..7) mod p.
+ *
+ * It has magnitude 1, unless d_i are all 0, in which case the magnitude is 0.
+ * It is normalized, unless sum(2^(i*32) * d_i, i=0..7) >= p.
+ *
+ * SECP256K1_FE_CONST_INNER is provided by the implementation.
+ */
+#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)) SECP256K1_FE_VERIFY_CONST((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)) }
+
+static const secp256k1_fe secp256k1_fe_one = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
+static const secp256k1_fe secp256k1_const_beta = SECP256K1_FE_CONST(
+    0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
+    0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
+);
+
+#ifndef VERIFY
+/* In non-VERIFY mode, we #define the fe operations to be identical to their
+ * internal field implementation, to avoid the potential overhead of a
+ * function call (even though presumably inlinable). */
+#  define secp256k1_fe_normalize secp256k1_fe_impl_normalize
+#  define secp256k1_fe_normalize_weak secp256k1_fe_impl_normalize_weak
+#  define secp256k1_fe_normalize_var secp256k1_fe_impl_normalize_var
+#  define secp256k1_fe_normalizes_to_zero secp256k1_fe_impl_normalizes_to_zero
+#  define secp256k1_fe_normalizes_to_zero_var secp256k1_fe_impl_normalizes_to_zero_var
+#  define secp256k1_fe_set_int secp256k1_fe_impl_set_int
+#  define secp256k1_fe_is_zero secp256k1_fe_impl_is_zero
+#  define secp256k1_fe_is_odd secp256k1_fe_impl_is_odd
+#  define secp256k1_fe_cmp_var secp256k1_fe_impl_cmp_var
+#  define secp256k1_fe_set_b32_mod secp256k1_fe_impl_set_b32_mod
+#  define secp256k1_fe_set_b32_limit secp256k1_fe_impl_set_b32_limit
+#  define secp256k1_fe_get_b32 secp256k1_fe_impl_get_b32
+#  define secp256k1_fe_negate_unchecked secp256k1_fe_impl_negate_unchecked
+#  define secp256k1_fe_mul_int_unchecked secp256k1_fe_impl_mul_int_unchecked
+#  define secp256k1_fe_add secp256k1_fe_impl_add
+#  define secp256k1_fe_mul secp256k1_fe_impl_mul
+#  define secp256k1_fe_sqr secp256k1_fe_impl_sqr
+#  define secp256k1_fe_cmov secp256k1_fe_impl_cmov
+#  define secp256k1_fe_to_storage secp256k1_fe_impl_to_storage
+#  define secp256k1_fe_from_storage secp256k1_fe_impl_from_storage
+#  define secp256k1_fe_inv secp256k1_fe_impl_inv
+#  define secp256k1_fe_inv_var secp256k1_fe_impl_inv_var
+#  define secp256k1_fe_get_bounds secp256k1_fe_impl_get_bounds
+#  define secp256k1_fe_half secp256k1_fe_impl_half
+#  define secp256k1_fe_add_int secp256k1_fe_impl_add_int
+#  define secp256k1_fe_is_square_var secp256k1_fe_impl_is_square_var
+#endif /* !defined(VERIFY) */
+
+/** Normalize a field element.
+ *
+ * On input, r must be a valid field element.
+ * On output, r represents the same value but has normalized=1 and magnitude=1.
+ */
+static void secp256k1_fe_normalize(secp256k1_fe *r);
+
+/** Give a field element magnitude 1.
+ *
+ * On input, r must be a valid field element.
+ * On output, r represents the same value but has magnitude=1. Normalized is unchanged.
+ */
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
+
+/** Normalize a field element, without constant-time guarantee.
+ *
+ * Identical in behavior to secp256k1_fe_normalize, but not constant time in r.
+ */
+static void secp256k1_fe_normalize_var(secp256k1_fe *r);
+
+/** Determine whether r represents field element 0.
+ *
+ * On input, r must be a valid field element.
+ * Returns whether r = 0 (mod p).
+ */
+static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r);
+
+/** Determine whether r represents field element 0, without constant-time guarantee.
+ *
+ * Identical in behavior to secp256k1_normalizes_to_zero, but not constant time in r.
+ */
+static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r);
+
+/** Set a field element to an integer in range [0,0x7FFF].
+ *
+ * On input, r does not need to be initialized, a must be in [0,0x7FFF].
+ * On output, r represents value a, is normalized and has magnitude (a!=0).
+ */
+static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
+
+/** Clear a field element to prevent leaking sensitive information. */
+static void secp256k1_fe_clear(secp256k1_fe *a);
+
+/** Determine whether a represents field element 0.
+ *
+ * On input, a must be a valid normalized field element.
+ * Returns whether a = 0 (mod p).
+ *
+ * This behaves identical to secp256k1_normalizes_to_zero{,_var}, but requires
+ * normalized input (and is much faster).
+ */
+static int secp256k1_fe_is_zero(const secp256k1_fe *a);
+
+/** Determine whether a (mod p) is odd.
+ *
+ * On input, a must be a valid normalized field element.
+ * Returns (int(a) mod p) & 1.
+ */
+static int secp256k1_fe_is_odd(const secp256k1_fe *a);
+
+/** Determine whether two field elements are equal.
+ *
+ * On input, a and b must be valid field elements with magnitudes not exceeding
+ * 1 and 31, respectively.
+ * Returns a = b (mod p).
+ */
+static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Compare the values represented by 2 field elements, without constant-time guarantee.
+ *
+ * On input, a and b must be valid normalized field elements.
+ * Returns 1 if a > b, -1 if a < b, and 0 if a = b (comparisons are done as integers
+ * in range 0..p-1).
+ */
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Set a field element equal to the element represented by a provided 32-byte big endian value
+ * interpreted modulo p.
+ *
+ * On input, r does not need to be initialized. a must be a pointer to an initialized 32-byte array.
+ * On output, r = a (mod p). It will have magnitude 1, and not be normalized.
+ */
+static void secp256k1_fe_set_b32_mod(secp256k1_fe *r, const unsigned char *a);
+
+/** Set a field element equal to a provided 32-byte big endian value, checking for overflow.
+ *
+ * On input, r does not need to be initialized. a must be a pointer to an initialized 32-byte array.
+ * On output, r = a if (a < p), it will be normalized with magnitude 1, and 1 is returned.
+ * If a >= p, 0 is returned, and r will be made invalid (and must not be used without overwriting).
+ */
+static int secp256k1_fe_set_b32_limit(secp256k1_fe *r, const unsigned char *a);
+
+/** Convert a field element to 32-byte big endian byte array.
+ * On input, a must be a valid normalized field element, and r a pointer to a 32-byte array.
+ * On output, r = a (mod p).
+ */
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
+
+/** Negate a field element.
+ *
+ * On input, r does not need to be initialized. a must be a valid field element with
+ * magnitude not exceeding m. m must be an integer constant expression in [0,31].
+ * Performs {r = -a}.
+ * On output, r will not be normalized, and will have magnitude m+1.
+ */
+#define secp256k1_fe_negate(r, a, m) ASSERT_INT_CONST_AND_DO(m, secp256k1_fe_negate_unchecked(r, a, m))
+
+/** Like secp256k1_fe_negate_unchecked but m is not checked to be an integer constant expression.
+ *
+ * Should not be called directly outside of tests.
+ */
+static void secp256k1_fe_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m);
+
+/** Add a small integer to a field element.
+ *
+ * Performs {r += a}. The magnitude of r increases by 1, and normalized is cleared.
+ * a must be in range [0,0x7FFF].
+ */
+static void secp256k1_fe_add_int(secp256k1_fe *r, int a);
+
+/** Multiply a field element with a small integer.
+ *
+ * On input, r must be a valid field element. a must be an integer constant expression in [0,32].
+ * The magnitude of r times a must not exceed 32.
+ * Performs {r *= a}.
+ * On output, r's magnitude is multiplied by a, and r will not be normalized.
+ */
+#define secp256k1_fe_mul_int(r, a) ASSERT_INT_CONST_AND_DO(a, secp256k1_fe_mul_int_unchecked(r, a))
+
+/** Like secp256k1_fe_mul_int but a is not checked to be an integer constant expression.
+ *
+ * Should not be called directly outside of tests.
+ */
+static void secp256k1_fe_mul_int_unchecked(secp256k1_fe *r, int a);
+
+/** Increment a field element by another.
+ *
+ * On input, r and a must be valid field elements, not necessarily normalized.
+ * The sum of their magnitudes must not exceed 32.
+ * Performs {r += a}.
+ * On output, r will not be normalized, and will have magnitude incremented by a's.
+ */
+static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Multiply two field elements.
+ *
+ * On input, a and b must be valid field elements; r does not need to be initialized.
+ * r and a may point to the same object, but neither may point to the object pointed
+ * to by b. The magnitudes of a and b must not exceed 8.
+ * Performs {r = a * b}
+ * On output, r will have magnitude 1, but won't be normalized.
+ */
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
+
+/** Square a field element.
+ *
+ * On input, a must be a valid field element; r does not need to be initialized. The magnitude
+ * of a must not exceed 8.
+ * Performs {r = a**2}
+ * On output, r will have magnitude 1, but won't be normalized.
+ */
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Compute a square root of a field element.
+ *
+ * On input, a must be a valid field element with magnitude<=8; r need not be initialized.
+ * If sqrt(a) exists, performs {r = sqrt(a)} and returns 1.
+ * Otherwise, sqrt(-a) exists. The function performs {r = sqrt(-a)} and returns 0.
+ * The resulting value represented by r will be a square itself.
+ * Variables r and a must not point to the same object.
+ * On output, r will have magnitude 1 but will not be normalized.
+ */
+static int secp256k1_fe_sqrt(secp256k1_fe * SECP256K1_RESTRICT r, const secp256k1_fe * SECP256K1_RESTRICT a);
+
+/** Compute the modular inverse of a field element.
+ *
+ * On input, a must be a valid field element; r need not be initialized.
+ * Performs {r = a**(p-2)} (which maps 0 to 0, and every other element to its
+ * inverse).
+ * On output, r will have magnitude (a.magnitude != 0) and be normalized.
+ */
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Compute the modular inverse of a field element, without constant-time guarantee.
+ *
+ * Behaves identically to secp256k1_fe_inv, but is not constant-time in a.
+ */
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
+
+/** Convert a field element to secp256k1_fe_storage.
+ *
+ * On input, a must be a valid normalized field element.
+ * Performs {r = a}.
+ */
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
+
+/** Convert a field element back from secp256k1_fe_storage.
+ *
+ * On input, r need not be initialized.
+ * Performs {r = a}.
+ * On output, r will be normalized and will have magnitude 1.
+ */
+static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
+
+/** If flag is 1, set *r equal to *a; if flag is 0, leave it. Constant-time.
+ * Both *r and *a must be initialized. Flag must be 0 or 1. */
+static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
+
+/** Conditionally move a field element in constant time.
+ *
+ * On input, both r and a must be valid field elements. Flag must be 0 or 1.
+ * Performs {r = flag ? a : r}.
+ *
+ * On output, r's magnitude will be the maximum of both input magnitudes.
+ * It will be normalized if and only if both inputs were normalized.
+ */
+static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
+
+/** Halve the value of a field element modulo the field prime in constant-time.
+ *
+ * On input, r must be a valid field element.
+ * On output, r will be normalized and have magnitude floor(m/2) + 1 where m is
+ * the magnitude of r on input.
+ */
+static void secp256k1_fe_half(secp256k1_fe *r);
+
+/** Sets r to a field element with magnitude m, normalized if (and only if) m==0.
+ *  The value is chosen so that it is likely to trigger edge cases related to
+ *  internal overflows. */
+static void secp256k1_fe_get_bounds(secp256k1_fe *r, int m);
+
+/** Determine whether a is a square (modulo p).
+ *
+ * On input, a must be a valid field element.
+ */
+static int secp256k1_fe_is_square_var(const secp256k1_fe *a);
+
+/** Check invariants on a field element (no-op unless VERIFY is enabled). */
+static void secp256k1_fe_verify(const secp256k1_fe *a);
+#define SECP256K1_FE_VERIFY(a) secp256k1_fe_verify(a)
+
+/** Check that magnitude of a is at most m (no-op unless VERIFY is enabled). */
+static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m);
+#define SECP256K1_FE_VERIFY_MAGNITUDE(a, m) secp256k1_fe_verify_magnitude(a, m)
+
+#endif /* SECP256K1_FIELD_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/field_10x26.h

@@ -0,0 +1,57 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_FIELD_REPR_H
+#define SECP256K1_FIELD_REPR_H
+
+#include <stdint.h>
+
+/** This field implementation represents the value as 10 uint32_t limbs in base
+ *  2^26. */
+typedef struct {
+   /* A field element f represents the sum(i=0..9, f.n[i] << (i*26)) mod p,
+    * where p is the field modulus, 2^256 - 2^32 - 977.
+    *
+    * The individual limbs f.n[i] can exceed 2^26; the field's magnitude roughly
+    * corresponds to how much excess is allowed. The value
+    * sum(i=0..9, f.n[i] << (i*26)) may exceed p, unless the field element is
+    * normalized. */
+    uint32_t n[10];
+    /*
+     * Magnitude m requires:
+     *     n[i] <= 2 * m * (2^26 - 1) for i=0..8
+     *     n[9] <= 2 * m * (2^22 - 1)
+     *
+     * Normalized requires:
+     *     n[i] <= (2^26 - 1) for i=0..8
+     *     sum(i=0..9, n[i] << (i*26)) < p
+     *     (together these imply n[9] <= 2^22 - 1)
+     */
+    SECP256K1_FE_VERIFY_FIELDS
+} secp256k1_fe;
+
+/* Unpacks a constant into a overlapping multi-limbed FE element. */
+#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
+    (d0) & 0x3FFFFFFUL, \
+    (((uint32_t)d0) >> 26) | (((uint32_t)(d1) & 0xFFFFFUL) << 6), \
+    (((uint32_t)d1) >> 20) | (((uint32_t)(d2) & 0x3FFFUL) << 12), \
+    (((uint32_t)d2) >> 14) | (((uint32_t)(d3) & 0xFFUL) << 18), \
+    (((uint32_t)d3) >> 8) | (((uint32_t)(d4) & 0x3UL) << 24), \
+    (((uint32_t)d4) >> 2) & 0x3FFFFFFUL, \
+    (((uint32_t)d4) >> 28) | (((uint32_t)(d5) & 0x3FFFFFUL) << 4), \
+    (((uint32_t)d5) >> 22) | (((uint32_t)(d6) & 0xFFFFUL) << 10), \
+    (((uint32_t)d6) >> 16) | (((uint32_t)(d7) & 0x3FFUL) << 16), \
+    (((uint32_t)d7) >> 10) \
+}
+
+typedef struct {
+    uint32_t n[8];
+} secp256k1_fe_storage;
+
+#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ (d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7) }}
+#define SECP256K1_FE_STORAGE_CONST_GET(d) d.n[7], d.n[6], d.n[5], d.n[4],d.n[3], d.n[2], d.n[1], d.n[0]
+
+#endif /* SECP256K1_FIELD_REPR_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/field_5x52.h

@@ -0,0 +1,62 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_FIELD_REPR_H
+#define SECP256K1_FIELD_REPR_H
+
+#include <stdint.h>
+
+/** This field implementation represents the value as 5 uint64_t limbs in base
+ *  2^52. */
+typedef struct {
+   /* A field element f represents the sum(i=0..4, f.n[i] << (i*52)) mod p,
+    * where p is the field modulus, 2^256 - 2^32 - 977.
+    *
+    * The individual limbs f.n[i] can exceed 2^52; the field's magnitude roughly
+    * corresponds to how much excess is allowed. The value
+    * sum(i=0..4, f.n[i] << (i*52)) may exceed p, unless the field element is
+    * normalized. */
+    uint64_t n[5];
+    /*
+     * Magnitude m requires:
+     *     n[i] <= 2 * m * (2^52 - 1) for i=0..3
+     *     n[4] <= 2 * m * (2^48 - 1)
+     *
+     * Normalized requires:
+     *     n[i] <= (2^52 - 1) for i=0..3
+     *     sum(i=0..4, n[i] << (i*52)) < p
+     *     (together these imply n[4] <= 2^48 - 1)
+     */
+    SECP256K1_FE_VERIFY_FIELDS
+} secp256k1_fe;
+
+/* Unpacks a constant into a overlapping multi-limbed FE element. */
+#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
+    (d0) | (((uint64_t)(d1) & 0xFFFFFUL) << 32), \
+    ((uint64_t)(d1) >> 20) | (((uint64_t)(d2)) << 12) | (((uint64_t)(d3) & 0xFFUL) << 44), \
+    ((uint64_t)(d3) >> 8) | (((uint64_t)(d4) & 0xFFFFFFFUL) << 24), \
+    ((uint64_t)(d4) >> 28) | (((uint64_t)(d5)) << 4) | (((uint64_t)(d6) & 0xFFFFUL) << 36), \
+    ((uint64_t)(d6) >> 16) | (((uint64_t)(d7)) << 16) \
+}
+
+typedef struct {
+    uint64_t n[4];
+} secp256k1_fe_storage;
+
+#define SECP256K1_FE_STORAGE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{ \
+    (d0) | (((uint64_t)(d1)) << 32), \
+    (d2) | (((uint64_t)(d3)) << 32), \
+    (d4) | (((uint64_t)(d5)) << 32), \
+    (d6) | (((uint64_t)(d7)) << 32) \
+}}
+
+#define SECP256K1_FE_STORAGE_CONST_GET(d) \
+    (uint32_t)(d.n[3] >> 32), (uint32_t)d.n[3], \
+    (uint32_t)(d.n[2] >> 32), (uint32_t)d.n[2], \
+    (uint32_t)(d.n[1] >> 32), (uint32_t)d.n[1], \
+    (uint32_t)(d.n[0] >> 32), (uint32_t)d.n[0]
+
+#endif /* SECP256K1_FIELD_REPR_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/field_5x52_impl.h

@@ -0,0 +1,524 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_FIELD_REPR_IMPL_H
+#define SECP256K1_FIELD_REPR_IMPL_H
+
+#include "checkmem.h"
+#include "util.h"
+#include "field.h"
+#include "modinv64_impl.h"
+
+#include "field_5x52_int128_impl.h"
+
+#ifdef VERIFY
+static void secp256k1_fe_impl_verify(const secp256k1_fe *a) {
+    const uint64_t *d = a->n;
+    int m = a->normalized ? 1 : 2 * a->magnitude;
+   /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+    VERIFY_CHECK(d[0] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[1] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[2] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[3] <= 0xFFFFFFFFFFFFFULL * m);
+    VERIFY_CHECK(d[4] <= 0x0FFFFFFFFFFFFULL * m);
+    if (a->normalized) {
+        if ((d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) {
+            VERIFY_CHECK(d[0] < 0xFFFFEFFFFFC2FULL);
+        }
+    }
+}
+#endif
+
+static void secp256k1_fe_impl_get_bounds(secp256k1_fe *r, int m) {
+    r->n[0] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * m;
+    r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * m;
+}
+
+static void secp256k1_fe_impl_normalize(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t m;
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
+        & (t0 >= 0xFFFFEFFFFFC2FULL));
+
+    /* Apply the final reduction (for constant-time behaviour, we do it always) */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+    /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
+    VERIFY_CHECK(t4 >> 48 == x);
+
+    /* Mask off the possible multiple of 2^256 from the final reduction */
+    t4 &= 0x0FFFFFFFFFFFFULL;
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+}
+
+static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+}
+
+static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t m;
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    /* At most a single final reduction is needed; check if the value is >= the field characteristic */
+    x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL)
+        & (t0 >= 0xFFFFEFFFFFC2FULL));
+
+    if (x) {
+        t0 += 0x1000003D1ULL;
+        t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL;
+        t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL;
+        t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL;
+        t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL;
+
+        /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */
+        VERIFY_CHECK(t4 >> 48 == x);
+
+        /* Mask off the possible multiple of 2^256 from the final reduction */
+        t4 &= 0x0FFFFFFFFFFFFULL;
+    }
+
+    r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4;
+}
+
+static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    uint64_t z0, z1;
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+    t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0  = t0; z1  = t0 ^ 0x1000003D0ULL;
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
+                                                z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
+}
+
+static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r) {
+    uint64_t t0, t1, t2, t3, t4;
+    uint64_t z0, z1;
+    uint64_t x;
+
+    t0 = r->n[0];
+    t4 = r->n[4];
+
+    /* Reduce t4 at the start so there will be at most a single carry from the first pass */
+    x = t4 >> 48;
+
+    /* The first pass ensures the magnitude is 1, ... */
+    t0 += x * 0x1000003D1ULL;
+
+    /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */
+    z0 = t0 & 0xFFFFFFFFFFFFFULL;
+    z1 = z0 ^ 0x1000003D0ULL;
+
+    /* Fast return path should catch the majority of cases */
+    if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) {
+        return 0;
+    }
+
+    t1 = r->n[1];
+    t2 = r->n[2];
+    t3 = r->n[3];
+
+    t4 &= 0x0FFFFFFFFFFFFULL;
+
+    t1 += (t0 >> 52);
+    t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1;
+    t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2;
+    t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3;
+                                                z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL;
+
+    /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */
+    VERIFY_CHECK(t4 >> 49 == 0);
+
+    return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL);
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a) {
+    r->n[0] = a;
+    r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0;
+}
+
+SECP256K1_INLINE static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a) {
+    const uint64_t *t = a->n;
+    return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0;
+}
+
+SECP256K1_INLINE static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a) {
+    return a->n[0] & 1;
+}
+
+static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    int i;
+    for (i = 4; i >= 0; i--) {
+        if (a->n[i] > b->n[i]) {
+            return 1;
+        }
+        if (a->n[i] < b->n[i]) {
+            return -1;
+        }
+    }
+    return 0;
+}
+
+static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
+    r->n[0] = (uint64_t)a[31]
+            | ((uint64_t)a[30] << 8)
+            | ((uint64_t)a[29] << 16)
+            | ((uint64_t)a[28] << 24)
+            | ((uint64_t)a[27] << 32)
+            | ((uint64_t)a[26] << 40)
+            | ((uint64_t)(a[25] & 0xF)  << 48);
+    r->n[1] = (uint64_t)((a[25] >> 4) & 0xF)
+            | ((uint64_t)a[24] << 4)
+            | ((uint64_t)a[23] << 12)
+            | ((uint64_t)a[22] << 20)
+            | ((uint64_t)a[21] << 28)
+            | ((uint64_t)a[20] << 36)
+            | ((uint64_t)a[19] << 44);
+    r->n[2] = (uint64_t)a[18]
+            | ((uint64_t)a[17] << 8)
+            | ((uint64_t)a[16] << 16)
+            | ((uint64_t)a[15] << 24)
+            | ((uint64_t)a[14] << 32)
+            | ((uint64_t)a[13] << 40)
+            | ((uint64_t)(a[12] & 0xF) << 48);
+    r->n[3] = (uint64_t)((a[12] >> 4) & 0xF)
+            | ((uint64_t)a[11] << 4)
+            | ((uint64_t)a[10] << 12)
+            | ((uint64_t)a[9]  << 20)
+            | ((uint64_t)a[8]  << 28)
+            | ((uint64_t)a[7]  << 36)
+            | ((uint64_t)a[6]  << 44);
+    r->n[4] = (uint64_t)a[5]
+            | ((uint64_t)a[4] << 8)
+            | ((uint64_t)a[3] << 16)
+            | ((uint64_t)a[2] << 24)
+            | ((uint64_t)a[1] << 32)
+            | ((uint64_t)a[0] << 40);
+}
+
+static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
+    secp256k1_fe_impl_set_b32_mod(r, a);
+    return !((r->n[4] == 0x0FFFFFFFFFFFFULL) & ((r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL) & (r->n[0] >= 0xFFFFEFFFFFC2FULL));
+}
+
+/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
+static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a) {
+    r[0] = (a->n[4] >> 40) & 0xFF;
+    r[1] = (a->n[4] >> 32) & 0xFF;
+    r[2] = (a->n[4] >> 24) & 0xFF;
+    r[3] = (a->n[4] >> 16) & 0xFF;
+    r[4] = (a->n[4] >> 8) & 0xFF;
+    r[5] = a->n[4] & 0xFF;
+    r[6] = (a->n[3] >> 44) & 0xFF;
+    r[7] = (a->n[3] >> 36) & 0xFF;
+    r[8] = (a->n[3] >> 28) & 0xFF;
+    r[9] = (a->n[3] >> 20) & 0xFF;
+    r[10] = (a->n[3] >> 12) & 0xFF;
+    r[11] = (a->n[3] >> 4) & 0xFF;
+    r[12] = ((a->n[2] >> 48) & 0xF) | ((a->n[3] & 0xF) << 4);
+    r[13] = (a->n[2] >> 40) & 0xFF;
+    r[14] = (a->n[2] >> 32) & 0xFF;
+    r[15] = (a->n[2] >> 24) & 0xFF;
+    r[16] = (a->n[2] >> 16) & 0xFF;
+    r[17] = (a->n[2] >> 8) & 0xFF;
+    r[18] = a->n[2] & 0xFF;
+    r[19] = (a->n[1] >> 44) & 0xFF;
+    r[20] = (a->n[1] >> 36) & 0xFF;
+    r[21] = (a->n[1] >> 28) & 0xFF;
+    r[22] = (a->n[1] >> 20) & 0xFF;
+    r[23] = (a->n[1] >> 12) & 0xFF;
+    r[24] = (a->n[1] >> 4) & 0xFF;
+    r[25] = ((a->n[0] >> 48) & 0xF) | ((a->n[1] & 0xF) << 4);
+    r[26] = (a->n[0] >> 40) & 0xFF;
+    r[27] = (a->n[0] >> 32) & 0xFF;
+    r[28] = (a->n[0] >> 24) & 0xFF;
+    r[29] = (a->n[0] >> 16) & 0xFF;
+    r[30] = (a->n[0] >> 8) & 0xFF;
+    r[31] = a->n[0] & 0xFF;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+    /* For all legal values of m (0..31), the following properties hold: */
+    VERIFY_CHECK(0xFFFFEFFFFFC2FULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
+    VERIFY_CHECK(0xFFFFFFFFFFFFFULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m);
+    VERIFY_CHECK(0x0FFFFFFFFFFFFULL * 2 * (m + 1) >= 0x0FFFFFFFFFFFFULL * 2 * m);
+
+    /* Due to the properties above, the left hand in the subtractions below is never less than
+     * the right hand. */
+    r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0];
+    r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1];
+    r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2];
+    r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3];
+    r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4];
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a) {
+    r->n[0] *= a;
+    r->n[1] *= a;
+    r->n[2] *= a;
+    r->n[3] *= a;
+    r->n[4] *= a;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a) {
+    r->n[0] += a;
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a) {
+    r->n[0] += a->n[0];
+    r->n[1] += a->n[1];
+    r->n[2] += a->n[2];
+    r->n[3] += a->n[3];
+    r->n[4] += a->n[4];
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
+    secp256k1_fe_mul_inner(r->n, a->n, b->n);
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
+    secp256k1_fe_sqr_inner(r->n, a->n);
+}
+
+SECP256K1_INLINE static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    uint64_t mask0, mask1;
+    volatile int vflag = flag;
+    VERIFY_CHECK(flag == 0 || flag == 1);
+    SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
+    mask0 = vflag + ~((uint64_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+    r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1);
+}
+
+static SECP256K1_INLINE void secp256k1_fe_impl_half(secp256k1_fe *r) {
+    uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4];
+    uint64_t one = (uint64_t)1;
+    uint64_t mask = -(t0 & one) >> 12;
+
+    /* Bounds analysis (over the rationals).
+     *
+     * Let m = r->magnitude
+     *     C = 0xFFFFFFFFFFFFFULL * 2
+     *     D = 0x0FFFFFFFFFFFFULL * 2
+     *
+     * Initial bounds: t0..t3 <= C * m
+     *                     t4 <= D * m
+     */
+
+    t0 += 0xFFFFEFFFFFC2FULL & mask;
+    t1 += mask;
+    t2 += mask;
+    t3 += mask;
+    t4 += mask >> 4;
+
+    VERIFY_CHECK((t0 & one) == 0);
+
+    /* t0..t3: added <= C/2
+     *     t4: added <= D/2
+     *
+     * Current bounds: t0..t3 <= C * (m + 1/2)
+     *                     t4 <= D * (m + 1/2)
+     */
+
+    r->n[0] = (t0 >> 1) + ((t1 & one) << 51);
+    r->n[1] = (t1 >> 1) + ((t2 & one) << 51);
+    r->n[2] = (t2 >> 1) + ((t3 & one) << 51);
+    r->n[3] = (t3 >> 1) + ((t4 & one) << 51);
+    r->n[4] = (t4 >> 1);
+
+    /* t0..t3: shifted right and added <= C/4 + 1/2
+     *     t4: shifted right
+     *
+     * Current bounds: t0..t3 <= C * (m/2 + 1/2)
+     *                     t4 <= D * (m/2 + 1/4)
+     *
+     * Therefore the output magnitude (M) has to be set such that:
+     *     t0..t3: C * M >= C * (m/2 + 1/2)
+     *         t4: D * M >= D * (m/2 + 1/4)
+     *
+     * It suffices for all limbs that, for any input magnitude m:
+     *     M >= m/2 + 1/2
+     *
+     * and since we want the smallest such integer value for M:
+     *     M == floor(m/2) + 1
+     */
+}
+
+static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) {
+    uint64_t mask0, mask1;
+    volatile int vflag = flag;
+    VERIFY_CHECK(flag == 0 || flag == 1);
+    SECP256K1_CHECKMEM_CHECK_VERIFY(r->n, sizeof(r->n));
+    mask0 = vflag + ~((uint64_t)0);
+    mask1 = ~mask0;
+    r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1);
+    r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1);
+    r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1);
+    r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1);
+}
+
+static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
+    r->n[0] = a->n[0] | a->n[1] << 52;
+    r->n[1] = a->n[1] >> 12 | a->n[2] << 40;
+    r->n[2] = a->n[2] >> 24 | a->n[3] << 28;
+    r->n[3] = a->n[3] >> 36 | a->n[4] << 16;
+}
+
+static SECP256K1_INLINE void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+    r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL;
+    r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL);
+    r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL);
+    r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL);
+    r->n[4] = a->n[3] >> 16;
+}
+
+static void secp256k1_fe_from_signed62(secp256k1_fe *r, const secp256k1_modinv64_signed62 *a) {
+    const uint64_t M52 = UINT64_MAX >> 12;
+    const uint64_t a0 = a->v[0], a1 = a->v[1], a2 = a->v[2], a3 = a->v[3], a4 = a->v[4];
+
+    /* The output from secp256k1_modinv64{_var} should be normalized to range [0,modulus), and
+     * have limbs in [0,2^62). The modulus is < 2^256, so the top limb must be below 2^(256-62*4).
+     */
+    VERIFY_CHECK(a0 >> 62 == 0);
+    VERIFY_CHECK(a1 >> 62 == 0);
+    VERIFY_CHECK(a2 >> 62 == 0);
+    VERIFY_CHECK(a3 >> 62 == 0);
+    VERIFY_CHECK(a4 >> 8 == 0);
+
+    r->n[0] =  a0                   & M52;
+    r->n[1] = (a0 >> 52 | a1 << 10) & M52;
+    r->n[2] = (a1 >> 42 | a2 << 20) & M52;
+    r->n[3] = (a2 >> 32 | a3 << 30) & M52;
+    r->n[4] = (a3 >> 22 | a4 << 40);
+}
+
+static void secp256k1_fe_to_signed62(secp256k1_modinv64_signed62 *r, const secp256k1_fe *a) {
+    const uint64_t M62 = UINT64_MAX >> 2;
+    const uint64_t a0 = a->n[0], a1 = a->n[1], a2 = a->n[2], a3 = a->n[3], a4 = a->n[4];
+
+    r->v[0] = (a0       | a1 << 52) & M62;
+    r->v[1] = (a1 >> 10 | a2 << 42) & M62;
+    r->v[2] = (a2 >> 20 | a3 << 32) & M62;
+    r->v[3] = (a3 >> 30 | a4 << 22) & M62;
+    r->v[4] =  a4 >> 40;
+}
+
+static const secp256k1_modinv64_modinfo secp256k1_const_modinfo_fe = {
+    {{-0x1000003D1LL, 0, 0, 0, 256}},
+    0x27C7F6E22DDACACFLL
+};
+
+static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x) {
+    secp256k1_fe tmp = *x;
+    secp256k1_modinv64_signed62 s;
+
+    secp256k1_fe_normalize(&tmp);
+    secp256k1_fe_to_signed62(&s, &tmp);
+    secp256k1_modinv64(&s, &secp256k1_const_modinfo_fe);
+    secp256k1_fe_from_signed62(r, &s);
+}
+
+static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
+    secp256k1_fe tmp = *x;
+    secp256k1_modinv64_signed62 s;
+
+    secp256k1_fe_normalize_var(&tmp);
+    secp256k1_fe_to_signed62(&s, &tmp);
+    secp256k1_modinv64_var(&s, &secp256k1_const_modinfo_fe);
+    secp256k1_fe_from_signed62(r, &s);
+}
+
+static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x) {
+    secp256k1_fe tmp;
+    secp256k1_modinv64_signed62 s;
+    int jac, ret;
+
+    tmp = *x;
+    secp256k1_fe_normalize_var(&tmp);
+    /* secp256k1_jacobi64_maybe_var cannot deal with input 0. */
+    if (secp256k1_fe_is_zero(&tmp)) return 1;
+    secp256k1_fe_to_signed62(&s, &tmp);
+    jac = secp256k1_jacobi64_maybe_var(&s, &secp256k1_const_modinfo_fe);
+    if (jac == 0) {
+        /* secp256k1_jacobi64_maybe_var failed to compute the Jacobi symbol. Fall back
+         * to computing a square root. This should be extremely rare with random
+         * input (except in VERIFY mode, where a lower iteration count is used). */
+        secp256k1_fe dummy;
+        ret = secp256k1_fe_sqrt(&dummy, &tmp);
+    } else {
+        ret = jac >= 0;
+    }
+    return ret;
+}
+
+#endif /* SECP256K1_FIELD_REPR_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/field_5x52_int128_impl.h

@@ -0,0 +1,274 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_FIELD_INNER5X52_IMPL_H
+#define SECP256K1_FIELD_INNER5X52_IMPL_H
+
+#include <stdint.h>
+
+#include "int128.h"
+#include "util.h"
+
+#define VERIFY_BITS(x, n) VERIFY_CHECK(((x) >> (n)) == 0)
+#define VERIFY_BITS_128(x, n) VERIFY_CHECK(secp256k1_u128_check_bits((x), (n)))
+
+SECP256K1_INLINE static void secp256k1_fe_mul_inner(uint64_t *r, const uint64_t *a, const uint64_t * SECP256K1_RESTRICT b) {
+    secp256k1_uint128 c, d;
+    uint64_t t3, t4, tx, u0;
+    uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
+    const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
+
+    VERIFY_BITS(a[0], 56);
+    VERIFY_BITS(a[1], 56);
+    VERIFY_BITS(a[2], 56);
+    VERIFY_BITS(a[3], 56);
+    VERIFY_BITS(a[4], 52);
+    VERIFY_BITS(b[0], 56);
+    VERIFY_BITS(b[1], 56);
+    VERIFY_BITS(b[2], 56);
+    VERIFY_BITS(b[3], 56);
+    VERIFY_BITS(b[4], 52);
+    VERIFY_CHECK(r != b);
+    VERIFY_CHECK(a != b);
+
+    /*  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
+     *  for 0 <= x <= 4, px is a shorthand for sum(a[i]*b[x-i], i=0..x).
+     *  for 4 <= x <= 8, px is a shorthand for sum(a[i]*b[x-i], i=(x-4)..4)
+     *  Note that [x 0 0 0 0 0] = [x*R].
+     */
+
+    secp256k1_u128_mul(&d, a0, b[3]);
+    secp256k1_u128_accum_mul(&d, a1, b[2]);
+    secp256k1_u128_accum_mul(&d, a2, b[1]);
+    secp256k1_u128_accum_mul(&d, a3, b[0]);
+    VERIFY_BITS_128(&d, 114);
+    /* [d 0 0 0] = [p3 0 0 0] */
+    secp256k1_u128_mul(&c, a4, b[4]);
+    VERIFY_BITS_128(&c, 112);
+    /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
+    VERIFY_BITS_128(&d, 115);
+    VERIFY_BITS_128(&c, 48);
+    /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS(t3, 52);
+    VERIFY_BITS_128(&d, 63);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+
+    secp256k1_u128_accum_mul(&d, a0, b[4]);
+    secp256k1_u128_accum_mul(&d, a1, b[3]);
+    secp256k1_u128_accum_mul(&d, a2, b[2]);
+    secp256k1_u128_accum_mul(&d, a3, b[1]);
+    secp256k1_u128_accum_mul(&d, a4, b[0]);
+    VERIFY_BITS_128(&d, 115);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
+    VERIFY_BITS_128(&d, 116);
+    /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS(t4, 52);
+    VERIFY_BITS_128(&d, 64);
+    /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    tx = (t4 >> 48); t4 &= (M >> 4);
+    VERIFY_BITS(tx, 4);
+    VERIFY_BITS(t4, 48);
+    /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+
+    secp256k1_u128_mul(&c, a0, b[0]);
+    VERIFY_BITS_128(&c, 112);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
+    secp256k1_u128_accum_mul(&d, a1, b[4]);
+    secp256k1_u128_accum_mul(&d, a2, b[3]);
+    secp256k1_u128_accum_mul(&d, a3, b[2]);
+    secp256k1_u128_accum_mul(&d, a4, b[1]);
+    VERIFY_BITS_128(&d, 114);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS(u0, 52);
+    VERIFY_BITS_128(&d, 62);
+    /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = (u0 << 4) | tx;
+    VERIFY_BITS(u0, 56);
+    /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    secp256k1_u128_accum_mul(&c, u0, R >> 4);
+    VERIFY_BITS_128(&c, 113);
+    /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[0], 52);
+    VERIFY_BITS_128(&c, 61);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
+
+    secp256k1_u128_accum_mul(&c, a0, b[1]);
+    secp256k1_u128_accum_mul(&c, a1, b[0]);
+    VERIFY_BITS_128(&c, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
+    secp256k1_u128_accum_mul(&d, a2, b[4]);
+    secp256k1_u128_accum_mul(&d, a3, b[3]);
+    secp256k1_u128_accum_mul(&d, a4, b[2]);
+    VERIFY_BITS_128(&d, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 62);
+    /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[1], 52);
+    VERIFY_BITS_128(&c, 63);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+
+    secp256k1_u128_accum_mul(&c, a0, b[2]);
+    secp256k1_u128_accum_mul(&c, a1, b[1]);
+    secp256k1_u128_accum_mul(&c, a2, b[0]);
+    VERIFY_BITS_128(&c, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
+    secp256k1_u128_accum_mul(&d, a3, b[4]);
+    secp256k1_u128_accum_mul(&d, a4, b[3]);
+    VERIFY_BITS_128(&d, 114);
+    /* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 50);
+    /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[2], 52);
+    VERIFY_BITS_128(&c, 63);
+    /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
+    secp256k1_u128_accum_u64(&c, t3);
+    VERIFY_BITS_128(&c, 100);
+    /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[3], 52);
+    VERIFY_BITS_128(&c, 48);
+    /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = secp256k1_u128_to_u64(&c) + t4;
+    VERIFY_BITS(r[4], 49);
+    /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+
+SECP256K1_INLINE static void secp256k1_fe_sqr_inner(uint64_t *r, const uint64_t *a) {
+    secp256k1_uint128 c, d;
+    uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
+    uint64_t t3, t4, tx, u0;
+    const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
+
+    VERIFY_BITS(a[0], 56);
+    VERIFY_BITS(a[1], 56);
+    VERIFY_BITS(a[2], 56);
+    VERIFY_BITS(a[3], 56);
+    VERIFY_BITS(a[4], 52);
+
+    /**  [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
+     *  px is a shorthand for sum(a[i]*a[x-i], i=0..x).
+     *  Note that [x 0 0 0 0 0] = [x*R].
+     */
+
+    secp256k1_u128_mul(&d, a0*2, a3);
+    secp256k1_u128_accum_mul(&d, a1*2, a2);
+    VERIFY_BITS_128(&d, 114);
+    /* [d 0 0 0] = [p3 0 0 0] */
+    secp256k1_u128_mul(&c, a4, a4);
+    VERIFY_BITS_128(&c, 112);
+    /* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    secp256k1_u128_accum_mul(&d, R, secp256k1_u128_to_u64(&c)); secp256k1_u128_rshift(&c, 64);
+    VERIFY_BITS_128(&d, 115);
+    VERIFY_BITS_128(&c, 48);
+    /* [(c<<12) 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+    t3 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS(t3, 52);
+    VERIFY_BITS_128(&d, 63);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
+
+    a4 *= 2;
+    secp256k1_u128_accum_mul(&d, a0, a4);
+    secp256k1_u128_accum_mul(&d, a1*2, a3);
+    secp256k1_u128_accum_mul(&d, a2, a2);
+    VERIFY_BITS_128(&d, 115);
+    /* [(c<<12) 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    secp256k1_u128_accum_mul(&d, R << 12, secp256k1_u128_to_u64(&c));
+    VERIFY_BITS_128(&d, 116);
+    /* [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    t4 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS(t4, 52);
+    VERIFY_BITS_128(&d, 64);
+    /* [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+    tx = (t4 >> 48); t4 &= (M >> 4);
+    VERIFY_BITS(tx, 4);
+    VERIFY_BITS(t4, 48);
+    /* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
+
+    secp256k1_u128_mul(&c, a0, a0);
+    VERIFY_BITS_128(&c, 112);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
+    secp256k1_u128_accum_mul(&d, a1, a4);
+    secp256k1_u128_accum_mul(&d, a2*2, a3);
+    VERIFY_BITS_128(&d, 114);
+    /* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = secp256k1_u128_to_u64(&d) & M; secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS(u0, 52);
+    VERIFY_BITS_128(&d, 62);
+    /* [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    /* [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    u0 = (u0 << 4) | tx;
+    VERIFY_BITS(u0, 56);
+    /* [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    secp256k1_u128_accum_mul(&c, u0, R >> 4);
+    VERIFY_BITS_128(&c, 113);
+    /* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
+    r[0] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[0], 52);
+    VERIFY_BITS_128(&c, 61);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
+
+    a0 *= 2;
+    secp256k1_u128_accum_mul(&c, a0, a1);
+    VERIFY_BITS_128(&c, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
+    secp256k1_u128_accum_mul(&d, a2, a4);
+    secp256k1_u128_accum_mul(&d, a3, a3);
+    VERIFY_BITS_128(&d, 114);
+    /* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    secp256k1_u128_accum_mul(&c, secp256k1_u128_to_u64(&d) & M, R); secp256k1_u128_rshift(&d, 52);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 62);
+    /* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+    r[1] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[1], 52);
+    VERIFY_BITS_128(&c, 63);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
+
+    secp256k1_u128_accum_mul(&c, a0, a2);
+    secp256k1_u128_accum_mul(&c, a1, a1);
+    VERIFY_BITS_128(&c, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
+    secp256k1_u128_accum_mul(&d, a3, a4);
+    VERIFY_BITS_128(&d, 114);
+    /* [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    secp256k1_u128_accum_mul(&c, R, secp256k1_u128_to_u64(&d)); secp256k1_u128_rshift(&d, 64);
+    VERIFY_BITS_128(&c, 115);
+    VERIFY_BITS_128(&d, 50);
+    /* [(d<<12) 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[2] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[2], 52);
+    VERIFY_BITS_128(&c, 63);
+    /* [(d<<12) 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+
+    secp256k1_u128_accum_mul(&c, R << 12, secp256k1_u128_to_u64(&d));
+    secp256k1_u128_accum_u64(&c, t3);
+    VERIFY_BITS_128(&c, 100);
+    /* [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[3] = secp256k1_u128_to_u64(&c) & M; secp256k1_u128_rshift(&c, 52);
+    VERIFY_BITS(r[3], 52);
+    VERIFY_BITS_128(&c, 48);
+    /* [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+    r[4] = secp256k1_u128_to_u64(&c) + t4;
+    VERIFY_BITS(r[4], 49);
+    /* [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
+}
+
+#endif /* SECP256K1_FIELD_INNER5X52_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/field_impl.h

@@ -0,0 +1,457 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_FIELD_IMPL_H
+#define SECP256K1_FIELD_IMPL_H
+
+#include "field.h"
+#include "util.h"
+
+#if defined(SECP256K1_WIDEMUL_INT128)
+#include "field_5x52_impl.h"
+#elif defined(SECP256K1_WIDEMUL_INT64)
+#include "field_10x26_impl.h"
+#else
+#error "Please select wide multiplication implementation"
+#endif
+
+SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) {
+    secp256k1_memclear_explicit(a, sizeof(secp256k1_fe));
+}
+
+SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
+    SECP256K1_FE_VERIFY(a);
+    SECP256K1_FE_VERIFY(b);
+    SECP256K1_FE_VERIFY_MAGNITUDE(a, 1);
+    SECP256K1_FE_VERIFY_MAGNITUDE(b, 31);
+
+    secp256k1_fe_negate(&na, a, 1);
+    secp256k1_fe_add(&na, b);
+    return secp256k1_fe_normalizes_to_zero(&na);
+}
+
+static int secp256k1_fe_sqrt(secp256k1_fe * SECP256K1_RESTRICT r, const secp256k1_fe * SECP256K1_RESTRICT a) {
+    /** Given that p is congruent to 3 mod 4, we can compute the square root of
+     *  a mod p as the (p+1)/4'th power of a.
+     *
+     *  As (p+1)/4 is an even number, it will have the same result for a and for
+     *  (-a). Only one of these two numbers actually has a square root however,
+     *  so we test at the end by squaring and comparing to the input.
+     *  Also because (p+1)/4 is an even number, the computed square root is
+     *  itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
+     */
+    secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+    int j, ret;
+
+    VERIFY_CHECK(r != a);
+    SECP256K1_FE_VERIFY(a);
+    SECP256K1_FE_VERIFY_MAGNITUDE(a, 8);
+
+    /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
+     *  { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
+     *  1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
+     */
+
+    secp256k1_fe_sqr(&x2, a);
+    secp256k1_fe_mul(&x2, &x2, a);
+
+    secp256k1_fe_sqr(&x3, &x2);
+    secp256k1_fe_mul(&x3, &x3, a);
+
+    x6 = x3;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x6, &x6);
+    }
+    secp256k1_fe_mul(&x6, &x6, &x3);
+
+    x9 = x6;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x9, &x9);
+    }
+    secp256k1_fe_mul(&x9, &x9, &x3);
+
+    x11 = x9;
+    for (j=0; j<2; j++) {
+        secp256k1_fe_sqr(&x11, &x11);
+    }
+    secp256k1_fe_mul(&x11, &x11, &x2);
+
+    x22 = x11;
+    for (j=0; j<11; j++) {
+        secp256k1_fe_sqr(&x22, &x22);
+    }
+    secp256k1_fe_mul(&x22, &x22, &x11);
+
+    x44 = x22;
+    for (j=0; j<22; j++) {
+        secp256k1_fe_sqr(&x44, &x44);
+    }
+    secp256k1_fe_mul(&x44, &x44, &x22);
+
+    x88 = x44;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x88, &x88);
+    }
+    secp256k1_fe_mul(&x88, &x88, &x44);
+
+    x176 = x88;
+    for (j=0; j<88; j++) {
+        secp256k1_fe_sqr(&x176, &x176);
+    }
+    secp256k1_fe_mul(&x176, &x176, &x88);
+
+    x220 = x176;
+    for (j=0; j<44; j++) {
+        secp256k1_fe_sqr(&x220, &x220);
+    }
+    secp256k1_fe_mul(&x220, &x220, &x44);
+
+    x223 = x220;
+    for (j=0; j<3; j++) {
+        secp256k1_fe_sqr(&x223, &x223);
+    }
+    secp256k1_fe_mul(&x223, &x223, &x3);
+
+    /* The final result is then assembled using a sliding window over the blocks. */
+
+    t1 = x223;
+    for (j=0; j<23; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x22);
+    for (j=0; j<6; j++) {
+        secp256k1_fe_sqr(&t1, &t1);
+    }
+    secp256k1_fe_mul(&t1, &t1, &x2);
+    secp256k1_fe_sqr(&t1, &t1);
+    secp256k1_fe_sqr(r, &t1);
+
+    /* Check that a square root was actually calculated */
+
+    secp256k1_fe_sqr(&t1, r);
+    ret = secp256k1_fe_equal(&t1, a);
+
+#ifdef VERIFY
+    if (!ret) {
+        secp256k1_fe_negate(&t1, &t1, 1);
+        secp256k1_fe_normalize_var(&t1);
+        VERIFY_CHECK(secp256k1_fe_equal(&t1, a));
+    }
+#endif
+    return ret;
+}
+
+#ifndef VERIFY
+static void secp256k1_fe_verify(const secp256k1_fe *a) { (void)a; }
+static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m) { (void)a; (void)m; }
+#else
+static void secp256k1_fe_impl_verify(const secp256k1_fe *a);
+static void secp256k1_fe_verify(const secp256k1_fe *a) {
+    /* Magnitude between 0 and 32. */
+    SECP256K1_FE_VERIFY_MAGNITUDE(a, 32);
+    /* Normalized is 0 or 1. */
+    VERIFY_CHECK((a->normalized == 0) || (a->normalized == 1));
+    /* If normalized, magnitude must be 0 or 1. */
+    if (a->normalized) SECP256K1_FE_VERIFY_MAGNITUDE(a, 1);
+    /* Invoke implementation-specific checks. */
+    secp256k1_fe_impl_verify(a);
+}
+
+static void secp256k1_fe_verify_magnitude(const secp256k1_fe *a, int m) {
+    VERIFY_CHECK(m >= 0);
+    VERIFY_CHECK(m <= 32);
+    VERIFY_CHECK(a->magnitude <= m);
+}
+
+static void secp256k1_fe_impl_normalize(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_normalize(secp256k1_fe *r) {
+    SECP256K1_FE_VERIFY(r);
+
+    secp256k1_fe_impl_normalize(r);
+    r->magnitude = 1;
+    r->normalized = 1;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_normalize_weak(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_normalize_weak(secp256k1_fe *r) {
+    SECP256K1_FE_VERIFY(r);
+
+    secp256k1_fe_impl_normalize_weak(r);
+    r->magnitude = 1;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_normalize_var(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_normalize_var(secp256k1_fe *r) {
+    SECP256K1_FE_VERIFY(r);
+
+    secp256k1_fe_impl_normalize_var(r);
+    r->magnitude = 1;
+    r->normalized = 1;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static int secp256k1_fe_impl_normalizes_to_zero(const secp256k1_fe *r);
+SECP256K1_INLINE static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r) {
+    SECP256K1_FE_VERIFY(r);
+
+    return secp256k1_fe_impl_normalizes_to_zero(r);
+}
+
+static int secp256k1_fe_impl_normalizes_to_zero_var(const secp256k1_fe *r);
+SECP256K1_INLINE static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r) {
+    SECP256K1_FE_VERIFY(r);
+
+    return secp256k1_fe_impl_normalizes_to_zero_var(r);
+}
+
+static void secp256k1_fe_impl_set_int(secp256k1_fe *r, int a);
+SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
+
+    secp256k1_fe_impl_set_int(r, a);
+    r->magnitude = (a != 0);
+    r->normalized = 1;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_add_int(secp256k1_fe *r, int a);
+SECP256K1_INLINE static void secp256k1_fe_add_int(secp256k1_fe *r, int a) {
+    VERIFY_CHECK(0 <= a && a <= 0x7FFF);
+    SECP256K1_FE_VERIFY(r);
+
+    secp256k1_fe_impl_add_int(r, a);
+    r->magnitude += 1;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static int secp256k1_fe_impl_is_zero(const secp256k1_fe *a);
+SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) {
+    SECP256K1_FE_VERIFY(a);
+    VERIFY_CHECK(a->normalized);
+
+    return secp256k1_fe_impl_is_zero(a);
+}
+
+static int secp256k1_fe_impl_is_odd(const secp256k1_fe *a);
+SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) {
+    SECP256K1_FE_VERIFY(a);
+    VERIFY_CHECK(a->normalized);
+
+    return secp256k1_fe_impl_is_odd(a);
+}
+
+static int secp256k1_fe_impl_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
+SECP256K1_INLINE static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+    SECP256K1_FE_VERIFY(a);
+    SECP256K1_FE_VERIFY(b);
+    VERIFY_CHECK(a->normalized);
+    VERIFY_CHECK(b->normalized);
+
+    return secp256k1_fe_impl_cmp_var(a, b);
+}
+
+static void secp256k1_fe_impl_set_b32_mod(secp256k1_fe *r, const unsigned char *a);
+SECP256K1_INLINE static void secp256k1_fe_set_b32_mod(secp256k1_fe *r, const unsigned char *a) {
+    secp256k1_fe_impl_set_b32_mod(r, a);
+    r->magnitude = 1;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static int secp256k1_fe_impl_set_b32_limit(secp256k1_fe *r, const unsigned char *a);
+SECP256K1_INLINE static int secp256k1_fe_set_b32_limit(secp256k1_fe *r, const unsigned char *a) {
+    if (secp256k1_fe_impl_set_b32_limit(r, a)) {
+        r->magnitude = 1;
+        r->normalized = 1;
+        SECP256K1_FE_VERIFY(r);
+        return 1;
+    } else {
+        /* Mark the output field element as invalid. */
+        r->magnitude = -1;
+        return 0;
+    }
+}
+
+static void secp256k1_fe_impl_get_b32(unsigned char *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) {
+    SECP256K1_FE_VERIFY(a);
+    VERIFY_CHECK(a->normalized);
+
+    secp256k1_fe_impl_get_b32(r, a);
+}
+
+static void secp256k1_fe_impl_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m);
+SECP256K1_INLINE static void secp256k1_fe_negate_unchecked(secp256k1_fe *r, const secp256k1_fe *a, int m) {
+    SECP256K1_FE_VERIFY(a);
+    VERIFY_CHECK(m >= 0 && m <= 31);
+    SECP256K1_FE_VERIFY_MAGNITUDE(a, m);
+
+    secp256k1_fe_impl_negate_unchecked(r, a, m);
+    r->magnitude = m + 1;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_mul_int_unchecked(secp256k1_fe *r, int a);
+SECP256K1_INLINE static void secp256k1_fe_mul_int_unchecked(secp256k1_fe *r, int a) {
+    SECP256K1_FE_VERIFY(r);
+
+    VERIFY_CHECK(a >= 0 && a <= 32);
+    VERIFY_CHECK(a*r->magnitude <= 32);
+    secp256k1_fe_impl_mul_int_unchecked(r, a);
+    r->magnitude *= a;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_add(secp256k1_fe *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) {
+    SECP256K1_FE_VERIFY(r);
+    SECP256K1_FE_VERIFY(a);
+    VERIFY_CHECK(r->magnitude + a->magnitude <= 32);
+
+    secp256k1_fe_impl_add(r, a);
+    r->magnitude += a->magnitude;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
+SECP256K1_INLINE static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) {
+    SECP256K1_FE_VERIFY(a);
+    SECP256K1_FE_VERIFY(b);
+    SECP256K1_FE_VERIFY_MAGNITUDE(a, 8);
+    SECP256K1_FE_VERIFY_MAGNITUDE(b, 8);
+    VERIFY_CHECK(r != b);
+    VERIFY_CHECK(a != b);
+
+    secp256k1_fe_impl_mul(r, a, b);
+    r->magnitude = 1;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_sqr(secp256k1_fe *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) {
+    SECP256K1_FE_VERIFY(a);
+    SECP256K1_FE_VERIFY_MAGNITUDE(a, 8);
+
+    secp256k1_fe_impl_sqr(r, a);
+    r->magnitude = 1;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
+SECP256K1_INLINE static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) {
+    VERIFY_CHECK(flag == 0 || flag == 1);
+    SECP256K1_FE_VERIFY(a);
+    SECP256K1_FE_VERIFY(r);
+
+    secp256k1_fe_impl_cmov(r, a, flag);
+    if (a->magnitude > r->magnitude) r->magnitude = a->magnitude;
+    if (!a->normalized) r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
+SECP256K1_INLINE static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) {
+    SECP256K1_FE_VERIFY(a);
+    VERIFY_CHECK(a->normalized);
+
+    secp256k1_fe_impl_to_storage(r, a);
+}
+
+static void secp256k1_fe_impl_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
+SECP256K1_INLINE static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) {
+    secp256k1_fe_impl_from_storage(r, a);
+    r->magnitude = 1;
+    r->normalized = 1;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_inv(secp256k1_fe *r, const secp256k1_fe *x);
+SECP256K1_INLINE static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *x) {
+    int input_is_zero = secp256k1_fe_normalizes_to_zero(x);
+    SECP256K1_FE_VERIFY(x);
+
+    secp256k1_fe_impl_inv(r, x);
+    r->magnitude = x->magnitude > 0;
+    r->normalized = 1;
+
+    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == input_is_zero);
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_inv_var(secp256k1_fe *r, const secp256k1_fe *x);
+SECP256K1_INLINE static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) {
+    int input_is_zero = secp256k1_fe_normalizes_to_zero(x);
+    SECP256K1_FE_VERIFY(x);
+
+    secp256k1_fe_impl_inv_var(r, x);
+    r->magnitude = x->magnitude > 0;
+    r->normalized = 1;
+
+    VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == input_is_zero);
+    SECP256K1_FE_VERIFY(r);
+}
+
+static int secp256k1_fe_impl_is_square_var(const secp256k1_fe *x);
+SECP256K1_INLINE static int secp256k1_fe_is_square_var(const secp256k1_fe *x) {
+    int ret;
+    secp256k1_fe tmp = *x, sqrt;
+    SECP256K1_FE_VERIFY(x);
+
+    ret = secp256k1_fe_impl_is_square_var(x);
+    secp256k1_fe_normalize_weak(&tmp);
+    VERIFY_CHECK(ret == secp256k1_fe_sqrt(&sqrt, &tmp));
+    return ret;
+}
+
+static void secp256k1_fe_impl_get_bounds(secp256k1_fe* r, int m);
+SECP256K1_INLINE static void secp256k1_fe_get_bounds(secp256k1_fe* r, int m) {
+    VERIFY_CHECK(m >= 0);
+    VERIFY_CHECK(m <= 32);
+
+    secp256k1_fe_impl_get_bounds(r, m);
+    r->magnitude = m;
+    r->normalized = (m == 0);
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+static void secp256k1_fe_impl_half(secp256k1_fe *r);
+SECP256K1_INLINE static void secp256k1_fe_half(secp256k1_fe *r) {
+    SECP256K1_FE_VERIFY(r);
+    SECP256K1_FE_VERIFY_MAGNITUDE(r, 31);
+
+    secp256k1_fe_impl_half(r);
+    r->magnitude = (r->magnitude >> 1) + 1;
+    r->normalized = 0;
+
+    SECP256K1_FE_VERIFY(r);
+}
+
+#endif /* defined(VERIFY) */
+
+#endif /* SECP256K1_FIELD_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/group.h

@@ -0,0 +1,218 @@
+/***********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                              *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_GROUP_H
+#define SECP256K1_GROUP_H
+
+#include "field.h"
+
+/** A group element in affine coordinates on the secp256k1 curve,
+ *  or occasionally on an isomorphic curve of the form y^2 = x^3 + 7*t^6.
+ *  Note: For exhaustive test mode, secp256k1 is replaced by a small subgroup of a different curve.
+ */
+typedef struct {
+    secp256k1_fe x;
+    secp256k1_fe y;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_ge;
+
+#define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
+#define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+/** A group element of the secp256k1 curve, in jacobian coordinates.
+ *  Note: For exhastive test mode, secp256k1 is replaced by a small subgroup of a different curve.
+ */
+typedef struct {
+    secp256k1_fe x; /* actual X: x/z^2 */
+    secp256k1_fe y; /* actual Y: y/z^3 */
+    secp256k1_fe z;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_gej;
+
+#define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
+#define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
+
+typedef struct {
+    secp256k1_fe_storage x;
+    secp256k1_fe_storage y;
+} secp256k1_ge_storage;
+
+#define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
+
+#define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
+
+/** Maximum allowed magnitudes for group element coordinates
+ *  in affine (x, y) and jacobian (x, y, z) representation. */
+#define SECP256K1_GE_X_MAGNITUDE_MAX  4
+#define SECP256K1_GE_Y_MAGNITUDE_MAX  3
+#define SECP256K1_GEJ_X_MAGNITUDE_MAX 4
+#define SECP256K1_GEJ_Y_MAGNITUDE_MAX 4
+#define SECP256K1_GEJ_Z_MAGNITUDE_MAX 1
+
+/** Set a group element equal to the point with given X and Y coordinates */
+static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
+
+/** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
+ *  for Y. Return value indicates whether the result is valid. */
+static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
+
+/** Determine whether x is a valid X coordinate on the curve. */
+static int secp256k1_ge_x_on_curve_var(const secp256k1_fe *x);
+
+/** Determine whether fraction xn/xd is a valid X coordinate on the curve (xd != 0). */
+static int secp256k1_ge_x_frac_on_curve_var(const secp256k1_fe *xn, const secp256k1_fe *xd);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
+
+/** Check whether a group element is valid (i.e., on the curve). */
+static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
+
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
+static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
+
+/** Set a group element equal to another which is given in jacobian coordinates. Constant time. */
+static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
+
+/** Set a group element equal to another which is given in jacobian coordinates. */
+static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a);
+
+/** Set group elements r[0:len] (affine) equal to group elements a[0:len] (jacobian).
+ * None of the group elements in a[0:len] may be infinity. Constant time. */
+static void secp256k1_ge_set_all_gej(secp256k1_ge *r, const secp256k1_gej *a, size_t len);
+
+/** Set group elements r[0:len] (affine) equal to group elements a[0:len] (jacobian). */
+static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len);
+
+/** Bring a batch of inputs to the same global z "denominator", based on ratios between
+ *  (omitted) z coordinates of adjacent elements.
+ *
+ *  Although the elements a[i] are _ge rather than _gej, they actually represent elements
+ *  in Jacobian coordinates with their z coordinates omitted.
+ *
+ *  Using the notation z(b) to represent the omitted z coordinate of b, the array zr of
+ *  z coordinate ratios must satisfy zr[i] == z(a[i]) / z(a[i-1]) for 0 < 'i' < len.
+ *  The zr[0] value is unused.
+ *
+ *  This function adjusts the coordinates of 'a' in place so that for all 'i', z(a[i]) == z(a[len-1]).
+ *  In other words, the initial value of z(a[len-1]) becomes the global z "denominator". Only the
+ *  a[i].x and a[i].y coordinates are explicitly modified; the adjustment of the omitted z coordinate is
+ *  implicit.
+ *
+ *  The coordinates of the final element a[len-1] are not changed.
+ */
+static void secp256k1_ge_table_set_globalz(size_t len, secp256k1_ge *a, const secp256k1_fe *zr);
+
+/** Check two group elements (affine) for equality in variable time. */
+static int secp256k1_ge_eq_var(const secp256k1_ge *a, const secp256k1_ge *b);
+
+/** Set a group element (affine) equal to the point at infinity. */
+static void secp256k1_ge_set_infinity(secp256k1_ge *r);
+
+/** Set a group element (jacobian) equal to the point at infinity. */
+static void secp256k1_gej_set_infinity(secp256k1_gej *r);
+
+/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
+static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
+
+/** Check two group elements (jacobian) for equality in variable time. */
+static int secp256k1_gej_eq_var(const secp256k1_gej *a, const secp256k1_gej *b);
+
+/** Check two group elements (jacobian and affine) for equality in variable time. */
+static int secp256k1_gej_eq_ge_var(const secp256k1_gej *a, const secp256k1_ge *b);
+
+/** Compare the X coordinate of a group element (jacobian).
+  * The magnitude of the group element's X coordinate must not exceed 31. */
+static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
+
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
+static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
+
+/** Set r equal to the double of a. Constant time. */
+static void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a);
+
+/** Set r equal to the double of a. If rzr is not-NULL this sets *rzr such that r->z == a->z * *rzr (where infinity means an implicit z = 0). */
+static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
+static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
+    than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
+    guarantee, and b is allowed to be infinity. If rzr is non-NULL this sets *rzr such that r->z == a->z * *rzr (a cannot be infinity in that case). */
+static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
+
+/** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
+static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
+
+/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
+static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
+
+/** Clear a secp256k1_gej to prevent leaking sensitive information. */
+static void secp256k1_gej_clear(secp256k1_gej *r);
+
+/** Clear a secp256k1_ge to prevent leaking sensitive information. */
+static void secp256k1_ge_clear(secp256k1_ge *r);
+
+/** Convert a group element to the storage type. */
+static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
+
+/** Convert a group element back from the storage type. */
+static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
+
+/** If flag is 1, set *r equal to *a; if flag is 0, leave it. Constant-time.
+ * Both *r and *a must be initialized. Flag must be 0 or 1. */
+static void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag);
+
+/** If flag is 1, set *r equal to *a; if flag is 0, leave it. Constant-time.
+ * Both *r and *a must be initialized. Flag must be 0 or 1. */
+static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
+
+/** Rescale a jacobian point by b which must be non-zero. Constant-time. */
+static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
+
+/** Convert a group element that is not infinity to a 64-byte array. The output
+ *  array is platform-dependent. */
+static void secp256k1_ge_to_bytes(unsigned char *buf, const secp256k1_ge *a);
+
+/** Convert a 64-byte array into group element. This function assumes that the
+ *  provided buffer correctly encodes a group element. */
+static void secp256k1_ge_from_bytes(secp256k1_ge *r, const unsigned char *buf);
+
+/** Convert a group element (that is allowed to be infinity) to a 64-byte
+ *  array. The output array is platform-dependent. */
+static void secp256k1_ge_to_bytes_ext(unsigned char *data, const secp256k1_ge *ge);
+
+/** Convert a 64-byte array into a group element. This function assumes that the
+ *  provided buffer is the output of secp256k1_ge_to_bytes_ext. */
+static void secp256k1_ge_from_bytes_ext(secp256k1_ge *ge, const unsigned char *data);
+
+/** Determine if a point (which is assumed to be on the curve) is in the correct (sub)group of the curve.
+ *
+ * In normal mode, the used group is secp256k1, which has cofactor=1 meaning that every point on the curve is in the
+ * group, and this function returns always true.
+ *
+ * When compiling in exhaustive test mode, a slightly different curve equation is used, leading to a group with a
+ * (very) small subgroup, and that subgroup is what is used for all cryptographic operations. In that mode, this
+ * function checks whether a point that is on the curve is in fact also in that subgroup.
+ */
+static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge* ge);
+
+/** Check invariants on an affine group element (no-op unless VERIFY is enabled). */
+static void secp256k1_ge_verify(const secp256k1_ge *a);
+#define SECP256K1_GE_VERIFY(a) secp256k1_ge_verify(a)
+
+/** Check invariants on a Jacobian group element (no-op unless VERIFY is enabled). */
+static void secp256k1_gej_verify(const secp256k1_gej *a);
+#define SECP256K1_GEJ_VERIFY(a) secp256k1_gej_verify(a)
+
+#endif /* SECP256K1_GROUP_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/hash.h

@@ -0,0 +1,54 @@
+/***********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_HASH_H
+#define SECP256K1_HASH_H
+
+#include <stdlib.h>
+#include <stdint.h>
+
+typedef struct {
+    secp256k1_sha256_compression_function fn_sha256_compression;
+} secp256k1_hash_ctx;
+
+static void secp256k1_hash_ctx_init(secp256k1_hash_ctx *hash_ctx);
+
+typedef struct {
+    uint32_t s[8];
+    unsigned char buf[64];
+    uint64_t bytes;
+} secp256k1_sha256;
+
+static void secp256k1_sha256_initialize(secp256k1_sha256 *hash);
+/* Initialize a SHA256 hash state with a precomputed midstate.
+ * The byte counter must be a multiple of 64, i.e., there must be no unwritten
+ * bytes in the buffer. */
+static void secp256k1_sha256_initialize_midstate(secp256k1_sha256 *hash, uint64_t bytes, const uint32_t state[8]);
+static void secp256k1_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, const unsigned char *data, size_t size);
+static void secp256k1_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, unsigned char *out32);
+static void secp256k1_sha256_clear(secp256k1_sha256 *hash);
+
+typedef struct {
+    secp256k1_sha256 inner, outer;
+} secp256k1_hmac_sha256;
+
+static void secp256k1_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t size);
+static void secp256k1_hmac_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size);
+static void secp256k1_hmac_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, unsigned char *out32);
+static void secp256k1_hmac_sha256_clear(secp256k1_hmac_sha256 *hash);
+
+typedef struct {
+    unsigned char v[32];
+    unsigned char k[32];
+    int retry;
+} secp256k1_rfc6979_hmac_sha256;
+
+static void secp256k1_rfc6979_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen);
+static void secp256k1_rfc6979_hmac_sha256_generate(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen);
+static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng);
+static void secp256k1_rfc6979_hmac_sha256_clear(secp256k1_rfc6979_hmac_sha256 *rng);
+
+#endif /* SECP256K1_HASH_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/hash_impl.h

@@ -0,0 +1,332 @@
+/***********************************************************************
+ * Copyright (c) 2014 Pieter Wuille                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_HASH_IMPL_H
+#define SECP256K1_HASH_IMPL_H
+
+#include "hash.h"
+#include "util.h"
+
+#include <stdlib.h>
+#include <stdint.h>
+#include <string.h>
+
+#define Ch(x,y,z) ((z) ^ ((x) & ((y) ^ (z))))
+#define Maj(x,y,z) (((x) & (y)) | ((z) & ((x) | (y))))
+#define Sigma0(x) (((x) >> 2 | (x) << 30) ^ ((x) >> 13 | (x) << 19) ^ ((x) >> 22 | (x) << 10))
+#define Sigma1(x) (((x) >> 6 | (x) << 26) ^ ((x) >> 11 | (x) << 21) ^ ((x) >> 25 | (x) << 7))
+#define sigma0(x) (((x) >> 7 | (x) << 25) ^ ((x) >> 18 | (x) << 14) ^ ((x) >> 3))
+#define sigma1(x) (((x) >> 17 | (x) << 15) ^ ((x) >> 19 | (x) << 13) ^ ((x) >> 10))
+
+#define Round(a,b,c,d,e,f,g,h,k,w) do { \
+    uint32_t t1 = (h) + Sigma1(e) + Ch((e), (f), (g)) + (k) + (w); \
+    uint32_t t2 = Sigma0(a) + Maj((a), (b), (c)); \
+    (d) += t1; \
+    (h) = t1 + t2; \
+} while(0)
+
+static void secp256k1_sha256_initialize(secp256k1_sha256 *hash) {
+    hash->s[0] = 0x6a09e667ul;
+    hash->s[1] = 0xbb67ae85ul;
+    hash->s[2] = 0x3c6ef372ul;
+    hash->s[3] = 0xa54ff53aul;
+    hash->s[4] = 0x510e527ful;
+    hash->s[5] = 0x9b05688cul;
+    hash->s[6] = 0x1f83d9abul;
+    hash->s[7] = 0x5be0cd19ul;
+    hash->bytes = 0;
+}
+
+static void secp256k1_sha256_initialize_midstate(secp256k1_sha256 *hash, uint64_t bytes, const uint32_t state[8]) {
+    VERIFY_CHECK((bytes & 0x3F) == 0);
+    VERIFY_CHECK(state != NULL);
+    memcpy(hash->s, state, sizeof(hash->s));
+    hash->bytes = bytes;
+}
+
+/** Perform one SHA-256 transformation, processing 16 big endian 32-bit words. */
+static void secp256k1_sha256_transform_impl(uint32_t* s, const unsigned char* buf) {
+    uint32_t a = s[0], b = s[1], c = s[2], d = s[3], e = s[4], f = s[5], g = s[6], h = s[7];
+    uint32_t w0, w1, w2, w3, w4, w5, w6, w7, w8, w9, w10, w11, w12, w13, w14, w15;
+
+    Round(a, b, c, d, e, f, g, h, 0x428a2f98,  w0 = secp256k1_read_be32(&buf[0]));
+    Round(h, a, b, c, d, e, f, g, 0x71374491,  w1 = secp256k1_read_be32(&buf[4]));
+    Round(g, h, a, b, c, d, e, f, 0xb5c0fbcf,  w2 = secp256k1_read_be32(&buf[8]));
+    Round(f, g, h, a, b, c, d, e, 0xe9b5dba5,  w3 = secp256k1_read_be32(&buf[12]));
+    Round(e, f, g, h, a, b, c, d, 0x3956c25b,  w4 = secp256k1_read_be32(&buf[16]));
+    Round(d, e, f, g, h, a, b, c, 0x59f111f1,  w5 = secp256k1_read_be32(&buf[20]));
+    Round(c, d, e, f, g, h, a, b, 0x923f82a4,  w6 = secp256k1_read_be32(&buf[24]));
+    Round(b, c, d, e, f, g, h, a, 0xab1c5ed5,  w7 = secp256k1_read_be32(&buf[28]));
+    Round(a, b, c, d, e, f, g, h, 0xd807aa98,  w8 = secp256k1_read_be32(&buf[32]));
+    Round(h, a, b, c, d, e, f, g, 0x12835b01,  w9 = secp256k1_read_be32(&buf[36]));
+    Round(g, h, a, b, c, d, e, f, 0x243185be, w10 = secp256k1_read_be32(&buf[40]));
+    Round(f, g, h, a, b, c, d, e, 0x550c7dc3, w11 = secp256k1_read_be32(&buf[44]));
+    Round(e, f, g, h, a, b, c, d, 0x72be5d74, w12 = secp256k1_read_be32(&buf[48]));
+    Round(d, e, f, g, h, a, b, c, 0x80deb1fe, w13 = secp256k1_read_be32(&buf[52]));
+    Round(c, d, e, f, g, h, a, b, 0x9bdc06a7, w14 = secp256k1_read_be32(&buf[56]));
+    Round(b, c, d, e, f, g, h, a, 0xc19bf174, w15 = secp256k1_read_be32(&buf[60]));
+
+    Round(a, b, c, d, e, f, g, h, 0xe49b69c1, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0xefbe4786, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x0fc19dc6, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x240ca1cc, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x2de92c6f, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x4a7484aa, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x5cb0a9dc, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x76f988da, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0x983e5152, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0xa831c66d, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0xb00327c8, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0xbf597fc7, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0xc6e00bf3, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xd5a79147, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0x06ca6351, w14 += sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0x14292967, w15 += sigma1(w13) + w8 + sigma0(w0));
+
+    Round(a, b, c, d, e, f, g, h, 0x27b70a85, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0x2e1b2138, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x4d2c6dfc, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x53380d13, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x650a7354, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x766a0abb, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x81c2c92e, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x92722c85, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0xa2bfe8a1, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0xa81a664b, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0xc24b8b70, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0xc76c51a3, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0xd192e819, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xd6990624, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0xf40e3585, w14 += sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0x106aa070, w15 += sigma1(w13) + w8 + sigma0(w0));
+
+    Round(a, b, c, d, e, f, g, h, 0x19a4c116, w0 += sigma1(w14) + w9 + sigma0(w1));
+    Round(h, a, b, c, d, e, f, g, 0x1e376c08, w1 += sigma1(w15) + w10 + sigma0(w2));
+    Round(g, h, a, b, c, d, e, f, 0x2748774c, w2 += sigma1(w0) + w11 + sigma0(w3));
+    Round(f, g, h, a, b, c, d, e, 0x34b0bcb5, w3 += sigma1(w1) + w12 + sigma0(w4));
+    Round(e, f, g, h, a, b, c, d, 0x391c0cb3, w4 += sigma1(w2) + w13 + sigma0(w5));
+    Round(d, e, f, g, h, a, b, c, 0x4ed8aa4a, w5 += sigma1(w3) + w14 + sigma0(w6));
+    Round(c, d, e, f, g, h, a, b, 0x5b9cca4f, w6 += sigma1(w4) + w15 + sigma0(w7));
+    Round(b, c, d, e, f, g, h, a, 0x682e6ff3, w7 += sigma1(w5) + w0 + sigma0(w8));
+    Round(a, b, c, d, e, f, g, h, 0x748f82ee, w8 += sigma1(w6) + w1 + sigma0(w9));
+    Round(h, a, b, c, d, e, f, g, 0x78a5636f, w9 += sigma1(w7) + w2 + sigma0(w10));
+    Round(g, h, a, b, c, d, e, f, 0x84c87814, w10 += sigma1(w8) + w3 + sigma0(w11));
+    Round(f, g, h, a, b, c, d, e, 0x8cc70208, w11 += sigma1(w9) + w4 + sigma0(w12));
+    Round(e, f, g, h, a, b, c, d, 0x90befffa, w12 += sigma1(w10) + w5 + sigma0(w13));
+    Round(d, e, f, g, h, a, b, c, 0xa4506ceb, w13 += sigma1(w11) + w6 + sigma0(w14));
+    Round(c, d, e, f, g, h, a, b, 0xbef9a3f7, w14 + sigma1(w12) + w7 + sigma0(w15));
+    Round(b, c, d, e, f, g, h, a, 0xc67178f2, w15 + sigma1(w13) + w8 + sigma0(w0));
+
+    s[0] += a;
+    s[1] += b;
+    s[2] += c;
+    s[3] += d;
+    s[4] += e;
+    s[5] += f;
+    s[6] += g;
+    s[7] += h;
+}
+
+static void secp256k1_sha256_transform(uint32_t *state, const unsigned char *blocks64, size_t n_blocks) {
+    while (n_blocks--) {
+        secp256k1_sha256_transform_impl(state, blocks64);
+        blocks64 += 64;
+    }
+}
+
+static void secp256k1_hash_ctx_init(secp256k1_hash_ctx *hash_ctx) {
+    VERIFY_CHECK(hash_ctx != NULL);
+    hash_ctx->fn_sha256_compression = secp256k1_sha256_transform;
+}
+
+static void secp256k1_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, const unsigned char *data, size_t len) {
+    size_t chunk_len;
+    size_t bufsize = hash->bytes & 0x3F;
+    hash->bytes += len;
+    VERIFY_CHECK(hash->bytes >= len);
+    VERIFY_CHECK(hash_ctx != NULL);
+    VERIFY_CHECK(hash_ctx->fn_sha256_compression != NULL);
+
+    /* If we exceed the 64-byte block size with this input, process it and wipe the buffer */
+    chunk_len = 64 - bufsize;
+    if (bufsize && len >= chunk_len) {
+        memcpy(hash->buf + bufsize, data, chunk_len);
+        data += chunk_len;
+        len -= chunk_len;
+        hash_ctx->fn_sha256_compression(hash->s, hash->buf, 1);
+        bufsize = 0;
+    }
+
+    /* If we still have data to process, invoke compression directly on the input */
+    if (len >= 64) {
+        const size_t n_blocks = len / 64;
+        const size_t advance = n_blocks * 64;
+        hash_ctx->fn_sha256_compression(hash->s, data, n_blocks);
+        data += advance;
+        len -= advance;
+    }
+
+    /* Fill the buffer with what remains */
+    if (len) {
+        memcpy(hash->buf + bufsize, data, len);
+    }
+}
+
+static void secp256k1_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, unsigned char *out32) {
+    static const unsigned char pad[64] = {0x80};
+    unsigned char sizedesc[8];
+    int i;
+    /* The maximum message size of SHA256 is 2^64-1 bits. */
+    VERIFY_CHECK(hash->bytes < ((uint64_t)1 << 61));
+    secp256k1_write_be32(&sizedesc[0], hash->bytes >> 29);
+    secp256k1_write_be32(&sizedesc[4], hash->bytes << 3);
+    secp256k1_sha256_write(hash_ctx, hash, pad, 1 + ((119 - (hash->bytes % 64)) % 64));
+    secp256k1_sha256_write(hash_ctx, hash, sizedesc, 8);
+    for (i = 0; i < 8; i++) {
+        secp256k1_write_be32(&out32[4*i], hash->s[i]);
+        hash->s[i] = 0;
+    }
+}
+
+/* Initializes a sha256 struct and writes the 64 byte string
+ * SHA256(tag)||SHA256(tag) into it. */
+static void secp256k1_sha256_initialize_tagged(const secp256k1_hash_ctx *hash_ctx, secp256k1_sha256 *hash, const unsigned char *tag, size_t taglen) {
+    unsigned char buf[32];
+    secp256k1_sha256_initialize(hash);
+    secp256k1_sha256_write(hash_ctx, hash, tag, taglen);
+    secp256k1_sha256_finalize(hash_ctx, hash, buf);
+
+    secp256k1_sha256_initialize(hash);
+    secp256k1_sha256_write(hash_ctx, hash, buf, 32);
+    secp256k1_sha256_write(hash_ctx, hash, buf, 32);
+}
+
+static void secp256k1_sha256_clear(secp256k1_sha256 *hash) {
+    secp256k1_memclear_explicit(hash, sizeof(*hash));
+}
+
+static void secp256k1_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *key, size_t keylen) {
+    size_t n;
+    unsigned char rkey[64];
+    if (keylen <= sizeof(rkey)) {
+        memcpy(rkey, key, keylen);
+        memset(rkey + keylen, 0, sizeof(rkey) - keylen);
+    } else {
+        secp256k1_sha256 sha256;
+        secp256k1_sha256_initialize(&sha256);
+        secp256k1_sha256_write(hash_ctx, &sha256, key, keylen);
+        secp256k1_sha256_finalize(hash_ctx, &sha256, rkey);
+        memset(rkey + 32, 0, 32);
+    }
+
+    secp256k1_sha256_initialize(&hash->outer);
+    for (n = 0; n < sizeof(rkey); n++) {
+        rkey[n] ^= 0x5c;
+    }
+    secp256k1_sha256_write(hash_ctx, &hash->outer, rkey, sizeof(rkey));
+
+    secp256k1_sha256_initialize(&hash->inner);
+    for (n = 0; n < sizeof(rkey); n++) {
+        rkey[n] ^= 0x5c ^ 0x36;
+    }
+    secp256k1_sha256_write(hash_ctx, &hash->inner, rkey, sizeof(rkey));
+    secp256k1_memclear_explicit(rkey, sizeof(rkey));
+}
+
+static void secp256k1_hmac_sha256_write(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, const unsigned char *data, size_t size) {
+    secp256k1_sha256_write(hash_ctx, &hash->inner, data, size);
+}
+
+static void secp256k1_hmac_sha256_finalize(const secp256k1_hash_ctx *hash_ctx, secp256k1_hmac_sha256 *hash, unsigned char *out32) {
+    unsigned char temp[32];
+    secp256k1_sha256_finalize(hash_ctx, &hash->inner, temp);
+    secp256k1_sha256_write(hash_ctx, &hash->outer, temp, 32);
+    secp256k1_memclear_explicit(temp, sizeof(temp));
+    secp256k1_sha256_finalize(hash_ctx, &hash->outer, out32);
+}
+
+static void secp256k1_hmac_sha256_clear(secp256k1_hmac_sha256 *hash) {
+    secp256k1_memclear_explicit(hash, sizeof(*hash));
+}
+
+static void secp256k1_rfc6979_hmac_sha256_initialize(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, const unsigned char *key, size_t keylen) {
+    secp256k1_hmac_sha256 hmac;
+    static const unsigned char zero[1] = {0x00};
+    static const unsigned char one[1] = {0x01};
+
+    memset(rng->v, 0x01, 32); /* RFC6979 3.2.b. */
+    memset(rng->k, 0x00, 32); /* RFC6979 3.2.c. */
+
+    /* RFC6979 3.2.d. */
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, zero, 1);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
+
+    /* RFC6979 3.2.f. */
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, one, 1);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, key, keylen);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->k);
+    secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+    secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+    secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
+    rng->retry = 0;
+}
+
+static void secp256k1_rfc6979_hmac_sha256_generate(const secp256k1_hash_ctx *hash_ctx, secp256k1_rfc6979_hmac_sha256 *rng, unsigned char *out, size_t outlen) {
+    /* RFC6979 3.2.h. */
+    static const unsigned char zero[1] = {0x00};
+    if (rng->retry) {
+        secp256k1_hmac_sha256 hmac;
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, zero, 1);
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->k);
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
+    }
+
+    while (outlen > 0) {
+        secp256k1_hmac_sha256 hmac;
+        size_t now = outlen;
+        secp256k1_hmac_sha256_initialize(hash_ctx, &hmac, rng->k, 32);
+        secp256k1_hmac_sha256_write(hash_ctx, &hmac, rng->v, 32);
+        secp256k1_hmac_sha256_finalize(hash_ctx, &hmac, rng->v);
+        if (now > 32) {
+            now = 32;
+        }
+        memcpy(out, rng->v, now);
+        out += now;
+        outlen -= now;
+    }
+
+    rng->retry = 1;
+}
+
+static void secp256k1_rfc6979_hmac_sha256_finalize(secp256k1_rfc6979_hmac_sha256 *rng) {
+    (void) rng;
+}
+
+static void secp256k1_rfc6979_hmac_sha256_clear(secp256k1_rfc6979_hmac_sha256 *rng) {
+    secp256k1_memclear_explicit(rng, sizeof(*rng));
+}
+
+#undef Round
+#undef sigma1
+#undef sigma0
+#undef Sigma1
+#undef Sigma0
+#undef Maj
+#undef Ch
+
+#endif /* SECP256K1_HASH_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/hsort.h

@@ -0,0 +1,33 @@
+/***********************************************************************
+ * Copyright (c) 2021 Russell O'Connor, Jonas Nick                     *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_HSORT_H
+#define SECP256K1_HSORT_H
+
+#include <stddef.h>
+#include <string.h>
+
+/* In-place, iterative heapsort with an interface matching glibc's qsort_r. This
+ * is preferred over standard library implementations because they generally
+ * make no guarantee about being fast for malicious inputs.
+ * Remember that heapsort is unstable.
+ *
+ * In/Out: ptr: pointer to the array to sort. The contents of the array are
+ *              sorted in ascending order according to the comparison function.
+ * In:   count: number of elements in the array.
+ *        size: size in bytes of each element.
+ *         cmp: pointer to a comparison function that is called with two
+ *              arguments that point to the objects being compared. The cmp_data
+ *              argument of secp256k1_hsort is passed as third argument. The
+ *              function must return an integer less than, equal to, or greater
+ *              than zero if the first argument is considered to be respectively
+ *              less than, equal to, or greater than the second.
+ *    cmp_data: pointer passed as third argument to cmp.
+ */
+static void secp256k1_hsort(void *ptr, size_t count, size_t size,
+                            int (*cmp)(const void *, const void *, void *),
+                            void *cmp_data);
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/hsort_impl.h

@@ -0,0 +1,125 @@
+/***********************************************************************
+ * Copyright (c) 2021 Russell O'Connor, Jonas Nick                     *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_HSORT_IMPL_H
+#define SECP256K1_HSORT_IMPL_H
+
+#include "hsort.h"
+
+/* An array is a heap when, for all non-zero indexes i, the element at index i
+ * compares as less than or equal to the element at index parent(i) = (i-1)/2.
+ */
+
+static SECP256K1_INLINE size_t secp256k1_heap_child1(size_t i) {
+    VERIFY_CHECK(i <= (SIZE_MAX - 1)/2);
+    return 2*i + 1;
+}
+
+static SECP256K1_INLINE size_t secp256k1_heap_child2(size_t i) {
+    VERIFY_CHECK(i <= SIZE_MAX/2 - 1);
+    return secp256k1_heap_child1(i)+1;
+}
+
+static SECP256K1_INLINE void secp256k1_heap_swap64(unsigned char *a, unsigned char *b, size_t len) {
+    unsigned char tmp[64];
+    VERIFY_CHECK(len <= 64);
+    memcpy(tmp, a, len);
+    memmove(a, b, len);
+    memcpy(b, tmp, len);
+}
+
+static SECP256K1_INLINE void secp256k1_heap_swap(unsigned char *arr, size_t i, size_t j, size_t stride) {
+    unsigned char *a = arr + i*stride;
+    unsigned char *b = arr + j*stride;
+    size_t len = stride;
+    while (64 < len) {
+        secp256k1_heap_swap64(a + (len - 64), b + (len - 64), 64);
+        len -= 64;
+    }
+    secp256k1_heap_swap64(a, b, len);
+}
+
+/* This function accepts an array arr containing heap_size elements, each of
+ * size stride. The elements in the array at indices >i satisfy the max-heap
+ * property, i.e., for any element at index j (where j > i), all of its children
+ * are smaller than the element itself. The purpose of the function is to update
+ * the array so that all elements at indices >=i satisfy the max-heap
+ * property. */
+static SECP256K1_INLINE void secp256k1_heap_down(unsigned char *arr, size_t i, size_t heap_size, size_t stride,
+                            int (*cmp)(const void *, const void *, void *), void *cmp_data) {
+    while (i < heap_size/2) {
+        VERIFY_CHECK(i <= SIZE_MAX/2 - 1);
+        /* Proof:
+         * i < heap_size/2
+         * i + 1 <= heap_size/2
+         * 2*i + 2 <= heap_size <= SIZE_MAX
+         * 2*i <= SIZE_MAX - 2
+         */
+
+        VERIFY_CHECK(secp256k1_heap_child1(i) < heap_size);
+        /* Proof:
+         * i < heap_size/2
+         * i + 1 <= heap_size/2
+         * 2*i + 2 <= heap_size
+         * 2*i + 1 < heap_size
+         * child1(i) < heap_size
+         */
+
+        /* Let [x] be notation for the contents at arr[x*stride].
+         *
+         * If [child1(i)] > [i] and [child2(i)] > [i],
+         *   swap [i] with the larger child to ensure the new parent is larger
+         *   than both children. When [child1(i)] == [child2(i)], swap [i] with
+         *   [child2(i)].
+         * Else if [child1(i)] > [i], swap [i] with [child1(i)].
+         * Else if [child2(i)] > [i], swap [i] with [child2(i)].
+         */
+        if (secp256k1_heap_child2(i) < heap_size
+                && 0 <= cmp(arr + secp256k1_heap_child2(i)*stride, arr + secp256k1_heap_child1(i)*stride, cmp_data)) {
+            if (0 < cmp(arr + secp256k1_heap_child2(i)*stride, arr + i*stride, cmp_data)) {
+                secp256k1_heap_swap(arr, i, secp256k1_heap_child2(i), stride);
+                i = secp256k1_heap_child2(i);
+            } else {
+                /* At this point we have [child2(i)] >= [child1(i)] and we have
+                 * [child2(i)] <= [i], and thus [child1(i)] <= [i] which means
+                 * that the next comparison can be skipped. */
+                return;
+            }
+        } else if (0 < cmp(arr + secp256k1_heap_child1(i)*stride, arr +         i*stride, cmp_data)) {
+            secp256k1_heap_swap(arr, i, secp256k1_heap_child1(i), stride);
+            i = secp256k1_heap_child1(i);
+        } else {
+            return;
+        }
+    }
+    /* heap_size/2 <= i
+     * heap_size/2 < i + 1
+     * heap_size < 2*i + 2
+     * heap_size <= 2*i + 1
+     * heap_size <= child1(i)
+     * Thus child1(i) and child2(i) are now out of bounds and we are at a leaf.
+     */
+}
+
+/* In-place heap sort. */
+static void secp256k1_hsort(void *ptr, size_t count, size_t size,
+                            int (*cmp)(const void *, const void *, void *),
+                            void *cmp_data) {
+    size_t i;
+
+    for (i = count/2; 0 < i; --i) {
+        secp256k1_heap_down(ptr, i-1, count, size, cmp, cmp_data);
+    }
+    for (i = count; 1 < i; --i) {
+        /* Extract the largest value from the heap */
+        secp256k1_heap_swap(ptr, 0, i-1, size);
+
+        /* Repair the heap condition */
+        secp256k1_heap_down(ptr, 0, i-1, size, cmp, cmp_data);
+    }
+}
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/int128.h

@@ -0,0 +1,90 @@
+#ifndef SECP256K1_INT128_H
+#define SECP256K1_INT128_H
+
+#include "util.h"
+
+#if defined(SECP256K1_WIDEMUL_INT128)
+#  if defined(SECP256K1_INT128_NATIVE)
+#    include "int128_native.h"
+#  elif defined(SECP256K1_INT128_STRUCT)
+#    include "int128_struct.h"
+#  else
+#    error "Please select int128 implementation"
+#  endif
+
+/* Construct an unsigned 128-bit value from a high and a low 64-bit value. */
+static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo);
+
+/* Multiply two unsigned 64-bit values a and b and write the result to r. */
+static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b);
+
+/* Multiply two unsigned 64-bit values a and b and add the result to r.
+ * The final result is taken modulo 2^128.
+ */
+static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b);
+
+/* Add an unsigned 64-bit value a to r.
+ * The final result is taken modulo 2^128.
+ */
+static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a);
+
+/* Unsigned (logical) right shift.
+ * Non-constant time in n.
+ */
+static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n);
+
+/* Return the low 64-bits of a 128-bit value as an unsigned 64-bit value. */
+static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a);
+
+/* Return the high 64-bits of a 128-bit value as an unsigned 64-bit value. */
+static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a);
+
+/* Write an unsigned 64-bit value to r. */
+static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a);
+
+/* Tests if r is strictly less than to 2^n.
+ * n must be strictly less than 128.
+ */
+static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n);
+
+/* Construct an signed 128-bit value from a high and a low 64-bit value. */
+static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo);
+
+/* Multiply two signed 64-bit values a and b and write the result to r. */
+static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b);
+
+/* Multiply two signed 64-bit values a and b and add the result to r.
+ * Overflow or underflow from the addition is undefined behaviour.
+ */
+static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b);
+
+/* Compute a*d - b*c from signed 64-bit values and write the result to r. */
+static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d);
+
+/* Signed (arithmetic) right shift.
+ * Non-constant time in b.
+ */
+static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int b);
+
+/* Return the input value modulo 2^64. */
+static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a);
+
+/* Return the value as a signed 64-bit value.
+ * Requires the input to be between INT64_MIN and INT64_MAX.
+ */
+static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a);
+
+/* Write a signed 64-bit value to r. */
+static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a);
+
+/* Compare two 128-bit values for equality. */
+static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b);
+
+/* Tests if r is equal to sign*2^n (sign must be 1 or -1).
+ * n must be strictly less than 127.
+ */
+static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign);
+
+#endif
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/int128_impl.h

@@ -0,0 +1,18 @@
+#ifndef SECP256K1_INT128_IMPL_H
+#define SECP256K1_INT128_IMPL_H
+
+#include "util.h"
+
+#include "int128.h"
+
+#if defined(SECP256K1_WIDEMUL_INT128)
+#  if defined(SECP256K1_INT128_NATIVE)
+#    include "int128_native_impl.h"
+#  elif defined(SECP256K1_INT128_STRUCT)
+#    include "int128_struct_impl.h"
+#  else
+#    error "Please select int128 implementation"
+#  endif
+#endif
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/int128_native.h

@@ -0,0 +1,19 @@
+#ifndef SECP256K1_INT128_NATIVE_H
+#define SECP256K1_INT128_NATIVE_H
+
+#include <stdint.h>
+#include "util.h"
+
+#if !defined(UINT128_MAX) && defined(__SIZEOF_INT128__)
+SECP256K1_GNUC_EXT typedef unsigned __int128 uint128_t;
+SECP256K1_GNUC_EXT typedef __int128 int128_t;
+# define UINT128_MAX ((uint128_t)(-1))
+# define INT128_MAX ((int128_t)(UINT128_MAX >> 1))
+# define INT128_MIN (-INT128_MAX - 1)
+/* No (U)INT128_C macros because compilers providing __int128 do not support 128-bit literals.  */
+#endif
+
+typedef uint128_t secp256k1_uint128;
+typedef int128_t secp256k1_int128;
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/int128_native_impl.h

@@ -0,0 +1,94 @@
+#ifndef SECP256K1_INT128_NATIVE_IMPL_H
+#define SECP256K1_INT128_NATIVE_IMPL_H
+
+#include "int128.h"
+#include "util.h"
+
+static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) {
+    *r = (((uint128_t)hi) << 64) + lo;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   *r = (uint128_t)a * b;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   *r += (uint128_t)a * b;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) {
+   *r += a;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   *r >>= n;
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) {
+   return (uint64_t)(*a);
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) {
+   return (uint64_t)(*a >> 64);
+}
+
+static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) {
+   *r = a;
+}
+
+static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   return (*r >> n == 0);
+}
+
+static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) {
+    *r = (((uint128_t)(uint64_t)hi) << 64) + lo;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   *r = (int128_t)a * b;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int128_t ab = (int128_t)a * b;
+   VERIFY_CHECK(0 <= ab ? *r <= INT128_MAX - ab : INT128_MIN - ab <= *r);
+   *r += ab;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) {
+   int128_t ad = (int128_t)a * d;
+   int128_t bc = (int128_t)b * c;
+   VERIFY_CHECK(0 <= bc ? INT128_MIN + bc <= ad : ad <= INT128_MAX + bc);
+   *r = ad - bc;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   *r >>= n;
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a) {
+   return (uint64_t)*a;
+}
+
+static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) {
+   VERIFY_CHECK(INT64_MIN <= *a && *a <= INT64_MAX);
+   return *a;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) {
+   *r = a;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) {
+   return *a == *b;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign) {
+   VERIFY_CHECK(n < 127);
+   VERIFY_CHECK(sign == 1 || sign == -1);
+   return (*r == (int128_t)((uint128_t)sign << n));
+}
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/int128_struct.h

@@ -0,0 +1,14 @@
+#ifndef SECP256K1_INT128_STRUCT_H
+#define SECP256K1_INT128_STRUCT_H
+
+#include <stdint.h>
+#include "util.h"
+
+typedef struct {
+  uint64_t lo;
+  uint64_t hi;
+} secp256k1_uint128;
+
+typedef secp256k1_uint128 secp256k1_int128;
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/int128_struct_impl.h

@@ -0,0 +1,205 @@
+#ifndef SECP256K1_INT128_STRUCT_IMPL_H
+#define SECP256K1_INT128_STRUCT_IMPL_H
+
+#include "int128.h"
+#include "util.h"
+
+#if defined(_MSC_VER) && (defined(_M_X64) || defined(_M_ARM64)) /* MSVC */
+#    include <intrin.h>
+#    if defined(_M_ARM64) || defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE)
+/* On ARM64 MSVC, use __(u)mulh for the upper half of 64x64 multiplications.
+   (Define SECP256K1_MSVC_MULH_TEST_OVERRIDE to test this code path on X64,
+   which supports both __(u)mulh and _umul128.) */
+#        if defined(SECP256K1_MSVC_MULH_TEST_OVERRIDE)
+#            pragma message(__FILE__ ": SECP256K1_MSVC_MULH_TEST_OVERRIDE is defined, forcing use of __(u)mulh.")
+#        endif
+static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) {
+    *hi = __umulh(a, b);
+    return a * b;
+}
+
+static SECP256K1_INLINE int64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) {
+    *hi = __mulh(a, b);
+    return (uint64_t)a * (uint64_t)b;
+}
+#    else
+/* On x84_64 MSVC, use native _(u)mul128 for 64x64->128 multiplications. */
+#        define secp256k1_umul128 _umul128
+#        define secp256k1_mul128 _mul128
+#    endif
+#else
+/* On other systems, emulate 64x64->128 multiplications using 32x32->64 multiplications. */
+static SECP256K1_INLINE uint64_t secp256k1_umul128(uint64_t a, uint64_t b, uint64_t* hi) {
+    uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b;
+    uint64_t lh = (uint32_t)a * (b >> 32);
+    uint64_t hl = (a >> 32) * (uint32_t)b;
+    uint64_t hh = (a >> 32) * (b >> 32);
+    uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl;
+    *hi = hh + (lh >> 32) + (hl >> 32) + (mid34 >> 32);
+    return (mid34 << 32) + (uint32_t)ll;
+}
+
+static SECP256K1_INLINE int64_t secp256k1_mul128(int64_t a, int64_t b, int64_t* hi) {
+    uint64_t ll = (uint64_t)(uint32_t)a * (uint32_t)b;
+    int64_t lh = (uint32_t)a * (b >> 32);
+    int64_t hl = (a >> 32) * (uint32_t)b;
+    int64_t hh = (a >> 32) * (b >> 32);
+    uint64_t mid34 = (ll >> 32) + (uint32_t)lh + (uint32_t)hl;
+    *hi = hh + (lh >> 32) + (hl >> 32) + (mid34 >> 32);
+    return (mid34 << 32) + (uint32_t)ll;
+}
+#endif
+
+static SECP256K1_INLINE void secp256k1_u128_load(secp256k1_uint128 *r, uint64_t hi, uint64_t lo) {
+    r->hi = hi;
+    r->lo = lo;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   r->lo = secp256k1_umul128(a, b, &r->hi);
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_mul(secp256k1_uint128 *r, uint64_t a, uint64_t b) {
+   uint64_t lo, hi;
+   lo = secp256k1_umul128(a, b, &hi);
+   r->lo += lo;
+   r->hi += hi + (r->lo < lo);
+}
+
+static SECP256K1_INLINE void secp256k1_u128_accum_u64(secp256k1_uint128 *r, uint64_t a) {
+   r->lo += a;
+   r->hi += r->lo < a;
+}
+
+/* Unsigned (logical) right shift.
+ * Non-constant time in n.
+ */
+static SECP256K1_INLINE void secp256k1_u128_rshift(secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   if (n >= 64) {
+     r->lo = r->hi >> (n-64);
+     r->hi = 0;
+   } else if (n > 0) {
+#if defined(_MSC_VER) && defined(_M_X64)
+     VERIFY_CHECK(n < 64);
+     r->lo = __shiftright128(r->lo, r->hi, n);
+#else
+     r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n;
+#endif
+     r->hi >>= n;
+   }
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_to_u64(const secp256k1_uint128 *a) {
+   return a->lo;
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_u128_hi_u64(const secp256k1_uint128 *a) {
+   return a->hi;
+}
+
+static SECP256K1_INLINE void secp256k1_u128_from_u64(secp256k1_uint128 *r, uint64_t a) {
+   r->hi = 0;
+   r->lo = a;
+}
+
+static SECP256K1_INLINE int secp256k1_u128_check_bits(const secp256k1_uint128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   return n >= 64 ? r->hi >> (n - 64) == 0
+                  : r->hi == 0 && r->lo >> n == 0;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_load(secp256k1_int128 *r, int64_t hi, uint64_t lo) {
+    r->hi = hi;
+    r->lo = lo;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int64_t hi;
+   r->lo = (uint64_t)secp256k1_mul128(a, b, &hi);
+   r->hi = (uint64_t)hi;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_accum_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int64_t hi;
+   uint64_t lo = (uint64_t)secp256k1_mul128(a, b, &hi);
+   r->lo += lo;
+   hi += r->lo < lo;
+   /* Verify no overflow.
+    * If r represents a positive value (the sign bit is not set) and the value we are adding is a positive value (the sign bit is not set),
+    * then we require that the resulting value also be positive (the sign bit is not set).
+    * Note that (X <= Y) means (X implies Y) when X and Y are boolean values (i.e. 0 or 1).
+    */
+   VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi <= 0x7fffffffffffffffu));
+   /* Verify no underflow.
+    * If r represents a negative value (the sign bit is set) and the value we are adding is a negative value (the sign bit is set),
+    * then we require that the resulting value also be negative (the sign bit is set).
+    */
+   VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi + (uint64_t)hi > 0x7fffffffffffffffu));
+   r->hi += hi;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_dissip_mul(secp256k1_int128 *r, int64_t a, int64_t b) {
+   int64_t hi;
+   uint64_t lo = (uint64_t)secp256k1_mul128(a, b, &hi);
+   hi += r->lo < lo;
+   /* Verify no overflow.
+    * If r represents a positive value (the sign bit is not set) and the value we are subtracting is a negative value (the sign bit is set),
+    * then we require that the resulting value also be positive (the sign bit is not set).
+    */
+   VERIFY_CHECK((r->hi <= 0x7fffffffffffffffu && (uint64_t)hi > 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi <= 0x7fffffffffffffffu));
+   /* Verify no underflow.
+    * If r represents a negative value (the sign bit is set) and the value we are subtracting is a positive value (the sign sign bit is not set),
+    * then we require that the resulting value also be negative (the sign bit is set).
+    */
+   VERIFY_CHECK((r->hi > 0x7fffffffffffffffu && (uint64_t)hi <= 0x7fffffffffffffffu) <= (r->hi - (uint64_t)hi > 0x7fffffffffffffffu));
+   r->hi -= hi;
+   r->lo -= lo;
+}
+
+static SECP256K1_INLINE void secp256k1_i128_det(secp256k1_int128 *r, int64_t a, int64_t b, int64_t c, int64_t d) {
+   secp256k1_i128_mul(r, a, d);
+   secp256k1_i128_dissip_mul(r, b, c);
+}
+
+/* Signed (arithmetic) right shift.
+ * Non-constant time in n.
+ */
+static SECP256K1_INLINE void secp256k1_i128_rshift(secp256k1_int128 *r, unsigned int n) {
+   VERIFY_CHECK(n < 128);
+   if (n >= 64) {
+     r->lo = (uint64_t)((int64_t)(r->hi) >> (n-64));
+     r->hi = (uint64_t)((int64_t)(r->hi) >> 63);
+   } else if (n > 0) {
+     r->lo = ((1U * r->hi) << (64-n)) | r->lo >> n;
+     r->hi = (uint64_t)((int64_t)(r->hi) >> n);
+   }
+}
+
+static SECP256K1_INLINE uint64_t secp256k1_i128_to_u64(const secp256k1_int128 *a) {
+   return a->lo;
+}
+
+static SECP256K1_INLINE int64_t secp256k1_i128_to_i64(const secp256k1_int128 *a) {
+   /* Verify that a represents a 64 bit signed value by checking that the high bits are a sign extension of the low bits. */
+   VERIFY_CHECK(a->hi == -(a->lo >> 63));
+   return (int64_t)secp256k1_i128_to_u64(a);
+}
+
+static SECP256K1_INLINE void secp256k1_i128_from_i64(secp256k1_int128 *r, int64_t a) {
+   r->hi = (uint64_t)(a >> 63);
+   r->lo = (uint64_t)a;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_eq_var(const secp256k1_int128 *a, const secp256k1_int128 *b) {
+   return a->hi == b->hi && a->lo == b->lo;
+}
+
+static SECP256K1_INLINE int secp256k1_i128_check_pow2(const secp256k1_int128 *r, unsigned int n, int sign) {
+    VERIFY_CHECK(n < 127);
+    VERIFY_CHECK(sign == 1 || sign == -1);
+    return n >= 64 ? r->hi == (uint64_t)sign << (n - 64) && r->lo == 0
+                   : r->hi == (uint64_t)(sign >> 1) && r->lo == (uint64_t)sign << n;
+}
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/modinv32.h

@@ -0,0 +1,43 @@
+/***********************************************************************
+ * Copyright (c) 2020 Peter Dettman                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODINV32_H
+#define SECP256K1_MODINV32_H
+
+#include "util.h"
+
+/* A signed 30-bit limb representation of integers.
+ *
+ * Its value is sum(v[i] * 2^(30*i), i=0..8). */
+typedef struct {
+    int32_t v[9];
+} secp256k1_modinv32_signed30;
+
+typedef struct {
+    /* The modulus in signed30 notation, must be odd and in [3, 2^256]. */
+    secp256k1_modinv32_signed30 modulus;
+
+    /* modulus^{-1} mod 2^30 */
+    uint32_t modulus_inv30;
+} secp256k1_modinv32_modinfo;
+
+/* Replace x with its modular inverse mod modinfo->modulus. x must be in range [0, modulus).
+ * If x is zero, the result will be zero as well. If not, the inverse must exist (i.e., the gcd of
+ * x and modulus must be 1). These rules are automatically satisfied if the modulus is prime.
+ *
+ * On output, all of x's limbs will be in [0, 2^30).
+ */
+static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo);
+
+/* Same as secp256k1_modinv32_var, but constant time in x (not in the modulus). */
+static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo);
+
+/* Compute the Jacobi symbol for (x | modinfo->modulus). x must be coprime with modulus (and thus
+ * cannot be 0, as modulus >= 3). All limbs of x must be non-negative. Returns 0 if the result
+ * cannot be computed. */
+static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo);
+
+#endif /* SECP256K1_MODINV32_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/modinv32_impl.h

@@ -0,0 +1,725 @@
+/***********************************************************************
+ * Copyright (c) 2020 Peter Dettman                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODINV32_IMPL_H
+#define SECP256K1_MODINV32_IMPL_H
+
+#include "modinv32.h"
+
+#include "util.h"
+
+#include <stdlib.h>
+
+/* This file implements modular inversion based on the paper "Fast constant-time gcd computation and
+ * modular inversion" by Daniel J. Bernstein and Bo-Yin Yang.
+ *
+ * For an explanation of the algorithm, see doc/safegcd_implementation.md. This file contains an
+ * implementation for N=30, using 30-bit signed limbs represented as int32_t.
+ */
+
+#ifdef VERIFY
+static const secp256k1_modinv32_signed30 SECP256K1_SIGNED30_ONE = {{1}};
+
+/* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^30). */
+static void secp256k1_modinv32_mul_30(secp256k1_modinv32_signed30 *r, const secp256k1_modinv32_signed30 *a, int alen, int32_t factor) {
+    const int32_t M30 = (int32_t)(UINT32_MAX >> 2);
+    int64_t c = 0;
+    int i;
+    for (i = 0; i < 8; ++i) {
+        if (i < alen) c += (int64_t)a->v[i] * factor;
+        r->v[i] = (int32_t)c & M30; c >>= 30;
+    }
+    if (8 < alen) c += (int64_t)a->v[8] * factor;
+    VERIFY_CHECK(c == (int32_t)c);
+    r->v[8] = (int32_t)c;
+}
+
+/* Return -1 for a<b*factor, 0 for a==b*factor, 1 for a>b*factor. A consists of alen limbs; b has 9. */
+static int secp256k1_modinv32_mul_cmp_30(const secp256k1_modinv32_signed30 *a, int alen, const secp256k1_modinv32_signed30 *b, int32_t factor) {
+    int i;
+    secp256k1_modinv32_signed30 am, bm;
+    secp256k1_modinv32_mul_30(&am, a, alen, 1); /* Normalize all but the top limb of a. */
+    secp256k1_modinv32_mul_30(&bm, b, 9, factor);
+    for (i = 0; i < 8; ++i) {
+        /* Verify that all but the top limb of a and b are normalized. */
+        VERIFY_CHECK(am.v[i] >> 30 == 0);
+        VERIFY_CHECK(bm.v[i] >> 30 == 0);
+    }
+    for (i = 8; i >= 0; --i) {
+        if (am.v[i] < bm.v[i]) return -1;
+        if (am.v[i] > bm.v[i]) return 1;
+    }
+    return 0;
+}
+#endif
+
+/* Take as input a signed30 number in range (-2*modulus,modulus), and add a multiple of the modulus
+ * to it to bring it to range [0,modulus). If sign < 0, the input will also be negated in the
+ * process. The input must have limbs in range (-2^30,2^30). The output will have limbs in range
+ * [0,2^30). */
+static void secp256k1_modinv32_normalize_30(secp256k1_modinv32_signed30 *r, int32_t sign, const secp256k1_modinv32_modinfo *modinfo) {
+    const int32_t M30 = (int32_t)(UINT32_MAX >> 2);
+    int32_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4],
+            r5 = r->v[5], r6 = r->v[6], r7 = r->v[7], r8 = r->v[8];
+    volatile int32_t cond_add, cond_negate;
+
+#ifdef VERIFY
+    /* Verify that all limbs are in range (-2^30,2^30). */
+    int i;
+    for (i = 0; i < 9; ++i) {
+        VERIFY_CHECK(r->v[i] >= -M30);
+        VERIFY_CHECK(r->v[i] <= M30);
+    }
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, -2) > 0); /* r > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, 1) < 0); /* r < modulus */
+#endif
+
+    /* In a first step, add the modulus if the input is negative, and then negate if requested.
+     * This brings r from range (-2*modulus,modulus) to range (-modulus,modulus). As all input
+     * limbs are in range (-2^30,2^30), this cannot overflow an int32_t. Note that the right
+     * shifts below are signed sign-extending shifts (see assumptions.h for tests that that is
+     * indeed the behavior of the right shift operator). */
+    cond_add = r8 >> 31;
+    r0 += modinfo->modulus.v[0] & cond_add;
+    r1 += modinfo->modulus.v[1] & cond_add;
+    r2 += modinfo->modulus.v[2] & cond_add;
+    r3 += modinfo->modulus.v[3] & cond_add;
+    r4 += modinfo->modulus.v[4] & cond_add;
+    r5 += modinfo->modulus.v[5] & cond_add;
+    r6 += modinfo->modulus.v[6] & cond_add;
+    r7 += modinfo->modulus.v[7] & cond_add;
+    r8 += modinfo->modulus.v[8] & cond_add;
+    cond_negate = sign >> 31;
+    r0 = (r0 ^ cond_negate) - cond_negate;
+    r1 = (r1 ^ cond_negate) - cond_negate;
+    r2 = (r2 ^ cond_negate) - cond_negate;
+    r3 = (r3 ^ cond_negate) - cond_negate;
+    r4 = (r4 ^ cond_negate) - cond_negate;
+    r5 = (r5 ^ cond_negate) - cond_negate;
+    r6 = (r6 ^ cond_negate) - cond_negate;
+    r7 = (r7 ^ cond_negate) - cond_negate;
+    r8 = (r8 ^ cond_negate) - cond_negate;
+    /* Propagate the top bits, to bring limbs back to range (-2^30,2^30). */
+    r1 += r0 >> 30; r0 &= M30;
+    r2 += r1 >> 30; r1 &= M30;
+    r3 += r2 >> 30; r2 &= M30;
+    r4 += r3 >> 30; r3 &= M30;
+    r5 += r4 >> 30; r4 &= M30;
+    r6 += r5 >> 30; r5 &= M30;
+    r7 += r6 >> 30; r6 &= M30;
+    r8 += r7 >> 30; r7 &= M30;
+
+    /* In a second step add the modulus again if the result is still negative, bringing r to range
+     * [0,modulus). */
+    cond_add = r8 >> 31;
+    r0 += modinfo->modulus.v[0] & cond_add;
+    r1 += modinfo->modulus.v[1] & cond_add;
+    r2 += modinfo->modulus.v[2] & cond_add;
+    r3 += modinfo->modulus.v[3] & cond_add;
+    r4 += modinfo->modulus.v[4] & cond_add;
+    r5 += modinfo->modulus.v[5] & cond_add;
+    r6 += modinfo->modulus.v[6] & cond_add;
+    r7 += modinfo->modulus.v[7] & cond_add;
+    r8 += modinfo->modulus.v[8] & cond_add;
+    /* And propagate again. */
+    r1 += r0 >> 30; r0 &= M30;
+    r2 += r1 >> 30; r1 &= M30;
+    r3 += r2 >> 30; r2 &= M30;
+    r4 += r3 >> 30; r3 &= M30;
+    r5 += r4 >> 30; r4 &= M30;
+    r6 += r5 >> 30; r5 &= M30;
+    r7 += r6 >> 30; r6 &= M30;
+    r8 += r7 >> 30; r7 &= M30;
+
+    r->v[0] = r0;
+    r->v[1] = r1;
+    r->v[2] = r2;
+    r->v[3] = r3;
+    r->v[4] = r4;
+    r->v[5] = r5;
+    r->v[6] = r6;
+    r->v[7] = r7;
+    r->v[8] = r8;
+
+    VERIFY_CHECK(r0 >> 30 == 0);
+    VERIFY_CHECK(r1 >> 30 == 0);
+    VERIFY_CHECK(r2 >> 30 == 0);
+    VERIFY_CHECK(r3 >> 30 == 0);
+    VERIFY_CHECK(r4 >> 30 == 0);
+    VERIFY_CHECK(r5 >> 30 == 0);
+    VERIFY_CHECK(r6 >> 30 == 0);
+    VERIFY_CHECK(r7 >> 30 == 0);
+    VERIFY_CHECK(r8 >> 30 == 0);
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, 0) >= 0); /* r >= 0 */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(r, 9, &modinfo->modulus, 1) < 0); /* r < modulus */
+}
+
+/* Data type for transition matrices (see section 3 of explanation).
+ *
+ * t = [ u  v ]
+ *     [ q  r ]
+ */
+typedef struct {
+    int32_t u, v, q, r;
+} secp256k1_modinv32_trans2x2;
+
+/* Compute the transition matrix and zeta for 30 divsteps.
+ *
+ * Input:  zeta: initial zeta
+ *         f0:   bottom limb of initial f
+ *         g0:   bottom limb of initial g
+ * Output: t: transition matrix
+ * Return: final zeta
+ *
+ * Implements the divsteps_n_matrix function from the explanation.
+ */
+static int32_t secp256k1_modinv32_divsteps_30(int32_t zeta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t) {
+    /* u,v,q,r are the elements of the transformation matrix being built up,
+     * starting with the identity matrix. Semantically they are signed integers
+     * in range [-2^30,2^30], but here represented as unsigned mod 2^32. This
+     * permits left shifting (which is UB for negative numbers). The range
+     * being inside [-2^31,2^31) means that casting to signed works correctly.
+     */
+    uint32_t u = 1, v = 0, q = 0, r = 1;
+    volatile uint32_t c1, c2;
+    uint32_t mask1, mask2, f = f0, g = g0, x, y, z;
+    int i;
+
+    for (i = 0; i < 30; ++i) {
+        VERIFY_CHECK((f & 1) == 1); /* f must always be odd */
+        VERIFY_CHECK((u * f0 + v * g0) == f << i);
+        VERIFY_CHECK((q * f0 + r * g0) == g << i);
+        /* Compute conditional masks for (zeta < 0) and for (g & 1). */
+        c1 = zeta >> 31;
+        mask1 = c1;
+        c2 = g & 1;
+        mask2 = -c2;
+        /* Compute x,y,z, conditionally negated versions of f,u,v. */
+        x = (f ^ mask1) - mask1;
+        y = (u ^ mask1) - mask1;
+        z = (v ^ mask1) - mask1;
+        /* Conditionally add x,y,z to g,q,r. */
+        g += x & mask2;
+        q += y & mask2;
+        r += z & mask2;
+        /* In what follows, mask1 is a condition mask for (zeta < 0) and (g & 1). */
+        mask1 &= mask2;
+        /* Conditionally change zeta into -zeta-2 or zeta-1. */
+        zeta = (zeta ^ mask1) - 1;
+        /* Conditionally add g,q,r to f,u,v. */
+        f += g & mask1;
+        u += q & mask1;
+        v += r & mask1;
+        /* Shifts */
+        g >>= 1;
+        u <<= 1;
+        v <<= 1;
+        /* Bounds on zeta that follow from the bounds on iteration count (max 20*30 divsteps). */
+        VERIFY_CHECK(zeta >= -601 && zeta <= 601);
+    }
+    /* Return data in t and return value. */
+    t->u = (int32_t)u;
+    t->v = (int32_t)v;
+    t->q = (int32_t)q;
+    t->r = (int32_t)r;
+    /* The determinant of t must be a power of two. This guarantees that multiplication with t
+     * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
+     * will be divided out again). As each divstep's individual matrix has determinant 2, the
+     * aggregate of 30 of them will have determinant 2^30. */
+    VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30);
+    return zeta;
+}
+
+/* secp256k1_modinv32_inv256[i] = -(2*i+1)^-1 (mod 256) */
+static const uint8_t secp256k1_modinv32_inv256[128] = {
+    0xFF, 0x55, 0x33, 0x49, 0xC7, 0x5D, 0x3B, 0x11, 0x0F, 0xE5, 0xC3, 0x59,
+    0xD7, 0xED, 0xCB, 0x21, 0x1F, 0x75, 0x53, 0x69, 0xE7, 0x7D, 0x5B, 0x31,
+    0x2F, 0x05, 0xE3, 0x79, 0xF7, 0x0D, 0xEB, 0x41, 0x3F, 0x95, 0x73, 0x89,
+    0x07, 0x9D, 0x7B, 0x51, 0x4F, 0x25, 0x03, 0x99, 0x17, 0x2D, 0x0B, 0x61,
+    0x5F, 0xB5, 0x93, 0xA9, 0x27, 0xBD, 0x9B, 0x71, 0x6F, 0x45, 0x23, 0xB9,
+    0x37, 0x4D, 0x2B, 0x81, 0x7F, 0xD5, 0xB3, 0xC9, 0x47, 0xDD, 0xBB, 0x91,
+    0x8F, 0x65, 0x43, 0xD9, 0x57, 0x6D, 0x4B, 0xA1, 0x9F, 0xF5, 0xD3, 0xE9,
+    0x67, 0xFD, 0xDB, 0xB1, 0xAF, 0x85, 0x63, 0xF9, 0x77, 0x8D, 0x6B, 0xC1,
+    0xBF, 0x15, 0xF3, 0x09, 0x87, 0x1D, 0xFB, 0xD1, 0xCF, 0xA5, 0x83, 0x19,
+    0x97, 0xAD, 0x8B, 0xE1, 0xDF, 0x35, 0x13, 0x29, 0xA7, 0x3D, 0x1B, 0xF1,
+    0xEF, 0xC5, 0xA3, 0x39, 0xB7, 0xCD, 0xAB, 0x01
+};
+
+/* Compute the transition matrix and eta for 30 divsteps (variable time).
+ *
+ * Input:  eta: initial eta
+ *         f0:  bottom limb of initial f
+ *         g0:  bottom limb of initial g
+ * Output: t: transition matrix
+ * Return: final eta
+ *
+ * Implements the divsteps_n_matrix_var function from the explanation.
+ */
+static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t) {
+    /* Transformation matrix; see comments in secp256k1_modinv32_divsteps_30. */
+    uint32_t u = 1, v = 0, q = 0, r = 1;
+    uint32_t f = f0, g = g0, m;
+    uint16_t w;
+    int i = 30, limit, zeros;
+
+    for (;;) {
+        /* Use a sentinel bit to count zeros only up to i. */
+        zeros = secp256k1_ctz32_var(g | (UINT32_MAX << i));
+        /* Perform zeros divsteps at once; they all just divide g by two. */
+        g >>= zeros;
+        u <<= zeros;
+        v <<= zeros;
+        eta -= zeros;
+        i -= zeros;
+         /* We're done once we've done 30 divsteps. */
+        if (i == 0) break;
+        VERIFY_CHECK((f & 1) == 1);
+        VERIFY_CHECK((g & 1) == 1);
+        VERIFY_CHECK((u * f0 + v * g0) == f << (30 - i));
+        VERIFY_CHECK((q * f0 + r * g0) == g << (30 - i));
+        /* Bounds on eta that follow from the bounds on iteration count (max 25*30 divsteps). */
+        VERIFY_CHECK(eta >= -751 && eta <= 751);
+        /* If eta is negative, negate it and replace f,g with g,-f. */
+        if (eta < 0) {
+            uint32_t tmp;
+            eta = -eta;
+            tmp = f; f = g; g = -tmp;
+            tmp = u; u = q; q = -tmp;
+            tmp = v; v = r; r = -tmp;
+        }
+        /* eta is now >= 0. In what follows we're going to cancel out the bottom bits of g. No more
+         * than i can be cancelled out (as we'd be done before that point), and no more than eta+1
+         * can be done as its sign will flip once that happens. */
+        limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
+        /* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */
+        VERIFY_CHECK(limit > 0 && limit <= 30);
+        m = (UINT32_MAX >> (32 - limit)) & 255U;
+        /* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */
+        w = (g * secp256k1_modinv32_inv256[(f >> 1) & 127]) & m;
+        /* Do so. */
+        g += f * w;
+        q += u * w;
+        r += v * w;
+        VERIFY_CHECK((g & m) == 0);
+    }
+    /* Return data in t and return value. */
+    t->u = (int32_t)u;
+    t->v = (int32_t)v;
+    t->q = (int32_t)q;
+    t->r = (int32_t)r;
+    /* The determinant of t must be a power of two. This guarantees that multiplication with t
+     * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
+     * will be divided out again). As each divstep's individual matrix has determinant 2, the
+     * aggregate of 30 of them will have determinant 2^30. */
+    VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30);
+    return eta;
+}
+
+/* Compute the transition matrix and eta for 30 posdivsteps (variable time, eta=-delta), and keeps track
+ * of the Jacobi symbol along the way. f0 and g0 must be f and g mod 2^32 rather than 2^30, because
+ * Jacobi tracking requires knowing (f mod 8) rather than just (f mod 2).
+ *
+ * Input:        eta: initial eta
+ *               f0:  bottom limb of initial f
+ *               g0:  bottom limb of initial g
+ * Output:       t: transition matrix
+ * Input/Output: (*jacp & 1) is bitflipped if and only if the Jacobi symbol of (f | g) changes sign
+ *               by applying the returned transformation matrix to it. The other bits of *jacp may
+ *               change, but are meaningless.
+ * Return: final eta
+ */
+static int32_t secp256k1_modinv32_posdivsteps_30_var(int32_t eta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t, int *jacp) {
+    /* Transformation matrix. */
+    uint32_t u = 1, v = 0, q = 0, r = 1;
+    uint32_t f = f0, g = g0, m;
+    uint16_t w;
+    int i = 30, limit, zeros;
+    int jac = *jacp;
+
+    for (;;) {
+        /* Use a sentinel bit to count zeros only up to i. */
+        zeros = secp256k1_ctz32_var(g | (UINT32_MAX << i));
+        /* Perform zeros divsteps at once; they all just divide g by two. */
+        g >>= zeros;
+        u <<= zeros;
+        v <<= zeros;
+        eta -= zeros;
+        i -= zeros;
+        /* Update the bottom bit of jac: when dividing g by an odd power of 2,
+         * if (f mod 8) is 3 or 5, the Jacobi symbol changes sign. */
+        jac ^= (zeros & ((f >> 1) ^ (f >> 2)));
+        /* We're done once we've done 30 posdivsteps. */
+        if (i == 0) break;
+        VERIFY_CHECK((f & 1) == 1);
+        VERIFY_CHECK((g & 1) == 1);
+        VERIFY_CHECK((u * f0 + v * g0) == f << (30 - i));
+        VERIFY_CHECK((q * f0 + r * g0) == g << (30 - i));
+        /* If eta is negative, negate it and replace f,g with g,f. */
+        if (eta < 0) {
+            uint32_t tmp;
+            eta = -eta;
+            /* Update bottom bit of jac: when swapping f and g, the Jacobi symbol changes sign
+             * if both f and g are 3 mod 4. */
+            jac ^= ((f & g) >> 1);
+            tmp = f; f = g; g = tmp;
+            tmp = u; u = q; q = tmp;
+            tmp = v; v = r; r = tmp;
+        }
+        /* eta is now >= 0. In what follows we're going to cancel out the bottom bits of g. No more
+         * than i can be cancelled out (as we'd be done before that point), and no more than eta+1
+         * can be done as its sign will flip once that happens. */
+        limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
+        /* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */
+        VERIFY_CHECK(limit > 0 && limit <= 30);
+        m = (UINT32_MAX >> (32 - limit)) & 255U;
+        /* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */
+        w = (g * secp256k1_modinv32_inv256[(f >> 1) & 127]) & m;
+        /* Do so. */
+        g += f * w;
+        q += u * w;
+        r += v * w;
+        VERIFY_CHECK((g & m) == 0);
+    }
+    /* Return data in t and return value. */
+    t->u = (int32_t)u;
+    t->v = (int32_t)v;
+    t->q = (int32_t)q;
+    t->r = (int32_t)r;
+    /* The determinant of t must be a power of two. This guarantees that multiplication with t
+     * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
+     * will be divided out again). As each divstep's individual matrix has determinant 2 or -2,
+     * the aggregate of 30 of them will have determinant 2^30 or -2^30. */
+    VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30 ||
+                 (int64_t)t->u * t->r - (int64_t)t->v * t->q == -(((int64_t)1) << 30));
+    *jacp = jac;
+    return eta;
+}
+
+/* Compute (t/2^30) * [d, e] mod modulus, where t is a transition matrix for 30 divsteps.
+ *
+ * On input and output, d and e are in range (-2*modulus,modulus). All output limbs will be in range
+ * (-2^30,2^30).
+ *
+ * This implements the update_de function from the explanation.
+ */
+static void secp256k1_modinv32_update_de_30(secp256k1_modinv32_signed30 *d, secp256k1_modinv32_signed30 *e, const secp256k1_modinv32_trans2x2 *t, const secp256k1_modinv32_modinfo* modinfo) {
+    const int32_t M30 = (int32_t)(UINT32_MAX >> 2);
+    const int32_t u = t->u, v = t->v, q = t->q, r = t->r;
+    int32_t di, ei, md, me, sd, se;
+    int64_t cd, ce;
+    int i;
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, 1) < 0);  /* d <    modulus */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, 1) < 0);  /* e <    modulus */
+    VERIFY_CHECK(labs(u) <= (M30 + 1 - labs(v))); /* |u|+|v| <= 2^30 */
+    VERIFY_CHECK(labs(q) <= (M30 + 1 - labs(r))); /* |q|+|r| <= 2^30 */
+
+    /* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */
+    sd = d->v[8] >> 31;
+    se = e->v[8] >> 31;
+    md = (u & sd) + (v & se);
+    me = (q & sd) + (r & se);
+    /* Begin computing t*[d,e]. */
+    di = d->v[0];
+    ei = e->v[0];
+    cd = (int64_t)u * di + (int64_t)v * ei;
+    ce = (int64_t)q * di + (int64_t)r * ei;
+    /* Correct md,me so that t*[d,e]+modulus*[md,me] has 30 zero bottom bits. */
+    md -= (modinfo->modulus_inv30 * (uint32_t)cd + md) & M30;
+    me -= (modinfo->modulus_inv30 * (uint32_t)ce + me) & M30;
+    /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */
+    cd += (int64_t)modinfo->modulus.v[0] * md;
+    ce += (int64_t)modinfo->modulus.v[0] * me;
+    /* Verify that the low 30 bits of the computation are indeed zero, and then throw them away. */
+    VERIFY_CHECK(((int32_t)cd & M30) == 0); cd >>= 30;
+    VERIFY_CHECK(((int32_t)ce & M30) == 0); ce >>= 30;
+    /* Now iteratively compute limb i=1..8 of t*[d,e]+modulus*[md,me], and store them in output
+     * limb i-1 (shifting down by 30 bits). */
+    for (i = 1; i < 9; ++i) {
+        di = d->v[i];
+        ei = e->v[i];
+        cd += (int64_t)u * di + (int64_t)v * ei;
+        ce += (int64_t)q * di + (int64_t)r * ei;
+        cd += (int64_t)modinfo->modulus.v[i] * md;
+        ce += (int64_t)modinfo->modulus.v[i] * me;
+        d->v[i - 1] = (int32_t)cd & M30; cd >>= 30;
+        e->v[i - 1] = (int32_t)ce & M30; ce >>= 30;
+    }
+    /* What remains is limb 9 of t*[d,e]+modulus*[md,me]; store it as output limb 8. */
+    d->v[8] = (int32_t)cd;
+    e->v[8] = (int32_t)ce;
+
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(d, 9, &modinfo->modulus, 1) < 0);  /* d <    modulus */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(e, 9, &modinfo->modulus, 1) < 0);  /* e <    modulus */
+}
+
+/* Compute (t/2^30) * [f, g], where t is a transition matrix for 30 divsteps.
+ *
+ * This implements the update_fg function from the explanation.
+ */
+static void secp256k1_modinv32_update_fg_30(secp256k1_modinv32_signed30 *f, secp256k1_modinv32_signed30 *g, const secp256k1_modinv32_trans2x2 *t) {
+    const int32_t M30 = (int32_t)(UINT32_MAX >> 2);
+    const int32_t u = t->u, v = t->v, q = t->q, r = t->r;
+    int32_t fi, gi;
+    int64_t cf, cg;
+    int i;
+    /* Start computing t*[f,g]. */
+    fi = f->v[0];
+    gi = g->v[0];
+    cf = (int64_t)u * fi + (int64_t)v * gi;
+    cg = (int64_t)q * fi + (int64_t)r * gi;
+    /* Verify that the bottom 30 bits of the result are zero, and then throw them away. */
+    VERIFY_CHECK(((int32_t)cf & M30) == 0); cf >>= 30;
+    VERIFY_CHECK(((int32_t)cg & M30) == 0); cg >>= 30;
+    /* Now iteratively compute limb i=1..8 of t*[f,g], and store them in output limb i-1 (shifting
+     * down by 30 bits). */
+    for (i = 1; i < 9; ++i) {
+        fi = f->v[i];
+        gi = g->v[i];
+        cf += (int64_t)u * fi + (int64_t)v * gi;
+        cg += (int64_t)q * fi + (int64_t)r * gi;
+        f->v[i - 1] = (int32_t)cf & M30; cf >>= 30;
+        g->v[i - 1] = (int32_t)cg & M30; cg >>= 30;
+    }
+    /* What remains is limb 9 of t*[f,g]; store it as output limb 8. */
+    f->v[8] = (int32_t)cf;
+    g->v[8] = (int32_t)cg;
+}
+
+/* Compute (t/2^30) * [f, g], where t is a transition matrix for 30 divsteps.
+ *
+ * Version that operates on a variable number of limbs in f and g.
+ *
+ * This implements the update_fg function from the explanation in modinv64_impl.h.
+ */
+static void secp256k1_modinv32_update_fg_30_var(int len, secp256k1_modinv32_signed30 *f, secp256k1_modinv32_signed30 *g, const secp256k1_modinv32_trans2x2 *t) {
+    const int32_t M30 = (int32_t)(UINT32_MAX >> 2);
+    const int32_t u = t->u, v = t->v, q = t->q, r = t->r;
+    int32_t fi, gi;
+    int64_t cf, cg;
+    int i;
+    VERIFY_CHECK(len > 0);
+    /* Start computing t*[f,g]. */
+    fi = f->v[0];
+    gi = g->v[0];
+    cf = (int64_t)u * fi + (int64_t)v * gi;
+    cg = (int64_t)q * fi + (int64_t)r * gi;
+    /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */
+    VERIFY_CHECK(((int32_t)cf & M30) == 0); cf >>= 30;
+    VERIFY_CHECK(((int32_t)cg & M30) == 0); cg >>= 30;
+    /* Now iteratively compute limb i=1..len of t*[f,g], and store them in output limb i-1 (shifting
+     * down by 30 bits). */
+    for (i = 1; i < len; ++i) {
+        fi = f->v[i];
+        gi = g->v[i];
+        cf += (int64_t)u * fi + (int64_t)v * gi;
+        cg += (int64_t)q * fi + (int64_t)r * gi;
+        f->v[i - 1] = (int32_t)cf & M30; cf >>= 30;
+        g->v[i - 1] = (int32_t)cg & M30; cg >>= 30;
+    }
+    /* What remains is limb (len) of t*[f,g]; store it as output limb (len-1). */
+    f->v[len - 1] = (int32_t)cf;
+    g->v[len - 1] = (int32_t)cg;
+}
+
+/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (constant time in x). */
+static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo) {
+    /* Start with d=0, e=1, f=modulus, g=x, zeta=-1. */
+    secp256k1_modinv32_signed30 d = {{0}};
+    secp256k1_modinv32_signed30 e = {{1}};
+    secp256k1_modinv32_signed30 f = modinfo->modulus;
+    secp256k1_modinv32_signed30 g = *x;
+    int i;
+    int32_t zeta = -1; /* zeta = -(delta+1/2); delta is initially 1/2. */
+
+    /* Do 20 iterations of 30 divsteps each = 600 divsteps. 590 suffices for 256-bit inputs. */
+    for (i = 0; i < 20; ++i) {
+        /* Compute transition matrix and new zeta after 30 divsteps. */
+        secp256k1_modinv32_trans2x2 t;
+        zeta = secp256k1_modinv32_divsteps_30(zeta, f.v[0], g.v[0], &t);
+        /* Update d,e using that transition matrix. */
+        secp256k1_modinv32_update_de_30(&d, &e, &t, modinfo);
+        /* Update f,g using that transition matrix. */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+
+        secp256k1_modinv32_update_fg_30(&f, &g, &t);
+
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+    }
+
+    /* At this point sufficient iterations have been performed that g must have reached 0
+     * and (if g was not originally 0) f must now equal +/- GCD of the initial f, g
+     * values i.e. +/- 1, and d now contains +/- the modular inverse. */
+
+    /* g == 0 */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, 9, &SECP256K1_SIGNED30_ONE, 0) == 0);
+    /* |f| == 1, or (x == 0 and d == 0 and f == modulus) */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, 9, &SECP256K1_SIGNED30_ONE, -1) == 0 ||
+                 secp256k1_modinv32_mul_cmp_30(&f, 9, &SECP256K1_SIGNED30_ONE, 1) == 0 ||
+                 (secp256k1_modinv32_mul_cmp_30(x, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
+                  secp256k1_modinv32_mul_cmp_30(&d, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
+                  secp256k1_modinv32_mul_cmp_30(&f, 9, &modinfo->modulus, 1) == 0));
+
+    /* Optionally negate d, normalize to [0,modulus), and return it. */
+    secp256k1_modinv32_normalize_30(&d, f.v[8], modinfo);
+    *x = d;
+}
+
+/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (variable time). */
+static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo) {
+    /* Start with d=0, e=1, f=modulus, g=x, eta=-1. */
+    secp256k1_modinv32_signed30 d = {{0, 0, 0, 0, 0, 0, 0, 0, 0}};
+    secp256k1_modinv32_signed30 e = {{1, 0, 0, 0, 0, 0, 0, 0, 0}};
+    secp256k1_modinv32_signed30 f = modinfo->modulus;
+    secp256k1_modinv32_signed30 g = *x;
+#ifdef VERIFY
+    int i = 0;
+#endif
+    int j, len = 9;
+    int32_t eta = -1; /* eta = -delta; delta is initially 1 (faster for the variable-time code) */
+    int32_t cond, fn, gn;
+
+    /* Do iterations of 30 divsteps each until g=0. */
+    while (1) {
+        /* Compute transition matrix and new eta after 30 divsteps. */
+        secp256k1_modinv32_trans2x2 t;
+        eta = secp256k1_modinv32_divsteps_30_var(eta, f.v[0], g.v[0], &t);
+        /* Update d,e using that transition matrix. */
+        secp256k1_modinv32_update_de_30(&d, &e, &t, modinfo);
+        /* Update f,g using that transition matrix. */
+
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+
+        secp256k1_modinv32_update_fg_30_var(len, &f, &g, &t);
+        /* If the bottom limb of g is 0, there is a chance g=0. */
+        if (g.v[0] == 0) {
+            cond = 0;
+            /* Check if all other limbs are also 0. */
+            for (j = 1; j < len; ++j) {
+                cond |= g.v[j];
+            }
+            /* If so, we're done. */
+            if (cond == 0) break;
+        }
+
+        /* Determine if len>1 and limb (len-1) of both f and g is 0 or -1. */
+        fn = f.v[len - 1];
+        gn = g.v[len - 1];
+        cond = ((int32_t)len - 2) >> 31;
+        cond |= fn ^ (fn >> 31);
+        cond |= gn ^ (gn >> 31);
+        /* If so, reduce length, propagating the sign of f and g's top limb into the one below. */
+        if (cond == 0) {
+            f.v[len - 2] |= (uint32_t)fn << 30;
+            g.v[len - 2] |= (uint32_t)gn << 30;
+            --len;
+        }
+
+        VERIFY_CHECK(++i < 25); /* We should never need more than 25*30 = 750 divsteps */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+    }
+
+    /* At this point g is 0 and (if g was not originally 0) f must now equal +/- GCD of
+     * the initial f, g values i.e. +/- 1, and d now contains +/- the modular inverse. */
+
+    /* g == 0 */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &SECP256K1_SIGNED30_ONE, 0) == 0);
+    /* |f| == 1, or (x == 0 and d == 0 and f == modulus) */
+    VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &SECP256K1_SIGNED30_ONE, -1) == 0 ||
+                 secp256k1_modinv32_mul_cmp_30(&f, len, &SECP256K1_SIGNED30_ONE, 1) == 0 ||
+                 (secp256k1_modinv32_mul_cmp_30(x, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
+                  secp256k1_modinv32_mul_cmp_30(&d, 9, &SECP256K1_SIGNED30_ONE, 0) == 0 &&
+                  secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) == 0));
+
+    /* Optionally negate d, normalize to [0,modulus), and return it. */
+    secp256k1_modinv32_normalize_30(&d, f.v[len - 1], modinfo);
+    *x = d;
+}
+
+/* Do up to 50 iterations of 30 posdivsteps (up to 1500 steps; more is extremely rare) each until f=1.
+ * In VERIFY mode use a lower number of iterations (750, close to the median 756), so failure actually occurs. */
+#ifdef VERIFY
+#define JACOBI32_ITERATIONS 25
+#else
+#define JACOBI32_ITERATIONS 50
+#endif
+
+/* Compute the Jacobi symbol of x modulo modinfo->modulus (variable time). gcd(x,modulus) must be 1. */
+static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo) {
+    /* Start with f=modulus, g=x, eta=-1. */
+    secp256k1_modinv32_signed30 f = modinfo->modulus;
+    secp256k1_modinv32_signed30 g = *x;
+    int j, len = 9;
+    int32_t eta = -1; /* eta = -delta; delta is initially 1 */
+    int32_t cond, fn, gn;
+    int jac = 0;
+    int count;
+
+    /* The input limbs must all be non-negative. */
+    VERIFY_CHECK(g.v[0] >= 0 && g.v[1] >= 0 && g.v[2] >= 0 && g.v[3] >= 0 && g.v[4] >= 0 && g.v[5] >= 0 && g.v[6] >= 0 && g.v[7] >= 0 && g.v[8] >= 0);
+
+    /* If x > 0, then if the loop below converges, it converges to f=g=gcd(x,modulus). Since we
+     * require that gcd(x,modulus)=1 and modulus>=3, x cannot be 0. Thus, we must reach f=1 (or
+     * time out). */
+    VERIFY_CHECK((g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4] | g.v[5] | g.v[6] | g.v[7] | g.v[8]) != 0);
+
+    for (count = 0; count < JACOBI32_ITERATIONS; ++count) {
+        /* Compute transition matrix and new eta after 30 posdivsteps. */
+        secp256k1_modinv32_trans2x2 t;
+        eta = secp256k1_modinv32_posdivsteps_30_var(eta, f.v[0] | ((uint32_t)f.v[1] << 30), g.v[0] | ((uint32_t)g.v[1] << 30), &t, &jac);
+        /* Update f,g using that transition matrix. */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0);  /* g < modulus */
+
+        secp256k1_modinv32_update_fg_30_var(len, &f, &g, &t);
+        /* If the bottom limb of f is 1, there is a chance that f=1. */
+        if (f.v[0] == 1) {
+            cond = 0;
+            /* Check if the other limbs are also 0. */
+            for (j = 1; j < len; ++j) {
+                cond |= f.v[j];
+            }
+            /* If so, we're done. If f=1, the Jacobi symbol (g | f)=1. */
+            if (cond == 0) return 1 - 2*(jac & 1);
+        }
+
+        /* Determine if len>1 and limb (len-1) of both f and g is 0. */
+        fn = f.v[len - 1];
+        gn = g.v[len - 1];
+        cond = ((int32_t)len - 2) >> 31;
+        cond |= fn;
+        cond |= gn;
+        /* If so, reduce length. */
+        if (cond == 0) --len;
+
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */
+        VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0);  /* g < modulus */
+    }
+
+    /* The loop failed to converge to f=g after 1500 iterations. Return 0, indicating unknown result. */
+    return 0;
+}
+
+#endif /* SECP256K1_MODINV32_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/modinv64.h

@@ -0,0 +1,47 @@
+/***********************************************************************
+ * Copyright (c) 2020 Peter Dettman                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODINV64_H
+#define SECP256K1_MODINV64_H
+
+#include "util.h"
+
+#ifndef SECP256K1_WIDEMUL_INT128
+#error "modinv64 requires 128-bit wide multiplication support"
+#endif
+
+/* A signed 62-bit limb representation of integers.
+ *
+ * Its value is sum(v[i] * 2^(62*i), i=0..4). */
+typedef struct {
+    int64_t v[5];
+} secp256k1_modinv64_signed62;
+
+typedef struct {
+    /* The modulus in signed62 notation, must be odd and in [3, 2^256]. */
+    secp256k1_modinv64_signed62 modulus;
+
+    /* modulus^{-1} mod 2^62 */
+    uint64_t modulus_inv62;
+} secp256k1_modinv64_modinfo;
+
+/* Replace x with its modular inverse mod modinfo->modulus. x must be in range [0, modulus).
+ * If x is zero, the result will be zero as well. If not, the inverse must exist (i.e., the gcd of
+ * x and modulus must be 1). These rules are automatically satisfied if the modulus is prime.
+ *
+ * On output, all of x's limbs will be in [0, 2^62).
+ */
+static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
+
+/* Same as secp256k1_modinv64_var, but constant time in x (not in the modulus). */
+static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
+
+/* Compute the Jacobi symbol for (x | modinfo->modulus). x must be coprime with modulus (and thus
+ * cannot be 0, as modulus >= 3). All limbs of x must be non-negative. Returns 0 if the result
+ * cannot be computed. */
+static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
+
+#endif /* SECP256K1_MODINV64_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/modinv64_impl.h

@@ -0,0 +1,780 @@
+/***********************************************************************
+ * Copyright (c) 2020 Peter Dettman                                    *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef SECP256K1_MODINV64_IMPL_H
+#define SECP256K1_MODINV64_IMPL_H
+
+#include "int128.h"
+#include "modinv64.h"
+
+/* This file implements modular inversion based on the paper "Fast constant-time gcd computation and
+ * modular inversion" by Daniel J. Bernstein and Bo-Yin Yang.
+ *
+ * For an explanation of the algorithm, see doc/safegcd_implementation.md. This file contains an
+ * implementation for N=62, using 62-bit signed limbs represented as int64_t.
+ */
+
+/* Data type for transition matrices (see section 3 of explanation).
+ *
+ * t = [ u  v ]
+ *     [ q  r ]
+ */
+typedef struct {
+    int64_t u, v, q, r;
+} secp256k1_modinv64_trans2x2;
+
+#ifdef VERIFY
+/* Helper function to compute the absolute value of an int64_t.
+ * (we don't use abs/labs/llabs as it depends on the int sizes). */
+static int64_t secp256k1_modinv64_abs(int64_t v) {
+    VERIFY_CHECK(v > INT64_MIN);
+    if (v < 0) return -v;
+    return v;
+}
+
+static const secp256k1_modinv64_signed62 SECP256K1_SIGNED62_ONE = {{1}};
+
+/* Compute a*factor and put it in r. All but the top limb in r will be in range [0,2^62). */
+static void secp256k1_modinv64_mul_62(secp256k1_modinv64_signed62 *r, const secp256k1_modinv64_signed62 *a, int alen, int64_t factor) {
+    const uint64_t M62 = UINT64_MAX >> 2;
+    secp256k1_int128 c, d;
+    int i;
+    secp256k1_i128_from_i64(&c, 0);
+    for (i = 0; i < 4; ++i) {
+        if (i < alen) secp256k1_i128_accum_mul(&c, a->v[i], factor);
+        r->v[i] = secp256k1_i128_to_u64(&c) & M62; secp256k1_i128_rshift(&c, 62);
+    }
+    if (4 < alen) secp256k1_i128_accum_mul(&c, a->v[4], factor);
+    secp256k1_i128_from_i64(&d, secp256k1_i128_to_i64(&c));
+    VERIFY_CHECK(secp256k1_i128_eq_var(&c, &d));
+    r->v[4] = secp256k1_i128_to_i64(&c);
+}
+
+/* Return -1 for a<b*factor, 0 for a==b*factor, 1 for a>b*factor. A has alen limbs; b has 5. */
+static int secp256k1_modinv64_mul_cmp_62(const secp256k1_modinv64_signed62 *a, int alen, const secp256k1_modinv64_signed62 *b, int64_t factor) {
+    int i;
+    secp256k1_modinv64_signed62 am, bm;
+    secp256k1_modinv64_mul_62(&am, a, alen, 1); /* Normalize all but the top limb of a. */
+    secp256k1_modinv64_mul_62(&bm, b, 5, factor);
+    for (i = 0; i < 4; ++i) {
+        /* Verify that all but the top limb of a and b are normalized. */
+        VERIFY_CHECK(am.v[i] >> 62 == 0);
+        VERIFY_CHECK(bm.v[i] >> 62 == 0);
+    }
+    for (i = 4; i >= 0; --i) {
+        if (am.v[i] < bm.v[i]) return -1;
+        if (am.v[i] > bm.v[i]) return 1;
+    }
+    return 0;
+}
+
+/* Check if the determinant of t is equal to 1 << n. If abs, check if |det t| == 1 << n. */
+static int secp256k1_modinv64_det_check_pow2(const secp256k1_modinv64_trans2x2 *t, unsigned int n, int abs) {
+    secp256k1_int128 a;
+    secp256k1_i128_det(&a, t->u, t->v, t->q, t->r);
+    if (secp256k1_i128_check_pow2(&a, n, 1)) return 1;
+    if (abs && secp256k1_i128_check_pow2(&a, n, -1)) return 1;
+    return 0;
+}
+#endif
+
+/* Take as input a signed62 number in range (-2*modulus,modulus), and add a multiple of the modulus
+ * to it to bring it to range [0,modulus). If sign < 0, the input will also be negated in the
+ * process. The input must have limbs in range (-2^62,2^62). The output will have limbs in range
+ * [0,2^62). */
+static void secp256k1_modinv64_normalize_62(secp256k1_modinv64_signed62 *r, int64_t sign, const secp256k1_modinv64_modinfo *modinfo) {
+    const int64_t M62 = (int64_t)(UINT64_MAX >> 2);
+    int64_t r0 = r->v[0], r1 = r->v[1], r2 = r->v[2], r3 = r->v[3], r4 = r->v[4];
+    volatile int64_t cond_add, cond_negate;
+
+#ifdef VERIFY
+    /* Verify that all limbs are in range (-2^62,2^62). */
+    int i;
+    for (i = 0; i < 5; ++i) {
+        VERIFY_CHECK(r->v[i] >= -M62);
+        VERIFY_CHECK(r->v[i] <= M62);
+    }
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, -2) > 0); /* r > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 1) < 0); /* r < modulus */
+#endif
+
+    /* In a first step, add the modulus if the input is negative, and then negate if requested.
+     * This brings r from range (-2*modulus,modulus) to range (-modulus,modulus). As all input
+     * limbs are in range (-2^62,2^62), this cannot overflow an int64_t. Note that the right
+     * shifts below are signed sign-extending shifts (see assumptions.h for tests that that is
+     * indeed the behavior of the right shift operator). */
+    cond_add = r4 >> 63;
+    r0 += modinfo->modulus.v[0] & cond_add;
+    r1 += modinfo->modulus.v[1] & cond_add;
+    r2 += modinfo->modulus.v[2] & cond_add;
+    r3 += modinfo->modulus.v[3] & cond_add;
+    r4 += modinfo->modulus.v[4] & cond_add;
+    cond_negate = sign >> 63;
+    r0 = (r0 ^ cond_negate) - cond_negate;
+    r1 = (r1 ^ cond_negate) - cond_negate;
+    r2 = (r2 ^ cond_negate) - cond_negate;
+    r3 = (r3 ^ cond_negate) - cond_negate;
+    r4 = (r4 ^ cond_negate) - cond_negate;
+    /* Propagate the top bits, to bring limbs back to range (-2^62,2^62). */
+    r1 += r0 >> 62; r0 &= M62;
+    r2 += r1 >> 62; r1 &= M62;
+    r3 += r2 >> 62; r2 &= M62;
+    r4 += r3 >> 62; r3 &= M62;
+
+    /* In a second step add the modulus again if the result is still negative, bringing
+     * r to range [0,modulus). */
+    cond_add = r4 >> 63;
+    r0 += modinfo->modulus.v[0] & cond_add;
+    r1 += modinfo->modulus.v[1] & cond_add;
+    r2 += modinfo->modulus.v[2] & cond_add;
+    r3 += modinfo->modulus.v[3] & cond_add;
+    r4 += modinfo->modulus.v[4] & cond_add;
+    /* And propagate again. */
+    r1 += r0 >> 62; r0 &= M62;
+    r2 += r1 >> 62; r1 &= M62;
+    r3 += r2 >> 62; r2 &= M62;
+    r4 += r3 >> 62; r3 &= M62;
+
+    r->v[0] = r0;
+    r->v[1] = r1;
+    r->v[2] = r2;
+    r->v[3] = r3;
+    r->v[4] = r4;
+
+    VERIFY_CHECK(r0 >> 62 == 0);
+    VERIFY_CHECK(r1 >> 62 == 0);
+    VERIFY_CHECK(r2 >> 62 == 0);
+    VERIFY_CHECK(r3 >> 62 == 0);
+    VERIFY_CHECK(r4 >> 62 == 0);
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 0) >= 0); /* r >= 0 */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(r, 5, &modinfo->modulus, 1) < 0); /* r < modulus */
+}
+
+/* Compute the transition matrix and eta for 59 divsteps (where zeta=-(delta+1/2)).
+ * Note that the transformation matrix is scaled by 2^62 and not 2^59.
+ *
+ * Input:  zeta: initial zeta
+ *         f0:   bottom limb of initial f
+ *         g0:   bottom limb of initial g
+ * Output: t: transition matrix
+ * Return: final zeta
+ *
+ * Implements the divsteps_n_matrix function from the explanation.
+ */
+static int64_t secp256k1_modinv64_divsteps_59(int64_t zeta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t) {
+    /* u,v,q,r are the elements of the transformation matrix being built up,
+     * starting with the identity matrix times 8 (because the caller expects
+     * a result scaled by 2^62). Semantically they are signed integers
+     * in range [-2^62,2^62], but here represented as unsigned mod 2^64. This
+     * permits left shifting (which is UB for negative numbers). The range
+     * being inside [-2^63,2^63) means that casting to signed works correctly.
+     */
+    uint64_t u = 8, v = 0, q = 0, r = 8;
+    volatile uint64_t c1, c2;
+    uint64_t mask1, mask2, f = f0, g = g0, x, y, z;
+    int i;
+
+    for (i = 3; i < 62; ++i) {
+        VERIFY_CHECK((f & 1) == 1); /* f must always be odd */
+        VERIFY_CHECK((u * f0 + v * g0) == f << i);
+        VERIFY_CHECK((q * f0 + r * g0) == g << i);
+        /* Compute conditional masks for (zeta < 0) and for (g & 1). */
+        c1 = zeta >> 63;
+        mask1 = c1;
+        c2 = g & 1;
+        mask2 = -c2;
+        /* Compute x,y,z, conditionally negated versions of f,u,v. */
+        x = (f ^ mask1) - mask1;
+        y = (u ^ mask1) - mask1;
+        z = (v ^ mask1) - mask1;
+        /* Conditionally add x,y,z to g,q,r. */
+        g += x & mask2;
+        q += y & mask2;
+        r += z & mask2;
+        /* In what follows, c1 is a condition mask for (zeta < 0) and (g & 1). */
+        mask1 &= mask2;
+        /* Conditionally change zeta into -zeta-2 or zeta-1. */
+        zeta = (zeta ^ mask1) - 1;
+        /* Conditionally add g,q,r to f,u,v. */
+        f += g & mask1;
+        u += q & mask1;
+        v += r & mask1;
+        /* Shifts */
+        g >>= 1;
+        u <<= 1;
+        v <<= 1;
+        /* Bounds on zeta that follow from the bounds on iteration count (max 10*59 divsteps). */
+        VERIFY_CHECK(zeta >= -591 && zeta <= 591);
+    }
+    /* Return data in t and return value. */
+    t->u = (int64_t)u;
+    t->v = (int64_t)v;
+    t->q = (int64_t)q;
+    t->r = (int64_t)r;
+
+    /* The determinant of t must be a power of two. This guarantees that multiplication with t
+     * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
+     * will be divided out again). As each divstep's individual matrix has determinant 2, the
+     * aggregate of 59 of them will have determinant 2^59. Multiplying with the initial
+     * 8*identity (which has determinant 2^6) means the overall outputs has determinant
+     * 2^65. */
+    VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 65, 0));
+
+    return zeta;
+}
+
+/* Compute the transition matrix and eta for 62 divsteps (variable time, eta=-delta).
+ *
+ * Input:  eta: initial eta
+ *         f0:  bottom limb of initial f
+ *         g0:  bottom limb of initial g
+ * Output: t: transition matrix
+ * Return: final eta
+ *
+ * Implements the divsteps_n_matrix_var function from the explanation.
+ */
+static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t) {
+    /* Transformation matrix; see comments in secp256k1_modinv64_divsteps_62. */
+    uint64_t u = 1, v = 0, q = 0, r = 1;
+    uint64_t f = f0, g = g0, m;
+    uint32_t w;
+    int i = 62, limit, zeros;
+
+    for (;;) {
+        /* Use a sentinel bit to count zeros only up to i. */
+        zeros = secp256k1_ctz64_var(g | (UINT64_MAX << i));
+        /* Perform zeros divsteps at once; they all just divide g by two. */
+        g >>= zeros;
+        u <<= zeros;
+        v <<= zeros;
+        eta -= zeros;
+        i -= zeros;
+        /* We're done once we've done 62 divsteps. */
+        if (i == 0) break;
+        VERIFY_CHECK((f & 1) == 1);
+        VERIFY_CHECK((g & 1) == 1);
+        VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i));
+        VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i));
+        /* Bounds on eta that follow from the bounds on iteration count (max 12*62 divsteps). */
+        VERIFY_CHECK(eta >= -745 && eta <= 745);
+        /* If eta is negative, negate it and replace f,g with g,-f. */
+        if (eta < 0) {
+            uint64_t tmp;
+            eta = -eta;
+            tmp = f; f = g; g = -tmp;
+            tmp = u; u = q; q = -tmp;
+            tmp = v; v = r; r = -tmp;
+            /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled
+             * out (as we'd be done before that point), and no more than eta+1 can be done as its
+             * sign will flip again once that happens. */
+            limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
+            VERIFY_CHECK(limit > 0 && limit <= 62);
+            /* m is a mask for the bottom min(limit, 6) bits. */
+            m = (UINT64_MAX >> (64 - limit)) & 63U;
+            /* Find what multiple of f must be added to g to cancel its bottom min(limit, 6)
+             * bits. */
+            w = (f * g * (f * f - 2)) & m;
+        } else {
+            /* In this branch, use a simpler formula that only lets us cancel up to 4 bits of g, as
+             * eta tends to be smaller here. */
+            limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
+            VERIFY_CHECK(limit > 0 && limit <= 62);
+            /* m is a mask for the bottom min(limit, 4) bits. */
+            m = (UINT64_MAX >> (64 - limit)) & 15U;
+            /* Find what multiple of f must be added to g to cancel its bottom min(limit, 4)
+             * bits. */
+            w = f + (((f + 1) & 4) << 1);
+            w = (-w * g) & m;
+        }
+        g += f * w;
+        q += u * w;
+        r += v * w;
+        VERIFY_CHECK((g & m) == 0);
+    }
+    /* Return data in t and return value. */
+    t->u = (int64_t)u;
+    t->v = (int64_t)v;
+    t->q = (int64_t)q;
+    t->r = (int64_t)r;
+
+    /* The determinant of t must be a power of two. This guarantees that multiplication with t
+     * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
+     * will be divided out again). As each divstep's individual matrix has determinant 2, the
+     * aggregate of 62 of them will have determinant 2^62. */
+    VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 62, 0));
+
+    return eta;
+}
+
+/* Compute the transition matrix and eta for 62 posdivsteps (variable time, eta=-delta), and keeps track
+ * of the Jacobi symbol along the way. f0 and g0 must be f and g mod 2^64 rather than 2^62, because
+ * Jacobi tracking requires knowing (f mod 8) rather than just (f mod 2).
+ *
+ * Input:        eta: initial eta
+ *               f0:  bottom limb of initial f
+ *               g0:  bottom limb of initial g
+ * Output:       t: transition matrix
+ * Input/Output: (*jacp & 1) is bitflipped if and only if the Jacobi symbol of (f | g) changes sign
+ *               by applying the returned transformation matrix to it. The other bits of *jacp may
+ *               change, but are meaningless.
+ * Return:       final eta
+ */
+static int64_t secp256k1_modinv64_posdivsteps_62_var(int64_t eta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t, int *jacp) {
+    /* Transformation matrix; see comments in secp256k1_modinv64_divsteps_62. */
+    uint64_t u = 1, v = 0, q = 0, r = 1;
+    uint64_t f = f0, g = g0, m;
+    uint32_t w;
+    int i = 62, limit, zeros;
+    int jac = *jacp;
+
+    for (;;) {
+        /* Use a sentinel bit to count zeros only up to i. */
+        zeros = secp256k1_ctz64_var(g | (UINT64_MAX << i));
+        /* Perform zeros divsteps at once; they all just divide g by two. */
+        g >>= zeros;
+        u <<= zeros;
+        v <<= zeros;
+        eta -= zeros;
+        i -= zeros;
+        /* Update the bottom bit of jac: when dividing g by an odd power of 2,
+         * if (f mod 8) is 3 or 5, the Jacobi symbol changes sign. */
+        jac ^= (zeros & ((f >> 1) ^ (f >> 2)));
+        /* We're done once we've done 62 posdivsteps. */
+        if (i == 0) break;
+        VERIFY_CHECK((f & 1) == 1);
+        VERIFY_CHECK((g & 1) == 1);
+        VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i));
+        VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i));
+        /* If eta is negative, negate it and replace f,g with g,f. */
+        if (eta < 0) {
+            uint64_t tmp;
+            eta = -eta;
+            tmp = f; f = g; g = tmp;
+            tmp = u; u = q; q = tmp;
+            tmp = v; v = r; r = tmp;
+            /* Update bottom bit of jac: when swapping f and g, the Jacobi symbol changes sign
+             * if both f and g are 3 mod 4. */
+            jac ^= ((f & g) >> 1);
+            /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled
+             * out (as we'd be done before that point), and no more than eta+1 can be done as its
+             * sign will flip again once that happens. */
+            limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
+            VERIFY_CHECK(limit > 0 && limit <= 62);
+            /* m is a mask for the bottom min(limit, 6) bits. */
+            m = (UINT64_MAX >> (64 - limit)) & 63U;
+            /* Find what multiple of f must be added to g to cancel its bottom min(limit, 6)
+             * bits. */
+            w = (f * g * (f * f - 2)) & m;
+        } else {
+            /* In this branch, use a simpler formula that only lets us cancel up to 4 bits of g, as
+             * eta tends to be smaller here. */
+            limit = ((int)eta + 1) > i ? i : ((int)eta + 1);
+            VERIFY_CHECK(limit > 0 && limit <= 62);
+            /* m is a mask for the bottom min(limit, 4) bits. */
+            m = (UINT64_MAX >> (64 - limit)) & 15U;
+            /* Find what multiple of f must be added to g to cancel its bottom min(limit, 4)
+             * bits. */
+            w = f + (((f + 1) & 4) << 1);
+            w = (-w * g) & m;
+        }
+        g += f * w;
+        q += u * w;
+        r += v * w;
+        VERIFY_CHECK((g & m) == 0);
+    }
+    /* Return data in t and return value. */
+    t->u = (int64_t)u;
+    t->v = (int64_t)v;
+    t->q = (int64_t)q;
+    t->r = (int64_t)r;
+
+    /* The determinant of t must be a power of two. This guarantees that multiplication with t
+     * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which
+     * will be divided out again). As each divstep's individual matrix has determinant 2 or -2,
+     * the aggregate of 62 of them will have determinant 2^62 or -2^62. */
+    VERIFY_CHECK(secp256k1_modinv64_det_check_pow2(t, 62, 1));
+
+    *jacp = jac;
+    return eta;
+}
+
+/* Compute (t/2^62) * [d, e] mod modulus, where t is a transition matrix scaled by 2^62.
+ *
+ * On input and output, d and e are in range (-2*modulus,modulus). All output limbs will be in range
+ * (-2^62,2^62).
+ *
+ * This implements the update_de function from the explanation.
+ */
+static void secp256k1_modinv64_update_de_62(secp256k1_modinv64_signed62 *d, secp256k1_modinv64_signed62 *e, const secp256k1_modinv64_trans2x2 *t, const secp256k1_modinv64_modinfo* modinfo) {
+    const uint64_t M62 = UINT64_MAX >> 2;
+    const int64_t d0 = d->v[0], d1 = d->v[1], d2 = d->v[2], d3 = d->v[3], d4 = d->v[4];
+    const int64_t e0 = e->v[0], e1 = e->v[1], e2 = e->v[2], e3 = e->v[3], e4 = e->v[4];
+    const int64_t u = t->u, v = t->v, q = t->q, r = t->r;
+    int64_t md, me, sd, se;
+    secp256k1_int128 cd, ce;
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0);  /* d <    modulus */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, 1) < 0);  /* e <    modulus */
+    VERIFY_CHECK(secp256k1_modinv64_abs(u) <= (((int64_t)1 << 62) - secp256k1_modinv64_abs(v))); /* |u|+|v| <= 2^62 */
+    VERIFY_CHECK(secp256k1_modinv64_abs(q) <= (((int64_t)1 << 62) - secp256k1_modinv64_abs(r))); /* |q|+|r| <= 2^62 */
+
+    /* [md,me] start as zero; plus [u,q] if d is negative; plus [v,r] if e is negative. */
+    sd = d4 >> 63;
+    se = e4 >> 63;
+    md = (u & sd) + (v & se);
+    me = (q & sd) + (r & se);
+    /* Begin computing t*[d,e]. */
+    secp256k1_i128_mul(&cd, u, d0);
+    secp256k1_i128_accum_mul(&cd, v, e0);
+    secp256k1_i128_mul(&ce, q, d0);
+    secp256k1_i128_accum_mul(&ce, r, e0);
+    /* Correct md,me so that t*[d,e]+modulus*[md,me] has 62 zero bottom bits. */
+    md -= (modinfo->modulus_inv62 * secp256k1_i128_to_u64(&cd) + md) & M62;
+    me -= (modinfo->modulus_inv62 * secp256k1_i128_to_u64(&ce) + me) & M62;
+    /* Update the beginning of computation for t*[d,e]+modulus*[md,me] now md,me are known. */
+    secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[0], md);
+    secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[0], me);
+    /* Verify that the low 62 bits of the computation are indeed zero, and then throw them away. */
+    VERIFY_CHECK((secp256k1_i128_to_u64(&cd) & M62) == 0); secp256k1_i128_rshift(&cd, 62);
+    VERIFY_CHECK((secp256k1_i128_to_u64(&ce) & M62) == 0); secp256k1_i128_rshift(&ce, 62);
+    /* Compute limb 1 of t*[d,e]+modulus*[md,me], and store it as output limb 0 (= down shift). */
+    secp256k1_i128_accum_mul(&cd, u, d1);
+    secp256k1_i128_accum_mul(&cd, v, e1);
+    secp256k1_i128_accum_mul(&ce, q, d1);
+    secp256k1_i128_accum_mul(&ce, r, e1);
+    if (modinfo->modulus.v[1]) { /* Optimize for the case where limb of modulus is zero. */
+        secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[1], md);
+        secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[1], me);
+    }
+    d->v[0] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[0] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
+    /* Compute limb 2 of t*[d,e]+modulus*[md,me], and store it as output limb 1. */
+    secp256k1_i128_accum_mul(&cd, u, d2);
+    secp256k1_i128_accum_mul(&cd, v, e2);
+    secp256k1_i128_accum_mul(&ce, q, d2);
+    secp256k1_i128_accum_mul(&ce, r, e2);
+    if (modinfo->modulus.v[2]) { /* Optimize for the case where limb of modulus is zero. */
+        secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[2], md);
+        secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[2], me);
+    }
+    d->v[1] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[1] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
+    /* Compute limb 3 of t*[d,e]+modulus*[md,me], and store it as output limb 2. */
+    secp256k1_i128_accum_mul(&cd, u, d3);
+    secp256k1_i128_accum_mul(&cd, v, e3);
+    secp256k1_i128_accum_mul(&ce, q, d3);
+    secp256k1_i128_accum_mul(&ce, r, e3);
+    if (modinfo->modulus.v[3]) { /* Optimize for the case where limb of modulus is zero. */
+        secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[3], md);
+        secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[3], me);
+    }
+    d->v[2] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[2] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
+    /* Compute limb 4 of t*[d,e]+modulus*[md,me], and store it as output limb 3. */
+    secp256k1_i128_accum_mul(&cd, u, d4);
+    secp256k1_i128_accum_mul(&cd, v, e4);
+    secp256k1_i128_accum_mul(&ce, q, d4);
+    secp256k1_i128_accum_mul(&ce, r, e4);
+    secp256k1_i128_accum_mul(&cd, modinfo->modulus.v[4], md);
+    secp256k1_i128_accum_mul(&ce, modinfo->modulus.v[4], me);
+    d->v[3] = secp256k1_i128_to_u64(&cd) & M62; secp256k1_i128_rshift(&cd, 62);
+    e->v[3] = secp256k1_i128_to_u64(&ce) & M62; secp256k1_i128_rshift(&ce, 62);
+    /* What remains is limb 5 of t*[d,e]+modulus*[md,me]; store it as output limb 4. */
+    d->v[4] = secp256k1_i128_to_i64(&cd);
+    e->v[4] = secp256k1_i128_to_i64(&ce);
+
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, -2) > 0); /* d > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(d, 5, &modinfo->modulus, 1) < 0);  /* d <    modulus */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, -2) > 0); /* e > -2*modulus */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(e, 5, &modinfo->modulus, 1) < 0);  /* e <    modulus */
+}
+
+/* Compute (t/2^62) * [f, g], where t is a transition matrix scaled by 2^62.
+ *
+ * This implements the update_fg function from the explanation.
+ */
+static void secp256k1_modinv64_update_fg_62(secp256k1_modinv64_signed62 *f, secp256k1_modinv64_signed62 *g, const secp256k1_modinv64_trans2x2 *t) {
+    const uint64_t M62 = UINT64_MAX >> 2;
+    const int64_t f0 = f->v[0], f1 = f->v[1], f2 = f->v[2], f3 = f->v[3], f4 = f->v[4];
+    const int64_t g0 = g->v[0], g1 = g->v[1], g2 = g->v[2], g3 = g->v[3], g4 = g->v[4];
+    const int64_t u = t->u, v = t->v, q = t->q, r = t->r;
+    secp256k1_int128 cf, cg;
+    /* Start computing t*[f,g]. */
+    secp256k1_i128_mul(&cf, u, f0);
+    secp256k1_i128_accum_mul(&cf, v, g0);
+    secp256k1_i128_mul(&cg, q, f0);
+    secp256k1_i128_accum_mul(&cg, r, g0);
+    /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */
+    VERIFY_CHECK((secp256k1_i128_to_u64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62);
+    VERIFY_CHECK((secp256k1_i128_to_u64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62);
+    /* Compute limb 1 of t*[f,g], and store it as output limb 0 (= down shift). */
+    secp256k1_i128_accum_mul(&cf, u, f1);
+    secp256k1_i128_accum_mul(&cf, v, g1);
+    secp256k1_i128_accum_mul(&cg, q, f1);
+    secp256k1_i128_accum_mul(&cg, r, g1);
+    f->v[0] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[0] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
+    /* Compute limb 2 of t*[f,g], and store it as output limb 1. */
+    secp256k1_i128_accum_mul(&cf, u, f2);
+    secp256k1_i128_accum_mul(&cf, v, g2);
+    secp256k1_i128_accum_mul(&cg, q, f2);
+    secp256k1_i128_accum_mul(&cg, r, g2);
+    f->v[1] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[1] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
+    /* Compute limb 3 of t*[f,g], and store it as output limb 2. */
+    secp256k1_i128_accum_mul(&cf, u, f3);
+    secp256k1_i128_accum_mul(&cf, v, g3);
+    secp256k1_i128_accum_mul(&cg, q, f3);
+    secp256k1_i128_accum_mul(&cg, r, g3);
+    f->v[2] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[2] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
+    /* Compute limb 4 of t*[f,g], and store it as output limb 3. */
+    secp256k1_i128_accum_mul(&cf, u, f4);
+    secp256k1_i128_accum_mul(&cf, v, g4);
+    secp256k1_i128_accum_mul(&cg, q, f4);
+    secp256k1_i128_accum_mul(&cg, r, g4);
+    f->v[3] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+    g->v[3] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
+    /* What remains is limb 5 of t*[f,g]; store it as output limb 4. */
+    f->v[4] = secp256k1_i128_to_i64(&cf);
+    g->v[4] = secp256k1_i128_to_i64(&cg);
+}
+
+/* Compute (t/2^62) * [f, g], where t is a transition matrix for 62 divsteps.
+ *
+ * Version that operates on a variable number of limbs in f and g.
+ *
+ * This implements the update_fg function from the explanation.
+ */
+static void secp256k1_modinv64_update_fg_62_var(int len, secp256k1_modinv64_signed62 *f, secp256k1_modinv64_signed62 *g, const secp256k1_modinv64_trans2x2 *t) {
+    const uint64_t M62 = UINT64_MAX >> 2;
+    const int64_t u = t->u, v = t->v, q = t->q, r = t->r;
+    int64_t fi, gi;
+    secp256k1_int128 cf, cg;
+    int i;
+    VERIFY_CHECK(len > 0);
+    /* Start computing t*[f,g]. */
+    fi = f->v[0];
+    gi = g->v[0];
+    secp256k1_i128_mul(&cf, u, fi);
+    secp256k1_i128_accum_mul(&cf, v, gi);
+    secp256k1_i128_mul(&cg, q, fi);
+    secp256k1_i128_accum_mul(&cg, r, gi);
+    /* Verify that the bottom 62 bits of the result are zero, and then throw them away. */
+    VERIFY_CHECK((secp256k1_i128_to_u64(&cf) & M62) == 0); secp256k1_i128_rshift(&cf, 62);
+    VERIFY_CHECK((secp256k1_i128_to_u64(&cg) & M62) == 0); secp256k1_i128_rshift(&cg, 62);
+    /* Now iteratively compute limb i=1..len of t*[f,g], and store them in output limb i-1 (shifting
+     * down by 62 bits). */
+    for (i = 1; i < len; ++i) {
+        fi = f->v[i];
+        gi = g->v[i];
+        secp256k1_i128_accum_mul(&cf, u, fi);
+        secp256k1_i128_accum_mul(&cf, v, gi);
+        secp256k1_i128_accum_mul(&cg, q, fi);
+        secp256k1_i128_accum_mul(&cg, r, gi);
+        f->v[i - 1] = secp256k1_i128_to_u64(&cf) & M62; secp256k1_i128_rshift(&cf, 62);
+        g->v[i - 1] = secp256k1_i128_to_u64(&cg) & M62; secp256k1_i128_rshift(&cg, 62);
+    }
+    /* What remains is limb (len) of t*[f,g]; store it as output limb (len-1). */
+    f->v[len - 1] = secp256k1_i128_to_i64(&cf);
+    g->v[len - 1] = secp256k1_i128_to_i64(&cg);
+}
+
+/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (constant time in x). */
+static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) {
+    /* Start with d=0, e=1, f=modulus, g=x, zeta=-1. */
+    secp256k1_modinv64_signed62 d = {{0, 0, 0, 0, 0}};
+    secp256k1_modinv64_signed62 e = {{1, 0, 0, 0, 0}};
+    secp256k1_modinv64_signed62 f = modinfo->modulus;
+    secp256k1_modinv64_signed62 g = *x;
+    int i;
+    int64_t zeta = -1; /* zeta = -(delta+1/2); delta starts at 1/2. */
+
+    /* Do 10 iterations of 59 divsteps each = 590 divsteps. This suffices for 256-bit inputs. */
+    for (i = 0; i < 10; ++i) {
+        /* Compute transition matrix and new zeta after 59 divsteps. */
+        secp256k1_modinv64_trans2x2 t;
+        zeta = secp256k1_modinv64_divsteps_59(zeta, f.v[0], g.v[0], &t);
+        /* Update d,e using that transition matrix. */
+        secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo);
+        /* Update f,g using that transition matrix. */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+
+        secp256k1_modinv64_update_fg_62(&f, &g, &t);
+
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+    }
+
+    /* At this point sufficient iterations have been performed that g must have reached 0
+     * and (if g was not originally 0) f must now equal +/- GCD of the initial f, g
+     * values i.e. +/- 1, and d now contains +/- the modular inverse. */
+
+    /* g == 0 */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, 5, &SECP256K1_SIGNED62_ONE, 0) == 0);
+    /* |f| == 1, or (x == 0 and d == 0 and f == modulus) */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, 5, &SECP256K1_SIGNED62_ONE, -1) == 0 ||
+                 secp256k1_modinv64_mul_cmp_62(&f, 5, &SECP256K1_SIGNED62_ONE, 1) == 0 ||
+                 (secp256k1_modinv64_mul_cmp_62(x, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
+                  secp256k1_modinv64_mul_cmp_62(&d, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
+                  secp256k1_modinv64_mul_cmp_62(&f, 5, &modinfo->modulus, 1) == 0));
+
+    /* Optionally negate d, normalize to [0,modulus), and return it. */
+    secp256k1_modinv64_normalize_62(&d, f.v[4], modinfo);
+    *x = d;
+}
+
+/* Compute the inverse of x modulo modinfo->modulus, and replace x with it (variable time). */
+static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) {
+    /* Start with d=0, e=1, f=modulus, g=x, eta=-1. */
+    secp256k1_modinv64_signed62 d = {{0, 0, 0, 0, 0}};
+    secp256k1_modinv64_signed62 e = {{1, 0, 0, 0, 0}};
+    secp256k1_modinv64_signed62 f = modinfo->modulus;
+    secp256k1_modinv64_signed62 g = *x;
+#ifdef VERIFY
+    int i = 0;
+#endif
+    int j, len = 5;
+    int64_t eta = -1; /* eta = -delta; delta is initially 1 */
+    int64_t cond, fn, gn;
+
+    /* Do iterations of 62 divsteps each until g=0. */
+    while (1) {
+        /* Compute transition matrix and new eta after 62 divsteps. */
+        secp256k1_modinv64_trans2x2 t;
+        eta = secp256k1_modinv64_divsteps_62_var(eta, f.v[0], g.v[0], &t);
+        /* Update d,e using that transition matrix. */
+        secp256k1_modinv64_update_de_62(&d, &e, &t, modinfo);
+        /* Update f,g using that transition matrix. */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+
+        secp256k1_modinv64_update_fg_62_var(len, &f, &g, &t);
+        /* If the bottom limb of g is zero, there is a chance that g=0. */
+        if (g.v[0] == 0) {
+            cond = 0;
+            /* Check if the other limbs are also 0. */
+            for (j = 1; j < len; ++j) {
+                cond |= g.v[j];
+            }
+            /* If so, we're done. */
+            if (cond == 0) break;
+        }
+
+        /* Determine if len>1 and limb (len-1) of both f and g is 0 or -1. */
+        fn = f.v[len - 1];
+        gn = g.v[len - 1];
+        cond = ((int64_t)len - 2) >> 63;
+        cond |= fn ^ (fn >> 63);
+        cond |= gn ^ (gn >> 63);
+        /* If so, reduce length, propagating the sign of f and g's top limb into the one below. */
+        if (cond == 0) {
+            f.v[len - 2] |= (uint64_t)fn << 62;
+            g.v[len - 2] |= (uint64_t)gn << 62;
+            --len;
+        }
+
+        VERIFY_CHECK(++i < 12); /* We should never need more than 12*62 = 744 divsteps */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, -1) > 0); /* f > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, -1) > 0); /* g > -modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0);  /* g <  modulus */
+    }
+
+    /* At this point g is 0 and (if g was not originally 0) f must now equal +/- GCD of
+     * the initial f, g values i.e. +/- 1, and d now contains +/- the modular inverse. */
+
+    /* g == 0 */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &SECP256K1_SIGNED62_ONE, 0) == 0);
+    /* |f| == 1, or (x == 0 and d == 0 and f == modulus) */
+    VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &SECP256K1_SIGNED62_ONE, -1) == 0 ||
+                 secp256k1_modinv64_mul_cmp_62(&f, len, &SECP256K1_SIGNED62_ONE, 1) == 0 ||
+                 (secp256k1_modinv64_mul_cmp_62(x, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
+                  secp256k1_modinv64_mul_cmp_62(&d, 5, &SECP256K1_SIGNED62_ONE, 0) == 0 &&
+                  secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) == 0));
+
+    /* Optionally negate d, normalize to [0,modulus), and return it. */
+    secp256k1_modinv64_normalize_62(&d, f.v[len - 1], modinfo);
+    *x = d;
+}
+
+/* Do up to 25 iterations of 62 posdivsteps (up to 1550 steps; more is extremely rare) each until f=1.
+ * In VERIFY mode use a lower number of iterations (744, close to the median 756), so failure actually occurs. */
+#ifdef VERIFY
+#define JACOBI64_ITERATIONS 12
+#else
+#define JACOBI64_ITERATIONS 25
+#endif
+
+/* Compute the Jacobi symbol of x modulo modinfo->modulus (variable time). gcd(x,modulus) must be 1. */
+static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) {
+    /* Start with f=modulus, g=x, eta=-1. */
+    secp256k1_modinv64_signed62 f = modinfo->modulus;
+    secp256k1_modinv64_signed62 g = *x;
+    int j, len = 5;
+    int64_t eta = -1; /* eta = -delta; delta is initially 1 */
+    int64_t cond, fn, gn;
+    int jac = 0;
+    int count;
+
+    /* The input limbs must all be non-negative. */
+    VERIFY_CHECK(g.v[0] >= 0 && g.v[1] >= 0 && g.v[2] >= 0 && g.v[3] >= 0 && g.v[4] >= 0);
+
+    /* If x > 0, then if the loop below converges, it converges to f=g=gcd(x,modulus). Since we
+     * require that gcd(x,modulus)=1 and modulus>=3, x cannot be 0. Thus, we must reach f=1 (or
+     * time out). */
+    VERIFY_CHECK((g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4]) != 0);
+
+    for (count = 0; count < JACOBI64_ITERATIONS; ++count) {
+        /* Compute transition matrix and new eta after 62 posdivsteps. */
+        secp256k1_modinv64_trans2x2 t;
+        eta = secp256k1_modinv64_posdivsteps_62_var(eta, f.v[0] | ((uint64_t)f.v[1] << 62), g.v[0] | ((uint64_t)g.v[1] << 62), &t, &jac);
+        /* Update f,g using that transition matrix. */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0);  /* g < modulus */
+
+        secp256k1_modinv64_update_fg_62_var(len, &f, &g, &t);
+        /* If the bottom limb of f is 1, there is a chance that f=1. */
+        if (f.v[0] == 1) {
+            cond = 0;
+            /* Check if the other limbs are also 0. */
+            for (j = 1; j < len; ++j) {
+                cond |= f.v[j];
+            }
+            /* If so, we're done. When f=1, the Jacobi symbol (g | f)=1. */
+            if (cond == 0) return 1 - 2*(jac & 1);
+        }
+
+        /* Determine if len>1 and limb (len-1) of both f and g is 0. */
+        fn = f.v[len - 1];
+        gn = g.v[len - 1];
+        cond = ((int64_t)len - 2) >> 63;
+        cond |= fn;
+        cond |= gn;
+        /* If so, reduce length. */
+        if (cond == 0) --len;
+
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */
+        VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0);  /* g < modulus */
+    }
+
+    /* The loop failed to converge to f=g after 1550 iterations. Return 0, indicating unknown result. */
+    return 0;
+}
+
+#endif /* SECP256K1_MODINV64_IMPL_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ecdh/Makefile.am.include

@@ -0,0 +1,5 @@
+include_HEADERS += include/secp256k1_ecdh.h
+noinst_HEADERS += src/modules/ecdh/main_impl.h
+noinst_HEADERS += src/modules/ecdh/tests_impl.h
+noinst_HEADERS += src/modules/ecdh/bench_impl.h
+noinst_HEADERS += src/wycheproof/ecdh_secp256k1_test.h

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ecdh/bench_impl.h

@@ -0,0 +1,54 @@
+/***********************************************************************
+ * Copyright (c) 2015 Pieter Wuille, Andrew Poelstra                   *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_MODULE_ECDH_BENCH_H
+#define SECP256K1_MODULE_ECDH_BENCH_H
+
+#include "../../../include/secp256k1_ecdh.h"
+
+typedef struct {
+    const secp256k1_context *ctx;
+    secp256k1_pubkey point;
+    unsigned char scalar[32];
+} bench_ecdh_data;
+
+static void bench_ecdh_setup(void* arg) {
+    int i;
+    bench_ecdh_data *data = (bench_ecdh_data*)arg;
+    const unsigned char point[] = {
+        0x03,
+        0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06,
+        0xc2, 0x39, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd,
+        0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb,
+        0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f
+    };
+
+    for (i = 0; i < 32; i++) {
+        data->scalar[i] = i + 1;
+    }
+    CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1);
+}
+
+static void bench_ecdh(void* arg, int iters) {
+    int i;
+    unsigned char res[32];
+    bench_ecdh_data *data = (bench_ecdh_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        CHECK(secp256k1_ecdh(data->ctx, res, &data->point, data->scalar, NULL, NULL) == 1);
+    }
+}
+
+static void run_ecdh_bench(int iters, int argc, char** argv) {
+    bench_ecdh_data data;
+    int d = argc == 1;
+
+    data.ctx = secp256k1_context_static;
+
+    if (d || have_flag(argc, argv, "ecdh")) run_benchmark("ecdh", bench_ecdh, bench_ecdh_setup, NULL, &data, 10, iters);
+}
+
+#endif /* SECP256K1_MODULE_ECDH_BENCH_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ecdh/main_impl.h

@@ -0,0 +1,79 @@
+/***********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                  *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_MODULE_ECDH_MAIN_H
+#define SECP256K1_MODULE_ECDH_MAIN_H
+
+#include "../../../include/secp256k1_ecdh.h"
+#include "../../ecmult_const_impl.h"
+
+static int ecdh_hash_function_sha256_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) {
+    unsigned char version = (y32[31] & 0x01) | 0x02;
+    secp256k1_sha256 sha;
+    (void)data;
+
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(hash_ctx, &sha, &version, 1);
+    secp256k1_sha256_write(hash_ctx, &sha, x32, 32);
+    secp256k1_sha256_finalize(hash_ctx, &sha, output);
+    secp256k1_sha256_clear(&sha);
+
+    return 1;
+}
+
+static int ecdh_hash_function_sha256(unsigned char *output, const unsigned char *x32, const unsigned char *y32, void *data) {
+    return ecdh_hash_function_sha256_impl(secp256k1_get_hash_context(secp256k1_context_static), output, x32, y32, data);
+}
+
+const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_sha256 = ecdh_hash_function_sha256;
+const secp256k1_ecdh_hash_function secp256k1_ecdh_hash_function_default = ecdh_hash_function_sha256;
+
+int secp256k1_ecdh(const secp256k1_context* ctx, unsigned char *output, const secp256k1_pubkey *point, const unsigned char *scalar, secp256k1_ecdh_hash_function hashfp, void *data) {
+    int ret = 0;
+    int overflow = 0;
+    secp256k1_gej res;
+    secp256k1_ge pt;
+    secp256k1_scalar s;
+    unsigned char x[32];
+    unsigned char y[32];
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(output != NULL);
+    ARG_CHECK(point != NULL);
+    ARG_CHECK(scalar != NULL);
+
+    secp256k1_pubkey_load(ctx, &pt, point);
+    secp256k1_scalar_set_b32(&s, scalar, &overflow);
+
+    overflow |= secp256k1_scalar_is_zero(&s);
+    secp256k1_scalar_cmov(&s, &secp256k1_scalar_one, overflow);
+
+    secp256k1_ecmult_const(&res, &pt, &s);
+    secp256k1_ge_set_gej(&pt, &res);
+
+    /* Compute a hash of the point */
+    secp256k1_fe_normalize(&pt.x);
+    secp256k1_fe_normalize(&pt.y);
+    secp256k1_fe_get_b32(x, &pt.x);
+    secp256k1_fe_get_b32(y, &pt.y);
+
+    if (hashfp == NULL) {
+        /* Use ctx-aware function by default */
+        ret = ecdh_hash_function_sha256_impl(secp256k1_get_hash_context(ctx), output, x, y, data);
+    } else {
+        ret = hashfp(output, x, y, data);
+    }
+
+    secp256k1_memclear_explicit(x, sizeof(x));
+    secp256k1_memclear_explicit(y, sizeof(y));
+    secp256k1_scalar_clear(&s);
+    secp256k1_ge_clear(&pt);
+    secp256k1_gej_clear(&res);
+
+    return !!ret & !overflow;
+}
+
+#endif /* SECP256K1_MODULE_ECDH_MAIN_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ecdh/tests_impl.h

@@ -0,0 +1,218 @@
+/***********************************************************************
+ * Copyright (c) 2015 Andrew Poelstra                                  *
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_MODULE_ECDH_TESTS_H
+#define SECP256K1_MODULE_ECDH_TESTS_H
+
+#include "../../unit_test.h"
+#include "../../testutil.h"
+
+static int ecdh_hash_function_test_xpassthru(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) {
+    (void)y;
+    (void)data;
+    memcpy(output, x, 32);
+    return 1;
+}
+
+static int ecdh_hash_function_test_fail(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) {
+    (void)output;
+    (void)x;
+    (void)y;
+    (void)data;
+    return 0;
+}
+
+static int ecdh_hash_function_custom(unsigned char *output, const unsigned char *x, const unsigned char *y, void *data) {
+    (void)data;
+    /* Save x and y as uncompressed public key */
+    output[0] = 0x04;
+    memcpy(output + 1, x, 32);
+    memcpy(output + 33, y, 32);
+    return 1;
+}
+
+static void test_ecdh_api(void) {
+    secp256k1_pubkey point;
+    unsigned char res[32];
+    unsigned char s_one[32] = { 0 };
+    s_one[31] = 1;
+
+    CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_one) == 1);
+
+    /* Check all NULLs are detected */
+    CHECK(secp256k1_ecdh(CTX, res, &point, s_one, NULL, NULL) == 1);
+    CHECK_ILLEGAL(CTX, secp256k1_ecdh(CTX, NULL, &point, s_one, NULL, NULL));
+    CHECK_ILLEGAL(CTX, secp256k1_ecdh(CTX, res, NULL, s_one, NULL, NULL));
+    CHECK_ILLEGAL(CTX, secp256k1_ecdh(CTX, res, &point, NULL, NULL, NULL));
+    CHECK(secp256k1_ecdh(CTX, res, &point, s_one, NULL, NULL) == 1);
+}
+
+static void test_ecdh_generator_basepoint(void) {
+    unsigned char s_one[32] = { 0 };
+    secp256k1_pubkey point[2];
+    int i;
+
+    s_one[31] = 1;
+    /* Check against pubkey creation when the basepoint is the generator */
+    for (i = 0; i < 2 * COUNT; ++i) {
+        secp256k1_sha256 sha;
+        unsigned char s_b32[32];
+        unsigned char output_ecdh[65];
+        unsigned char output_ser[32];
+        unsigned char point_ser[65];
+        size_t point_ser_len = sizeof(point_ser);
+        secp256k1_scalar s;
+
+        testutil_random_scalar_order(&s);
+        secp256k1_scalar_get_b32(s_b32, &s);
+
+        CHECK(secp256k1_ec_pubkey_create(CTX, &point[0], s_one) == 1);
+        CHECK(secp256k1_ec_pubkey_create(CTX, &point[1], s_b32) == 1);
+
+        /* compute using ECDH function with custom hash function */
+        CHECK(secp256k1_ecdh(CTX, output_ecdh, &point[0], s_b32, ecdh_hash_function_custom, NULL) == 1);
+        /* compute "explicitly" */
+        CHECK(secp256k1_ec_pubkey_serialize(CTX, point_ser, &point_ser_len, &point[1], SECP256K1_EC_UNCOMPRESSED) == 1);
+        /* compare */
+        CHECK(secp256k1_memcmp_var(output_ecdh, point_ser, 65) == 0);
+
+        /* compute using ECDH function with default hash function */
+        CHECK(secp256k1_ecdh(CTX, output_ecdh, &point[0], s_b32, NULL, NULL) == 1);
+        /* compute "explicitly" */
+        CHECK(secp256k1_ec_pubkey_serialize(CTX, point_ser, &point_ser_len, &point[1], SECP256K1_EC_COMPRESSED) == 1);
+        secp256k1_sha256_initialize(&sha);
+        secp256k1_sha256_write(secp256k1_get_hash_context(CTX), &sha, point_ser, point_ser_len);
+        secp256k1_sha256_finalize(secp256k1_get_hash_context(CTX), &sha, output_ser);
+        /* compare */
+        CHECK(secp256k1_memcmp_var(output_ecdh, output_ser, 32) == 0);
+    }
+}
+
+DEFINE_SHA256_TRANSFORM_PROBE(sha256_ecdh)
+static void test_ecdh_ctx_sha256(void) {
+    /* Check ctx-provided SHA256 compression override takes effect */
+    secp256k1_context *ctx = secp256k1_context_clone(CTX);
+    unsigned char out_default[65], out_custom[65];
+    const unsigned char sk[32] = {1};
+    secp256k1_pubkey pubkey;
+    CHECK(secp256k1_ec_pubkey_create(ctx, &pubkey, sk) == 1);
+
+    /* Default behavior */
+    CHECK(secp256k1_ecdh(ctx, out_default, &pubkey, sk, NULL, NULL) == 1);
+    CHECK(!sha256_ecdh_called);
+
+    /* Override SHA256 compression directly, bypassing the ctx setter sanity checks */
+    ctx->hash_ctx.fn_sha256_compression = sha256_ecdh;
+    CHECK(secp256k1_ecdh(ctx, out_custom, &pubkey, sk, NULL, NULL) == 1);
+
+    /* Outputs must differ if custom compression was used */
+    CHECK(secp256k1_memcmp_var(out_default, out_custom, 32) != 0);
+    CHECK(sha256_ecdh_called);
+
+    secp256k1_context_destroy(ctx);
+}
+
+static void test_bad_scalar(void) {
+    unsigned char s_zero[32] = { 0 };
+    unsigned char s_overflow[32] = { 0 };
+    unsigned char s_rand[32] = { 0 };
+    unsigned char output[32];
+    secp256k1_scalar rand;
+    secp256k1_pubkey point;
+
+    /* Create random point */
+    testutil_random_scalar_order(&rand);
+    secp256k1_scalar_get_b32(s_rand, &rand);
+    CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_rand) == 1);
+
+    /* Try to multiply it by bad values */
+    memcpy(s_overflow, secp256k1_group_order_bytes, 32);
+    CHECK(secp256k1_ecdh(CTX, output, &point, s_zero, NULL, NULL) == 0);
+    CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, NULL, NULL) == 0);
+    /* ...and a good one */
+    s_overflow[31] -= 1;
+    CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, NULL, NULL) == 1);
+
+    /* Hash function failure results in ecdh failure */
+    CHECK(secp256k1_ecdh(CTX, output, &point, s_overflow, ecdh_hash_function_test_fail, NULL) == 0);
+}
+
+/** Test that ECDH(sG, 1/s) == ECDH((1/s)G, s) == ECDH(G, 1) for a few random s. */
+static void test_result_basepoint(void) {
+    secp256k1_pubkey point;
+    secp256k1_scalar rand;
+    unsigned char s[32];
+    unsigned char s_inv[32];
+    unsigned char out[32];
+    unsigned char out_inv[32];
+    unsigned char out_base[32];
+    int i;
+
+    unsigned char s_one[32] = { 0 };
+    s_one[31] = 1;
+    CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_one) == 1);
+    CHECK(secp256k1_ecdh(CTX, out_base, &point, s_one, NULL, NULL) == 1);
+
+    for (i = 0; i < 2 * COUNT; i++) {
+        testutil_random_scalar_order(&rand);
+        secp256k1_scalar_get_b32(s, &rand);
+        secp256k1_scalar_inverse(&rand, &rand);
+        secp256k1_scalar_get_b32(s_inv, &rand);
+
+        CHECK(secp256k1_ec_pubkey_create(CTX, &point, s) == 1);
+        CHECK(secp256k1_ecdh(CTX, out, &point, s_inv, NULL, NULL) == 1);
+        CHECK(secp256k1_memcmp_var(out, out_base, 32) == 0);
+
+        CHECK(secp256k1_ec_pubkey_create(CTX, &point, s_inv) == 1);
+        CHECK(secp256k1_ecdh(CTX, out_inv, &point, s, NULL, NULL) == 1);
+        CHECK(secp256k1_memcmp_var(out_inv, out_base, 32) == 0);
+    }
+}
+
+static void test_ecdh_wycheproof(void) {
+#include "../../wycheproof/ecdh_secp256k1_test.h"
+    int t;
+    for (t = 0; t < SECP256K1_ECDH_WYCHEPROOF_NUMBER_TESTVECTORS; t++) {
+        int parsed_ok;
+        secp256k1_pubkey point;
+        const unsigned char *pk;
+        const unsigned char *sk;
+        const unsigned char *expected_shared_secret;
+        unsigned char output_ecdh[65] = { 0 };
+
+        int expected_result;
+
+        memset(&point, 0, sizeof(point));
+        pk = &wycheproof_ecdh_public_keys[testvectors[t].pk_offset];
+        parsed_ok = secp256k1_ec_pubkey_parse(CTX, &point, pk, testvectors[t].pk_len);
+
+        expected_result = testvectors[t].expected_result;
+        CHECK(parsed_ok == expected_result);
+        if (!parsed_ok) {
+            continue;
+        }
+
+        sk = &wycheproof_ecdh_private_keys[testvectors[t].sk_offset];
+        CHECK(testvectors[t].sk_len == 32);
+
+        CHECK(secp256k1_ecdh(CTX, output_ecdh, &point, sk, ecdh_hash_function_test_xpassthru, NULL) == 1);
+        expected_shared_secret = &wycheproof_ecdh_shared_secrets[testvectors[t].shared_offset];
+
+        CHECK(secp256k1_memcmp_var(output_ecdh, expected_shared_secret, testvectors[t].shared_len) == 0);
+    }
+}
+
+/* --- Test registry --- */
+static const struct tf_test_entry tests_ecdh[] = {
+    CASE1(test_ecdh_api),
+    CASE1(test_ecdh_generator_basepoint),
+    CASE1(test_bad_scalar),
+    CASE1(test_result_basepoint),
+    CASE1(test_ecdh_wycheproof),
+    CASE1(test_ecdh_ctx_sha256),
+};
+
+#endif /* SECP256K1_MODULE_ECDH_TESTS_H */

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ellswift/Makefile.am.include

@@ -0,0 +1,5 @@
+include_HEADERS += include/secp256k1_ellswift.h
+noinst_HEADERS += src/modules/ellswift/bench_impl.h
+noinst_HEADERS += src/modules/ellswift/main_impl.h
+noinst_HEADERS += src/modules/ellswift/tests_impl.h
+noinst_HEADERS += src/modules/ellswift/tests_exhaustive_impl.h

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ellswift/bench_impl.h

@@ -0,0 +1,106 @@
+/***********************************************************************
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_MODULE_ELLSWIFT_BENCH_H
+#define SECP256K1_MODULE_ELLSWIFT_BENCH_H
+
+#include "../../../include/secp256k1_ellswift.h"
+
+typedef struct {
+    secp256k1_context *ctx;
+    secp256k1_pubkey point[256];
+    unsigned char rnd64[64];
+} bench_ellswift_data;
+
+static void bench_ellswift_setup(void *arg) {
+    int i;
+    bench_ellswift_data *data = (bench_ellswift_data*)arg;
+    static const unsigned char init[64] = {
+        0x78, 0x1f, 0xb7, 0xd4, 0x67, 0x7f, 0x08, 0x68,
+        0xdb, 0xe3, 0x1d, 0x7f, 0x1b, 0xb0, 0xf6, 0x9e,
+        0x0a, 0x64, 0xca, 0x32, 0x9e, 0xc6, 0x20, 0x79,
+        0x03, 0xf3, 0xd0, 0x46, 0x7a, 0x0f, 0xd2, 0x21,
+        0xb0, 0x2c, 0x46, 0xd8, 0xba, 0xca, 0x26, 0x4f,
+        0x8f, 0x8c, 0xd4, 0xdd, 0x2d, 0x04, 0xbe, 0x30,
+        0x48, 0x51, 0x1e, 0xd4, 0x16, 0xfd, 0x42, 0x85,
+        0x62, 0xc9, 0x02, 0xf9, 0x89, 0x84, 0xff, 0xdc
+    };
+    memcpy(data->rnd64, init, 64);
+    for (i = 0; i < 256; ++i) {
+        int j;
+        CHECK(secp256k1_ellswift_decode(data->ctx, &data->point[i], data->rnd64));
+        for (j = 0; j < 64; ++j) {
+            data->rnd64[j] += 1;
+        }
+    }
+    CHECK(secp256k1_ellswift_encode(data->ctx, data->rnd64, &data->point[255], init + 16));
+}
+
+static void bench_ellswift_encode(void *arg, int iters) {
+    int i;
+    bench_ellswift_data *data = (bench_ellswift_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        CHECK(secp256k1_ellswift_encode(data->ctx, data->rnd64, &data->point[i & 255], data->rnd64 + 16));
+    }
+}
+
+static void bench_ellswift_create(void *arg, int iters) {
+    int i;
+    bench_ellswift_data *data = (bench_ellswift_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        unsigned char buf[64];
+        CHECK(secp256k1_ellswift_create(data->ctx, buf, data->rnd64, data->rnd64 + 32));
+        memcpy(data->rnd64, buf, 64);
+    }
+}
+
+static void bench_ellswift_decode(void *arg, int iters) {
+    int i;
+    secp256k1_pubkey out;
+    size_t len;
+    bench_ellswift_data *data = (bench_ellswift_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        CHECK(secp256k1_ellswift_decode(data->ctx, &out, data->rnd64) == 1);
+        len = 33;
+        CHECK(secp256k1_ec_pubkey_serialize(data->ctx, data->rnd64 + (i % 32), &len, &out, SECP256K1_EC_COMPRESSED));
+    }
+}
+
+static void bench_ellswift_xdh(void *arg, int iters) {
+    int i;
+    bench_ellswift_data *data = (bench_ellswift_data*)arg;
+
+    for (i = 0; i < iters; i++) {
+        int party = i & 1;
+        CHECK(secp256k1_ellswift_xdh(data->ctx,
+                                     data->rnd64 + (i % 33),
+                                     data->rnd64,
+                                     data->rnd64,
+                                     data->rnd64 + ((i + 16) % 33),
+                                     party,
+                                     secp256k1_ellswift_xdh_hash_function_bip324,
+                                     NULL) == 1);
+    }
+}
+
+void run_ellswift_bench(int iters, int argc, char **argv) {
+    bench_ellswift_data data;
+    int d = argc == 1;
+
+    /* create a context with signing capabilities */
+    data.ctx = secp256k1_context_create(SECP256K1_CONTEXT_NONE);
+
+    if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "encode") || have_flag(argc, argv, "ellswift_encode")) run_benchmark("ellswift_encode", bench_ellswift_encode, bench_ellswift_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "decode") || have_flag(argc, argv, "ellswift_decode")) run_benchmark("ellswift_decode", bench_ellswift_decode, bench_ellswift_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "keygen") || have_flag(argc, argv, "ellswift_keygen")) run_benchmark("ellswift_keygen", bench_ellswift_create, bench_ellswift_setup, NULL, &data, 10, iters);
+    if (d || have_flag(argc, argv, "ellswift") || have_flag(argc, argv, "ecdh") || have_flag(argc, argv, "ellswift_ecdh")) run_benchmark("ellswift_ecdh", bench_ellswift_xdh, bench_ellswift_setup, NULL, &data, 10, iters);
+
+    secp256k1_context_destroy(data.ctx);
+}
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ellswift/main_impl.h

@@ -0,0 +1,581 @@
+/***********************************************************************
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_MODULE_ELLSWIFT_MAIN_H
+#define SECP256K1_MODULE_ELLSWIFT_MAIN_H
+
+#include "../../../include/secp256k1.h"
+#include "../../../include/secp256k1_ellswift.h"
+#include "../../eckey.h"
+#include "../../hash.h"
+
+/** c1 = (sqrt(-3)-1)/2 */
+static const secp256k1_fe secp256k1_ellswift_c1 = SECP256K1_FE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa40);
+/** c2 = (-sqrt(-3)-1)/2 = -(c1+1) */
+static const secp256k1_fe secp256k1_ellswift_c2 = SECP256K1_FE_CONST(0x7ae96a2b, 0x657c0710, 0x6e64479e, 0xac3434e9, 0x9cf04975, 0x12f58995, 0xc1396c28, 0x719501ee);
+/** c3 = (-sqrt(-3)+1)/2 = -c1 = c2+1 */
+static const secp256k1_fe secp256k1_ellswift_c3 = SECP256K1_FE_CONST(0x7ae96a2b, 0x657c0710, 0x6e64479e, 0xac3434e9, 0x9cf04975, 0x12f58995, 0xc1396c28, 0x719501ef);
+/** c4 = (sqrt(-3)+1)/2 = -c2 = c1+1 */
+static const secp256k1_fe secp256k1_ellswift_c4 = SECP256K1_FE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa41);
+
+/** Decode ElligatorSwift encoding (u, t) to a fraction xn/xd representing a curve X coordinate. */
+static void secp256k1_ellswift_xswiftec_frac_var(secp256k1_fe *xn, secp256k1_fe *xd, const secp256k1_fe *u, const secp256k1_fe *t) {
+    /* The implemented algorithm is the following (all operations in GF(p)):
+     *
+     * - Let c0 = sqrt(-3) = 0xa2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f852.
+     * - If u = 0, set u = 1.
+     * - If t = 0, set t = 1.
+     * - If u^3+7+t^2 = 0, set t = 2*t.
+     * - Let X = (u^3+7-t^2)/(2*t).
+     * - Let Y = (X+t)/(c0*u).
+     * - If x3 = u+4*Y^2 is a valid x coordinate, return it.
+     * - If x2 = (-X/Y-u)/2 is a valid x coordinate, return it.
+     * - Return x1 = (X/Y-u)/2 (which is now guaranteed to be a valid x coordinate).
+     *
+     * Introducing s=t^2, g=u^3+7, and simplifying x1=-(x2+u) we get:
+     *
+     * - Let c0 = ...
+     * - If u = 0, set u = 1.
+     * - If t = 0, set t = 1.
+     * - Let s = t^2
+     * - Let g = u^3+7
+     * - If g+s = 0, set t = 2*t, s = 4*s
+     * - Let X = (g-s)/(2*t).
+     * - Let Y = (X+t)/(c0*u) = (g+s)/(2*c0*t*u).
+     * - If x3 = u+4*Y^2 is a valid x coordinate, return it.
+     * - If x2 = (-X/Y-u)/2 is a valid x coordinate, return it.
+     * - Return x1 = -(x2+u).
+     *
+     * Now substitute Y^2 = -(g+s)^2/(12*s*u^2) and X/Y = c0*u*(g-s)/(g+s). This
+     * means X and Y do not need to be evaluated explicitly anymore.
+     *
+     * - ...
+     * - If g+s = 0, set s = 4*s.
+     * - If x3 = u-(g+s)^2/(3*s*u^2) is a valid x coordinate, return it.
+     * - If x2 = (-c0*u*(g-s)/(g+s)-u)/2 is a valid x coordinate, return it.
+     * - Return x1 = -(x2+u).
+     *
+     * Simplifying x2 using 2 additional constants:
+     *
+     * - Let c1 = (c0-1)/2 = 0x851695d49a83f8ef919bb86153cbcb16630fb68aed0a766a3ec693d68e6afa40.
+     * - Let c2 = (-c0-1)/2 = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee.
+     * - ...
+     * - If x2 = u*(c1*s+c2*g)/(g+s) is a valid x coordinate, return it.
+     * - ...
+     *
+     * Writing x3 as a fraction:
+     *
+     * - ...
+     * - If x3 = (3*s*u^3-(g+s)^2)/(3*s*u^2) ...
+     * - ...
+
+     * Overall, we get:
+     *
+     * - Let c1 = 0x851695d49a83f8ef919bb86153cbcb16630fb68aed0a766a3ec693d68e6afa40.
+     * - Let c2 = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee.
+     * - If u = 0, set u = 1.
+     * - If t = 0, set s = 1, else set s = t^2.
+     * - Let g = u^3+7.
+     * - If g+s = 0, set s = 4*s.
+     * - If x3 = (3*s*u^3-(g+s)^2)/(3*s*u^2) is a valid x coordinate, return it.
+     * - If x2 = u*(c1*s+c2*g)/(g+s) is a valid x coordinate, return it.
+     * - Return x1 = -(x2+u).
+     */
+    secp256k1_fe u1, s, g, p, d, n, l;
+    u1 = *u;
+    if (EXPECT(secp256k1_fe_normalizes_to_zero_var(&u1), 0)) u1 = secp256k1_fe_one;
+    secp256k1_fe_sqr(&s, t);
+    if (EXPECT(secp256k1_fe_normalizes_to_zero_var(t), 0)) s = secp256k1_fe_one;
+    secp256k1_fe_sqr(&l, &u1);                                   /* l = u^2 */
+    secp256k1_fe_mul(&g, &l, &u1);                               /* g = u^3 */
+    secp256k1_fe_add_int(&g, SECP256K1_B);                       /* g = u^3 + 7 */
+    p = g;                                                       /* p = g */
+    secp256k1_fe_add(&p, &s);                                    /* p = g+s */
+    if (EXPECT(secp256k1_fe_normalizes_to_zero_var(&p), 0)) {
+        secp256k1_fe_mul_int(&s, 4);
+        /* Recompute p = g+s */
+        p = g;                                                   /* p = g */
+        secp256k1_fe_add(&p, &s);                                /* p = g+s */
+    }
+    secp256k1_fe_mul(&d, &s, &l);                                /* d = s*u^2 */
+    secp256k1_fe_mul_int(&d, 3);                                 /* d = 3*s*u^2 */
+    secp256k1_fe_sqr(&l, &p);                                    /* l = (g+s)^2 */
+    secp256k1_fe_negate(&l, &l, 1);                              /* l = -(g+s)^2 */
+    secp256k1_fe_mul(&n, &d, &u1);                               /* n = 3*s*u^3 */
+    secp256k1_fe_add(&n, &l);                                    /* n = 3*s*u^3-(g+s)^2 */
+    if (secp256k1_ge_x_frac_on_curve_var(&n, &d)) {
+        /* Return x3 = n/d = (3*s*u^3-(g+s)^2)/(3*s*u^2) */
+        *xn = n;
+        *xd = d;
+        return;
+    }
+    *xd = p;
+    secp256k1_fe_mul(&l, &secp256k1_ellswift_c1, &s);            /* l = c1*s */
+    secp256k1_fe_mul(&n, &secp256k1_ellswift_c2, &g);            /* n = c2*g */
+    secp256k1_fe_add(&n, &l);                                    /* n = c1*s+c2*g */
+    secp256k1_fe_mul(&n, &n, &u1);                               /* n = u*(c1*s+c2*g) */
+    /* Possible optimization: in the invocation below, p^2 = (g+s)^2 is computed,
+     * which we already have computed above. This could be deduplicated. */
+    if (secp256k1_ge_x_frac_on_curve_var(&n, &p)) {
+        /* Return x2 = n/p = u*(c1*s+c2*g)/(g+s) */
+        *xn = n;
+        return;
+    }
+    secp256k1_fe_mul(&l, &p, &u1);                               /* l = u*(g+s) */
+    secp256k1_fe_add(&n, &l);                                    /* n = u*(c1*s+c2*g)+u*(g+s) */
+    secp256k1_fe_negate(xn, &n, 2);                              /* n = -u*(c1*s+c2*g)-u*(g+s) */
+
+    VERIFY_CHECK(secp256k1_ge_x_frac_on_curve_var(xn, &p));
+    /* Return x3 = n/p = -(u*(c1*s+c2*g)/(g+s)+u) */
+}
+
+/** Decode ElligatorSwift encoding (u, t) to X coordinate. */
+static void secp256k1_ellswift_xswiftec_var(secp256k1_fe *x, const secp256k1_fe *u, const secp256k1_fe *t) {
+    secp256k1_fe xn, xd;
+    secp256k1_ellswift_xswiftec_frac_var(&xn, &xd, u, t);
+    secp256k1_fe_inv_var(&xd, &xd);
+    secp256k1_fe_mul(x, &xn, &xd);
+}
+
+/** Decode ElligatorSwift encoding (u, t) to point P. */
+static void secp256k1_ellswift_swiftec_var(secp256k1_ge *p, const secp256k1_fe *u, const secp256k1_fe *t) {
+    secp256k1_fe x;
+    secp256k1_ellswift_xswiftec_var(&x, u, t);
+    secp256k1_ge_set_xo_var(p, &x, secp256k1_fe_is_odd(t));
+}
+
+/* Try to complete an ElligatorSwift encoding (u, t) for X coordinate x, given u and x.
+ *
+ * There may be up to 8 distinct t values such that (u, t) decodes back to x, but also
+ * fewer, or none at all. Each such partial inverse can be accessed individually using a
+ * distinct input argument c (in range 0-7), and some or all of these may return failure.
+ * The following guarantees exist:
+ * - Given (x, u), no two distinct c values give the same successful result t.
+ * - Every successful result maps back to x through secp256k1_ellswift_xswiftec_var.
+ * - Given (x, u), all t values that map back to x can be reached by combining the
+ *   successful results from this function over all c values, with the exception of:
+ *   - this function cannot be called with u=0
+ *   - no result with t=0 will be returned
+ *   - no result for which u^3 + t^2 + 7 = 0 will be returned.
+ *
+ * The rather unusual encoding of bits in c (a large "if" based on the middle bit, and then
+ * using the low and high bits to pick signs of square roots) is to match the paper's
+ * encoding more closely: c=0 through c=3 match branches 1..4 in the paper, while c=4 through
+ * c=7 are copies of those with an additional negation of sqrt(w).
+ */
+static int secp256k1_ellswift_xswiftec_inv_var(secp256k1_fe *t, const secp256k1_fe *x_in, const secp256k1_fe *u_in, int c) {
+    /* The implemented algorithm is this (all arithmetic, except involving c, is mod p):
+     *
+     * - If (c & 2) = 0:
+     *   - If (-x-u) is a valid X coordinate, fail.
+     *   - Let s=-(u^3+7)/(u^2+u*x+x^2).
+     *   - If s is not square, fail.
+     *   - Let v=x.
+     * - If (c & 2) = 2:
+     *   - Let s=x-u.
+     *   - If s is not square, fail.
+     *   - Let r=sqrt(-s*(4*(u^3+7)+3*u^2*s)); fail if it doesn't exist.
+     *   - If (c & 1) = 1 and r = 0, fail.
+     *   - If s=0, fail.
+     *   - Let v=(r/s-u)/2.
+     * - Let w=sqrt(s).
+     * - If (c & 5) = 0: return -w*(c3*u + v).
+     * - If (c & 5) = 1: return  w*(c4*u + v).
+     * - If (c & 5) = 4: return  w*(c3*u + v).
+     * - If (c & 5) = 5: return -w*(c4*u + v).
+     */
+    secp256k1_fe x = *x_in, u = *u_in, g, v, s, m, r, q;
+    int ret;
+
+    secp256k1_fe_normalize_weak(&x);
+    secp256k1_fe_normalize_weak(&u);
+
+    VERIFY_CHECK(c >= 0 && c < 8);
+    VERIFY_CHECK(secp256k1_ge_x_on_curve_var(&x));
+
+    if (!(c & 2)) {
+        /* c is in {0, 1, 4, 5}. In this case we look for an inverse under the x1 (if c=0 or
+         * c=4) formula, or x2 (if c=1 or c=5) formula. */
+
+        /* If -u-x is a valid X coordinate, fail. This would yield an encoding that roundtrips
+         * back under the x3 formula instead (which has priority over x1 and x2, so the decoding
+         * would not match x). */
+        m = x;                                          /* m = x */
+        secp256k1_fe_add(&m, &u);                       /* m = u+x */
+        secp256k1_fe_negate(&m, &m, 2);                 /* m = -u-x */
+        /* Test if (-u-x) is a valid X coordinate. If so, fail. */
+        if (secp256k1_ge_x_on_curve_var(&m)) return 0;
+
+        /* Let s = -(u^3 + 7)/(u^2 + u*x + x^2) [first part] */
+        secp256k1_fe_sqr(&s, &m);                       /* s = (u+x)^2 */
+        secp256k1_fe_negate(&s, &s, 1);                 /* s = -(u+x)^2 */
+        secp256k1_fe_mul(&m, &u, &x);                   /* m = u*x */
+        secp256k1_fe_add(&s, &m);                       /* s = -(u^2 + u*x + x^2) */
+
+        /* Note that at this point, s = 0 is impossible. If it were the case:
+         *             s = -(u^2 + u*x + x^2) = 0
+         * =>                 u^2 + u*x + x^2 = 0
+         * =>   (u + 2*x) * (u^2 + u*x + x^2) = 0
+         * => 2*x^3 + 3*x^2*u + 3*x*u^2 + u^3 = 0
+         * =>                 (x + u)^3 + x^3 = 0
+         * =>                             x^3 = -(x + u)^3
+         * =>                         x^3 + B = (-u - x)^3 + B
+         *
+         * However, we know x^3 + B is square (because x is on the curve) and
+         * that (-u-x)^3 + B is not square (the secp256k1_ge_x_on_curve_var(&m)
+         * test above would have failed). This is a contradiction, and thus the
+         * assumption s=0 is false. */
+        VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero_var(&s));
+
+        /* If s is not square, fail. We have not fully computed s yet, but s is square iff
+         * -(u^3+7)*(u^2+u*x+x^2) is square (because a/b is square iff a*b is square and b is
+         * nonzero). */
+        secp256k1_fe_sqr(&g, &u);                       /* g = u^2 */
+        secp256k1_fe_mul(&g, &g, &u);                   /* g = u^3 */
+        secp256k1_fe_add_int(&g, SECP256K1_B);          /* g = u^3+7 */
+        secp256k1_fe_mul(&m, &s, &g);                   /* m = -(u^3 + 7)*(u^2 + u*x + x^2) */
+        if (!secp256k1_fe_is_square_var(&m)) return 0;
+
+        /* Let s = -(u^3 + 7)/(u^2 + u*x + x^2) [second part] */
+        secp256k1_fe_inv_var(&s, &s);                   /* s = -1/(u^2 + u*x + x^2) [no div by 0] */
+        secp256k1_fe_mul(&s, &s, &g);                   /* s = -(u^3 + 7)/(u^2 + u*x + x^2) */
+
+        /* Let v = x. */
+        v = x;
+    } else {
+        /* c is in {2, 3, 6, 7}. In this case we look for an inverse under the x3 formula. */
+
+        /* Let s = x-u. */
+        secp256k1_fe_negate(&m, &u, 1);                 /* m = -u */
+        s = m;                                          /* s = -u */
+        secp256k1_fe_add(&s, &x);                       /* s = x-u */
+
+        /* If s is not square, fail. */
+        if (!secp256k1_fe_is_square_var(&s)) return 0;
+
+        /* Let r = sqrt(-s*(4*(u^3+7)+3*u^2*s)); fail if it doesn't exist. */
+        secp256k1_fe_sqr(&g, &u);                       /* g = u^2 */
+        secp256k1_fe_mul(&q, &s, &g);                   /* q = s*u^2 */
+        secp256k1_fe_mul_int(&q, 3);                    /* q = 3*s*u^2 */
+        secp256k1_fe_mul(&g, &g, &u);                   /* g = u^3 */
+        secp256k1_fe_mul_int(&g, 4);                    /* g = 4*u^3 */
+        secp256k1_fe_add_int(&g, 4 * SECP256K1_B);      /* g = 4*(u^3+7) */
+        secp256k1_fe_add(&q, &g);                       /* q = 4*(u^3+7)+3*s*u^2 */
+        secp256k1_fe_mul(&q, &q, &s);                   /* q = s*(4*(u^3+7)+3*u^2*s) */
+        secp256k1_fe_negate(&q, &q, 1);                 /* q = -s*(4*(u^3+7)+3*u^2*s) */
+        if (!secp256k1_fe_is_square_var(&q)) return 0;
+        ret = secp256k1_fe_sqrt(&r, &q);                /* r = sqrt(-s*(4*(u^3+7)+3*u^2*s)) */
+#ifdef VERIFY
+        VERIFY_CHECK(ret);
+#else
+        (void)ret;
+#endif
+
+        /* If (c & 1) = 1 and r = 0, fail. */
+        if (EXPECT((c & 1) && secp256k1_fe_normalizes_to_zero_var(&r), 0)) return 0;
+
+        /* If s = 0, fail. */
+        if (EXPECT(secp256k1_fe_normalizes_to_zero_var(&s), 0)) return 0;
+
+        /* Let v = (r/s-u)/2. */
+        secp256k1_fe_inv_var(&v, &s);                   /* v = 1/s [no div by 0] */
+        secp256k1_fe_mul(&v, &v, &r);                   /* v = r/s */
+        secp256k1_fe_add(&v, &m);                       /* v = r/s-u */
+        secp256k1_fe_half(&v);                          /* v = (r/s-u)/2 */
+    }
+
+    /* Let w = sqrt(s). */
+    ret = secp256k1_fe_sqrt(&m, &s);                    /* m = sqrt(s) = w */
+    VERIFY_CHECK(ret);
+
+    /* Return logic. */
+    if ((c & 5) == 0 || (c & 5) == 5) {
+        secp256k1_fe_negate(&m, &m, 1);                 /* m = -w */
+    }
+    /* Now m = {-w if c&5=0 or c&5=5; w otherwise}. */
+    secp256k1_fe_mul(&u, &u, c&1 ? &secp256k1_ellswift_c4 : &secp256k1_ellswift_c3);
+    /* u = {c4 if c&1=1; c3 otherwise}*u */
+    secp256k1_fe_add(&u, &v);                           /* u = {c4 if c&1=1; c3 otherwise}*u + v */
+    secp256k1_fe_mul(t, &m, &u);
+    return 1;
+}
+
+/** Use SHA256 as a PRNG, returning SHA256(hasher || cnt).
+ *
+ * hasher is a SHA256 object to which an incrementing 4-byte counter is written to generate randomness.
+ * Writing 13 bytes (4 bytes for counter, plus 9 bytes for the SHA256 padding) cannot cross a
+ * 64-byte block size boundary (to make sure it only triggers a single SHA256 compression). */
+static void secp256k1_ellswift_prng(const secp256k1_hash_ctx *hash_ctx, unsigned char* out32, const secp256k1_sha256 *hasher, uint32_t cnt) {
+    secp256k1_sha256 hash = *hasher;
+    unsigned char buf4[4];
+#ifdef VERIFY
+    size_t blocks = hash.bytes >> 6;
+#endif
+    buf4[0] = cnt;
+    buf4[1] = cnt >> 8;
+    buf4[2] = cnt >> 16;
+    buf4[3] = cnt >> 24;
+    secp256k1_sha256_write(hash_ctx, &hash, buf4, 4);
+    secp256k1_sha256_finalize(hash_ctx, &hash, out32);
+
+    /* Writing and finalizing together should trigger exactly one SHA256 compression. */
+    VERIFY_CHECK(((hash.bytes) >> 6) == (blocks + 1));
+}
+
+/** Find an ElligatorSwift encoding (u, t) for X coordinate x, and random Y coordinate.
+ *
+ * u32 is the 32-byte big endian encoding of u; t is the output field element t that still
+ * needs encoding.
+ *
+ * hasher is a hasher in the secp256k1_ellswift_prng sense, with the same restrictions. */
+static void secp256k1_ellswift_xelligatorswift_var(const secp256k1_context *ctx, unsigned char *u32, secp256k1_fe *t, const secp256k1_fe *x, const secp256k1_sha256 *hasher) {
+    /* Pool of 3-bit branch values. */
+    unsigned char branch_hash[32];
+    /* Number of 3-bit values in branch_hash left. */
+    int branches_left = 0;
+    /* Field elements u and branch values are extracted from RNG based on hasher for consecutive
+     * values of cnt. cnt==0 is first used to populate a pool of 64 4-bit branch values. The 64
+     * cnt values that follow are used to generate field elements u. cnt==65 (and multiples
+     * thereof) are used to repopulate the pool and start over, if that were ever necessary.
+     * On average, 4 iterations are needed. */
+    uint32_t cnt = 0;
+    while (1) {
+        int branch;
+        secp256k1_fe u;
+        /* If the pool of branch values is empty, populate it. */
+        if (branches_left == 0) {
+            secp256k1_ellswift_prng(secp256k1_get_hash_context(ctx), branch_hash, hasher, cnt++);
+            branches_left = 64;
+        }
+        /* Take a 3-bit branch value from the branch pool (top bit is discarded). */
+        --branches_left;
+        branch = (branch_hash[branches_left >> 1] >> ((branches_left & 1) << 2)) & 7;
+        /* Compute a new u value by hashing. */
+        secp256k1_ellswift_prng(secp256k1_get_hash_context(ctx), u32, hasher, cnt++);
+        /* overflow is not a problem (we prefer uniform u32 over uniform u). */
+        secp256k1_fe_set_b32_mod(&u, u32);
+        /* Since u is the output of a hash, it should practically never be 0. We could apply the
+         * u=0 to u=1 correction here too to deal with that case still, but it's such a low
+         * probability event that we do not bother. */
+        VERIFY_CHECK(!secp256k1_fe_normalizes_to_zero_var(&u));
+
+        /* Find a remainder t, and return it if found. */
+        if (EXPECT(secp256k1_ellswift_xswiftec_inv_var(t, x, &u, branch), 0)) break;
+    }
+}
+
+/** Find an ElligatorSwift encoding (u, t) for point P.
+ *
+ * This is similar secp256k1_ellswift_xelligatorswift_var, except it takes a full group element p
+ * as input, and returns an encoding that matches the provided Y coordinate rather than a random
+ * one.
+ */
+static void secp256k1_ellswift_elligatorswift_var(const secp256k1_context *ctx, unsigned char *u32, secp256k1_fe *t, const secp256k1_ge *p, const secp256k1_sha256 *hasher) {
+    secp256k1_ellswift_xelligatorswift_var(ctx, u32, t, &p->x, hasher);
+    secp256k1_fe_normalize_var(t);
+    if (secp256k1_fe_is_odd(t) != secp256k1_fe_is_odd(&p->y)) {
+        secp256k1_fe_negate(t, t, 1);
+        secp256k1_fe_normalize_var(t);
+    }
+}
+
+/** Set hash state to the BIP340 tagged hash midstate for "secp256k1_ellswift_encode". */
+static void secp256k1_ellswift_sha256_init_encode(secp256k1_sha256* hash) {
+    static const uint32_t midstate[8] = {
+        0xd1a6524bul, 0x028594b3ul, 0x96e42f4eul, 0x1037a177ul,
+        0x1b8fcb8bul, 0x56023885ul, 0x2560ede1ul, 0xd626b715ul
+    };
+    secp256k1_sha256_initialize_midstate(hash, 64, midstate);
+}
+
+int secp256k1_ellswift_encode(const secp256k1_context *ctx, unsigned char *ell64, const secp256k1_pubkey *pubkey, const unsigned char *rnd32) {
+    secp256k1_ge p;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(ell64 != NULL);
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(rnd32 != NULL);
+
+    if (secp256k1_pubkey_load(ctx, &p, pubkey)) {
+        secp256k1_fe t;
+        unsigned char p64[64] = {0};
+        secp256k1_sha256 hash;
+
+        /* Set up hasher state; the used RNG is H(pubkey || "\x00"*31 || rnd32 || cnt++), using
+         * BIP340 tagged hash with tag "secp256k1_ellswift_encode". */
+        secp256k1_ellswift_sha256_init_encode(&hash);
+        secp256k1_eckey_pubkey_serialize33(&p, p64);
+        secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, p64, sizeof(p64));
+        secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, rnd32, 32);
+
+        /* Compute ElligatorSwift encoding and construct output. */
+        secp256k1_ellswift_elligatorswift_var(ctx, ell64, &t, &p, &hash); /* puts u in ell64[0..32] */
+        secp256k1_fe_get_b32(ell64 + 32, &t); /* puts t in ell64[32..64] */
+        return 1;
+    }
+    /* Only reached in case the provided pubkey is invalid. */
+    memset(ell64, 0, 64);
+    return 0;
+}
+
+/** Set hash state to the BIP340 tagged hash midstate for "secp256k1_ellswift_create". */
+static void secp256k1_ellswift_sha256_init_create(secp256k1_sha256* hash) {
+    static const uint32_t midstate[8] = {
+        0xd29e1bf5ul, 0xf7025f42ul, 0x9b024773ul, 0x094cb7d5ul,
+        0xe59ed789ul, 0x03bc9786ul, 0x68335b35ul, 0x4e363b53ul
+    };
+    secp256k1_sha256_initialize_midstate(hash, 64, midstate);
+}
+
+int secp256k1_ellswift_create(const secp256k1_context *ctx, unsigned char *ell64, const unsigned char *seckey32, const unsigned char *auxrnd32) {
+    secp256k1_ge p;
+    secp256k1_fe t;
+    secp256k1_sha256 hash;
+    secp256k1_scalar seckey_scalar;
+    int ret;
+    static const unsigned char zero32[32] = {0};
+
+    /* Sanity check inputs. */
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(ell64 != NULL);
+    memset(ell64, 0, 64);
+    ARG_CHECK(secp256k1_ecmult_gen_context_is_built(&ctx->ecmult_gen_ctx));
+    ARG_CHECK(seckey32 != NULL);
+
+    /* Compute (affine) public key */
+    ret = secp256k1_ec_pubkey_create_helper(&ctx->ecmult_gen_ctx, &seckey_scalar, &p, seckey32);
+    secp256k1_declassify(ctx, &p, sizeof(p)); /* not constant time in produced pubkey */
+    secp256k1_fe_normalize_var(&p.x);
+    secp256k1_fe_normalize_var(&p.y);
+
+    /* Set up hasher state. The used RNG is H(privkey || "\x00"*32 [|| auxrnd32] || cnt++),
+     * using BIP340 tagged hash with tag "secp256k1_ellswift_create". */
+    secp256k1_ellswift_sha256_init_create(&hash);
+    secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, seckey32, 32);
+    secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, zero32, sizeof(zero32));
+    secp256k1_declassify(ctx, &hash, sizeof(hash)); /* private key is hashed now */
+    if (auxrnd32) secp256k1_sha256_write(secp256k1_get_hash_context(ctx), &hash, auxrnd32, 32);
+
+    /* Compute ElligatorSwift encoding and construct output. */
+    secp256k1_ellswift_elligatorswift_var(ctx, ell64, &t, &p, &hash); /* puts u in ell64[0..32] */
+    secp256k1_fe_get_b32(ell64 + 32, &t); /* puts t in ell64[32..64] */
+
+    secp256k1_memczero(ell64, 64, !ret);
+    secp256k1_scalar_clear(&seckey_scalar);
+
+    return ret;
+}
+
+int secp256k1_ellswift_decode(const secp256k1_context *ctx, secp256k1_pubkey *pubkey, const unsigned char *ell64) {
+    secp256k1_fe u, t;
+    secp256k1_ge p;
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(pubkey != NULL);
+    ARG_CHECK(ell64 != NULL);
+
+    secp256k1_fe_set_b32_mod(&u, ell64);
+    secp256k1_fe_set_b32_mod(&t, ell64 + 32);
+    secp256k1_fe_normalize_var(&t);
+    secp256k1_ellswift_swiftec_var(&p, &u, &t);
+    secp256k1_pubkey_save(pubkey, &p);
+    return 1;
+}
+
+static int ellswift_xdh_hash_function_prefix_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+    secp256k1_sha256 sha;
+
+    secp256k1_sha256_initialize(&sha);
+    secp256k1_sha256_write(hash_ctx, &sha, data, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_a64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_b64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, x32, 32);
+    secp256k1_sha256_finalize(hash_ctx, &sha, output);
+    secp256k1_sha256_clear(&sha);
+
+    return 1;
+}
+
+static int ellswift_xdh_hash_function_prefix(unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+    return ellswift_xdh_hash_function_prefix_impl(secp256k1_get_hash_context(secp256k1_context_static), output, x32, ell_a64, ell_b64, data);
+}
+
+/** Set hash state to the BIP340 tagged hash midstate for "bip324_ellswift_xonly_ecdh". */
+static void secp256k1_ellswift_sha256_init_bip324(secp256k1_sha256* hash) {
+    static const uint32_t midstate[8] = {
+        0x8c12d730ul, 0x827bd392ul, 0x9e4fb2eeul, 0x207b373eul,
+        0x2292bd7aul, 0xaa5441bcul, 0x15c3779ful, 0xcfb52549ul
+    };
+    secp256k1_sha256_initialize_midstate(hash, 64, midstate);
+}
+
+static int ellswift_xdh_hash_function_bip324_impl(const secp256k1_hash_ctx *hash_ctx, unsigned char* output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+    secp256k1_sha256 sha;
+
+    (void)data;
+
+    secp256k1_ellswift_sha256_init_bip324(&sha);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_a64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, ell_b64, 64);
+    secp256k1_sha256_write(hash_ctx, &sha, x32, 32);
+    secp256k1_sha256_finalize(hash_ctx, &sha, output);
+    secp256k1_sha256_clear(&sha);
+
+    return 1;
+}
+
+static int ellswift_xdh_hash_function_bip324(unsigned char* output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+    return ellswift_xdh_hash_function_bip324_impl(secp256k1_get_hash_context(secp256k1_context_static), output, x32, ell_a64, ell_b64, data);
+}
+
+const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_prefix = ellswift_xdh_hash_function_prefix;
+const secp256k1_ellswift_xdh_hash_function secp256k1_ellswift_xdh_hash_function_bip324 = ellswift_xdh_hash_function_bip324;
+
+int secp256k1_ellswift_xdh(const secp256k1_context *ctx, unsigned char *output, const unsigned char *ell_a64, const unsigned char *ell_b64, const unsigned char *seckey32, int party, secp256k1_ellswift_xdh_hash_function hashfp, void *data) {
+    int ret = 0;
+    int overflow;
+    secp256k1_scalar s;
+    secp256k1_fe xn, xd, px, u, t;
+    unsigned char sx[32];
+    const unsigned char* theirs64;
+
+    VERIFY_CHECK(ctx != NULL);
+    ARG_CHECK(output != NULL);
+    ARG_CHECK(ell_a64 != NULL);
+    ARG_CHECK(ell_b64 != NULL);
+    ARG_CHECK(seckey32 != NULL);
+    ARG_CHECK(hashfp != NULL);
+
+    /* Load remote public key (as fraction). */
+    theirs64 = party ? ell_a64 : ell_b64;
+    secp256k1_fe_set_b32_mod(&u, theirs64);
+    secp256k1_fe_set_b32_mod(&t, theirs64 + 32);
+    secp256k1_ellswift_xswiftec_frac_var(&xn, &xd, &u, &t);
+
+    /* Load private key (using one if invalid). */
+    secp256k1_scalar_set_b32(&s, seckey32, &overflow);
+    overflow |= secp256k1_scalar_is_zero(&s);
+    secp256k1_scalar_cmov(&s, &secp256k1_scalar_one, overflow);
+
+    /* Compute shared X coordinate. */
+    secp256k1_ecmult_const_xonly(&px, &xn, &xd, &s, 1);
+    secp256k1_fe_normalize(&px);
+    secp256k1_fe_get_b32(sx, &px);
+
+    /* Invoke hasher. Use ctx-aware function by default */
+    if (hashfp == secp256k1_ellswift_xdh_hash_function_bip324) {
+        ret = ellswift_xdh_hash_function_bip324_impl(secp256k1_get_hash_context(ctx), output, sx, ell_a64, ell_b64, data);
+    } else if (hashfp == secp256k1_ellswift_xdh_hash_function_prefix) {
+        ret = ellswift_xdh_hash_function_prefix_impl(secp256k1_get_hash_context(ctx), output, sx, ell_a64, ell_b64, data);
+    } else {
+        ret = hashfp(output, sx, ell_a64, ell_b64, data);
+    }
+
+    secp256k1_memclear_explicit(sx, sizeof(sx));
+    secp256k1_fe_clear(&px);
+    secp256k1_scalar_clear(&s);
+
+    return !!ret & !overflow;
+}
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ellswift/tests_exhaustive_impl.h

@@ -0,0 +1,39 @@
+/***********************************************************************
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_MODULE_ELLSWIFT_TESTS_EXHAUSTIVE_H
+#define SECP256K1_MODULE_ELLSWIFT_TESTS_EXHAUSTIVE_H
+
+#include "../../../include/secp256k1_ellswift.h"
+#include "main_impl.h"
+
+static void test_exhaustive_ellswift(const secp256k1_context *ctx, const secp256k1_ge *group) {
+    int i;
+
+    /* Note that SwiftEC/ElligatorSwift are inherently curve operations, not
+     * group operations, and this test only checks the curve points which are in
+     * a tiny subgroup. In that sense it can't be really seen as exhaustive as
+     * it doesn't (and for computational reasons obviously cannot) test the
+     * entire domain ellswift operates under. */
+    for (i = 1; i < EXHAUSTIVE_TEST_ORDER; i++) {
+        secp256k1_scalar scalar_i;
+        unsigned char sec32[32];
+        unsigned char ell64[64];
+        secp256k1_pubkey pub_decoded;
+        secp256k1_ge ge_decoded;
+
+        /* Construct ellswift pubkey from exhaustive loop scalar i. */
+        secp256k1_scalar_set_int(&scalar_i, i);
+        secp256k1_scalar_get_b32(sec32, &scalar_i);
+        CHECK(secp256k1_ellswift_create(ctx, ell64, sec32, NULL));
+
+        /* Decode ellswift pubkey and check that it matches the precomputed group element. */
+        secp256k1_ellswift_decode(ctx, &pub_decoded, ell64);
+        secp256k1_pubkey_load(ctx, &ge_decoded, &pub_decoded);
+        CHECK(secp256k1_ge_eq_var(&ge_decoded, &group[i]));
+    }
+}
+
+#endif

firmware/kb2040_hidden_signer/src/secp256k1/src/modules/ellswift/tests_impl.h

@@ -0,0 +1,544 @@
+/***********************************************************************
+ * Distributed under the MIT software license, see the accompanying    *
+ * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
+ ***********************************************************************/
+
+#ifndef SECP256K1_MODULE_ELLSWIFT_TESTS_H
+#define SECP256K1_MODULE_ELLSWIFT_TESTS_H
+
+#include "../../../include/secp256k1_ellswift.h"
+#include "../../unit_test.h"
+#include "../../util.h"
+
+struct ellswift_xswiftec_inv_test {
+    int enc_bitmap;
+    secp256k1_fe u;
+    secp256k1_fe x;
+    secp256k1_fe encs[8];
+};
+
+struct ellswift_decode_test {
+    unsigned char enc[64];
+    secp256k1_fe x;
+    int odd_y;
+};
+
+struct ellswift_xdh_test {
+    unsigned char priv_ours[32];
+    unsigned char ellswift_ours[64];
+    unsigned char ellswift_theirs[64];
+    int initiating;
+    unsigned char shared_secret[32];
+};
+
+/* Set of (point, encodings) test vectors, selected to maximize branch coverage, part of the BIP324
+ * test vectors. Created using an independent implementation, and tested decoding against paper
+ * authors' code. */
+static const struct ellswift_xswiftec_inv_test ellswift_xswiftec_inv_tests[] = {
+    {0xcc, SECP256K1_FE_CONST(0x05ff6bda, 0xd900fc32, 0x61bc7fe3, 0x4e2fb0f5, 0x69f06e09, 0x1ae437d3, 0xa52e9da0, 0xcbfb9590), SECP256K1_FE_CONST(0x80cdf637, 0x74ec7022, 0xc89a5a85, 0x58e373a2, 0x79170285, 0xe0ab2741, 0x2dbce510, 0xbdfe23fc), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x45654798, 0xece071ba, 0x79286d04, 0xf7f3eb1c, 0x3f1d17dd, 0x883610f2, 0xad2efd82, 0xa287466b), SECP256K1_FE_CONST(0x0aeaa886, 0xf6b76c71, 0x58452418, 0xcbf5033a, 0xdc5747e9, 0xe9b5d3b2, 0x303db969, 0x36528557), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xba9ab867, 0x131f8e45, 0x86d792fb, 0x080c14e3, 0xc0e2e822, 0x77c9ef0d, 0x52d1027c, 0x5d78b5c4), SECP256K1_FE_CONST(0xf5155779, 0x0948938e, 0xa7badbe7, 0x340afcc5, 0x23a8b816, 0x164a2c4d, 0xcfc24695, 0xc9ad76d8)}},
+    {0x33, SECP256K1_FE_CONST(0x1737a85f, 0x4c8d146c, 0xec96e3ff, 0xdca76d99, 0x03dcf3bd, 0x53061868, 0xd478c78c, 0x63c2aa9e), SECP256K1_FE_CONST(0x39e48dd1, 0x50d2f429, 0xbe088dfd, 0x5b61882e, 0x7e840748, 0x3702ae9a, 0x5ab35927, 0xb15f85ea), {SECP256K1_FE_CONST(0x1be8cc0b, 0x04be0c68, 0x1d0c6a68, 0xf733f82c, 0x6c896e0c, 0x8a262fcd, 0x392918e3, 0x03a7abf4), SECP256K1_FE_CONST(0x605b5814, 0xbf9b8cb0, 0x66667c9e, 0x5480d22d, 0xc5b6c92f, 0x14b4af3e, 0xe0a9eb83, 0xb03685e3), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xe41733f4, 0xfb41f397, 0xe2f39597, 0x08cc07d3, 0x937691f3, 0x75d9d032, 0xc6d6e71b, 0xfc58503b), SECP256K1_FE_CONST(0x9fa4a7eb, 0x4064734f, 0x99998361, 0xab7f2dd2, 0x3a4936d0, 0xeb4b50c1, 0x1f56147b, 0x4fc9764c), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x00, SECP256K1_FE_CONST(0x1aaa1cce, 0xbf9c7241, 0x91033df3, 0x66b36f69, 0x1c4d902c, 0x228033ff, 0x4516d122, 0xb2564f68), SECP256K1_FE_CONST(0xc7554125, 0x9d3ba98f, 0x207eaa30, 0xc69634d1, 0x87d0b6da, 0x594e719e, 0x420f4898, 0x638fc5b0), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x33, SECP256K1_FE_CONST(0x2323a1d0, 0x79b0fd72, 0xfc8bb62e, 0xc34230a8, 0x15cb0596, 0xc2bfac99, 0x8bd6b842, 0x60f5dc26), SECP256K1_FE_CONST(0x239342df, 0xb675500a, 0x34a19631, 0x0b8d87d5, 0x4f49dcac, 0x9da50c17, 0x43ceab41, 0xa7b249ff), {SECP256K1_FE_CONST(0xf63580b8, 0xaa49c484, 0x6de56e39, 0xe1b3e73f, 0x171e881e, 0xba8c66f6, 0x14e67e5c, 0x975dfc07), SECP256K1_FE_CONST(0xb6307b33, 0x2e699f1c, 0xf77841d9, 0x0af25365, 0x404deb7f, 0xed5edb30, 0x90db49e6, 0x42a156b6), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x09ca7f47, 0x55b63b7b, 0x921a91c6, 0x1e4c18c0, 0xe8e177e1, 0x45739909, 0xeb1981a2, 0x68a20028), SECP256K1_FE_CONST(0x49cf84cc, 0xd19660e3, 0x0887be26, 0xf50dac9a, 0xbfb21480, 0x12a124cf, 0x6f24b618, 0xbd5ea579), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x33, SECP256K1_FE_CONST(0x2dc90e64, 0x0cb646ae, 0x9164c0b5, 0xa9ef0169, 0xfebe34dc, 0x4437d6e4, 0x6acb0e27, 0xe219d1e8), SECP256K1_FE_CONST(0xd236f19b, 0xf349b951, 0x6e9b3f4a, 0x5610fe96, 0x0141cb23, 0xbbc8291b, 0x9534f1d7, 0x1de62a47), {SECP256K1_FE_CONST(0xe69df7d9, 0xc026c366, 0x00ebdf58, 0x80726758, 0x47c0c431, 0xc8eb7306, 0x82533e96, 0x4b6252c9), SECP256K1_FE_CONST(0x4f18bbdf, 0x7c2d6c5f, 0x818c1880, 0x2fa35cd0, 0x69eaa79f, 0xff74e4fc, 0x837c80d9, 0x3fece2f8), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x19620826, 0x3fd93c99, 0xff1420a7, 0x7f8d98a7, 0xb83f3bce, 0x37148cf9, 0x7dacc168, 0xb49da966), SECP256K1_FE_CONST(0xb0e74420, 0x83d293a0, 0x7e73e77f, 0xd05ca32f, 0x96155860, 0x008b1b03, 0x7c837f25, 0xc0131937), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0xcc, SECP256K1_FE_CONST(0x3edd7b39, 0x80e2f2f3, 0x4d1409a2, 0x07069f88, 0x1fda5f96, 0xf08027ac, 0x4465b63d, 0xc278d672), SECP256K1_FE_CONST(0x053a98de, 0x4a27b196, 0x1155822b, 0x3a3121f0, 0x3b2a1445, 0x8bd80eb4, 0xa560c4c7, 0xa85c149c), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xb3dae4b7, 0xdcf858e4, 0xc6968057, 0xcef2b156, 0x46543152, 0x6538199c, 0xf52dc1b2, 0xd62fda30), SECP256K1_FE_CONST(0x4aa77dd5, 0x5d6b6d3c, 0xfa10cc9d, 0x0fe42f79, 0x232e4575, 0x661049ae, 0x36779c1d, 0x0c666d88), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x4c251b48, 0x2307a71b, 0x39697fa8, 0x310d4ea9, 0xb9abcead, 0x9ac7e663, 0x0ad23e4c, 0x29d021ff), SECP256K1_FE_CONST(0xb558822a, 0xa29492c3, 0x05ef3362, 0xf01bd086, 0xdcd1ba8a, 0x99efb651, 0xc98863e1, 0xf3998ea7)}},
+    {0x00, SECP256K1_FE_CONST(0x4295737e, 0xfcb1da6f, 0xb1d96b9c, 0xa7dcd1e3, 0x20024b37, 0xa736c494, 0x8b625981, 0x73069f70), SECP256K1_FE_CONST(0xfa7ffe4f, 0x25f88362, 0x831c087a, 0xfe2e8a9b, 0x0713e2ca, 0xc1ddca6a, 0x383205a2, 0x66f14307), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0xff, SECP256K1_FE_CONST(0x587c1a0c, 0xee91939e, 0x7f784d23, 0xb963004a, 0x3bf44f5d, 0x4e32a008, 0x1995ba20, 0xb0fca59e), SECP256K1_FE_CONST(0x2ea98853, 0x0715e8d1, 0x0363907f, 0xf2512452, 0x4d471ba2, 0x454d5ce3, 0xbe3f0419, 0x4dfd3a3c), {SECP256K1_FE_CONST(0xcfd5a094, 0xaa0b9b88, 0x91b76c6a, 0xb9438f66, 0xaa1c095a, 0x65f9f701, 0x35e81712, 0x92245e74), SECP256K1_FE_CONST(0xa89057d7, 0xc6563f0d, 0x6efa19ae, 0x84412b8a, 0x7b47e791, 0xa191ecdf, 0xdf2af84f, 0xd97bc339), SECP256K1_FE_CONST(0x475d0ae9, 0xef46920d, 0xf07b3411, 0x7be5a081, 0x7de1023e, 0x3cc32689, 0xe9be145b, 0x406b0aef), SECP256K1_FE_CONST(0xa0759178, 0xad802324, 0x54f827ef, 0x05ea3e72, 0xad8d7541, 0x8e6d4cc1, 0xcd4f5306, 0xc5e7c453), SECP256K1_FE_CONST(0x302a5f6b, 0x55f46477, 0x6e489395, 0x46bc7099, 0x55e3f6a5, 0x9a0608fe, 0xca17e8ec, 0x6ddb9dbb), SECP256K1_FE_CONST(0x576fa828, 0x39a9c0f2, 0x9105e651, 0x7bbed475, 0x84b8186e, 0x5e6e1320, 0x20d507af, 0x268438f6), SECP256K1_FE_CONST(0xb8a2f516, 0x10b96df2, 0x0f84cbee, 0x841a5f7e, 0x821efdc1, 0xc33cd976, 0x1641eba3, 0xbf94f140), SECP256K1_FE_CONST(0x5f8a6e87, 0x527fdcdb, 0xab07d810, 0xfa15c18d, 0x52728abe, 0x7192b33e, 0x32b0acf8, 0x3a1837dc)}},
+    {0xcc, SECP256K1_FE_CONST(0x5fa88b33, 0x65a635cb, 0xbcee003c, 0xce9ef51d, 0xd1a310de, 0x277e441a, 0xbccdb7be, 0x1e4ba249), SECP256K1_FE_CONST(0x79461ff6, 0x2bfcbcac, 0x4249ba84, 0xdd040f2c, 0xec3c63f7, 0x25204dc7, 0xf464c16b, 0xf0ff3170), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x6bb700e1, 0xf4d7e236, 0xe8d193ff, 0x4a76c1b3, 0xbcd4e2b2, 0x5acac3d5, 0x1c8dac65, 0x3fe909a0), SECP256K1_FE_CONST(0xf4c73410, 0x633da7f6, 0x3a4f1d55, 0xaec6dd32, 0xc4c6d89e, 0xe74075ed, 0xb5515ed9, 0x0da9e683), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x9448ff1e, 0x0b281dc9, 0x172e6c00, 0xb5893e4c, 0x432b1d4d, 0xa5353c2a, 0xe3725399, 0xc016f28f), SECP256K1_FE_CONST(0x0b38cbef, 0x9cc25809, 0xc5b0e2aa, 0x513922cd, 0x3b392761, 0x18bf8a12, 0x4aaea125, 0xf25615ac)}},
+    {0xcc, SECP256K1_FE_CONST(0x6fb31c75, 0x31f03130, 0xb42b155b, 0x952779ef, 0xbb46087d, 0xd9807d24, 0x1a48eac6, 0x3c3d96d6), SECP256K1_FE_CONST(0x56f81be7, 0x53e8d4ae, 0x4940ea6f, 0x46f6ec9f, 0xda66a6f9, 0x6cc95f50, 0x6cb2b574, 0x90e94260), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x59059774, 0x795bdb7a, 0x837fbe11, 0x40a5fa59, 0x984f48af, 0x8df95d57, 0xdd6d1c05, 0x437dcec1), SECP256K1_FE_CONST(0x22a644db, 0x79376ad4, 0xe7b3a009, 0xe58b3f13, 0x137c54fd, 0xf911122c, 0xc93667c4, 0x7077d784), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xa6fa688b, 0x86a42485, 0x7c8041ee, 0xbf5a05a6, 0x67b0b750, 0x7206a2a8, 0x2292e3f9, 0xbc822d6e), SECP256K1_FE_CONST(0xdd59bb24, 0x86c8952b, 0x184c5ff6, 0x1a74c0ec, 0xec83ab02, 0x06eeedd3, 0x36c9983a, 0x8f8824ab)}},
+    {0x00, SECP256K1_FE_CONST(0x704cd226, 0xe71cb682, 0x6a590e80, 0xdac90f2d, 0x2f5830f0, 0xfdf135a3, 0xeae3965b, 0xff25ff12), SECP256K1_FE_CONST(0x138e0afa, 0x68936ee6, 0x70bd2b8d, 0xb53aedbb, 0x7bea2a85, 0x97388b24, 0xd0518edd, 0x22ad66ec), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x33, SECP256K1_FE_CONST(0x725e9147, 0x92cb8c89, 0x49e7e116, 0x8b7cdd8a, 0x8094c91c, 0x6ec2202c, 0xcd53a6a1, 0x8771edeb), SECP256K1_FE_CONST(0x8da16eb8, 0x6d347376, 0xb6181ee9, 0x74832275, 0x7f6b36e3, 0x913ddfd3, 0x32ac595d, 0x788e0e44), {SECP256K1_FE_CONST(0xdd357786, 0xb9f68733, 0x30391aa5, 0x62580965, 0x4e43116e, 0x82a5a5d8, 0x2ffd1d66, 0x24101fc4), SECP256K1_FE_CONST(0xa0b7efca, 0x01814594, 0xc59c9aae, 0x8e497001, 0x86ca5d95, 0xe88bcc80, 0x399044d9, 0xc2d8613d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x22ca8879, 0x460978cc, 0xcfc6e55a, 0x9da7f69a, 0xb1bcee91, 0x7d5a5a27, 0xd002e298, 0xdbefdc6b), SECP256K1_FE_CONST(0x5f481035, 0xfe7eba6b, 0x3a636551, 0x71b68ffe, 0x7935a26a, 0x1774337f, 0xc66fbb25, 0x3d279af2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x00, SECP256K1_FE_CONST(0x78fe6b71, 0x7f2ea4a3, 0x2708d79c, 0x151bf503, 0xa5312a18, 0xc0963437, 0xe865cc6e, 0xd3f6ae97), SECP256K1_FE_CONST(0x8701948e, 0x80d15b5c, 0xd8f72863, 0xeae40afc, 0x5aced5e7, 0x3f69cbc8, 0x179a3390, 0x2c094d98), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x44, SECP256K1_FE_CONST(0x7c37bb9c, 0x5061dc07, 0x413f11ac, 0xd5a34006, 0xe64c5c45, 0x7fdb9a43, 0x8f217255, 0xa961f50d), SECP256K1_FE_CONST(0x5c1a76b4, 0x4568eb59, 0xd6789a74, 0x42d9ed7c, 0xdc6226b7, 0x752b4ff8, 0xeaf8e1a9, 0x5736e507), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xb94d30cd, 0x7dbff60b, 0x64620c17, 0xca0fafaa, 0x40b3d1f5, 0x2d077a60, 0xa2e0cafd, 0x145086c2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x46b2cf32, 0x824009f4, 0x9b9df3e8, 0x35f05055, 0xbf4c2e0a, 0xd2f8859f, 0x5d1f3501, 0xebaf756d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x00, SECP256K1_FE_CONST(0x82388888, 0x967f82a6, 0xb444438a, 0x7d44838e, 0x13c0d478, 0xb9ca060d, 0xa95a41fb, 0x94303de6), SECP256K1_FE_CONST(0x29e96541, 0x70628fec, 0x8b497289, 0x8b113cf9, 0x8807f460, 0x9274f4f3, 0x140d0674, 0x157c90a0), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x33, SECP256K1_FE_CONST(0x91298f57, 0x70af7a27, 0xf0a47188, 0xd24c3b7b, 0xf98ab299, 0x0d84b0b8, 0x98507e3c, 0x561d6472), SECP256K1_FE_CONST(0x144f4ccb, 0xd9a74698, 0xa88cbf6f, 0xd00ad886, 0xd339d29e, 0xa19448f2, 0xc572cac0, 0xa07d5562), {SECP256K1_FE_CONST(0xe6a0ffa3, 0x807f09da, 0xdbe71e0f, 0x4be4725f, 0x2832e76c, 0xad8dc1d9, 0x43ce8393, 0x75eff248), SECP256K1_FE_CONST(0x837b8e68, 0xd4917544, 0x764ad090, 0x3cb11f86, 0x15d2823c, 0xefbb06d8, 0x9049dbab, 0xc69befda), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x195f005c, 0x7f80f625, 0x2418e1f0, 0xb41b8da0, 0xd7cd1893, 0x52723e26, 0xbc317c6b, 0x8a1009e7), SECP256K1_FE_CONST(0x7c847197, 0x2b6e8abb, 0x89b52f6f, 0xc34ee079, 0xea2d7dc3, 0x1044f927, 0x6fb62453, 0x39640c55), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x00, SECP256K1_FE_CONST(0xb682f3d0, 0x3bbb5dee, 0x4f54b5eb, 0xfba931b4, 0xf52f6a19, 0x1e5c2f48, 0x3c73c66e, 0x9ace97e1), SECP256K1_FE_CONST(0x904717bf, 0x0bc0cb78, 0x73fcdc38, 0xaa97f19e, 0x3a626309, 0x72acff92, 0xb24cc6dd, 0xa197cb96), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x77, SECP256K1_FE_CONST(0xc17ec69e, 0x665f0fb0, 0xdbab48d9, 0xc2f94d12, 0xec8a9d7e, 0xacb58084, 0x83309180, 0x1eb0b80b), SECP256K1_FE_CONST(0x147756e6, 0x6d96e31c, 0x426d3cc8, 0x5ed0c4cf, 0xbef6341d, 0xd8b28558, 0x5aa574ea, 0x0204b55e), {SECP256K1_FE_CONST(0x6f4aea43, 0x1a0043bd, 0xd03134d6, 0xd9159119, 0xce034b88, 0xc32e50e8, 0xe36c4ee4, 0x5eac7ae9), SECP256K1_FE_CONST(0xfd5be16d, 0x4ffa2690, 0x126c67c3, 0xef7cb9d2, 0x9b74d397, 0xc78b06b3, 0x605fda34, 0xdc9696a6), SECP256K1_FE_CONST(0x5e9c6079, 0x2a2f000e, 0x45c6250f, 0x296f875e, 0x174efc0e, 0x9703e628, 0x706103a9, 0xdd2d82c7), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x90b515bc, 0xe5ffbc42, 0x2fcecb29, 0x26ea6ee6, 0x31fcb477, 0x3cd1af17, 0x1c93b11a, 0xa1538146), SECP256K1_FE_CONST(0x02a41e92, 0xb005d96f, 0xed93983c, 0x1083462d, 0x648b2c68, 0x3874f94c, 0x9fa025ca, 0x23696589), SECP256K1_FE_CONST(0xa1639f86, 0xd5d0fff1, 0xba39daf0, 0xd69078a1, 0xe8b103f1, 0x68fc19d7, 0x8f9efc55, 0x22d27968), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0xcc, SECP256K1_FE_CONST(0xc25172fc, 0x3f29b6fc, 0x4a1155b8, 0x57523315, 0x5486b274, 0x64b74b8b, 0x260b499a, 0x3f53cb14), SECP256K1_FE_CONST(0x1ea9cbdb, 0x35cf6e03, 0x29aa31b0, 0xbb0a702a, 0x65123ed0, 0x08655a93, 0xb7dcd528, 0x0e52e1ab), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x7422edc7, 0x843136af, 0x0053bb88, 0x54448a82, 0x99994f9d, 0xdcefd3a9, 0xa92d4546, 0x2c59298a), SECP256K1_FE_CONST(0x78c7774a, 0x266f8b97, 0xea23d05d, 0x064f033c, 0x77319f92, 0x3f6b78bc, 0xe4e20bf0, 0x5fa5398d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x8bdd1238, 0x7bcec950, 0xffac4477, 0xabbb757d, 0x6666b062, 0x23102c56, 0x56d2bab8, 0xd3a6d2a5), SECP256K1_FE_CONST(0x873888b5, 0xd9907468, 0x15dc2fa2, 0xf9b0fcc3, 0x88ce606d, 0xc0948743, 0x1b1df40e, 0xa05ac2a2)}},
+    {0x00, SECP256K1_FE_CONST(0xcab6626f, 0x832a4b12, 0x80ba7add, 0x2fc5322f, 0xf011caed, 0xedf7ff4d, 0xb6735d50, 0x26dc0367), SECP256K1_FE_CONST(0x2b2bef08, 0x52c6f7c9, 0x5d72ac99, 0xa23802b8, 0x75029cd5, 0x73b248d1, 0xf1b3fc80, 0x33788eb6), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x33, SECP256K1_FE_CONST(0xd8621b4f, 0xfc85b9ed, 0x56e99d8d, 0xd1dd24ae, 0xdcecb147, 0x63b861a1, 0x7112dc77, 0x1a104fd2), SECP256K1_FE_CONST(0x812cabe9, 0x72a22aa6, 0x7c7da0c9, 0x4d8a9362, 0x96eb9949, 0xd70c37cb, 0x2b248757, 0x4cb3ce58), {SECP256K1_FE_CONST(0xfbc5febc, 0x6fdbc9ae, 0x3eb88a93, 0xb982196e, 0x8b6275a6, 0xd5a73c17, 0x387e000c, 0x711bd0e3), SECP256K1_FE_CONST(0x8724c96b, 0xd4e5527f, 0x2dd195a5, 0x1c468d2d, 0x211ba2fa, 0xc7cbe0b4, 0xb3434253, 0x409fb42d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x043a0143, 0x90243651, 0xc147756c, 0x467de691, 0x749d8a59, 0x2a58c3e8, 0xc781fff2, 0x8ee42b4c), SECP256K1_FE_CONST(0x78db3694, 0x2b1aad80, 0xd22e6a5a, 0xe3b972d2, 0xdee45d05, 0x38341f4b, 0x4cbcbdab, 0xbf604802), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x00, SECP256K1_FE_CONST(0xda463164, 0xc6f4bf71, 0x29ee5f0e, 0xc00f65a6, 0x75a8adf1, 0xbd931b39, 0xb64806af, 0xdcda9a22), SECP256K1_FE_CONST(0x25b9ce9b, 0x390b408e, 0xd611a0f1, 0x3ff09a59, 0x8a57520e, 0x426ce4c6, 0x49b7f94f, 0x2325620d), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0xcc, SECP256K1_FE_CONST(0xdafc971e, 0x4a3a7b6d, 0xcfb42a08, 0xd9692d82, 0xad9e7838, 0x523fcbda, 0x1d4827e1, 0x4481ae2d), SECP256K1_FE_CONST(0x250368e1, 0xb5c58492, 0x304bd5f7, 0x2696d27d, 0x526187c7, 0xadc03425, 0xe2b7d81d, 0xbb7e4e02), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x370c28f1, 0xbe665efa, 0xcde6aa43, 0x6bf86fe2, 0x1e6e314c, 0x1e53dd04, 0x0e6c73a4, 0x6b4c8c49), SECP256K1_FE_CONST(0xcd8acee9, 0x8ffe5653, 0x1a84d7eb, 0x3e48fa40, 0x34206ce8, 0x25ace907, 0xd0edf0ea, 0xeb5e9ca2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xc8f3d70e, 0x4199a105, 0x321955bc, 0x9407901d, 0xe191ceb3, 0xe1ac22fb, 0xf1938c5a, 0x94b36fe6), SECP256K1_FE_CONST(0x32753116, 0x7001a9ac, 0xe57b2814, 0xc1b705bf, 0xcbdf9317, 0xda5316f8, 0x2f120f14, 0x14a15f8d)}},
+    {0x44, SECP256K1_FE_CONST(0xe0294c8b, 0xc1a36b41, 0x66ee92bf, 0xa70a5c34, 0x976fa982, 0x9405efea, 0x8f9cd54d, 0xcb29b99e), SECP256K1_FE_CONST(0xae9690d1, 0x3b8d20a0, 0xfbbf37be, 0xd8474f67, 0xa04e142f, 0x56efd787, 0x70a76b35, 0x9165d8a1), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xdcd45d93, 0x5613916a, 0xf167b029, 0x058ba3a7, 0x00d37150, 0xb9df3472, 0x8cb05412, 0xc16d4182), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x232ba26c, 0xa9ec6e95, 0x0e984fd6, 0xfa745c58, 0xff2c8eaf, 0x4620cb8d, 0x734fabec, 0x3e92baad), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0x00, SECP256K1_FE_CONST(0xe148441c, 0xd7b92b8b, 0x0e4fa3bd, 0x68712cfd, 0x0d709ad1, 0x98cace61, 0x1493c10e, 0x97f5394e), SECP256K1_FE_CONST(0x164a6397, 0x94d74c53, 0xafc4d329, 0x4e79cdb3, 0xcd25f99f, 0x6df45c00, 0x0f758aba, 0x54d699c0), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0xff, SECP256K1_FE_CONST(0xe4b00ec9, 0x7aadcca9, 0x7644d3b0, 0xc8a931b1, 0x4ce7bcf7, 0xbc877954, 0x6d6e35aa, 0x5937381c), SECP256K1_FE_CONST(0x94e9588d, 0x41647b3f, 0xcc772dc8, 0xd83c67ce, 0x3be00353, 0x8517c834, 0x103d2cd4, 0x9d62ef4d), {SECP256K1_FE_CONST(0xc88d25f4, 0x1407376b, 0xb2c03a7f, 0xffeb3ec7, 0x811cc434, 0x91a0c3aa, 0xc0378cdc, 0x78357bee), SECP256K1_FE_CONST(0x51c02636, 0xce00c234, 0x5ecd89ad, 0xb6089fe4, 0xd5e18ac9, 0x24e3145e, 0x6669501c, 0xd37a00d4), SECP256K1_FE_CONST(0x205b3512, 0xdb40521c, 0xb200952e, 0x67b46f67, 0xe09e7839, 0xe0de4400, 0x4138329e, 0xbd9138c5), SECP256K1_FE_CONST(0x58aab390, 0xab6fb55c, 0x1d1b8089, 0x7a207ce9, 0x4a78fa5b, 0x4aa61a33, 0x398bcae9, 0xadb20d3e), SECP256K1_FE_CONST(0x3772da0b, 0xebf8c894, 0x4d3fc580, 0x0014c138, 0x7ee33bcb, 0x6e5f3c55, 0x3fc87322, 0x87ca8041), SECP256K1_FE_CONST(0xae3fd9c9, 0x31ff3dcb, 0xa1327652, 0x49f7601b, 0x2a1e7536, 0xdb1ceba1, 0x9996afe2, 0x2c85fb5b), SECP256K1_FE_CONST(0xdfa4caed, 0x24bfade3, 0x4dff6ad1, 0x984b9098, 0x1f6187c6, 0x1f21bbff, 0xbec7cd60, 0x426ec36a), SECP256K1_FE_CONST(0xa7554c6f, 0x54904aa3, 0xe2e47f76, 0x85df8316, 0xb58705a4, 0xb559e5cc, 0xc6743515, 0x524deef1)}},
+    {0x00, SECP256K1_FE_CONST(0xe5bbb9ef, 0x360d0a50, 0x1618f006, 0x7d36dceb, 0x75f5be9a, 0x620232aa, 0x9fd5139d, 0x0863fde5), SECP256K1_FE_CONST(0xe5bbb9ef, 0x360d0a50, 0x1618f006, 0x7d36dceb, 0x75f5be9a, 0x620232aa, 0x9fd5139d, 0x0863fde5), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0xff, SECP256K1_FE_CONST(0xe6bcb5c3, 0xd63467d4, 0x90bfa54f, 0xbbc6092a, 0x7248c25e, 0x11b248dc, 0x2964a6e1, 0x5edb1457), SECP256K1_FE_CONST(0x19434a3c, 0x29cb982b, 0x6f405ab0, 0x4439f6d5, 0x8db73da1, 0xee4db723, 0xd69b591d, 0xa124e7d8), {SECP256K1_FE_CONST(0x67119877, 0x832ab8f4, 0x59a82165, 0x6d8261f5, 0x44a553b8, 0x9ae4f25c, 0x52a97134, 0xb70f3426), SECP256K1_FE_CONST(0xffee02f5, 0xe649c07f, 0x0560eff1, 0x867ec7b3, 0x2d0e595e, 0x9b1c0ea6, 0xe2a4fc70, 0xc97cd71f), SECP256K1_FE_CONST(0xb5e0c189, 0xeb5b4bac, 0xd025b744, 0x4d74178b, 0xe8d5246c, 0xfa4a9a20, 0x7964a057, 0xee969992), SECP256K1_FE_CONST(0x5746e459, 0x1bf7f4c3, 0x044609ea, 0x372e9086, 0x03975d27, 0x9fdef834, 0x9f0b08d3, 0x2f07619d), SECP256K1_FE_CONST(0x98ee6788, 0x7cd5470b, 0xa657de9a, 0x927d9e0a, 0xbb5aac47, 0x651b0da3, 0xad568eca, 0x48f0c809), SECP256K1_FE_CONST(0x0011fd0a, 0x19b63f80, 0xfa9f100e, 0x7981384c, 0xd2f1a6a1, 0x64e3f159, 0x1d5b038e, 0x36832510), SECP256K1_FE_CONST(0x4a1f3e76, 0x14a4b453, 0x2fda48bb, 0xb28be874, 0x172adb93, 0x05b565df, 0x869b5fa7, 0x1169629d), SECP256K1_FE_CONST(0xa8b91ba6, 0xe4080b3c, 0xfbb9f615, 0xc8d16f79, 0xfc68a2d8, 0x602107cb, 0x60f4f72b, 0xd0f89a92)}},
+    {0x33, SECP256K1_FE_CONST(0xf28fba64, 0xaf766845, 0xeb2f4302, 0x456e2b9f, 0x8d80affe, 0x57e7aae4, 0x2738d7cd, 0xdb1c2ce6), SECP256K1_FE_CONST(0xf28fba64, 0xaf766845, 0xeb2f4302, 0x456e2b9f, 0x8d80affe, 0x57e7aae4, 0x2738d7cd, 0xdb1c2ce6), {SECP256K1_FE_CONST(0x4f867ad8, 0xbb3d8404, 0x09d26b67, 0x307e6210, 0x0153273f, 0x72fa4b74, 0x84becfa1, 0x4ebe7408), SECP256K1_FE_CONST(0x5bbc4f59, 0xe452cc5f, 0x22a99144, 0xb10ce898, 0x9a89a995, 0xec3cea1c, 0x91ae10e8, 0xf721bb5d), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xb0798527, 0x44c27bfb, 0xf62d9498, 0xcf819def, 0xfeacd8c0, 0x8d05b48b, 0x7b41305d, 0xb1418827), SECP256K1_FE_CONST(0xa443b0a6, 0x1bad33a0, 0xdd566ebb, 0x4ef31767, 0x6576566a, 0x13c315e3, 0x6e51ef16, 0x08de40d2), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+    {0xcc, SECP256K1_FE_CONST(0xf455605b, 0xc85bf48e, 0x3a908c31, 0x023faf98, 0x381504c6, 0xc6d3aeb9, 0xede55f8d, 0xd528924d), SECP256K1_FE_CONST(0xd31fbcd5, 0xcdb798f6, 0xc00db669, 0x2f8fe896, 0x7fa9c79d, 0xd10958f4, 0xa194f013, 0x74905e99), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0x0c00c571, 0x5b56fe63, 0x2d814ad8, 0xa77f8e66, 0x628ea47a, 0x6116834f, 0x8c1218f3, 0xa03cbd50), SECP256K1_FE_CONST(0xdf88e44f, 0xac84fa52, 0xdf4d59f4, 0x8819f18f, 0x6a8cd415, 0x1d162afa, 0xf773166f, 0x57c7ff46), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0xf3ff3a8e, 0xa4a9019c, 0xd27eb527, 0x58807199, 0x9d715b85, 0x9ee97cb0, 0x73ede70b, 0x5fc33edf), SECP256K1_FE_CONST(0x20771bb0, 0x537b05ad, 0x20b2a60b, 0x77e60e70, 0x95732bea, 0xe2e9d505, 0x088ce98f, 0xa837fce9)}},
+    {0xff, SECP256K1_FE_CONST(0xf58cd4d9, 0x830bad32, 0x2699035e, 0x8246007d, 0x4be27e19, 0xb6f53621, 0x317b4f30, 0x9b3daa9d), SECP256K1_FE_CONST(0x78ec2b3d, 0xc0948de5, 0x60148bbc, 0x7c6dc963, 0x3ad5df70, 0xa5a5750c, 0xbed72180, 0x4f082a3b), {SECP256K1_FE_CONST(0x6c4c580b, 0x76c75940, 0x43569f9d, 0xae16dc28, 0x01c16a1f, 0xbe128608, 0x81b75f8e, 0xf929bce5), SECP256K1_FE_CONST(0x94231355, 0xe7385c5f, 0x25ca436a, 0xa6419147, 0x1aea4393, 0xd6e86ab7, 0xa35fe2af, 0xacaefd0d), SECP256K1_FE_CONST(0xdff2a195, 0x1ada6db5, 0x74df8340, 0x48149da3, 0x397a75b8, 0x29abf58c, 0x7e69db1b, 0x41ac0989), SECP256K1_FE_CONST(0xa52b66d3, 0xc9070355, 0x48028bf8, 0x04711bf4, 0x22aba95f, 0x1a666fc8, 0x6f4648e0, 0x5f29caae), SECP256K1_FE_CONST(0x93b3a7f4, 0x8938a6bf, 0xbca96062, 0x51e923d7, 0xfe3e95e0, 0x41ed79f7, 0x7e48a070, 0x06d63f4a), SECP256K1_FE_CONST(0x6bdcecaa, 0x18c7a3a0, 0xda35bc95, 0x59be6eb8, 0xe515bc6c, 0x29179548, 0x5ca01d4f, 0x5350ff22), SECP256K1_FE_CONST(0x200d5e6a, 0xe525924a, 0x8b207cbf, 0xb7eb625c, 0xc6858a47, 0xd6540a73, 0x819624e3, 0xbe53f2a6), SECP256K1_FE_CONST(0x5ad4992c, 0x36f8fcaa, 0xb7fd7407, 0xfb8ee40b, 0xdd5456a0, 0xe5999037, 0x90b9b71e, 0xa0d63181)}},
+    {0x00, SECP256K1_FE_CONST(0xfd7d912a, 0x40f182a3, 0x588800d6, 0x9ebfb504, 0x8766da20, 0x6fd7ebc8, 0xd2436c81, 0xcbef6421), SECP256K1_FE_CONST(0x8d37c862, 0x054debe7, 0x31694536, 0xff46b273, 0xec122b35, 0xa9bf1445, 0xac3c4ff9, 0xf262c952), {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0)}},
+};
+
+/* Set of (encoding, xcoord) test vectors, selected to maximize branch coverage, part of the BIP324
+ * test vectors. Created using an independent implementation, and tested decoding against the paper
+ * authors' code. */
+static const struct ellswift_decode_test ellswift_decode_tests[] = {
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01, 0xd3, 0x47, 0x5b, 0xf7, 0x65, 0x5b, 0x0f, 0xb2, 0xd8, 0x52, 0x92, 0x10, 0x35, 0xb2, 0xef, 0x60, 0x7f, 0x49, 0x06, 0x9b, 0x97, 0x45, 0x4e, 0x67, 0x95, 0x25, 0x10, 0x62, 0x74, 0x17, 0x71}, SECP256K1_FE_CONST(0xb5da00b7, 0x3cd65605, 0x20e7c364, 0x086e7cd2, 0x3a34bf60, 0xd0e707be, 0x9fc34d4c, 0xd5fdfa2c), 1},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x82, 0x27, 0x7c, 0x4a, 0x71, 0xf9, 0xd2, 0x2e, 0x66, 0xec, 0xe5, 0x23, 0xf8, 0xfa, 0x08, 0x74, 0x1a, 0x7c, 0x09, 0x12, 0xc6, 0x6a, 0x69, 0xce, 0x68, 0x51, 0x4b, 0xfd, 0x35, 0x15, 0xb4, 0x9f}, SECP256K1_FE_CONST(0xf482f2e2, 0x41753ad0, 0xfb89150d, 0x8491dc1e, 0x34ff0b8a, 0xcfbb442c, 0xfe999e2e, 0x5e6fd1d2), 1},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x84, 0x21, 0xcc, 0x93, 0x0e, 0x77, 0xc9, 0xf5, 0x14, 0xb6, 0x91, 0x5c, 0x3d, 0xbe, 0x2a, 0x94, 0xc6, 0xd8, 0xf6, 0x90, 0xb5, 0xb7, 0x39, 0x86, 0x4b, 0xa6, 0x78, 0x9f, 0xb8, 0xa5, 0x5d, 0xd0}, SECP256K1_FE_CONST(0x9f59c402, 0x75f5085a, 0x006f05da, 0xe77eb98c, 0x6fd0db1a, 0xb4a72ac4, 0x7eae90a4, 0xfc9e57e0), 0},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xbd, 0xe7, 0x0d, 0xf5, 0x19, 0x39, 0xb9, 0x4c, 0x9c, 0x24, 0x97, 0x9f, 0xa7, 0xdd, 0x04, 0xeb, 0xd9, 0xb3, 0x57, 0x2d, 0xa7, 0x80, 0x22, 0x90, 0x43, 0x8a, 0xf2, 0xa6, 0x81, 0x89, 0x54, 0x41}, SECP256K1_FE_CONST(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaa9, 0xfffffd6b), 1},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xd1, 0x9c, 0x18, 0x2d, 0x27, 0x59, 0xcd, 0x99, 0x82, 0x42, 0x28, 0xd9, 0x47, 0x99, 0xf8, 0xc6, 0x55, 0x7c, 0x38, 0xa1, 0xc0, 0xd6, 0x77, 0x9b, 0x9d, 0x4b, 0x72, 0x9c, 0x6f, 0x1c, 0xcc, 0x42}, SECP256K1_FE_CONST(0x70720db7, 0xe238d041, 0x21f5b1af, 0xd8cc5ad9, 0xd18944c6, 0xbdc94881, 0xf502b7a3, 0xaf3aecff), 0},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x26, 0x64, 0xbb, 0xd5}, SECP256K1_FE_CONST(0x50873db3, 0x1badcc71, 0x890e4f67, 0x753a6575, 0x7f97aaa7, 0xdd5f1e82, 0xb753ace3, 0x2219064b), 0},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x70, 0x28, 0xde, 0x7d}, SECP256K1_FE_CONST(0x1eea9cc5, 0x9cfcf2fa, 0x151ac6c2, 0x74eea411, 0x0feb4f7b, 0x68c59657, 0x32e9992e, 0x976ef68e), 0},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xcb, 0xcf, 0xb7, 0xe7}, SECP256K1_FE_CONST(0x12303941, 0xaedc2088, 0x80735b1f, 0x1795c8e5, 0x5be520ea, 0x93e10335, 0x7b5d2adb, 0x7ed59b8e), 0},
+    {{0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf3, 0x11, 0x3a, 0xd9}, SECP256K1_FE_CONST(0x7eed6b70, 0xe7b0767c, 0x7d7feac0, 0x4e57aa2a, 0x12fef5e0, 0xf48f878f, 0xcbb88b3b, 0x6b5e0783), 0},
+    {{0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c, 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x532167c1, 0x1200b08c, 0x0e84a354, 0xe74dcc40, 0xf8b25f4f, 0xe686e308, 0x69526366, 0x278a0688), 0},
+    {{0x0a, 0x2d, 0x2b, 0xa9, 0x35, 0x07, 0xf1, 0xdf, 0x23, 0x37, 0x70, 0xc2, 0xa7, 0x97, 0x96, 0x2c, 0xc6, 0x1f, 0x6d, 0x15, 0xda, 0x14, 0xec, 0xd4, 0x7d, 0x8d, 0x27, 0xae, 0x1c, 0xd5, 0xf8, 0x53, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x532167c1, 0x1200b08c, 0x0e84a354, 0xe74dcc40, 0xf8b25f4f, 0xe686e308, 0x69526366, 0x278a0688), 0},
+    {{0x0f, 0xfd, 0xe9, 0xca, 0x81, 0xd7, 0x51, 0xe9, 0xcd, 0xaf, 0xfc, 0x1a, 0x50, 0x77, 0x92, 0x45, 0x32, 0x0b, 0x28, 0x99, 0x6d, 0xba, 0xf3, 0x2f, 0x82, 0x2f, 0x20, 0x11, 0x7c, 0x22, 0xfb, 0xd6, 0xc7, 0x4d, 0x99, 0xef, 0xce, 0xaa, 0x55, 0x0f, 0x1a, 0xd1, 0xc0, 0xf4, 0x3f, 0x46, 0xe7, 0xff, 0x1e, 0xe3, 0xbd, 0x01, 0x62, 0xb7, 0xbf, 0x55, 0xf2, 0x96, 0x5d, 0xa9, 0xc3, 0x45, 0x06, 0x46}, SECP256K1_FE_CONST(0x74e880b3, 0xffd18fe3, 0xcddf7902, 0x522551dd, 0xf97fa4a3, 0x5a3cfda8, 0x197f9470, 0x81a57b8f), 0},
+    {{0x0f, 0xfd, 0xe9, 0xca, 0x81, 0xd7, 0x51, 0xe9, 0xcd, 0xaf, 0xfc, 0x1a, 0x50, 0x77, 0x92, 0x45, 0x32, 0x0b, 0x28, 0x99, 0x6d, 0xba, 0xf3, 0x2f, 0x82, 0x2f, 0x20, 0x11, 0x7c, 0x22, 0xfb, 0xd6, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x15, 0x6c, 0xa8, 0x96}, SECP256K1_FE_CONST(0x377b643f, 0xce2271f6, 0x4e5c8101, 0x566107c1, 0xbe498074, 0x50917838, 0x04f65478, 0x1ac9217c), 1},
+    {{0x12, 0x36, 0x58, 0x44, 0x4f, 0x32, 0xbe, 0x8f, 0x02, 0xea, 0x20, 0x34, 0xaf, 0xa7, 0xef, 0x4b, 0xbe, 0x8a, 0xdc, 0x91, 0x8c, 0xeb, 0x49, 0xb1, 0x27, 0x73, 0xb6, 0x25, 0xf4, 0x90, 0xb3, 0x68, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x8d, 0xc5, 0xfe, 0x11}, SECP256K1_FE_CONST(0xed16d65c, 0xf3a9538f, 0xcb2c139f, 0x1ecbc143, 0xee148271, 0x20cbc265, 0x9e667256, 0x800b8142), 0},
+    {{0x14, 0x6f, 0x92, 0x46, 0x4d, 0x15, 0xd3, 0x6e, 0x35, 0x38, 0x2b, 0xd3, 0xca, 0x5b, 0x0f, 0x97, 0x6c, 0x95, 0xcb, 0x08, 0xac, 0xdc, 0xf2, 0xd5, 0xb3, 0x57, 0x06, 0x17, 0x99, 0x08, 0x39, 0xd7, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x31, 0x45, 0xe9, 0x3b}, SECP256K1_FE_CONST(0x0d5cd840, 0x427f941f, 0x65193079, 0xab8e2e83, 0x024ef2ee, 0x7ca558d8, 0x8879ffd8, 0x79fb6657), 0},
+    {{0x15, 0xfd, 0xf5, 0xcf, 0x09, 0xc9, 0x07, 0x59, 0xad, 0xd2, 0x27, 0x2d, 0x57, 0x4d, 0x2b, 0xb5, 0xfe, 0x14, 0x29, 0xf9, 0xf3, 0xc1, 0x4c, 0x65, 0xe3, 0x19, 0x4b, 0xf6, 0x1b, 0x82, 0xaa, 0x73, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x04, 0xcf, 0xd9, 0x06}, SECP256K1_FE_CONST(0x16d0e439, 0x46aec93f, 0x62d57eb8, 0xcde68951, 0xaf136cf4, 0xb307938d, 0xd1447411, 0xe07bffe1), 1},
+    {{0x1f, 0x67, 0xed, 0xf7, 0x79, 0xa8, 0xa6, 0x49, 0xd6, 0xde, 0xf6, 0x00, 0x35, 0xf2, 0xfa, 0x22, 0xd0, 0x22, 0xdd, 0x35, 0x90, 0x79, 0xa1, 0xa1, 0x44, 0x07, 0x3d, 0x84, 0xf1, 0x9b, 0x92, 0xd5, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x025661f9, 0xaba9d15c, 0x3118456b, 0xbe980e3e, 0x1b8ba2e0, 0x47c737a4, 0xeb48a040, 0xbb566f6c), 0},
+    {{0x1f, 0x67, 0xed, 0xf7, 0x79, 0xa8, 0xa6, 0x49, 0xd6, 0xde, 0xf6, 0x00, 0x35, 0xf2, 0xfa, 0x22, 0xd0, 0x22, 0xdd, 0x35, 0x90, 0x79, 0xa1, 0xa1, 0x44, 0x07, 0x3d, 0x84, 0xf1, 0x9b, 0x92, 0xd5, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x025661f9, 0xaba9d15c, 0x3118456b, 0xbe980e3e, 0x1b8ba2e0, 0x47c737a4, 0xeb48a040, 0xbb566f6c), 0},
+    {{0x1f, 0xe1, 0xe5, 0xef, 0x3f, 0xce, 0xb5, 0xc1, 0x35, 0xab, 0x77, 0x41, 0x33, 0x3c, 0xe5, 0xa6, 0xe8, 0x0d, 0x68, 0x16, 0x76, 0x53, 0xf6, 0xb2, 0xb2, 0x4b, 0xcb, 0xcf, 0xaa, 0xaf, 0xf5, 0x07, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x98bec3b2, 0xa351fa96, 0xcfd191c1, 0x77835193, 0x1b9e9ba9, 0xad1149f6, 0xd9eadca8, 0x0981b801), 0},
+    {{0x40, 0x56, 0xa3, 0x4a, 0x21, 0x0e, 0xec, 0x78, 0x92, 0xe8, 0x82, 0x06, 0x75, 0xc8, 0x60, 0x09, 0x9f, 0x85, 0x7b, 0x26, 0xaa, 0xd8, 0x54, 0x70, 0xee, 0x6d, 0x3c, 0xf1, 0x30, 0x4a, 0x9d, 0xcf, 0x37, 0x5e, 0x70, 0x37, 0x42, 0x71, 0xf2, 0x0b, 0x13, 0xc9, 0x98, 0x6e, 0xd7, 0xd3, 0xc1, 0x77, 0x99, 0x69, 0x8c, 0xfc, 0x43, 0x5d, 0xbe, 0xd3, 0xa9, 0xf3, 0x4b, 0x38, 0xc8, 0x23, 0xc2, 0xb4}, SECP256K1_FE_CONST(0x868aac20, 0x03b29dbc, 0xad1a3e80, 0x3855e078, 0xa89d1654, 0x3ac64392, 0xd1224172, 0x98cec76e), 0},
+    {{0x41, 0x97, 0xec, 0x37, 0x23, 0xc6, 0x54, 0xcf, 0xdd, 0x32, 0xab, 0x07, 0x55, 0x06, 0x64, 0x8b, 0x2f, 0xf5, 0x07, 0x03, 0x62, 0xd0, 0x1a, 0x4f, 0xff, 0x14, 0xb3, 0x36, 0xb7, 0x8f, 0x96, 0x3f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xb3, 0xab, 0x1e, 0x95}, SECP256K1_FE_CONST(0xba5a6314, 0x502a8952, 0xb8f456e0, 0x85928105, 0xf665377a, 0x8ce27726, 0xa5b0eb7e, 0xc1ac0286), 0},
+    {{0x47, 0xeb, 0x3e, 0x20, 0x8f, 0xed, 0xcd, 0xf8, 0x23, 0x4c, 0x94, 0x21, 0xe9, 0xcd, 0x9a, 0x7a, 0xe8, 0x73, 0xbf, 0xbd, 0xbc, 0x39, 0x37, 0x23, 0xd1, 0xba, 0x1e, 0x1e, 0x6a, 0x8e, 0x6b, 0x24, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x7c, 0xd1, 0x2c, 0xb1}, SECP256K1_FE_CONST(0xd192d520, 0x07e541c9, 0x807006ed, 0x0468df77, 0xfd214af0, 0xa795fe11, 0x9359666f, 0xdcf08f7c), 0},
+    {{0x5e, 0xb9, 0x69, 0x6a, 0x23, 0x36, 0xfe, 0x2c, 0x3c, 0x66, 0x6b, 0x02, 0xc7, 0x55, 0xdb, 0x4c, 0x0c, 0xfd, 0x62, 0x82, 0x5c, 0x7b, 0x58, 0x9a, 0x7b, 0x7b, 0xb4, 0x42, 0xe1, 0x41, 0xc1, 0xd6, 0x93, 0x41, 0x3f, 0x00, 0x52, 0xd4, 0x9e, 0x64, 0xab, 0xec, 0x6d, 0x58, 0x31, 0xd6, 0x6c, 0x43, 0x61, 0x28, 0x30, 0xa1, 0x7d, 0xf1, 0xfe, 0x43, 0x83, 0xdb, 0x89, 0x64, 0x68, 0x10, 0x02, 0x21}, SECP256K1_FE_CONST(0xef6e1da6, 0xd6c7627e, 0x80f7a723, 0x4cb08a02, 0x2c1ee1cf, 0x29e4d0f9, 0x642ae924, 0xcef9eb38), 1},
+    {{0x7b, 0xf9, 0x6b, 0x7b, 0x6d, 0xa1, 0x5d, 0x34, 0x76, 0xa2, 0xb1, 0x95, 0x93, 0x4b, 0x69, 0x0a, 0x3a, 0x3d, 0xe3, 0xe8, 0xab, 0x84, 0x74, 0x85, 0x68, 0x63, 0xb0, 0xde, 0x3a, 0xf9, 0x0b, 0x0e, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x50851dfc, 0x9f418c31, 0x4a437295, 0xb24feeea, 0x27af3d0c, 0xd2308348, 0xfda6e21c, 0x463e46ff), 0},
+    {{0x7b, 0xf9, 0x6b, 0x7b, 0x6d, 0xa1, 0x5d, 0x34, 0x76, 0xa2, 0xb1, 0x95, 0x93, 0x4b, 0x69, 0x0a, 0x3a, 0x3d, 0xe3, 0xe8, 0xab, 0x84, 0x74, 0x85, 0x68, 0x63, 0xb0, 0xde, 0x3a, 0xf9, 0x0b, 0x0e, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x50851dfc, 0x9f418c31, 0x4a437295, 0xb24feeea, 0x27af3d0c, 0xd2308348, 0xfda6e21c, 0x463e46ff), 0},
+    {{0x85, 0x1b, 0x1c, 0xa9, 0x45, 0x49, 0x37, 0x1c, 0x4f, 0x1f, 0x71, 0x87, 0x32, 0x1d, 0x39, 0xbf, 0x51, 0xc6, 0xb7, 0xfb, 0x61, 0xf7, 0xcb, 0xf0, 0x27, 0xc9, 0xda, 0x62, 0x02, 0x1b, 0x7a, 0x65, 0xfc, 0x54, 0xc9, 0x68, 0x37, 0xfb, 0x22, 0xb3, 0x62, 0xed, 0xa6, 0x3e, 0xc5, 0x2e, 0xc8, 0x3d, 0x81, 0xbe, 0xdd, 0x16, 0x0c, 0x11, 0xb2, 0x2d, 0x96, 0x5d, 0x9f, 0x4a, 0x6d, 0x64, 0xd2, 0x51}, SECP256K1_FE_CONST(0x3e731051, 0xe12d3323, 0x7eb324f2, 0xaa5b16bb, 0x868eb49a, 0x1aa1fadc, 0x19b6e876, 0x1b5a5f7b), 1},
+    {{0x94, 0x3c, 0x2f, 0x77, 0x51, 0x08, 0xb7, 0x37, 0xfe, 0x65, 0xa9, 0x53, 0x1e, 0x19, 0xf2, 0xfc, 0x2a, 0x19, 0x7f, 0x56, 0x03, 0xe3, 0xa2, 0x88, 0x1d, 0x1d, 0x83, 0xe4, 0x00, 0x8f, 0x91, 0x25, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x311c61f0, 0xab2f32b7, 0xb1f0223f, 0xa72f0a78, 0x752b8146, 0xe46107f8, 0x876dd9c4, 0xf92b2942), 0},
+    {{0x94, 0x3c, 0x2f, 0x77, 0x51, 0x08, 0xb7, 0x37, 0xfe, 0x65, 0xa9, 0x53, 0x1e, 0x19, 0xf2, 0xfc, 0x2a, 0x19, 0x7f, 0x56, 0x03, 0xe3, 0xa2, 0x88, 0x1d, 0x1d, 0x83, 0xe4, 0x00, 0x8f, 0x91, 0x25, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x311c61f0, 0xab2f32b7, 0xb1f0223f, 0xa72f0a78, 0x752b8146, 0xe46107f8, 0x876dd9c4, 0xf92b2942), 0},
+    {{0xa0, 0xf1, 0x84, 0x92, 0x18, 0x3e, 0x61, 0xe8, 0x06, 0x3e, 0x57, 0x36, 0x06, 0x59, 0x14, 0x21, 0xb0, 0x6b, 0xc3, 0x51, 0x36, 0x31, 0x57, 0x8a, 0x73, 0xa3, 0x9c, 0x1c, 0x33, 0x06, 0x23, 0x9f, 0x2f, 0x32, 0x90, 0x4f, 0x0d, 0x2a, 0x33, 0xec, 0xca, 0x8a, 0x54, 0x51, 0x70, 0x5b, 0xb5, 0x37, 0xd3, 0xbf, 0x44, 0xe0, 0x71, 0x22, 0x60, 0x25, 0xcd, 0xbf, 0xd2, 0x49, 0xfe, 0x0f, 0x7a, 0xd6}, SECP256K1_FE_CONST(0x97a09cf1, 0xa2eae7c4, 0x94df3c6f, 0x8a9445bf, 0xb8c09d60, 0x832f9b0b, 0x9d5eabe2, 0x5fbd14b9), 0},
+    {{0xa1, 0xed, 0x0a, 0x0b, 0xd7, 0x9d, 0x8a, 0x23, 0xcf, 0xe4, 0xec, 0x5f, 0xef, 0x5b, 0xa5, 0xcc, 0xcf, 0xd8, 0x44, 0xe4, 0xff, 0x5c, 0xb4, 0xb0, 0xf2, 0xe7, 0x16, 0x27, 0x34, 0x1f, 0x1c, 0x5b, 0x17, 0xc4, 0x99, 0x24, 0x9e, 0x0a, 0xc0, 0x8d, 0x5d, 0x11, 0xea, 0x1c, 0x2c, 0x8c, 0xa7, 0x00, 0x16, 0x16, 0x55, 0x9a, 0x79, 0x94, 0xea, 0xde, 0xc9, 0xca, 0x10, 0xfb, 0x4b, 0x85, 0x16, 0xdc}, SECP256K1_FE_CONST(0x65a89640, 0x744192cd, 0xac64b2d2, 0x1ddf989c, 0xdac75007, 0x25b645be, 0xf8e2200a, 0xe39691f2), 0},
+    {{0xba, 0x94, 0x59, 0x4a, 0x43, 0x27, 0x21, 0xaa, 0x35, 0x80, 0xb8, 0x4c, 0x16, 0x1d, 0x0d, 0x13, 0x4b, 0xc3, 0x54, 0xb6, 0x90, 0x40, 0x4d, 0x7c, 0xd4, 0xec, 0x57, 0xc1, 0x6d, 0x3f, 0xbe, 0x98, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xea, 0x50, 0x7d, 0xd7}, SECP256K1_FE_CONST(0x5e0d7656, 0x4aae92cb, 0x347e01a6, 0x2afd389a, 0x9aa401c7, 0x6c8dd227, 0x543dc9cd, 0x0efe685a), 0},
+    {{0xbc, 0xaf, 0x72, 0x19, 0xf2, 0xf6, 0xfb, 0xf5, 0x5f, 0xe5, 0xe0, 0x62, 0xdc, 0xe0, 0xe4, 0x8c, 0x18, 0xf6, 0x81, 0x03, 0xf1, 0x0b, 0x81, 0x98, 0xe9, 0x74, 0xc1, 0x84, 0x75, 0x0e, 0x1b, 0xe3, 0x93, 0x20, 0x16, 0xcb, 0xf6, 0x9c, 0x44, 0x71, 0xbd, 0x1f, 0x65, 0x6c, 0x6a, 0x10, 0x7f, 0x19, 0x73, 0xde, 0x4a, 0xf7, 0x08, 0x6d, 0xb8, 0x97, 0x27, 0x70, 0x60, 0xe2, 0x56, 0x77, 0xf1, 0x9a}, SECP256K1_FE_CONST(0x2d97f96c, 0xac882dfe, 0x73dc44db, 0x6ce0f1d3, 0x1d624135, 0x8dd5d74e, 0xb3d3b500, 0x03d24c2b), 0},
+    {{0xbc, 0xaf, 0x72, 0x19, 0xf2, 0xf6, 0xfb, 0xf5, 0x5f, 0xe5, 0xe0, 0x62, 0xdc, 0xe0, 0xe4, 0x8c, 0x18, 0xf6, 0x81, 0x03, 0xf1, 0x0b, 0x81, 0x98, 0xe9, 0x74, 0xc1, 0x84, 0x75, 0x0e, 0x1b, 0xe3, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x65, 0x07, 0xd0, 0x9a}, SECP256K1_FE_CONST(0xe7008afe, 0x6e8cbd50, 0x55df120b, 0xd748757c, 0x686dadb4, 0x1cce75e4, 0xaddcc5e0, 0x2ec02b44), 1},
+    {{0xc5, 0x98, 0x1b, 0xae, 0x27, 0xfd, 0x84, 0x40, 0x1c, 0x72, 0xa1, 0x55, 0xe5, 0x70, 0x7f, 0xbb, 0x81, 0x1b, 0x2b, 0x62, 0x06, 0x45, 0xd1, 0x02, 0x8e, 0xa2, 0x70, 0xcb, 0xe0, 0xee, 0x22, 0x5d, 0x4b, 0x62, 0xaa, 0x4d, 0xca, 0x65, 0x06, 0xc1, 0xac, 0xdb, 0xec, 0xc0, 0x55, 0x25, 0x69, 0xb4, 0xb2, 0x14, 0x36, 0xa5, 0x69, 0x2e, 0x25, 0xd9, 0x0d, 0x3b, 0xc2, 0xeb, 0x7c, 0xe2, 0x40, 0x78}, SECP256K1_FE_CONST(0x948b40e7, 0x181713bc, 0x018ec170, 0x2d3d054d, 0x15746c59, 0xa7020730, 0xdd13ecf9, 0x85a010d7), 0},
+    {{0xc8, 0x94, 0xce, 0x48, 0xbf, 0xec, 0x43, 0x30, 0x14, 0xb9, 0x31, 0xa6, 0xad, 0x42, 0x26, 0xd7, 0xdb, 0xd8, 0xea, 0xa7, 0xb6, 0xe3, 0xfa, 0xa8, 0xd0, 0xef, 0x94, 0x05, 0x2b, 0xcf, 0x8c, 0xff, 0x33, 0x6e, 0xeb, 0x39, 0x19, 0xe2, 0xb4, 0xef, 0xb7, 0x46, 0xc7, 0xf7, 0x1b, 0xbc, 0xa7, 0xe9, 0x38, 0x32, 0x30, 0xfb, 0xbc, 0x48, 0xff, 0xaf, 0xe7, 0x7e, 0x8b, 0xcc, 0x69, 0x54, 0x24, 0x71}, SECP256K1_FE_CONST(0xf1c91acd, 0xc2525330, 0xf9b53158, 0x434a4d43, 0xa1c547cf, 0xf29f1550, 0x6f5da4eb, 0x4fe8fa5a), 1},
+    {{0xcb, 0xb0, 0xde, 0xab, 0x12, 0x57, 0x54, 0xf1, 0xfd, 0xb2, 0x03, 0x8b, 0x04, 0x34, 0xed, 0x9c, 0xb3, 0xfb, 0x53, 0xab, 0x73, 0x53, 0x91, 0x12, 0x99, 0x94, 0xa5, 0x35, 0xd9, 0x25, 0xf6, 0x73, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x872d81ed, 0x8831d999, 0x8b67cb71, 0x05243edb, 0xf86c10ed, 0xfebb786c, 0x110b02d0, 0x7b2e67cd), 0},
+    {{0xd9, 0x17, 0xb7, 0x86, 0xda, 0xc3, 0x56, 0x70, 0xc3, 0x30, 0xc9, 0xc5, 0xae, 0x59, 0x71, 0xdf, 0xb4, 0x95, 0xc8, 0xae, 0x52, 0x3e, 0xd9, 0x7e, 0xe2, 0x42, 0x01, 0x17, 0xb1, 0x71, 0xf4, 0x1e, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x20, 0x01, 0xf6, 0xf6}, SECP256K1_FE_CONST(0xe45b71e1, 0x10b831f2, 0xbdad8651, 0x994526e5, 0x8393fde4, 0x328b1ec0, 0x4d598971, 0x42584691), 1},
+    {{0xe2, 0x8b, 0xd8, 0xf5, 0x92, 0x9b, 0x46, 0x7e, 0xb7, 0x0e, 0x04, 0x33, 0x23, 0x74, 0xff, 0xb7, 0xe7, 0x18, 0x02, 0x18, 0xad, 0x16, 0xea, 0xa4, 0x6b, 0x71, 0x61, 0xaa, 0x67, 0x9e, 0xb4, 0x26, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x66b8c980, 0xa75c72e5, 0x98d383a3, 0x5a62879f, 0x844242ad, 0x1e73ff12, 0xedaa59f4, 0xe58632b5), 0},
+    {{0xe2, 0x8b, 0xd8, 0xf5, 0x92, 0x9b, 0x46, 0x7e, 0xb7, 0x0e, 0x04, 0x33, 0x23, 0x74, 0xff, 0xb7, 0xe7, 0x18, 0x02, 0x18, 0xad, 0x16, 0xea, 0xa4, 0x6b, 0x71, 0x61, 0xaa, 0x67, 0x9e, 0xb4, 0x26, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x66b8c980, 0xa75c72e5, 0x98d383a3, 0x5a62879f, 0x844242ad, 0x1e73ff12, 0xedaa59f4, 0xe58632b5), 0},
+    {{0xe7, 0xee, 0x58, 0x14, 0xc1, 0x70, 0x6b, 0xf8, 0xa8, 0x93, 0x96, 0xa9, 0xb0, 0x32, 0xbc, 0x01, 0x4c, 0x2c, 0xac, 0x9c, 0x12, 0x11, 0x27, 0xdb, 0xf6, 0xc9, 0x92, 0x78, 0xf8, 0xbb, 0x53, 0xd1, 0xdf, 0xd0, 0x4d, 0xbc, 0xda, 0x8e, 0x35, 0x24, 0x66, 0xb6, 0xfc, 0xd5, 0xf2, 0xde, 0xa3, 0xe1, 0x7d, 0x5e, 0x13, 0x31, 0x15, 0x88, 0x6e, 0xda, 0x20, 0xdb, 0x8a, 0x12, 0xb5, 0x4d, 0xe7, 0x1b}, SECP256K1_FE_CONST(0xe842c6e3, 0x529b2342, 0x70a5e977, 0x44edc34a, 0x04d7ba94, 0xe44b6d25, 0x23c9cf01, 0x95730a50), 1},
+    {{0xf2, 0x92, 0xe4, 0x68, 0x25, 0xf9, 0x22, 0x5a, 0xd2, 0x3d, 0xc0, 0x57, 0xc1, 0xd9, 0x1c, 0x4f, 0x57, 0xfc, 0xb1, 0x38, 0x6f, 0x29, 0xef, 0x10, 0x48, 0x1c, 0xb1, 0xd2, 0x25, 0x18, 0x59, 0x3f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x70, 0x11, 0xc9, 0x89}, SECP256K1_FE_CONST(0x3cea2c53, 0xb8b01701, 0x66ac7da6, 0x7194694a, 0xdacc84d5, 0x6389225e, 0x330134da, 0xb85a4d55), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x01, 0xd3, 0x47, 0x5b, 0xf7, 0x65, 0x5b, 0x0f, 0xb2, 0xd8, 0x52, 0x92, 0x10, 0x35, 0xb2, 0xef, 0x60, 0x7f, 0x49, 0x06, 0x9b, 0x97, 0x45, 0x4e, 0x67, 0x95, 0x25, 0x10, 0x62, 0x74, 0x17, 0x71}, SECP256K1_FE_CONST(0xb5da00b7, 0x3cd65605, 0x20e7c364, 0x086e7cd2, 0x3a34bf60, 0xd0e707be, 0x9fc34d4c, 0xd5fdfa2c), 1},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x42, 0x18, 0xf2, 0x0a, 0xe6, 0xc6, 0x46, 0xb3, 0x63, 0xdb, 0x68, 0x60, 0x58, 0x22, 0xfb, 0x14, 0x26, 0x4c, 0xa8, 0xd2, 0x58, 0x7f, 0xdd, 0x6f, 0xbc, 0x75, 0x0d, 0x58, 0x7e, 0x76, 0xa7, 0xee}, SECP256K1_FE_CONST(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaa9, 0xfffffd6b), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x82, 0x27, 0x7c, 0x4a, 0x71, 0xf9, 0xd2, 0x2e, 0x66, 0xec, 0xe5, 0x23, 0xf8, 0xfa, 0x08, 0x74, 0x1a, 0x7c, 0x09, 0x12, 0xc6, 0x6a, 0x69, 0xce, 0x68, 0x51, 0x4b, 0xfd, 0x35, 0x15, 0xb4, 0x9f}, SECP256K1_FE_CONST(0xf482f2e2, 0x41753ad0, 0xfb89150d, 0x8491dc1e, 0x34ff0b8a, 0xcfbb442c, 0xfe999e2e, 0x5e6fd1d2), 1},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x84, 0x21, 0xcc, 0x93, 0x0e, 0x77, 0xc9, 0xf5, 0x14, 0xb6, 0x91, 0x5c, 0x3d, 0xbe, 0x2a, 0x94, 0xc6, 0xd8, 0xf6, 0x90, 0xb5, 0xb7, 0x39, 0x86, 0x4b, 0xa6, 0x78, 0x9f, 0xb8, 0xa5, 0x5d, 0xd0}, SECP256K1_FE_CONST(0x9f59c402, 0x75f5085a, 0x006f05da, 0xe77eb98c, 0x6fd0db1a, 0xb4a72ac4, 0x7eae90a4, 0xfc9e57e0), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xd1, 0x9c, 0x18, 0x2d, 0x27, 0x59, 0xcd, 0x99, 0x82, 0x42, 0x28, 0xd9, 0x47, 0x99, 0xf8, 0xc6, 0x55, 0x7c, 0x38, 0xa1, 0xc0, 0xd6, 0x77, 0x9b, 0x9d, 0x4b, 0x72, 0x9c, 0x6f, 0x1c, 0xcc, 0x42}, SECP256K1_FE_CONST(0x70720db7, 0xe238d041, 0x21f5b1af, 0xd8cc5ad9, 0xd18944c6, 0xbdc94881, 0xf502b7a3, 0xaf3aecff), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0xedd1fd3e, 0x327ce90c, 0xc7a35426, 0x14289aee, 0x9682003e, 0x9cf7dcc9, 0xcf2ca974, 0x3be5aa0c), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x26, 0x64, 0xbb, 0xd5}, SECP256K1_FE_CONST(0x50873db3, 0x1badcc71, 0x890e4f67, 0x753a6575, 0x7f97aaa7, 0xdd5f1e82, 0xb753ace3, 0x2219064b), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x70, 0x28, 0xde, 0x7d}, SECP256K1_FE_CONST(0x1eea9cc5, 0x9cfcf2fa, 0x151ac6c2, 0x74eea411, 0x0feb4f7b, 0x68c59657, 0x32e9992e, 0x976ef68e), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xcb, 0xcf, 0xb7, 0xe7}, SECP256K1_FE_CONST(0x12303941, 0xaedc2088, 0x80735b1f, 0x1795c8e5, 0x5be520ea, 0x93e10335, 0x7b5d2adb, 0x7ed59b8e), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf3, 0x11, 0x3a, 0xd9}, SECP256K1_FE_CONST(0x7eed6b70, 0xe7b0767c, 0x7d7feac0, 0x4e57aa2a, 0x12fef5e0, 0xf48f878f, 0xcbb88b3b, 0x6b5e0783), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x13, 0xce, 0xa4, 0xa7, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x64998443, 0x5b62b4a2, 0x5d40c613, 0x3e8d9ab8, 0xc53d4b05, 0x9ee8a154, 0xa3be0fcf, 0x4e892edb), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x13, 0xce, 0xa4, 0xa7, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x64998443, 0x5b62b4a2, 0x5d40c613, 0x3e8d9ab8, 0xc53d4b05, 0x9ee8a154, 0xa3be0fcf, 0x4e892edb), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x15, 0x02, 0x8c, 0x59, 0x00, 0x63, 0xf6, 0x4d, 0x5a, 0x7f, 0x1c, 0x14, 0x91, 0x5c, 0xd6, 0x1e, 0xac, 0x88, 0x6a, 0xb2, 0x95, 0xbe, 0xbd, 0x91, 0x99, 0x25, 0x04, 0xcf, 0x77, 0xed, 0xb0, 0x28, 0xbd, 0xd6, 0x26, 0x7f}, SECP256K1_FE_CONST(0x3fde5713, 0xf8282eea, 0xd7d39d42, 0x01f44a7c, 0x85a5ac8a, 0x0681f35e, 0x54085c6b, 0x69543374), 1},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x27, 0x15, 0xde, 0x86, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x3524f77f, 0xa3a6eb43, 0x89c3cb5d, 0x27f1f914, 0x62086429, 0xcd6c0cb0, 0xdf43ea8f, 0x1e7b3fb4), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x27, 0x15, 0xde, 0x86, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x3524f77f, 0xa3a6eb43, 0x89c3cb5d, 0x27f1f914, 0x62086429, 0xcd6c0cb0, 0xdf43ea8f, 0x1e7b3fb4), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x2c, 0x2c, 0x57, 0x09, 0xe7, 0x15, 0x6c, 0x41, 0x77, 0x17, 0xf2, 0xfe, 0xab, 0x14, 0x71, 0x41, 0xec, 0x3d, 0xa1, 0x9f, 0xb7, 0x59, 0x57, 0x5c, 0xc6, 0xe3, 0x7b, 0x2e, 0xa5, 0xac, 0x93, 0x09, 0xf2, 0x6f, 0x0f, 0x66}, SECP256K1_FE_CONST(0xd2469ab3, 0xe04acbb2, 0x1c65a180, 0x9f39caaf, 0xe7a77c13, 0xd10f9dd3, 0x8f391c01, 0xdc499c52), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3a, 0x08, 0xcc, 0x1e, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf7, 0x60, 0xe9, 0xf0}, SECP256K1_FE_CONST(0x38e2a5ce, 0x6a93e795, 0xe16d2c39, 0x8bc99f03, 0x69202ce2, 0x1e8f09d5, 0x6777b40f, 0xc512bccc), 1},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x3e, 0x91, 0x25, 0x7d, 0x93, 0x20, 0x16, 0xcb, 0xf6, 0x9c, 0x44, 0x71, 0xbd, 0x1f, 0x65, 0x6c, 0x6a, 0x10, 0x7f, 0x19, 0x73, 0xde, 0x4a, 0xf7, 0x08, 0x6d, 0xb8, 0x97, 0x27, 0x70, 0x60, 0xe2, 0x56, 0x77, 0xf1, 0x9a}, SECP256K1_FE_CONST(0x864b3dc9, 0x02c37670, 0x9c10a93a, 0xd4bbe29f, 0xce0012f3, 0xdc8672c6, 0x286bba28, 0xd7d6d6fc), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x79, 0x5d, 0x6c, 0x1c, 0x32, 0x2c, 0xad, 0xf5, 0x99, 0xdb, 0xb8, 0x64, 0x81, 0x52, 0x2b, 0x3c, 0xc5, 0x5f, 0x15, 0xa6, 0x79, 0x32, 0xdb, 0x2a, 0xfa, 0x01, 0x11, 0xd9, 0xed, 0x69, 0x81, 0xbc, 0xd1, 0x24, 0xbf, 0x44}, SECP256K1_FE_CONST(0x766dfe4a, 0x700d9bee, 0x288b903a, 0xd58870e3, 0xd4fe2f0e, 0xf780bcac, 0x5c823f32, 0x0d9a9bef), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x8e, 0x42, 0x6f, 0x03, 0x92, 0x38, 0x90, 0x78, 0xc1, 0x2b, 0x1a, 0x89, 0xe9, 0x54, 0x2f, 0x05, 0x93, 0xbc, 0x96, 0xb6, 0xbf, 0xde, 0x82, 0x24, 0xf8, 0x65, 0x4e, 0xf5, 0xd5, 0xcd, 0xa9, 0x35, 0xa3, 0x58, 0x21, 0x94}, SECP256K1_FE_CONST(0xfaec7bc1, 0x987b6323, 0x3fbc5f95, 0x6edbf37d, 0x54404e74, 0x61c58ab8, 0x631bc68e, 0x451a0478), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x91, 0x19, 0x21, 0x39, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x45, 0xf0, 0xf1, 0xeb}, SECP256K1_FE_CONST(0xec29a50b, 0xae138dbf, 0x7d8e2482, 0x5006bb5f, 0xc1a2cc12, 0x43ba335b, 0xc6116fb9, 0xe498ec1f), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x98, 0xeb, 0x9a, 0xb7, 0x6e, 0x84, 0x49, 0x9c, 0x48, 0x3b, 0x3b, 0xf0, 0x62, 0x14, 0xab, 0xfe, 0x06, 0x5d, 0xdd, 0xf4, 0x3b, 0x86, 0x01, 0xde, 0x59, 0x6d, 0x63, 0xb9, 0xe4, 0x5a, 0x16, 0x6a, 0x58, 0x05, 0x41, 0xfe}, SECP256K1_FE_CONST(0x1e0ff2de, 0xe9b09b13, 0x6292a9e9, 0x10f0d6ac, 0x3e552a64, 0x4bba39e6, 0x4e9dd3e3, 0xbbd3d4d4), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x9b, 0x77, 0xb7, 0xf2, 0xc7, 0x4d, 0x99, 0xef, 0xce, 0xaa, 0x55, 0x0f, 0x1a, 0xd1, 0xc0, 0xf4, 0x3f, 0x46, 0xe7, 0xff, 0x1e, 0xe3, 0xbd, 0x01, 0x62, 0xb7, 0xbf, 0x55, 0xf2, 0x96, 0x5d, 0xa9, 0xc3, 0x45, 0x06, 0x46}, SECP256K1_FE_CONST(0x8b7dd5c3, 0xedba9ee9, 0x7b70eff4, 0x38f22dca, 0x9849c825, 0x4a2f3345, 0xa0a572ff, 0xeaae0928), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x9b, 0x77, 0xb7, 0xf2, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x15, 0x6c, 0xa8, 0x96}, SECP256K1_FE_CONST(0x0881950c, 0x8f51d6b9, 0xa6387465, 0xd5f12609, 0xef1bb254, 0x12a08a74, 0xcb2dfb20, 0x0c74bfbf), 1},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xa2, 0xf5, 0xcd, 0x83, 0x88, 0x16, 0xc1, 0x6c, 0x4f, 0xe8, 0xa1, 0x66, 0x1d, 0x60, 0x6f, 0xdb, 0x13, 0xcf, 0x9a, 0xf0, 0x4b, 0x97, 0x9a, 0x2e, 0x15, 0x9a, 0x09, 0x40, 0x9e, 0xbc, 0x86, 0x45, 0xd5, 0x8f, 0xde, 0x02}, SECP256K1_FE_CONST(0x2f083207, 0xb9fd9b55, 0x0063c31c, 0xd62b8746, 0xbd543bdc, 0x5bbf10e3, 0xa35563e9, 0x27f440c8), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xb1, 0x3f, 0x75, 0xc0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x4f51e0be, 0x078e0cdd, 0xab274215, 0x6adba7e7, 0xa148e731, 0x57072fd6, 0x18cd6094, 0x2b146bd0), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xb1, 0x3f, 0x75, 0xc0, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x4f51e0be, 0x078e0cdd, 0xab274215, 0x6adba7e7, 0xa148e731, 0x57072fd6, 0x18cd6094, 0x2b146bd0), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe7, 0xbc, 0x1f, 0x8d, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, SECP256K1_FE_CONST(0x16c2ccb5, 0x4352ff4b, 0xd794f6ef, 0xd613c721, 0x97ab7082, 0xda5b563b, 0xdf9cb3ed, 0xaafe74c2), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xe7, 0xbc, 0x1f, 0x8d, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f}, SECP256K1_FE_CONST(0x16c2ccb5, 0x4352ff4b, 0xd794f6ef, 0xd613c721, 0x97ab7082, 0xda5b563b, 0xdf9cb3ed, 0xaafe74c2), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xef, 0x64, 0xd1, 0x62, 0x75, 0x05, 0x46, 0xce, 0x42, 0xb0, 0x43, 0x13, 0x61, 0xe5, 0x2d, 0x4f, 0x52, 0x42, 0xd8, 0xf2, 0x4f, 0x33, 0xe6, 0xb1, 0xf9, 0x9b, 0x59, 0x16, 0x47, 0xcb, 0xc8, 0x08, 0xf4, 0x62, 0xaf, 0x51}, SECP256K1_FE_CONST(0xd41244d1, 0x1ca4f652, 0x40687759, 0xf95ca9ef, 0xbab767ed, 0xedb38fd1, 0x8c36e18c, 0xd3b6f6a9), 1},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf0, 0xe5, 0xbe, 0x52, 0x37, 0x2d, 0xd6, 0xe8, 0x94, 0xb2, 0xa3, 0x26, 0xfc, 0x36, 0x05, 0xa6, 0xe8, 0xf3, 0xc6, 0x9c, 0x71, 0x0b, 0xf2, 0x7d, 0x63, 0x0d, 0xfe, 0x20, 0x04, 0x98, 0x8b, 0x78, 0xeb, 0x6e, 0xab, 0x36}, SECP256K1_FE_CONST(0x64bf84dd, 0x5e03670f, 0xdb24c0f5, 0xd3c2c365, 0x736f51db, 0x6c92d950, 0x10716ad2, 0xd36134c8), 0},
+    {{0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xfb, 0xb9, 0x82, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf6, 0xd6, 0xdb, 0x1f}, SECP256K1_FE_CONST(0x1c92ccdf, 0xcf4ac550, 0xc28db57c, 0xff0c8515, 0xcb26936c, 0x786584a7, 0x0114008d, 0x6c33a34b), 0},
+};
+
+/* Set of expected ellswift_xdh BIP324 shared secrets, given private key, encodings, initiating,
+ * taken from the BIP324 test vectors. Created using an independent implementation, and tested
+ * against the paper authors' decoding code. */
+static const struct ellswift_xdh_test ellswift_xdh_tests_bip324[] = {
+    {{0x61, 0x06, 0x2e, 0xa5, 0x07, 0x1d, 0x80, 0x0b, 0xbf, 0xd5, 0x9e, 0x2e, 0x8b, 0x53, 0xd4, 0x7d, 0x19, 0x4b, 0x09, 0x5a, 0xe5, 0xa4, 0xdf, 0x04, 0x93, 0x6b, 0x49, 0x77, 0x2e, 0xf0, 0xd4, 0xd7}, {0xec, 0x0a, 0xdf, 0xf2, 0x57, 0xbb, 0xfe, 0x50, 0x0c, 0x18, 0x8c, 0x80, 0xb4, 0xfd, 0xd6, 0x40, 0xf6, 0xb4, 0x5a, 0x48, 0x2b, 0xbc, 0x15, 0xfc, 0x7c, 0xef, 0x59, 0x31, 0xde, 0xff, 0x0a, 0xa1, 0x86, 0xf6, 0xeb, 0x9b, 0xba, 0x7b, 0x85, 0xdc, 0x4d, 0xcc, 0x28, 0xb2, 0x87, 0x22, 0xde, 0x1e, 0x3d, 0x91, 0x08, 0xb9, 0x85, 0xe2, 0x96, 0x70, 0x45, 0x66, 0x8f, 0x66, 0x09, 0x8e, 0x47, 0x5b}, {0xa4, 0xa9, 0x4d, 0xfc, 0xe6, 0x9b, 0x4a, 0x2a, 0x0a, 0x09, 0x93, 0x13, 0xd1, 0x0f, 0x9f, 0x7e, 0x7d, 0x64, 0x9d, 0x60, 0x50, 0x1c, 0x9e, 0x1d, 0x27, 0x4c, 0x30, 0x0e, 0x0d, 0x89, 0xaa, 0xfa, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x8f, 0xaf, 0x88, 0xd5}, 1, {0xc6, 0x99, 0x2a, 0x11, 0x7f, 0x5e, 0xdb, 0xea, 0x70, 0xc3, 0xf5, 0x11, 0xd3, 0x2d, 0x26, 0xb9, 0x79, 0x8b, 0xe4, 0xb8, 0x1a, 0x62, 0xea, 0xee, 0x1a, 0x5a, 0xca, 0xa8, 0x45, 0x9a, 0x35, 0x92}},
+    {{0x1f, 0x9c, 0x58, 0x1b, 0x35, 0x23, 0x18, 0x38, 0xf0, 0xf1, 0x7c, 0xf0, 0xc9, 0x79, 0x83, 0x5b, 0xac, 0xcb, 0x7f, 0x3a, 0xbb, 0xbb, 0x96, 0xff, 0xcc, 0x31, 0x8a, 0xb7, 0x1e, 0x6e, 0x12, 0x6f}, {0xa1, 0x85, 0x5e, 0x10, 0xe9, 0x4e, 0x00, 0xba, 0xa2, 0x30, 0x41, 0xd9, 0x16, 0xe2, 0x59, 0xf7, 0x04, 0x4e, 0x49, 0x1d, 0xa6, 0x17, 0x12, 0x69, 0x69, 0x47, 0x63, 0xf0, 0x18, 0xc7, 0xe6, 0x36, 0x93, 0xd2, 0x95, 0x75, 0xdc, 0xb4, 0x64, 0xac, 0x81, 0x6b, 0xaa, 0x1b, 0xe3, 0x53, 0xba, 0x12, 0xe3, 0x87, 0x6c, 0xba, 0x76, 0x28, 0xbd, 0x0b, 0xd8, 0xe7, 0x55, 0xe7, 0x21, 0xeb, 0x01, 0x40}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xfc, 0x2f, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, 0, {0xa0, 0x13, 0x8f, 0x56, 0x4f, 0x74, 0xd0, 0xad, 0x70, 0xbc, 0x33, 0x7d, 0xac, 0xc9, 0xd0, 0xbf, 0x1d, 0x23, 0x49, 0x36, 0x4c, 0xaf, 0x11, 0x88, 0xa1, 0xe6, 0xe8, 0xdd, 0xb3, 0xb7, 0xb1, 0x84}},
+    {{0x02, 0x86, 0xc4, 0x1c, 0xd3, 0x09, 0x13, 0xdb, 0x0f, 0xdf, 0xf7, 0xa6, 0x4e, 0xbd, 0xa5, 0xc8, 0xe3, 0xe7, 0xce, 0xf1, 0x0f, 0x2a, 0xeb, 0xc0, 0x0a, 0x76, 0x50, 0x44, 0x3c, 0xf4, 0xc6, 0x0d}, {0xd1, 0xee, 0x8a, 0x93, 0xa0, 0x11, 0x30, 0xcb, 0xf2, 0x99, 0x24, 0x9a, 0x25, 0x8f, 0x94, 0xfe, 0xb5, 0xf4, 0x69, 0xe7, 0xd0, 0xf2, 0xf2, 0x8f, 0x69, 0xee, 0x5e, 0x9a, 0xa8, 0xf9, 0xb5, 0x4a, 0x60, 0xf2, 0xc3, 0xff, 0x2d, 0x02, 0x36, 0x34, 0xec, 0x7f, 0x41, 0x27, 0xa9, 0x6c, 0xc1, 0x16, 0x62, 0xe4, 0x02, 0x89, 0x4c, 0xf1, 0xf6, 0x94, 0xfb, 0x9a, 0x7e, 0xaa, 0x5f, 0x1d, 0x92, 0x44}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x22, 0xd5, 0xe4, 0x41, 0x52, 0x4d, 0x57, 0x1a, 0x52, 0xb3, 0xde, 0xf1, 0x26, 0x18, 0x9d, 0x3f, 0x41, 0x68, 0x90, 0xa9, 0x9d, 0x4d, 0xa6, 0xed, 0xe2, 0xb0, 0xcd, 0xe1, 0x76, 0x0c, 0xe2, 0xc3, 0xf9, 0x84, 0x57, 0xae}, 1, {0x25, 0x0b, 0x93, 0x57, 0x0d, 0x41, 0x11, 0x49, 0x10, 0x5a, 0xb8, 0xcb, 0x0b, 0xc5, 0x07, 0x99, 0x14, 0x90, 0x63, 0x06, 0x36, 0x8c, 0x23, 0xe9, 0xd7, 0x7c, 0x2a, 0x33, 0x26, 0x5b, 0x99, 0x4c}},
+    {{0x6c, 0x77, 0x43, 0x2d, 0x1f, 0xda, 0x31, 0xe9, 0xf9, 0x42, 0xf8, 0xaf, 0x44, 0x60, 0x7e, 0x10, 0xf3, 0xad, 0x38, 0xa6, 0x5f, 0x8a, 0x4b, 0xdd, 0xae, 0x82, 0x3e, 0x5e, 0xff, 0x90, 0xdc, 0x38}, {0xd2, 0x68, 0x50, 0x70, 0xc1, 0xe6, 0x37, 0x6e, 0x63, 0x3e, 0x82, 0x52, 0x96, 0x63, 0x4f, 0xd4, 0x61, 0xfa, 0x9e, 0x5b, 0xdf, 0x21, 0x09, 0xbc, 0xeb, 0xd7, 0x35, 0xe5, 0xa9, 0x1f, 0x3e, 0x58, 0x7c, 0x5c, 0xb7, 0x82, 0xab, 0xb7, 0x97, 0xfb, 0xf6, 0xbb, 0x50, 0x74, 0xfd, 0x15, 0x42, 0xa4, 0x74, 0xf2, 0xa4, 0x5b, 0x67, 0x37, 0x63, 0xec, 0x2d, 0xb7, 0xfb, 0x99, 0xb7, 0x37, 0xbb, 0xb9}, {0x56, 0xbd, 0x0c, 0x06, 0xf1, 0x03, 0x52, 0xc3, 0xa1, 0xa9, 0xf4, 0xb4, 0xc9, 0x2f, 0x6f, 0xa2, 0xb2, 0x6d, 0xf1, 0x24, 0xb5, 0x78, 0x78, 0x35, 0x3c, 0x1f, 0xc6, 0x91, 0xc5, 0x1a, 0xbe, 0xa7, 0x7c, 0x88, 0x17, 0xda, 0xee, 0xb9, 0xfa, 0x54, 0x6b, 0x77, 0xc8, 0xda, 0xf7, 0x9d, 0x89, 0xb2, 0x2b, 0x0e, 0x1b, 0x87, 0x57, 0x4e, 0xce, 0x42, 0x37, 0x1f, 0x00, 0x23, 0x7a, 0xa9, 0xd8, 0x3a}, 0, {0x19, 0x18, 0xb7, 0x41, 0xef, 0x5f, 0x9d, 0x1d, 0x76, 0x70, 0xb0, 0x50, 0xc1, 0x52, 0xb4, 0xa4, 0xea, 0xd2, 0xc3, 0x1b, 0xe9, 0xae, 0xcb, 0x06, 0x81, 0xc0, 0xcd, 0x43, 0x24, 0x15, 0x08, 0x53}},
+    {{0xa6, 0xec, 0x25, 0x12, 0x7c, 0xa1, 0xaa, 0x4c, 0xf1, 0x6b, 0x20, 0x08, 0x4b, 0xa1, 0xe6, 0x51, 0x6b, 0xaa, 0xe4, 0xd3, 0x24, 0x22, 0x28, 0x8e, 0x9b, 0x36, 0xd8, 0xbd, 0xdd, 0x2d, 0xe3, 0x5a}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x05, 0x3d, 0x7e, 0xcc, 0xa5, 0x3e, 0x33, 0xe1, 0x85, 0xa8, 0xb9, 0xbe, 0x4e, 0x76, 0x99, 0xa9, 0x7c, 0x6f, 0xf4, 0xc7, 0x95, 0x52, 0x2e, 0x59, 0x18, 0xab, 0x7c, 0xd6, 0xb6, 0x88, 0x4f, 0x67, 0xe6, 0x83, 0xf3, 0xdc}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xa7, 0x73, 0x0b, 0xe3, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00}, 1, {0xdd, 0x21, 0x0a, 0xa6, 0x62, 0x9f, 0x20, 0xbb, 0x32, 0x8e, 0x5d, 0x89, 0xda, 0xa6, 0xeb, 0x2a, 0xc3, 0xd1, 0xc6, 0x58, 0xa7, 0x25, 0x53, 0x6f, 0xf1, 0x54, 0xf3, 0x1b, 0x53, 0x6c, 0x23, 0xb2}},
+    {{0x0a, 0xf9, 0x52, 0x65, 0x9e, 0xd7, 0x6f, 0x80, 0xf5, 0x85, 0x96, 0x6b, 0x95, 0xab, 0x6e, 0x6f, 0xd6, 0x86, 0x54, 0x67, 0x28, 0x27, 0x87, 0x86, 0x84, 0xc8, 0xb5, 0x47, 0xb1, 0xb9, 0x4f, 0x5a}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xc8, 0x10, 0x17, 0xfd, 0x92, 0xfd, 0x31, 0x63, 0x7c, 0x26, 0xc9, 0x06, 0xb4, 0x20, 0x92, 0xe1, 0x1c, 0xc0, 0xd3, 0xaf, 0xae, 0x8d, 0x90, 0x19, 0xd2, 0x57, 0x8a, 0xf2, 0x27, 0x35, 0xce, 0x7b, 0xc4, 0x69, 0xc7, 0x2d}, {0x96, 0x52, 0xd7, 0x8b, 0xae, 0xfc, 0x02, 0x8c, 0xd3, 0x7a, 0x6a, 0x92, 0x62, 0x5b, 0x8b, 0x8f, 0x85, 0xfd, 0xe1, 0xe4, 0xc9, 0x44, 0xad, 0x3f, 0x20, 0xe1, 0x98, 0xbe, 0xf8, 0xc0, 0x2f, 0x19, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xf2, 0xe9, 0x18, 0x70}, 0, {0x35, 0x68, 0xf2, 0xae, 0xa2, 0xe1, 0x4e, 0xf4, 0xee, 0x4a, 0x3c, 0x2a, 0x8b, 0x8d, 0x31, 0xbc, 0x5e, 0x31, 0x87, 0xba, 0x86, 0xdb, 0x10, 0x73, 0x9b, 0x4f, 0xf8, 0xec, 0x92, 0xff, 0x66, 0x55}},
+    {{0xf9, 0x0e, 0x08, 0x0c, 0x64, 0xb0, 0x58, 0x24, 0xc5, 0xa2, 0x4b, 0x25, 0x01, 0xd5, 0xae, 0xaf, 0x08, 0xaf, 0x38, 0x72, 0xee, 0x86, 0x0a, 0xa8, 0x0b, 0xdc, 0xd4, 0x30, 0xf7, 0xb6, 0x34, 0x94}, {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x11, 0x51, 0x73, 0x76, 0x5d, 0xc2, 0x02, 0xcf, 0x02, 0x9a, 0xd3, 0xf1, 0x54, 0x79, 0x73, 0x5d, 0x57, 0x69, 0x7a, 0xf1, 0x2b, 0x01, 0x31, 0xdd, 0x21, 0x43, 0x0d, 0x57, 0x72, 0xe4, 0xef, 0x11, 0x47, 0x4d, 0x58, 0xb9}, {0x12, 0xa5, 0x0f, 0x3f, 0xaf, 0xea, 0x7c, 0x1e, 0xea, 0xda, 0x4c, 0xf8, 0xd3, 0x37, 0x77, 0x70, 0x4b, 0x77, 0x36, 0x14, 0x53, 0xaf, 0xc8, 0x3b, 0xda, 0x91, 0xee, 0xf3, 0x49, 0xae, 0x04, 0x4d, 0x20, 0x12, 0x6c, 0x62, 0x00, 0x54, 0x7e, 0xa5, 0xa6, 0x91, 0x17, 0x76, 0xc0, 0x5d, 0xee, 0x2a, 0x7f, 0x1a, 0x9b, 0xa7, 0xdf, 0xba, 0xbb, 0xbd, 0x27, 0x3c, 0x3e, 0xf2, 0x9e, 0xf4, 0x6e, 0x46}, 1, {0xe2, 0x54, 0x61, 0xfb, 0x0e, 0x4c, 0x16, 0x2e, 0x18, 0x12, 0x3e, 0xcd, 0xe8, 0x83, 0x42, 0xd5, 0x4d, 0x44, 0x96, 0x31, 0xe9, 0xb7, 0x5a, 0x26, 0x6f, 0xd9, 0x26, 0x0c, 0x2b, 0xb2, 0xf4, 0x1d}},
+};
+
+/** This is a hasher for ellswift_xdh which just returns the shared X coordinate.
+ *
+ * This is generally a bad idea as it means changes to the encoding of the
+ * exchanged public keys do not affect the shared secret. However, it's used here
+ * in tests to be able to verify the X coordinate through other means.
+ */
+static int ellswift_xdh_hash_x32(unsigned char *output, const unsigned char *x32, const unsigned char *ell_a64, const unsigned char *ell_b64, void *data) {
+    (void)ell_a64;
+    (void)ell_b64;
+    (void)data;
+    memcpy(output, x32, 32);
+    return 1;
+}
+
+/* Run the test vectors for ellswift encoding */
+void ellswift_encoding_test_vectors_tests(void) {
+    int i;
+    for (i = 0; (unsigned)i < ARRAY_SIZE(ellswift_xswiftec_inv_tests); ++i) {
+        const struct ellswift_xswiftec_inv_test *testcase = &ellswift_xswiftec_inv_tests[i];
+        int c;
+        for (c = 0; c < 8; ++c) {
+            secp256k1_fe t;
+            int ret = secp256k1_ellswift_xswiftec_inv_var(&t, &testcase->x, &testcase->u, c);
+            CHECK(ret == ((testcase->enc_bitmap >> c) & 1));
+            if (ret) {
+                secp256k1_fe x2;
+                CHECK(fe_equal(&t, &testcase->encs[c]));
+                secp256k1_ellswift_xswiftec_var(&x2, &testcase->u, &testcase->encs[c]);
+                CHECK(fe_equal(&testcase->x, &x2));
+            }
+        }
+    }
+}
+
+/* Run the test vectors for ellswift decoding */
+void ellswift_decoding_test_vectors_tests(void) {
+    int i;
+    for (i = 0; (unsigned)i < ARRAY_SIZE(ellswift_decode_tests); ++i) {
+        const struct ellswift_decode_test *testcase = &ellswift_decode_tests[i];
+        secp256k1_pubkey pubkey;
+        secp256k1_ge ge;
+        int ret;
+        ret = secp256k1_ellswift_decode(CTX, &pubkey, testcase->enc);
+        CHECK(ret);
+        ret = secp256k1_pubkey_load(CTX, &ge, &pubkey);
+        CHECK(ret);
+        CHECK(fe_equal(&testcase->x, &ge.x));
+        CHECK(secp256k1_fe_is_odd(&ge.y) == testcase->odd_y);
+    }
+}
+
+/* Run the test vectors for ellswift expected xdh BIP324 shared secrets */
+void ellswift_xdh_test_vectors_tests(void) {
+    int i;
+    for (i = 0; (unsigned)i < ARRAY_SIZE(ellswift_xdh_tests_bip324); ++i) {
+        const struct ellswift_xdh_test *test = &ellswift_xdh_tests_bip324[i];
+        unsigned char shared_secret[32];
+        int ret;
+        int party = !test->initiating;
+        const unsigned char* ell_a64 = party ? test->ellswift_theirs : test->ellswift_ours;
+        const unsigned char* ell_b64 = party ? test->ellswift_ours   : test->ellswift_theirs;
+        ret = secp256k1_ellswift_xdh(CTX, shared_secret,
+                                     ell_a64, ell_b64,
+                                     test->priv_ours,
+                                     party,
+                                     secp256k1_ellswift_xdh_hash_function_bip324,
+                                     NULL);
+        CHECK(ret);
+        CHECK(secp256k1_memcmp_var(shared_secret, test->shared_secret, 32) == 0);
+    }
+}
+
+/* Verify that secp256k1_ellswift_encode + decode roundtrips */
+void ellswift_encode_decode_roundtrip_tests(void) {
+    int i;
+    for (i = 0; i < 1000 * COUNT; i++) {
+        unsigned char rnd32[32];
+        unsigned char ell64[64];
+        secp256k1_ge g, g2;
+        secp256k1_pubkey pubkey, pubkey2;
+        /* Generate random public key and random randomizer. */
+        testutil_random_ge_test(&g);
+        secp256k1_pubkey_save(&pubkey, &g);
+        testrand256(rnd32);
+        /* Convert the public key to ElligatorSwift and back. */
+        secp256k1_ellswift_encode(CTX, ell64, &pubkey, rnd32);
+        secp256k1_ellswift_decode(CTX, &pubkey2, ell64);
+        secp256k1_pubkey_load(CTX, &g2, &pubkey2);
+        /* Compare with original. */
+        CHECK(secp256k1_ge_eq_var(&g, &g2));
+    }
+}
+
+/* Verify the behavior of secp256k1_ellswift_create */
+void ellswift_create_tests(void) {
+    int i;
+    for (i = 0; i < 400 * COUNT; i++) {
+        unsigned char auxrnd32[32], sec32[32];
+        secp256k1_scalar sec;
+        secp256k1_gej res;
+        secp256k1_ge dec;
+        secp256k1_pubkey pub;
+        unsigned char ell64[64];
+        int ret;
+        /* Generate random secret key and random randomizer. */
+        if (i & 1) testrand256_test(auxrnd32);
+        testutil_random_scalar_order_test(&sec);
+        secp256k1_scalar_get_b32(sec32, &sec);
+        /* Construct ElligatorSwift-encoded public keys for that key. */
+        ret = secp256k1_ellswift_create(CTX, ell64, sec32, (i & 1) ? auxrnd32 : NULL);
+        CHECK(ret);
+        /* Decode it, and compare with traditionally-computed public key. */
+        secp256k1_ellswift_decode(CTX, &pub, ell64);
+        secp256k1_pubkey_load(CTX, &dec, &pub);
+        secp256k1_ecmult(&res, NULL, &secp256k1_scalar_zero, &sec);
+        CHECK(secp256k1_gej_eq_ge_var(&res, &dec));
+    }
+}
+
+/* Verify that secp256k1_ellswift_xdh computes the right shared X coordinate */
+void ellswift_compute_shared_secret_tests(void) {
+    int i;
+    for (i = 0; i < 800 * COUNT; i++) {
+        unsigned char ell64[64], sec32[32], share32[32];
+        secp256k1_scalar sec;
+        secp256k1_ge dec, res;
+        secp256k1_fe share_x;
+        secp256k1_gej decj, resj;
+        secp256k1_pubkey pub;
+        int ret;
+        /* Generate random secret key. */
+        testutil_random_scalar_order_test(&sec);
+        secp256k1_scalar_get_b32(sec32, &sec);
+        /* Generate random ElligatorSwift encoding for the remote key and decode it. */
+        testrand256_test(ell64);
+        testrand256_test(ell64 + 32);
+        secp256k1_ellswift_decode(CTX, &pub, ell64);
+        secp256k1_pubkey_load(CTX, &dec, &pub);
+        secp256k1_gej_set_ge(&decj, &dec);
+        /* Compute the X coordinate of seckey*pubkey using ellswift_xdh. Note that we
+         * pass ell64 as claimed (but incorrect) encoding for sec32 here; this works
+         * because the "hasher" function we use here ignores the ell64 arguments. */
+        ret = secp256k1_ellswift_xdh(CTX, share32, ell64, ell64, sec32, i & 1, &ellswift_xdh_hash_x32, NULL);
+        CHECK(ret);
+        (void)secp256k1_fe_set_b32_limit(&share_x, share32); /* no overflow is possible */
+        SECP256K1_FE_VERIFY(&share_x);
+        /* Compute seckey*pubkey directly. */
+        secp256k1_ecmult(&resj, &decj, &sec, NULL);
+        secp256k1_ge_set_gej(&res, &resj);
+        /* Compare. */
+        CHECK(fe_equal(&res.x, &share_x));
+    }
+}
+
+void ellswift_xdh_correctness_tests(void) {
+    int i;
+    /* Verify the joint behavior of secp256k1_ellswift_xdh */
+    for (i = 0; i < 200 * COUNT; i++) {
+        unsigned char auxrnd32a[32], auxrnd32b[32], auxrnd32a_bad[32], auxrnd32b_bad[32];
+        unsigned char sec32a[32], sec32b[32], sec32a_bad[32], sec32b_bad[32];
+        secp256k1_scalar seca, secb;
+        unsigned char ell64a[64], ell64b[64], ell64a_bad[64], ell64b_bad[64];
+        unsigned char share32a[32], share32b[32], share32_bad[32];
+        unsigned char prefix64[64];
+        secp256k1_ellswift_xdh_hash_function hash_function;
+        void* data;
+        int ret;
+
+        /* Pick hasher to use. */
+        if ((i % 3) == 0) {
+            hash_function = ellswift_xdh_hash_x32;
+            data = NULL;
+        } else if ((i % 3) == 1) {
+            hash_function = secp256k1_ellswift_xdh_hash_function_bip324;
+            data = NULL;
+        } else {
+            hash_function = secp256k1_ellswift_xdh_hash_function_prefix;
+            testrand256_test(prefix64);
+            testrand256_test(prefix64 + 32);
+            data = prefix64;
+        }
+
+        /* Generate random secret keys and random randomizers. */
+        testrand256_test(auxrnd32a);
+        testrand256_test(auxrnd32b);
+        testutil_random_scalar_order_test(&seca);
+        /* Draw secb uniformly at random to make sure that the secret keys
+         * differ */
+        testutil_random_scalar_order(&secb);
+        secp256k1_scalar_get_b32(sec32a, &seca);
+        secp256k1_scalar_get_b32(sec32b, &secb);
+
+        /* Construct ElligatorSwift-encoded public keys for those keys. */
+        /* For A: */
+        ret = secp256k1_ellswift_create(CTX, ell64a, sec32a, auxrnd32a);
+        CHECK(ret);
+        /* For B: */
+        ret = secp256k1_ellswift_create(CTX, ell64b, sec32b, auxrnd32b);
+        CHECK(ret);
+
+        /* Compute the shared secret both ways and compare with each other. */
+        /* For A: */
+        ret = secp256k1_ellswift_xdh(CTX, share32a, ell64a, ell64b, sec32a, 0, hash_function, data);
+        CHECK(ret);
+        /* For B: */
+        ret = secp256k1_ellswift_xdh(CTX, share32b, ell64a, ell64b, sec32b, 1, hash_function, data);
+        CHECK(ret);
+        /* And compare: */
+        CHECK(secp256k1_memcmp_var(share32a, share32b, 32) == 0);
+
+        /* Verify that the shared secret doesn't match if other side's public key is incorrect. */
+        /* For A (using a bad public key for B): */
+        memcpy(ell64b_bad, ell64b, sizeof(ell64a_bad));
+        testrand_flip(ell64b_bad, sizeof(ell64b_bad));
+        ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b_bad, sec32a, 0, hash_function, data);
+        CHECK(ret); /* Mismatching encodings don't get detected by secp256k1_ellswift_xdh. */
+        CHECK(secp256k1_memcmp_var(share32_bad, share32a, 32) != 0);
+        /* For B (using a bad public key for A): */
+        memcpy(ell64a_bad, ell64a, sizeof(ell64a_bad));
+        testrand_flip(ell64a_bad, sizeof(ell64a_bad));
+        ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a_bad, ell64b, sec32b, 1, hash_function, data);
+        CHECK(ret);
+        CHECK(secp256k1_memcmp_var(share32_bad, share32b, 32) != 0);
+
+        /* Verify that the shared secret doesn't match if the private key is incorrect. */
+        /* For A: */
+        memcpy(sec32a_bad, sec32a, sizeof(sec32a_bad));
+        testrand_flip(sec32a_bad, sizeof(sec32a_bad));
+        ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32a_bad, 0, hash_function, data);
+        CHECK(!ret || secp256k1_memcmp_var(share32_bad, share32a, 32) != 0);
+        /* For B: */
+        memcpy(sec32b_bad, sec32b, sizeof(sec32b_bad));
+        testrand_flip(sec32b_bad, sizeof(sec32b_bad));
+        ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32b_bad, 1, hash_function, data);
+        CHECK(!ret || secp256k1_memcmp_var(share32_bad, share32b, 32) != 0);
+
+        if (hash_function != ellswift_xdh_hash_x32) {
+            /* Verify that the shared secret doesn't match when a different encoding of the same public key is used. */
+            /* For A (changing B's public key): */
+            memcpy(auxrnd32b_bad, auxrnd32b, sizeof(auxrnd32b_bad));
+            testrand_flip(auxrnd32b_bad, sizeof(auxrnd32b_bad));
+            ret = secp256k1_ellswift_create(CTX, ell64b_bad, sec32b, auxrnd32b_bad);
+            CHECK(ret);
+            ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b_bad, sec32a, 0, hash_function, data);
+            CHECK(ret);
+            CHECK(secp256k1_memcmp_var(share32_bad, share32a, 32) != 0);
+            /* For B (changing A's public key): */
+            memcpy(auxrnd32a_bad, auxrnd32a, sizeof(auxrnd32a_bad));
+            testrand_flip(auxrnd32a_bad, sizeof(auxrnd32a_bad));
+            ret = secp256k1_ellswift_create(CTX, ell64a_bad, sec32a, auxrnd32a_bad);
+            CHECK(ret);
+            ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a_bad, ell64b, sec32b, 1, hash_function, data);
+            CHECK(ret);
+            CHECK(secp256k1_memcmp_var(share32_bad, share32b, 32) != 0);
+
+            /* Verify that swapping sides changes the shared secret. */
+            /* For A (claiming to be B): */
+            ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32a, 1, hash_function, data);
+            CHECK(ret);
+            CHECK(secp256k1_memcmp_var(share32_bad, share32a, 32) != 0);
+            /* For B (claiming to be A): */
+            ret = secp256k1_ellswift_xdh(CTX, share32_bad, ell64a, ell64b, sec32b, 0, hash_function, data);
+            CHECK(ret);
+            CHECK(secp256k1_memcmp_var(share32_bad, share32b, 32) != 0);
+        }
+    }
+}
+
+DEFINE_SHA256_TRANSFORM_PROBE(sha256_ellswift_xdh)
+void ellswift_xdh_ctx_sha256_tests(void) {
+    /* Check ctx-provided SHA256 compression override takes effect */
+    secp256k1_context *ctx = secp256k1_context_clone(CTX);
+    unsigned char out_default[65], out_custom[65];
+    const unsigned char skA[32] = {1}, skB[32] = {2};
+    unsigned char keyA[64], keyB[64], data[64] = {0};
+    secp256k1_ellswift_xdh_hash_function hash_fn;
+    int i;
+
+    CHECK(secp256k1_ellswift_create(ctx, keyA, skA, NULL));
+    CHECK(secp256k1_ellswift_create(ctx, keyB, skB, NULL));
+
+    for (i = 0; i < 2; i++) {
+        if (i == 0) {
+            hash_fn = secp256k1_ellswift_xdh_hash_function_bip324;
+        } else {
+            hash_fn = secp256k1_ellswift_xdh_hash_function_prefix;
+        }
+        /* Default behavior. No ctx-provided SHA256 compression */
+        CHECK(secp256k1_ellswift_xdh(ctx, out_default, keyA, keyB, skA, 0, hash_fn, data));
+        CHECK(!sha256_ellswift_xdh_called);
+
+        /* Override SHA256 compression directly, bypassing the ctx setter sanity checks */
+        ctx->hash_ctx.fn_sha256_compression = sha256_ellswift_xdh;
+        CHECK(secp256k1_ellswift_xdh(ctx, out_custom, keyA, keyB, skA, 0, hash_fn, data));
+        CHECK(sha256_ellswift_xdh_called);
+        /* Outputs must differ if custom compression was used */
+        CHECK(secp256k1_memcmp_var(out_default, out_custom, 32) != 0);
+
+        /* Restore defaults */
+        sha256_ellswift_xdh_called = 0;
+        secp256k1_context_set_sha256_compression(ctx, NULL);
+    }
+
+    secp256k1_context_destroy(ctx);
+}
+
+/* Test hash initializers */
+void ellswift_hash_init_tests(void) {
+    secp256k1_sha256 sha_optimized;
+    const secp256k1_hash_ctx *hash_ctx = secp256k1_get_hash_context(CTX);
+    /* "secp256k1_ellswift_encode" */
+    static const unsigned char encode_tag[] = {'s', 'e', 'c', 'p', '2', '5', '6', 'k', '1', '_', 'e', 'l', 'l', 's', 'w', 'i', 'f', 't', '_', 'e', 'n', 'c', 'o', 'd', 'e'};
+    /* "secp256k1_ellswift_create" */
+    static const unsigned char create_tag[] = {'s', 'e', 'c', 'p', '2', '5', '6', 'k', '1', '_', 'e', 'l', 'l', 's', 'w', 'i', 'f', 't', '_', 'c', 'r', 'e', 'a', 't', 'e'};
+    /* "bip324_ellswift_xonly_ecdh" */
+    static const unsigned char bip324_tag[] = {'b', 'i', 'p', '3', '2', '4', '_', 'e', 'l', 'l', 's', 'w', 'i', 'f', 't', '_', 'x', 'o', 'n', 'l', 'y', '_', 'e', 'c', 'd', 'h'};
+
+    /* Check that hash initialized by
+     * secp256k1_ellswift_sha256_init_encode has the expected
+     * state. */
+    secp256k1_ellswift_sha256_init_encode(&sha_optimized);
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, encode_tag, sizeof(encode_tag));
+
+    /* Check that hash initialized by
+     * secp256k1_ellswift_sha256_init_create has the expected
+     * state. */
+    secp256k1_ellswift_sha256_init_create(&sha_optimized);
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, create_tag, sizeof(create_tag));
+
+    /* Check that hash initialized by
+     * secp256k1_ellswift_sha256_init_bip324 has the expected
+     * state. */
+    secp256k1_ellswift_sha256_init_bip324(&sha_optimized);
+    test_sha256_tag_midstate(hash_ctx, &sha_optimized, bip324_tag, sizeof(bip324_tag));
+}
+
+void ellswift_xdh_bad_scalar_tests(void) {
+    unsigned char s_zero[32] = { 0 };
+    unsigned char s_overflow_minus1[32] = { 0 };
+    unsigned char s_overflow_plus1[32] = { 0 };
+    unsigned char s_good[32] = { 0 };
+    unsigned char ell_a64[64], ell_b64[64];
+    unsigned char output[32];
+    secp256k1_scalar rand_scalar;
+
+    testutil_random_scalar_order(&rand_scalar);
+    secp256k1_scalar_get_b32(s_good, &rand_scalar);
+
+    CHECK(secp256k1_ellswift_create(CTX, ell_a64, s_good, NULL) == 1);
+
+    testrand256_test(ell_b64);
+    testrand256_test(ell_b64 + 32);
+
+    memcpy(s_overflow_minus1, secp256k1_group_order_bytes, 32);
+    s_overflow_minus1[31] -= 1;
+    memcpy(s_overflow_plus1, secp256k1_group_order_bytes, 32);
+    s_overflow_plus1[31] += 1;
+    CHECK(secp256k1_ellswift_xdh(CTX, output, ell_a64, ell_b64, s_zero, 0, &ellswift_xdh_hash_x32, NULL) == 0);
+    CHECK(secp256k1_ellswift_xdh(CTX, output, ell_a64, ell_b64, secp256k1_group_order_bytes, 0, &ellswift_xdh_hash_x32, NULL) == 0);
+    CHECK(secp256k1_ellswift_xdh(CTX, output, ell_a64, ell_b64, s_overflow_plus1, 0, &ellswift_xdh_hash_x32, NULL) == 0);
+    CHECK(secp256k1_ellswift_xdh(CTX, output, ell_a64, ell_b64, s_overflow_minus1, 0, &ellswift_xdh_hash_x32, NULL) == 1);
+}
+
+/* --- Test registry --- */
+static const struct tf_test_entry tests_ellswift[] = {
+    CASE1(ellswift_encoding_test_vectors_tests),
+    CASE1(ellswift_decoding_test_vectors_tests),
+    CASE1(ellswift_xdh_test_vectors_tests),
+    CASE1(ellswift_encode_decode_roundtrip_tests),
+    CASE1(ellswift_create_tests),
+    CASE1(ellswift_compute_shared_secret_tests),
+    CASE1(ellswift_xdh_correctness_tests),
+    CASE1(ellswift_hash_init_tests),
+    CASE1(ellswift_xdh_bad_scalar_tests),
+    CASE1(ellswift_xdh_ctx_sha256_tests),
+};
+
+#endif