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13 Commits

Author SHA1 Message Date
Laan Tungir
6cf3255d56 This is a meaningful git commit message 2026-07-12 10:11:00 -04:00
Laan Tungir
57863fddcd Fix worker unresponsiveness: fire-and-forget cache writes + remove per-event console.log 2026-07-03 06:29:34 -04:00
Laan Tungir
7d500495a7 post.html: comment button now opens post-feed.html like feed.html 2026-07-01 18:55:25 -04:00
Laan Tungir
7da3b7047c Remove debug logging from notifications menu 2026-07-01 17:30:39 -04:00
Laan Tungir
360a4d83db Add debug logging for notification menu items 2026-07-01 16:54:24 -04:00
Laan Tungir
9400508f3e Fix notifications: keep interaction bar detached so only dropdown menu shows 2026-07-01 16:50:21 -04:00
Laan Tungir
7edee38ea1 Add Like/Zap/Nutzap/Comment/Quote to notification dropdown menu via hidden interaction bar 2026-07-01 15:56:16 -04:00
Laan Tungir
1a17bef1ac Implement Phase 1 remaining tasks: notifications append-only, listener leak fix, memory caps
Task 1.2: Append-only rendering for notifications page
- Extracted buildNotificationRow(item) helper from renderNotifications()
- Added prependNotificationRow(item) with sorted insertion by created_at
- addNotificationFromEvent uses prepend when DOM has children

Task 1.3: Fix notification document.click listener leak
- Removed per-row document.addEventListener('click') that leaked on every render
- Added single delegated click listener in main() using .notif-menu-panel class
- Menu panels still close when clicking outside .notif-right

Task 1.4: Cap posts[] and postIds with rolling eviction
- Added MAX_STORED_POSTS=500 constant to feed.html and post.html
- Added prunePostsArray() that sorts, slices, rebuilds postIds/renderedPostIds
- Called in upsertFeedPost/upsertPost with +50 batch threshold
- post.html skips pruning in event mode

Task 1.5: Cap notificationsById/unreadNotificationsById with periodic pruning
- Added MAX_STORED_NOTIFICATIONS=500, MAX_POST_IMAGE_CACHE=200
- Added pruneNotificationMaps() that prunes both Maps and LRU-caps postImageCache
- Called in addNotificationFromEvent, hydrateNotificationsFromCache/Relays

Updated plan checklist marking all Phase 1 tasks complete.
2026-07-01 09:33:29 -04:00
Laan Tungir
04405da933 Fix feed page dropped posts: out-of-order events and race condition
prependPostCard() now inserts posts in the correct sorted position within
the existing DOM instead of falling back to a full renderFeed() rebuild
when a post is older than the first visible post. This handles relays
that deliver events out of order without wiping the feed.

Also fixed a race condition in fetchFeedWindow: the fire-and-forget
ndkFetchEvents callback was calling renderFeed() after bootstrap
completed, which wiped prepended live posts and caused concurrent
rebuild races. Now it only calls renderFeed() if the feed hasn't been
rendered yet (renderedPostIds.size === 0).

Same prependPostCard sorted-insert fix applied to post.html.
2026-07-01 09:22:33 -04:00
Laan Tungir
ee0077063d Implement append-only rendering for feed and post pages (task 1.1)
Split renderFeed() into full rebuild + prependPostCard() on both feed.html
and post.html. New live events now prepend a single card at the top of the
feed without rebuilding existing cards, eliminating O(n) DOM rebuilds on
every incoming event. DOM is trimmed to displayCount on overflow with
renderedPostIds kept in sync. Full rebuild path preserved for See More,
mute removal, bootstrap completion, and event mode.

Also added implementation checklist to plans/long-running-memory-bloat-fix.md.
2026-07-01 07:59:39 -04:00
Laan Tungir
b09bf0d839 Fix ReferenceError: move publishStartTime to outer scope so silent failure detection can access it 2026-06-30 11:36:36 -04:00
Laan Tungir
d04844cce8 Detect silent relay failures: after each batch, mark relays with no response as timed out (catches DNS errors, connection refused, HTTP handshake failures that NDK doesn't emit relay:publish:failed for) 2026-06-30 11:24:45 -04:00
Laan Tungir
b03b848909 Add debug logging: per-relay publish/timeout/reject with elapsed time, batch start/end timing 2026-06-30 11:07:27 -04:00
368 changed files with 120000 additions and 631 deletions

36
build-pq-bundle.js Normal file
View File

@@ -0,0 +1,36 @@
/**
* Build script for the post-quantum crypto bundle.
* Bundles pq-crypto.mjs and all its dependencies into a single
* ESM file that can be loaded directly in the browser.
*
* Usage: node build-pq-bundle.js
*/
const esbuild = require('esbuild');
const path = require('path');
async function build() {
console.log('🔧 Building PQ crypto bundle...');
await esbuild.build({
entryPoints: ['www/js/pq-crypto.mjs'],
bundle: true,
format: 'esm',
target: ['es2020'],
outfile: 'www/pq-crypto.bundle.js',
sourcemap: true,
minify: false, // keep readable for demo
logLevel: 'info',
// Pure JS — no WASM files to handle
define: {
'process.env.NODE_ENV': '"production"'
}
});
console.log('✅ PQ crypto bundle built: www/pq-crypto.bundle.js');
}
build().catch(err => {
console.error('❌ Build failed:', err);
process.exit(1);
});

494
node_modules/.package-lock.json generated vendored
View File

@@ -1,296 +1,8 @@
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The MIT License (MIT)
Copyright (c) 2022 Paul Miller (https://paulmillr.com)
Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
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.

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# noble-ciphers
Audited & minimal JS implementation of Salsa20, ChaCha and AES.
- 🔒 [**Audited**](#security) by an independent security firm
- 🔻 Tree-shakeable: unused code is excluded from your builds
- 🏎 Fast: hand-optimized for caveats of JS engines
- 🔍 Reliable: property-based / cross-library / wycheproof tests ensure correctness
- 💼 AES: ECB, CBC, CTR, CFB, GCM, SIV (nonce misuse-resistant), AESKW, AESKWP
- 💃 Salsa20, ChaCha, XSalsa20, XChaCha, ChaCha8, ChaCha12, Poly1305
- 🥈 Two AES implementations: pure JS or friendly WebCrypto wrapper
- 🪶 11KB (gzipped) for everything, 3KB for ChaCha-only build
Use [awasm-noble](https://github.com/paulmillr/awasm-noble) if you need an even faster (WASM) alternative. Check out [Upgrading](#upgrading) for information about upgrading from previous versions.
Take a glance at [GitHub Discussions](https://github.com/paulmillr/noble-ciphers/discussions) for questions and support.
### This library belongs to _noble_ cryptography
> **noble cryptography** — high-security, easily auditable set of contained cryptographic libraries and tools.
- Zero or minimal dependencies
- Highly readable TypeScript / JS code
- PGP-signed releases and transparent NPM builds
- All libraries:
[ciphers](https://github.com/paulmillr/noble-ciphers),
[curves](https://github.com/paulmillr/noble-curves),
[hashes](https://github.com/paulmillr/noble-hashes),
[post-quantum](https://github.com/paulmillr/noble-post-quantum),
5kb [secp256k1](https://github.com/paulmillr/noble-secp256k1) /
[ed25519](https://github.com/paulmillr/noble-ed25519)
- [Check out the homepage](https://paulmillr.com/noble/)
for reading resources, documentation, and apps built with noble
## Usage
> `npm install @noble/ciphers`
> `deno add jsr:@noble/ciphers`
We support all major platforms and runtimes.
For React Native, you may need a
[polyfill for getRandomValues](https://github.com/LinusU/react-native-get-random-values).
A standalone file
[noble-ciphers.js](https://github.com/paulmillr/noble-ciphers/releases) is also available.
```ts
// import * from '@noble/ciphers'; // Error: use sub-imports, to ensure small app size
import { gcm, gcmsiv } from '@noble/ciphers/aes.js';
import { chacha20poly1305, xchacha20poly1305 } from '@noble/ciphers/chacha.js';
import { xsalsa20poly1305 } from '@noble/ciphers/salsa.js';
// Unauthenticated encryption: make sure to use HMAC or similar
import { ctr, cfb, cbc, ecb } from '@noble/ciphers/aes.js';
import { salsa20, xsalsa20 } from '@noble/ciphers/salsa.js';
import { chacha20, xchacha20, chacha8, chacha12 } from '@noble/ciphers/chacha.js';
import { aeskw, aeskwp } from '@noble/ciphers/aes.js'; // KW
import { bytesToHex, hexToBytes, managedNonce, randomBytes } from '@noble/ciphers/utils.js';
```
- [Examples](#examples)
- [XChaCha20-Poly1305 encryption](#xchacha20-poly1305-encryption)
- [AES-256-GCM encryption](#aes-256-gcm-encryption)
- [managedNonce: automatic nonce handling](#managednonce-automatic-nonce-handling)
- [AES: gcm, siv, ctr, cfb, cbc, ecb, aeskw](#aes-gcm-siv-ctr-cfb-cbc-ecb-aeskw)
- [AES: friendly WebCrypto wrapper](#aes-friendly-webcrypto-wrapper)
- [Reuse array for input and output](#reuse-array-for-input-and-output)
- [Use password for encryption](#use-password-for-encryption)
- [Internals](#internals)
- [Picking a cipher](#picking-a-cipher)
- [How to encrypt properly](#how-to-encrypt-properly)
- [Nonces](#nonces)
- [Encryption limits](#encryption-limits)
- [AES block modes](#aes-block-modes)
- [Implemented primitives](#implemented-primitives)
- [Security](#security)
- [Speed](#speed)
- [Upgrading](#upgrading)
- [Contributing & testing](#contributing--testing)
- [License](#license)
## Examples
> [!NOTE]
> Use different nonce every time `encrypt()` is done.
#### XChaCha20-Poly1305 encryption
```js
import { xchacha20poly1305 } from '@noble/ciphers/chacha.js';
import { randomBytes } from '@noble/ciphers/utils.js';
const key = randomBytes(32); // random key
// const key = new Uint8Array([ // existing key
// 169, 88, 160, 139, 168, 29, 147, 196, 14, 88, 237, 76, 243, 177, 109, 140,
// 195, 140, 80, 10, 216, 134, 215, 71, 191, 48, 20, 104, 189, 37, 38, 55,
// ]);
// import { hexToBytes } from '@noble/ciphers/utils.js'; // hex key
// const key = hexToBytes('4b7f89bac90a1086fef73f5da2cbe93b2fae9dfbf7678ae1f3e75fd118ddf999');
const nonce = randomBytes(24);
const chacha = xchacha20poly1305(key, nonce);
const data = new TextEncoder().encode('hello noble');
const ciphertext = chacha.encrypt(data);
const data_ = chacha.decrypt(ciphertext); // new TextDecoder().decode(data_) === data
```
#### AES-256-GCM encryption
```js
import { gcm } from '@noble/ciphers/aes.js';
import { randomBytes } from '@noble/ciphers/utils.js';
const key = randomBytes(32);
const nonce = randomBytes(24);
const data = new TextEncoder().encode('hello noble');
const aes = gcm(key, nonce);
const ciphertext = aes.encrypt(data);
const data_ = aes.decrypt(ciphertext); // new TextDecoder().decode(data_) === data
```
#### managedNonce: automatic nonce handling
We provide API that manages nonce internally instead of exposing them to library's user.
For `encrypt`: a `nonceBytes`-length buffer is fetched from CSPRNG and prenended to encrypted ciphertext.
For `decrypt`: first `nonceBytes` of ciphertext are treated as nonce.
> [!NOTE]
> AES-GCM & ChaCha (NOT XChaCha) [limit amount of messages](#encryption-limits)
> encryptable under the same key.
```js
import { xchacha20poly1305 } from '@noble/ciphers/chacha.js';
import { hexToBytes, managedNonce } from '@noble/ciphers/utils.js';
const key = hexToBytes('fa686bfdffd3758f6377abbc23bf3d9bdc1a0dda4a6e7f8dbdd579fa1ff6d7e1');
const chacha = managedNonce(xchacha20poly1305)(key); // manages nonces for you
const data = new TextEncoder().encode('hello noble');
const ciphertext = chacha.encrypt(data);
const data_ = chacha.decrypt(ciphertext);
```
#### AES: gcm, siv, ctr, cfb, cbc, ecb, aeskw
```js
import { gcm, gcmsiv, aessiv, ctr, cfb, cbc, ecb } from '@noble/ciphers/aes.js';
import { randomBytes } from '@noble/ciphers/utils.js';
const plaintext = new Uint8Array(32).fill(16);
for (let cipher of [gcm, gcmsiv, aessiv]) {
const key = randomBytes(32); // 24 for AES-192, 16 for AES-128
const nonce = randomBytes(12);
const ciphertext_ = cipher(key, nonce).encrypt(plaintext);
const plaintext_ = cipher(key, nonce).decrypt(ciphertext_);
}
for (const cipher of [ctr, cbc, cfb]) {
const key = randomBytes(32); // 24 for AES-192, 16 for AES-128
const nonce = randomBytes(16);
const ciphertext_ = cipher(key, nonce).encrypt(plaintext);
const plaintext_ = cipher(key, nonce).decrypt(ciphertext_);
}
for (const cipher of [ecb]) {
const key = randomBytes(32); // 24 for AES-192, 16 for AES-128
const ciphertext_ = cipher(key).encrypt(plaintext);
const plaintext_ = cipher(key).decrypt(ciphertext_);
}
// AESKW, AESKWP
import { aeskw, aeskwp } from '@noble/ciphers/aes.js';
import { hexToBytes } from '@noble/ciphers/utils.js';
const kek = hexToBytes('000102030405060708090A0B0C0D0E0F');
const keyData = hexToBytes('00112233445566778899AABBCCDDEEFF');
const ciphertext = aeskw(kek).encrypt(keyData);
```
#### AES: friendly WebCrypto wrapper
Noble implements AES. Sometimes people want to use built-in `crypto.subtle` instead. However, it has terrible API. We simplify access to built-ins.
> [!NOTE]
> Webcrypto methods are always async.
```js
import { gcm, ctr, cbc } from '@noble/ciphers/webcrypto.js';
import { randomBytes } from '@noble/ciphers/utils.js';
const plaintext = new Uint8Array(32).fill(16);
const key = randomBytes(32);
for (const cipher of [gcm]) {
const nonce = randomBytes(12);
const ciphertext_ = await cipher(key, nonce).encrypt(plaintext);
const plaintext_ = await cipher(key, nonce).decrypt(ciphertext_);
}
for (const cipher of [ctr, cbc]) {
const nonce = randomBytes(16);
const ciphertext_ = await cipher(key, nonce).encrypt(plaintext);
const plaintext_ = await cipher(key, nonce).decrypt(ciphertext_);
}
```
#### Reuse array for input and output
To avoid additional allocations, Uint8Array can be reused
between encryption and decryption calls.
> [!NOTE]
> Some ciphers don't support unaligned (`byteOffset % 4 !== 0`) Uint8Array as
> destination. It can decrease performance, making the optimization pointless.
```js
import { chacha20poly1305 } from '@noble/ciphers/chacha.js';
import { randomBytes } from '@noble/ciphers/utils.js';
const key = randomBytes(32);
const nonce = randomBytes(12);
const chacha = chacha20poly1305(key, nonce);
const input = new TextEncoder().encode('hello noble'); // length == 12
const inputLength = input.length;
const tagLength = 16;
const buf = new Uint8Array(inputLength + tagLength);
const start = buf.subarray(0, inputLength);
start.set(input); // copy input to buf
chacha.encrypt(start, buf); // encrypt into `buf`
chacha.decrypt(buf, start); // decrypt into `start`
```
xsalsa20poly1305 also supports this, but requires 32 additional bytes for encryption / decryption,
due to its inner workings.
#### Randomness generation
We provide userspace CSPRNG (cryptographically secure pseudorandom number generator).
It's best to limit their usage to non-production, non-critical cases: for example, test-only usage.
ChaCha-based CSPRNG does not have a specification as per 2025, which makes it less secure.
```js
import { randomBytes } from '@noble/ciphers/utils.js';
import { rngAesCtrDrbg256 } from '@noble/ciphers/aes.js';
import { rngChacha8, rngChacha20 } from '@noble/ciphers/chacha.js';
// 1. Best: WebCrypto
const rnd1 = randomBytes(32);
// 2. AES-CTR DRBG
const seed2 = randomBytes(48);
const rnd2 = rngAesCtrDrbg256(seed2).randomBytes(1024);
// 3. ChaCha8 CSPRNG
const seed3 = randomBytes(32);
const rnd3 = rngChacha8(seed3).randomBytes(1024);
```
#### Use password for encryption
It is not safe to convert password into Uint8Array.
Instead, KDF stretching function like PBKDF2 / Scrypt / Argon2id
should be applied to convert password to AES key.
Make sure to use salt (app-specific secret) in addition to password.
> `npm install @noble/hashes`
```js
import { xchacha20poly1305 } from '@noble/ciphers/chacha.js';
import { managedNonce } from '@noble/ciphers/utils.js';
import { scrypt } from '@noble/hashes/scrypt.js';
// Convert password into 32-byte key using scrypt
const PASSWORD = 'correct-horse-battery-staple';
const APP_SPECIFIC_SECRET = 'salt-12345678-secret';
const SECURITY_LEVEL = 2 ** 20; // requires 1GB of RAM to calculate
// sync, but scryptAsync is also available
const key = scrypt(PASSWORD, APP_SPECIFIC_SECRET, { N: SECURITY_LEVEL, r: 8, p: 1, dkLen: 32 });
// Use random, managed nonce
const chacha = managedNonce(xchacha20poly1305)(key);
const data = new TextEncoder().encode('hello noble');
const ciphertext = chacha.encrypt(data);
const data_ = chacha.decrypt(ciphertext);
```
## Internals
### Picking a cipher
We suggest to use **XChaCha20-Poly1305** because it's very fast and allows random keys.
**AES-GCM-SIV** is also a good idea, because it provides resistance against nonce reuse.
**AES-GCM** is a good option when those two are not available.
### How to encrypt properly
- Use unpredictable key with enough entropy
- Random key must be using cryptographically secure random number generator (CSPRNG), not `Math.random` etc.
- Non-random key generated from KDF is fine
- Re-using key is fine, but be aware of rules for cryptographic key wear-out and [encryption limits](#encryption-limits)
- Use new nonce every time and [don't repeat it](#nonces)
- chacha and salsa20 are fine for sequential counters that _never_ repeat: `01, 02...`
- xchacha and xsalsa20 can use random nonces instead
- AES-GCM should use 12-byte nonces: smaller nonces are security risk
- Prefer authenticated encryption (AEAD)
- Good: chacha20poly1305, GCM, GCM-SIV, ChaCha+HMAC, CTR+HMAC, CBC+HMAC
- Bad: chacha20, raw CTR, raw CBC
- Flipping bits or ciphertext substitution won't be detected in unauthenticated ciphers
- Polynomial MACs are not perfect for every situation:
they lack Random Key Robustness: the MAC can be forged, and can't
be used in PAKE schemes. See
[invisible salamanders attack](https://keymaterial.net/2020/09/07/invisible-salamanders-in-aes-gcm-siv/).
To combat salamanders, `hash(key)` can be included in ciphertext,
however, this would violate ciphertext indistinguishability:
an attacker would know which key was used - so `HKDF(key, i)`
could be used instead.
- Don't re-use keys between different protocols
- For example, using ECDH key in AES can be bad
- Use hkdf or, at least, a hash function to create sub-key instead
### Nonces
Most ciphers need a key and a nonce (aka initialization vector / IV) to encrypt a data.
Repeating (key, nonce) pair with different plaintexts would allow an attacker to decrypt it.
ciphertext_a = encrypt(plaintext_a, key, nonce)
ciphertext_b = encrypt(plaintext_b, key, nonce)
stream_diff = xor(ciphertext_a, ciphertext_b) # Break encryption
One way of not repeating nonces is using counters:
for i in 0..:
ciphertext[i] = encrypt(plaintexts[i], key, i)
Another is generating random nonce every time:
for i in 0..:
rand_nonces[i] = random()
ciphertext[i] = encrypt(plaintexts[i], key, rand_nonces[i])
- Counters are OK, but it's not always possible to store current counter value:
e.g. in decentralized, unsyncable systems.
- Randomness is OK, but there's a catch:
ChaCha20 and AES-GCM use 96-bit / 12-byte nonces, which implies higher chance of collision.
In the example above, `random()` can collide and produce repeating nonce.
Chance is even higher for 64-bit nonces, which GCM allows - don't use them.
- To safely use random nonces, utilize XSalsa20 or XChaCha:
they increased nonce length to 192-bit, minimizing a chance of collision.
AES-SIV is also fine. In situations where you can't use eXtended-nonce
algorithms, key rotation is advised. hkdf would work great for this case.
### Encryption limits
A "protected message" would mean a probability of `2**-50` that a passive attacker
successfully distinguishes the ciphertext outputs of the AEAD scheme from the outputs
of a random function.
- Max message size:
- AES-GCM: ~68GB, `2**36-256`
- Salsa, ChaCha, XSalsa, XChaCha: ~256GB, `2**38-64`
- Max amount of protected messages, under same key:
- AES-GCM: `2**32.5`
- Salsa, ChaCha: `2**46`, but only integrity (MAC) is affected, not confidentiality (encryption)
- XSalsa, XChaCha: `2**72`
- Max amount of protected messages, across all keys:
- AES-GCM: `2**69/B` where B is max blocks encrypted by a key. Meaning
`2**59` for 1KB, `2**49` for 1MB, `2**39` for 1GB
- Salsa, ChaCha, XSalsa, XChaCha: `2**100`
- Max amount of protected messages, under same key, using **random nonce**:
- Relevant for 12-byte nonces with `managedNonce`: AES-GCM, ChaCha
- `2**23` (8M) messages for `2**-50` chance, `2**32.5` (4B) for `2**-32.5` chance
Check out [draft-irtf-cfrg-aead-limits](https://datatracker.ietf.org/doc/draft-irtf-cfrg-aead-limits/) for details.
### Implemented primitives
- Salsa20 stream cipher, released in 2005.
Salsa's goal was to implement AES replacement that does not rely on S-Boxes,
which are hard to implement in a constant-time manner.
Salsa20 is usually faster than AES, a big deal on slow, budget mobile phones.
- [XSalsa20](https://cr.yp.to/snuffle/xsalsa-20110204.pdf), extended-nonce
variant was released in 2008. It switched nonces from 96-bit to 192-bit,
and became safe to be picked at random.
- Nacl / Libsodium popularized term "secretbox", - which is just xsalsa20poly1305.
We provide the alias and corresponding seal / open methods.
"crypto_box" and "sealedbox" are available in package [noble-sodium](https://github.com/serenity-kit/noble-sodium).
- Check out [PDF](https://cr.yp.to/snuffle/salsafamily-20071225.pdf)
and [website](https://cr.yp.to/snuffle.html).
- ChaCha20 stream cipher, released in 2008. Developed after Salsa20,
ChaCha aims to increase diffusion per round.
- [XChaCha20](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha)
extended-nonce variant is also provided. Similar to XSalsa, it's safe to use with
randomly-generated nonces.
- Check out
[RFC 8439](https://www.rfc-editor.org/rfc/rfc8439),
[PDF](http://cr.yp.to/chacha/chacha-20080128.pdf) and
[website](https://cr.yp.to/chacha.html).
- AES is a variant of Rijndael block cipher, standardized by NIST in 2001.
We provide the fastest available pure JS implementation.
- We support AES-128, AES-192 and AES-256: the mode is selected dynamically,
based on key length (16, 24, 32).
- AES-GCM-SIV nonce-misuse-resistant mode is also provided. Our implementation of SIV
has the same speed as GCM: there is no performance hit.
The mode is described in [RFC 8452](https://www.rfc-editor.org/rfc/rfc8452).
- There is a separate AES-SIV mode, described in [RFC 5297](https://www.rfc-editor.org/rfc/rfc5297)
- We also have AESKW and AESKWP from
[RFC 3394](https://www.rfc-editor.org/rfc/rfc3394) & [RFC 5649](https://www.rfc-editor.org/rfc/rfc5649)
- Format-preserving encryption algorithm (FPE-FF1) specified in
[NIST SP 800-38G](https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-38G.pdf).
- Check out [AES block modes](#aes-block-modes),
[FIPS 197](https://csrc.nist.gov/files/pubs/fips/197/final/docs/fips-197.pdf) and
[original proposal](https://csrc.nist.gov/csrc/media/projects/cryptographic-standards-and-guidelines/documents/aes-development/rijndael-ammended.pdf).
- Polynomial-evaluation MACs are available: Poly1305, AES-GCM's GHash and AES-SIV's Polyval.
- Poly1305 ([PDF](https://cr.yp.to/mac/poly1305-20050329.pdf),
[website](https://cr.yp.to/mac.html))
is a fast and parallel secret-key message-authentication code suitable for
a wide variety of applications. It was standardized in
[RFC 8439](https://www.rfc-editor.org/rfc/rfc8439) and is now used in TLS 1.3.
- Ghash is used in AES-GCM: see NIST SP 800-38G
- Polyval is used in AES-GCM-SIV: see [RFC 8452](https://www.rfc-editor.org/rfc/rfc8452)
##### AES block modes
For non-deterministic (not ECB) schemes, initialization vector (IV) is mixed to block/key;
and each new round either depends on previous block's key, or on some counter.
- **ECB** (Electronic Codebook): Deterministic encryption; identical plaintext blocks yield identical ciphertexts. Not secure due to pattern leakage. due to pattern leakage.
See [AES Penguin](https://words.filippo.io/the-ecb-penguin/)
- **CBC** (Cipher Block Chaining): Each plaintext block is XORed with the previous block of ciphertext
before encryption. Hard to use: requires proper padding and an IV. Unauthenticated: needs MAC.
- **CTR** (Counter Mode): Turns a block cipher into a stream cipher using a counter and IV (nonce).
Efficient and parallelizable. Requires a unique nonce per encryption. Unauthenticated: needs MAC.
- **GCM** (Galois/Counter Mode): Combines CTR mode with polynomial MAC. Efficient and widely used. Not perfect:
a) conservative key wear-out is `2**32` (4B) msgs.
b) key wear-out under random nonces is even smaller: `2**23` (8M) messages for `2**-50` chance.
c) MAC can be forged: see Poly1305 documentation.
- **SIV** (Synthetic IV): GCM with nonce-misuse resistance; repeating nonces reveal only the fact plaintexts
are identical. Also suffers from GCM issues: key wear-out limits & MAC forging.
- **XTS**: Designed for disk encryption.
Similar to ECB (deterministic), but has `[i][j]` tweak arguments corresponding to
sector i and 16-byte block (part of sector) j. Lacks MAC.
## Security
The library has been audited:
- at version 2.2.0, in Apr 2026, by ourselves (self-audited)
- Scope: everything
- [Changes since audit](https://github.com/paulmillr/noble-ciphers/compare/2.2.0..main)
- at version 1.0.0, in Sep 2024, independently, by [cure53](https://cure53.de)
- PDFs: [website](https://cure53.de/audit-report_noble-crypto-libs.pdf), [in-repo](./audit/2024-09-cure53-audit-nbl4.pdf)
- [Changes since audit](https://github.com/paulmillr/noble-ciphers/compare/1.0.0..main)
- Scope: everything
- The audit has been funded by [OpenSats](https://opensats.org)
It is tested against property-based, cross-library and Wycheproof vectors,
and is being fuzzed in [the separate repo](https://github.com/paulmillr/fuzzing).
If you see anything unusual: investigate and report.
### Constant-timeness
We're targetting algorithmic constant time. _JIT-compiler_ and _Garbage Collector_ make "constant time"
extremely hard to achieve [timing attack](https://en.wikipedia.org/wiki/Timing_attack) resistance
in a scripting language. Which means _any other JS library can't have
constant-timeness_. Even statically typed Rust, a language without GC,
[makes it harder to achieve constant-time](https://www.chosenplaintext.ca/open-source/rust-timing-shield/security)
for some cases. If your goal is absolute security, don't use any JS lib — including bindings to native ones.
Use low-level libraries & languages.
The library uses T-tables for AES, which
[leak access timings](https://cr.yp.to/antiforgery/cachetiming-20050414.pdf).
This is also done in [OpenSSL](https://github.com/openssl/openssl/blob/2f33265039cdbd0e4589c80970e02e208f3f94d2/crypto/aes/aes_core.c#L706) and
[Go stdlib](https://cs.opensource.google/go/go/+/refs/tags/go1.22.6:src/crypto/aes/const.go;l=90) for performance reasons.
The analysis was mentioned in [hal-04652991](https://hal.science/hal-04652991/document).
### Supply chain security
- **Commits** are signed with PGP keys to prevent forgery. Be sure to verify the commit signatures
- **Releases** are made transparently through token-less GitHub CI and Trusted Publishing. Be sure to verify the [provenance logs](https://docs.npmjs.com/generating-provenance-statements) for authenticity.
- **Rare releasing** is practiced to minimize the need for re-audits by end-users.
- **Dependencies** are minimized and strictly pinned to reduce supply-chain risk.
- We use as few dependencies as possible.
- Version ranges are locked, and changes are checked with npm-diff.
- **Dev dependencies** are excluded from end-user installs; theyre only used for development and build steps.
For this package, there are 0 dependencies; and a few dev dependencies:
- jsbt is used for benchmarking / testing / build tooling and developed by the same author
- prettier, fast-check and typescript are used for code quality / test generation / ts compilation
### Randomness
We rely on the built-in
[`crypto.getRandomValues`](https://developer.mozilla.org/en-US/docs/Web/API/Crypto/getRandomValues),
which is considered a cryptographically secure PRNG.
Browsers have had weaknesses in the past - and could again - but implementing a userspace CSPRNG is even worse, as theres no reliable userspace source of high-quality entropy.
### Quantum computers
Cryptographically relevant quantum computer, if built, will allow to
utilize Grover's algorithm to break ciphers in 2^n/2 operations, instead of 2^n.
This means AES128 should be replaced with AES256. Salsa and ChaCha are already safe.
Australian ASD prohibits AES128 [after 2030](https://www.cyber.gov.au/resources-business-and-government/essential-cyber-security/ism/cyber-security-guidelines/guidelines-cryptography).
## Speed
```sh
npm run bench
```
Benchmarks measured on Apple M4.
If you need truly exemplar performance, switch to [awasm-noble](https://github.com/paulmillr/awasm-noble).
```
64B
xsalsa20poly1305 x 735,835 ops/sec @ 1μs/op
chacha20poly1305 x 581,395 ops/sec @ 1μs/op
xchacha20poly1305 x 468,384 ops/sec @ 2μs/op
aes-256-gcm x 201,126 ops/sec @ 4μs/op
aes-256-gcm-siv x 162,284 ops/sec @ 6μs/op
# Unauthenticated encryption
salsa20 x 1,655,629 ops/sec @ 604ns/op
xsalsa20 x 1,400,560 ops/sec @ 714ns/op
chacha20 x 1,996,007 ops/sec @ 501ns/op
xchacha20 x 1,404,494 ops/sec @ 712ns/op
chacha8 x 2,145,922 ops/sec @ 466ns/op
chacha12 x 2,036,659 ops/sec @ 491ns/op
aes-ecb-256 x 1,019,367 ops/sec @ 981ns/op
aes-cbc-256 x 931,966 ops/sec @ 1μs/op
aes-ctr-256 x 954,198 ops/sec @ 1μs/op
1MB
xsalsa20poly1305 x 334 ops/sec @ 2ms/op
chacha20poly1305 x 333 ops/sec @ 2ms/op
xchacha20poly1305 x 334 ops/sec @ 2ms/op
aes-256-gcm x 94 ops/sec @ 10ms/op
aes-256-gcm-siv x 90 ops/sec @ 11ms/op
# Unauthenticated encryption
salsa20 x 831 ops/sec @ 1ms/op
xsalsa20 x 830 ops/sec @ 1ms/op
chacha20 x 804 ops/sec @ 1ms/op
xchacha20 x 797 ops/sec @ 1ms/op
chacha8 x 1,495 ops/sec @ 668μs/op
chacha12 x 1,148 ops/sec @ 871μs/op
aes-ecb-256 x 289 ops/sec @ 3ms/op
aes-cbc-256 x 114 ops/sec @ 8ms/op
aes-ctr-256 x 127 ops/sec @ 7ms/op
# Wrapper over built-in webcrypto
webcrypto ctr-256 x 6,508 ops/sec @ 153μs/op
webcrypto cbc-256 x 1,820 ops/sec @ 549μs/op
webcrypto gcm-256 x 5,106 ops/sec @ 195μs/op
```
Compare to other implementations:
```
xsalsa20poly1305 (encrypt, 1MB)
├─tweetnacl x 196 mb/sec
├─awasm-noble_threads x 2,318 mb/sec
├─awasm-noble_no_threads x 1,196 mb/sec
└─noble x 305 mb/sec
aes-ctr-256 (encrypt, 1MB)
├─stablelib x 123 mb/sec
├─aesjs x 42 mb/sec
├─awasm-noble_thread x 2,105 mb/sec
├─awasm-noble_no_threads x 272 mb/sec
├─noble_webcrypto x 5,965 mb/sec
└─noble x 124 mb/sec
```
## Upgrading
Supported node.js versions:
- v2: v20.19+ (ESM-only)
- v1: v14.21+ (ESM & CJS)
Changelog of v2, when upgrading from ciphers v1:
- The package is now ESM-only. ESM can finally be loaded from common.js on node v20.19+
- `.js` extension must be used for all modules
- Old: `@noble/ciphers/aes`
- New: `@noble/ciphers/aes.js`
- This simplifies working in browsers natively without transpilers
- webcrypto: move `randomBytes` and `managedNonce` to `utils.js`
- ghash, poly1305, polyval: only allow Uint8Array as hash inputs, prohibit `string`
- utils: new abytes; remove ahash, toBytes
- Remove modules `_assert` (use `utils`), `_micro` and `crypto` (use `webcrypto`)
- Bump TS compilation target from es2020 to es2022
- Massively improve error messages, make them more descriptive
## Contributing & testing
- `npm install && npm run build && npm test` will build the code and run tests.
- `npm run lint` / `npm run format` will run linter / fix linter issues.
- `npm run bench` will run benchmarks
- `npm run build:release` will build single file
See [paulmillr.com/noble](https://paulmillr.com/noble/)
for useful resources, articles, documentation and demos
related to the library.
## License
The MIT License (MIT)
Copyright (c) 2023 Paul Miller [(https://paulmillr.com)](https://paulmillr.com)
Copyright (c) 2016 Thomas Pornin <pornin@bolet.org>
See LICENSE file.

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/**
* Basic utils for ARX (add-rotate-xor) salsa and chacha ciphers.
RFC8439 requires multi-step cipher stream, where
authKey starts with counter: 0, actual msg with counter: 1.
For this, we need a way to re-use nonce / counter:
const counter = new Uint8Array(4);
chacha(..., counter, ...); // counter is now 1
chacha(..., counter, ...); // counter is now 2
This is complicated:
- 32-bit counters are enough, no need for 64-bit: max ArrayBuffer size in JS is 4GB
- Original papers don't allow mutating counters
- Counter overflow is undefined [^1]
- Idea A: allow providing (nonce | counter) instead of just nonce, re-use it
- Caveat: Cannot be re-used through all cases:
- * chacha has (counter | nonce)
- * xchacha has (nonce16 | counter | nonce16)
- Idea B: separate nonce / counter and provide separate API for counter re-use
- Caveat: there are different counter sizes depending on an algorithm.
- salsa & chacha also differ in structures of key & sigma:
salsa20: s[0] | k(4) | s[1] | nonce(2) | cnt(2) | s[2] | k(4) | s[3]
chacha: s(4) | k(8) | cnt(1) | nonce(3)
chacha20orig: s(4) | k(8) | cnt(2) | nonce(2)
- Idea C: helper method such as `setSalsaState(key, nonce, sigma, data)`
- Caveat: we can't re-use counter array
xchacha uses the subkey and remaining 8 byte nonce with ChaCha20 as normal
(prefixed by 4 NUL bytes, since RFC8439 specifies a 12-byte nonce).
Counter overflow is undefined; see {@link https://mailarchive.ietf.org/arch/msg/cfrg/gsOnTJzcbgG6OqD8Sc0GO5aR_tU/ | the CFRG thread}.
Current noble policy is strict non-wrap for the shared 32-bit counter path:
exported ARX ciphers reject initial `0xffffffff` and stop before any implicit
wrap back to zero.
See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha#appendix-A.2 | the XChaCha appendix} for the extended-nonce construction.
* @module
*/
import { type PRG, type TArg, type TRet, type XorStream } from './utils.ts';
/**
* Rotates a 32-bit word left.
* @param a - Input word.
* @param b - Rotation count in bits.
* @returns Rotated 32-bit word.
* @example
* Moves the top byte of `0x12345678` into the low byte position.
* ```ts
* rotl(0x12345678, 8);
* ```
*/
export declare function rotl(a: number, b: number): number;
/**
* ARX core function operating on 32-bit words. Ciphers must use u32 for efficiency.
* @param sigma - Sigma constants for the selected cipher layout.
* @param key - Expanded key words.
* @param nonce - Nonce and counter words prepared for the round function.
* @param output - Output block written in place.
* @param counter - Block counter value.
* @param rounds - Optional round count override.
*/
export type CipherCoreFn = (sigma: TArg<Uint32Array>, key: TArg<Uint32Array>, nonce: TArg<Uint32Array>, output: TArg<Uint32Array>, counter: number, rounds?: number) => void;
/**
* Nonce-extension function used by XChaCha and XSalsa.
* @param sigma - Sigma constants for the selected cipher layout.
* @param key - Expanded key words.
* @param input - Input nonce words used for subkey derivation.
* @param output - Output buffer written with the derived nonce words.
*/
export type ExtendNonceFn = (sigma: TArg<Uint32Array>, key: TArg<Uint32Array>, input: TArg<Uint32Array>, output: TArg<Uint32Array>) => void;
/** ARX cipher options.
* * `allowShortKeys` for 16-byte keys
* * `counterLength` in bytes
* * `counterRight`: right: `nonce|counter`; left: `counter|nonce`
* */
export type CipherOpts = {
/** Whether 16-byte keys are accepted for legacy Salsa and ChaCha variants. */
allowShortKeys?: boolean;
/** Optional nonce-expansion hook used by extended-nonce variants. */
extendNonceFn?: ExtendNonceFn;
/** Counter length in bytes inside the nonce/counter layout. */
counterLength?: number;
/** Whether the layout is `nonce|counter` instead of `counter|nonce`. */
counterRight?: boolean;
/** Number of core rounds to execute. */
rounds?: number;
};
/**
* Creates an ARX stream cipher from a 32-bit core permutation.
* Used internally to build the exported Salsa and ChaCha stream ciphers.
* @param core - Core function that fills one keystream block.
* @param opts - Cipher layout and nonce-extension options. See {@link CipherOpts}.
* @returns Stream cipher function over byte arrays.
* @throws If the core callback, key size, counter, or output sizing is invalid. {@link Error}
*/
export declare function createCipher(core: TArg<CipherCoreFn>, opts: TArg<CipherOpts>): TRet<XorStream>;
/** Internal class which wraps chacha20 or chacha8 to create CSPRNG. */
export declare class _XorStreamPRG implements PRG {
readonly blockLen: number;
readonly keyLen: number;
readonly nonceLen: number;
private state;
private buf;
private key;
private nonce;
private pos;
private ctr;
private cipher;
constructor(cipher: TArg<XorStream>, blockLen: number, keyLen: number, nonceLen: number, seed: TArg<Uint8Array>);
private reseed;
addEntropy(seed: TArg<Uint8Array>): void;
randomBytes(len: number): TRet<Uint8Array>;
clone(): _XorStreamPRG;
clean(): void;
}
/**
* PRG constructor backed by an ARX stream cipher.
* @param seed - Optional seed bytes mixed into the initial state. When omitted, exactly 32
* random bytes are mixed in by default: larger states keep a zero tail, while smaller states
* wrap those bytes through `reseed()`'s XOR schedule.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
*/
export type XorPRG = (seed?: TArg<Uint8Array>) => TRet<_XorStreamPRG>;
/**
* Creates a PRG constructor from a stream cipher.
* @param cipher - Stream cipher used to fill output blocks.
* @param blockLen - Keystream block length in bytes.
* @param keyLen - Internal key length in bytes.
* @param nonceLen - Internal nonce length in bytes.
* @returns PRG factory for seeded concrete `_XorStreamPRG` instances.
* @example
* Builds a PRG from XChaCha20 and reads bytes from a randomly seeded instance.
* ```ts
* import { xchacha20 } from '@noble/ciphers/chacha.js';
* import { createPRG } from '@noble/ciphers/_arx.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const init = createPRG(xchacha20, 64, 32, 24);
* const prg = init(seed);
* prg.randomBytes(8);
* ```
*/
export declare const createPRG: (cipher: TArg<XorStream>, blockLen: number, keyLen: number, nonceLen: number) => TRet<XorPRG>;
//# sourceMappingURL=_arx.d.ts.map

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/**
* Basic utils for ARX (add-rotate-xor) salsa and chacha ciphers.
RFC8439 requires multi-step cipher stream, where
authKey starts with counter: 0, actual msg with counter: 1.
For this, we need a way to re-use nonce / counter:
const counter = new Uint8Array(4);
chacha(..., counter, ...); // counter is now 1
chacha(..., counter, ...); // counter is now 2
This is complicated:
- 32-bit counters are enough, no need for 64-bit: max ArrayBuffer size in JS is 4GB
- Original papers don't allow mutating counters
- Counter overflow is undefined [^1]
- Idea A: allow providing (nonce | counter) instead of just nonce, re-use it
- Caveat: Cannot be re-used through all cases:
- * chacha has (counter | nonce)
- * xchacha has (nonce16 | counter | nonce16)
- Idea B: separate nonce / counter and provide separate API for counter re-use
- Caveat: there are different counter sizes depending on an algorithm.
- salsa & chacha also differ in structures of key & sigma:
salsa20: s[0] | k(4) | s[1] | nonce(2) | cnt(2) | s[2] | k(4) | s[3]
chacha: s(4) | k(8) | cnt(1) | nonce(3)
chacha20orig: s(4) | k(8) | cnt(2) | nonce(2)
- Idea C: helper method such as `setSalsaState(key, nonce, sigma, data)`
- Caveat: we can't re-use counter array
xchacha uses the subkey and remaining 8 byte nonce with ChaCha20 as normal
(prefixed by 4 NUL bytes, since RFC8439 specifies a 12-byte nonce).
Counter overflow is undefined; see {@link https://mailarchive.ietf.org/arch/msg/cfrg/gsOnTJzcbgG6OqD8Sc0GO5aR_tU/ | the CFRG thread}.
Current noble policy is strict non-wrap for the shared 32-bit counter path:
exported ARX ciphers reject initial `0xffffffff` and stop before any implicit
wrap back to zero.
See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha#appendix-A.2 | the XChaCha appendix} for the extended-nonce construction.
* @module
*/
import { abool, abytes, anumber, checkOpts, clean, copyBytes, getOutput, isAligned32, isLE, randomBytes, swap32IfBE, u32, } from "./utils.js";
// Replaces `TextEncoder` for ASCII literals, which is enough for sigma constants.
// Non-ASCII input would not match UTF-8 `TextEncoder` output.
const encodeStr = (str) => Uint8Array.from(str.split(''), (c) => c.charCodeAt(0));
// Raw `createCipher(...)` exports consume these native-endian `u32(...)` views directly.
// Public `wrapCipher(...)` APIs reject non-little-endian platforms before reaching this path.
// RFC 8439 §2.3 / RFC 7539 §2.3 only define the 256-bit-key constants; this 16-byte sigma is
// kept for legacy allowShortKeys Salsa/ChaCha variants.
const sigma16_32 = /* @__PURE__ */ (() => swap32IfBE(u32(encodeStr('expand 16-byte k'))))();
// RFC 8439 §2.3 / RFC 7539 §2.3 define words 0-3 as
// `0x61707865 0x3320646e 0x79622d32 0x6b206574`, i.e. `expand 32-byte k`.
const sigma32_32 = /* @__PURE__ */ (() => swap32IfBE(u32(encodeStr('expand 32-byte k'))))();
/**
* Rotates a 32-bit word left.
* @param a - Input word.
* @param b - Rotation count in bits.
* @returns Rotated 32-bit word.
* @example
* Moves the top byte of `0x12345678` into the low byte position.
* ```ts
* rotl(0x12345678, 8);
* ```
*/
export function rotl(a, b) {
return (a << b) | (a >>> (32 - b));
}
// Salsa and Chacha block length is always 512-bit
const BLOCK_LEN = 64;
// RFC 8439 §2.2 / RFC 7539 §2.2: the ChaCha state has 16 32-bit words.
const BLOCK_LEN32 = 16;
// Counter policy for the shared public `counter` argument:
// - RFC/IETF ChaCha20 uses a 32-bit counter.
// - OpenSSL/Node `chacha20` instead treat the full 16-byte IV as a 128-bit
// counter state and carry into the next word.
// - Raw `chacha20orig`, `salsa20`, `xsalsa20`, and `xchacha20` use 64-bit counters in libsodium
// and libtomcrypt, while some libs (for example libtomcrypt's RFC/IETF path) reject the max
// boundary instead of carrying.
// - AEAD wrappers diverge too: libsodium `xchacha20poly1305` uses the IETF payload counter from
// block 1, while `secretstream_xchacha20poly1305` is a different protocol with rekey/reset.
// Noble intentionally throws instead of silently picking one wrap model for users. In the default
// path, even a 32-bit boundary would take 2^32 blocks * 64 bytes = 256 GiB, which is practically
// unreachable for normal JS callers; advanced users who pass `counter` explicitly can implement
// whatever wider carry / wrap policy they need on top.
const MAX_COUNTER = /* @__PURE__ */ (() => 2 ** 32 - 1)();
const U32_EMPTY = /* @__PURE__ */ Uint32Array.of();
function runCipher(core, sigma, key, nonce, data, output, counter, rounds) {
const len = data.length;
const block = new Uint8Array(BLOCK_LEN);
const b32 = u32(block);
// Make sure that buffers aligned to 4 bytes
const isAligned = isLE && isAligned32(data) && isAligned32(output);
const d32 = isAligned ? u32(data) : U32_EMPTY;
const o32 = isAligned ? u32(output) : U32_EMPTY;
// RFC 8439 §2.4.1 / RFC 7539 §2.4.1 allow XORing one keystream block at a time and
// truncating the final partial block instead of materializing the whole keystream.
if (!isLE) {
for (let pos = 0; pos < len; counter++) {
core(sigma, key, nonce, b32, counter, rounds);
// RFC 8439 §2.4 / RFC 7539 §2.4 serialize keystream words in little-endian order.
swap32IfBE(b32);
if (counter >= MAX_COUNTER)
throw new Error('arx: counter overflow');
const take = Math.min(BLOCK_LEN, len - pos);
for (let j = 0, posj; j < take; j++) {
posj = pos + j;
output[posj] = data[posj] ^ block[j];
}
pos += take;
}
return;
}
for (let pos = 0; pos < len; counter++) {
core(sigma, key, nonce, b32, counter, rounds);
// See MAX_COUNTER policy note above: never silently wrap the shared public counter.
if (counter >= MAX_COUNTER)
throw new Error('arx: counter overflow');
const take = Math.min(BLOCK_LEN, len - pos);
// aligned to 4 bytes
if (isAligned && take === BLOCK_LEN) {
const pos32 = pos / 4;
if (pos % 4 !== 0)
throw new Error('arx: invalid block position');
for (let j = 0, posj; j < BLOCK_LEN32; j++) {
posj = pos32 + j;
o32[posj] = d32[posj] ^ b32[j];
}
pos += BLOCK_LEN;
continue;
}
for (let j = 0, posj; j < take; j++) {
posj = pos + j;
output[posj] = data[posj] ^ block[j];
}
pos += take;
}
}
/**
* Creates an ARX stream cipher from a 32-bit core permutation.
* Used internally to build the exported Salsa and ChaCha stream ciphers.
* @param core - Core function that fills one keystream block.
* @param opts - Cipher layout and nonce-extension options. See {@link CipherOpts}.
* @returns Stream cipher function over byte arrays.
* @throws If the core callback, key size, counter, or output sizing is invalid. {@link Error}
*/
export function createCipher(core, opts) {
const { allowShortKeys, extendNonceFn, counterLength, counterRight, rounds } = checkOpts({ allowShortKeys: false, counterLength: 8, counterRight: false, rounds: 20 }, opts);
if (typeof core !== 'function')
throw new Error('core must be a function');
anumber(counterLength);
anumber(rounds);
abool(counterRight);
abool(allowShortKeys);
return (key, nonce, data, output, counter = 0) => {
abytes(key, undefined, 'key');
abytes(nonce, undefined, 'nonce');
abytes(data, undefined, 'data');
const len = data.length;
// Raw XorStream APIs return ciphertext/plaintext bytes directly, so caller-provided outputs
// must match the logical result length exactly instead of returning an oversized workspace.
output = getOutput(len, output, false);
anumber(counter);
// See MAX_COUNTER policy note above: reject advanced explicit-counter requests before any wrap.
if (counter < 0 || counter >= MAX_COUNTER)
throw new Error('arx: counter overflow');
const toClean = [];
// Key & sigma
// key=16 -> sigma16, k=key|key
// key=32 -> sigma32, k=key
let l = key.length;
let k;
let sigma;
if (l === 32) {
// Copy caller keys too: big-endian normalization, extended-nonce subkey derivation, and
// final clean(...) all mutate or wipe the temporary buffer in place.
toClean.push((k = copyBytes(key)));
sigma = sigma32_32;
}
else if (l === 16 && allowShortKeys) {
k = new Uint8Array(32);
k.set(key);
k.set(key, 16);
sigma = sigma16_32;
toClean.push(k);
}
else {
abytes(key, 32, 'arx key');
throw new Error('invalid key size');
// throw new Error(`"arx key" expected Uint8Array of length 32, got length=${l}`);
}
// Nonce
// salsa20: 8 (8-byte counter)
// chacha20orig: 8 (8-byte counter)
// chacha20: 12 (4-byte counter)
// xsalsa20: 24 (16 -> hsalsa, 8 -> old nonce)
// xchacha20: 24 (16 -> hchacha, 8 -> old nonce)
// Copy before taking u32(...) views on misaligned inputs, and on big-endian so later
// swap32IfBE(...) never mutates caller nonce bytes in place.
if (!isLE || !isAligned32(nonce))
toClean.push((nonce = copyBytes(nonce)));
let k32 = u32(k);
// hsalsa & hchacha: handle extended nonce
if (extendNonceFn) {
if (nonce.length !== 24)
throw new Error(`arx: extended nonce must be 24 bytes`);
const n16 = nonce.subarray(0, 16);
if (isLE)
extendNonceFn(sigma, k32, u32(n16), k32);
else {
const sigmaRaw = swap32IfBE(Uint32Array.from(sigma));
extendNonceFn(sigmaRaw, k32, u32(n16), k32);
clean(sigmaRaw);
swap32IfBE(k32);
}
nonce = nonce.subarray(16);
}
else if (!isLE)
swap32IfBE(k32);
// Handle nonce counter
const nonceNcLen = 16 - counterLength;
if (nonceNcLen !== nonce.length)
throw new Error(`arx: nonce must be ${nonceNcLen} or 16 bytes`);
// Normalize 64-bit-nonce layouts to the 12-byte core input: ChaCha/XChaCha prefix 4 zero
// counter bytes, while Salsa/XSalsa append them after the nonce words.
if (nonceNcLen !== 12) {
const nc = new Uint8Array(12);
nc.set(nonce, counterRight ? 0 : 12 - nonce.length);
nonce = nc;
toClean.push(nonce);
}
const n32 = swap32IfBE(u32(nonce));
// Ensure temporary key/nonce copies are wiped even if the remaining
// runtime guard in runCipher(...) throws on counter overflow.
try {
runCipher(core, sigma, k32, n32, data, output, counter, rounds);
return output;
}
finally {
clean(...toClean);
}
};
}
/** Internal class which wraps chacha20 or chacha8 to create CSPRNG. */
export class _XorStreamPRG {
blockLen;
keyLen;
nonceLen;
state;
buf;
key;
nonce;
pos;
ctr;
cipher;
constructor(cipher, blockLen, keyLen, nonceLen, seed) {
this.cipher = cipher;
this.blockLen = blockLen;
this.keyLen = keyLen;
this.nonceLen = nonceLen;
this.state = new Uint8Array(this.keyLen + this.nonceLen);
this.reseed(seed);
this.ctr = 0;
this.pos = this.blockLen;
this.buf = new Uint8Array(this.blockLen);
// Keep a single key||nonce backing buffer so reseed/addEntropy/clean update the live cipher
// inputs in place through these subarray views.
this.key = this.state.subarray(0, this.keyLen);
this.nonce = this.state.subarray(this.keyLen);
}
reseed(seed) {
abytes(seed);
if (!seed || seed.length === 0)
throw new Error('entropy required');
// Mix variable-length entropy cyclically across the whole key||nonce state, then restart the
// keystream so buffered leftovers from the previous state are never reused.
for (let i = 0; i < seed.length; i++)
this.state[i % this.state.length] ^= seed[i];
this.ctr = 0;
this.pos = this.blockLen;
}
addEntropy(seed) {
// Reject empty entropy before re-keying, otherwise a throwing call would still advance state.
abytes(seed);
if (seed.length === 0)
throw new Error('entropy required');
// Re-key from the current stream first, then mix external entropy into the fresh key||nonce
// state through reseed() so stale buffered bytes are discarded.
this.state.set(this.randomBytes(this.state.length));
this.reseed(seed);
}
randomBytes(len) {
anumber(len);
if (len === 0)
return new Uint8Array(0);
const avail = this.pos < this.blockLen ? this.blockLen - this.pos : 0;
const blocks = Math.ceil(Math.max(0, len - avail) / this.blockLen);
// Preflight overflow so failed reads don't partially consume keystream
// and leave the PRG repeating blocks.
if (blocks > 0 && this.ctr > MAX_COUNTER - blocks)
throw new Error('arx: counter overflow');
const out = new Uint8Array(len);
let outPos = 0;
// `out` starts zero-filled, and `buf.fill(0)` below does the same for leftovers: XOR-stream
// ciphers then emit raw keystream bytes directly into those buffers.
// Serve buffered leftovers first so split reads stay identical to one larger read.
if (this.pos < this.blockLen) {
const take = Math.min(len, this.blockLen - this.pos);
out.set(this.buf.subarray(this.pos, this.pos + take), 0);
this.pos += take;
outPos += take;
if (outPos === len)
return out; // fast path
}
// Full blocks directly to out
const full = Math.floor((len - outPos) / this.blockLen);
if (full > 0) {
const blockBytes = full * this.blockLen;
const b = out.subarray(outPos, outPos + blockBytes);
this.cipher(this.key, this.nonce, b, b, this.ctr);
this.ctr += full;
outPos += blockBytes;
}
// Save leftovers
const left = len - outPos;
if (left > 0) {
this.buf.fill(0);
// NOTE: cipher will handle overflow
this.cipher(this.key, this.nonce, this.buf, this.buf, this.ctr++);
out.set(this.buf.subarray(0, left), outPos);
this.pos = left;
}
return out;
}
// Clone seeds the new instance from this stream, so the source PRG advances too.
clone() {
return new _XorStreamPRG(this.cipher, this.blockLen, this.keyLen, this.nonceLen, this.randomBytes(this.state.length));
}
// Zeroes the current state and leftover buffer, but does not make the instance unusable:
// Later reads first drain zeros from the cleared buffer and then continue
// from zero key||nonce state.
clean() {
this.pos = 0;
this.ctr = 0;
this.buf.fill(0);
this.state.fill(0);
}
}
/**
* Creates a PRG constructor from a stream cipher.
* @param cipher - Stream cipher used to fill output blocks.
* @param blockLen - Keystream block length in bytes.
* @param keyLen - Internal key length in bytes.
* @param nonceLen - Internal nonce length in bytes.
* @returns PRG factory for seeded concrete `_XorStreamPRG` instances.
* @example
* Builds a PRG from XChaCha20 and reads bytes from a randomly seeded instance.
* ```ts
* import { xchacha20 } from '@noble/ciphers/chacha.js';
* import { createPRG } from '@noble/ciphers/_arx.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const init = createPRG(xchacha20, 64, 32, 24);
* const prg = init(seed);
* prg.randomBytes(8);
* ```
*/
export const createPRG = (cipher, blockLen, keyLen, nonceLen) => {
return ((seed = randomBytes(32)) => new _XorStreamPRG(cipher, blockLen, keyLen, nonceLen, seed));
};
//# sourceMappingURL=_arx.js.map

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/**
* Poly1305 ({@link https://cr.yp.to/mac/poly1305-20050329.pdf | PDF},
* {@link https://en.wikipedia.org/wiki/Poly1305 | wiki})
* is a fast and parallel secret-key message-authentication code suitable for
* a wide variety of applications. It was standardized in
* {@link https://www.rfc-editor.org/rfc/rfc8439 | RFC 8439} and is now used in TLS 1.3.
*
* Polynomial MACs are not perfect for every situation:
* they lack Random Key Robustness: the MAC can be forged, and can't be used in PAKE schemes.
* See {@link https://keymaterial.net/2020/09/07/invisible-salamanders-in-aes-gcm-siv/ | the invisible salamanders attack writeup}.
* To combat invisible salamanders, `hash(key)` can be included in ciphertext,
* however, this would violate ciphertext indistinguishability:
* an attacker would know which key was used - so `HKDF(key, i)`
* could be used instead.
*
* Check out the {@link https://cr.yp.to/mac.html | original website}.
* Based on public-domain {@link https://github.com/floodyberry/poly1305-donna | poly1305-donna}.
* @module
*/
import { type CMac, type IHash2, type TArg, type TRet } from './utils.ts';
/**
* Incremental Poly1305 MAC state.
* Prefer `poly1305()` for one-shot use.
* @param key - 32-byte Poly1305 one-time key.
* @example
* Feeds one chunk into an incremental Poly1305 state with a fresh one-time key.
*
* ```ts
* import { Poly1305 } from '@noble/ciphers/_poly1305.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const mac = new Poly1305(key);
* mac.update(new Uint8Array([1, 2, 3]));
* mac.digest();
* ```
*/
export declare class Poly1305 implements IHash2 {
readonly blockLen = 16;
readonly outputLen = 16;
private buffer;
private r;
private h;
private pad;
private pos;
protected finished: boolean;
protected destroyed: boolean;
constructor(key: TArg<Uint8Array>);
private process;
private finalize;
update(data: TArg<Uint8Array>): this;
destroy(): void;
digestInto(out: TArg<Uint8Array>): void;
digest(): TRet<Uint8Array>;
}
/** One-shot keyed hash helper with `.create()`. */
export type CHash = CMac<Poly1305>;
/**
* Poly1305 MAC from RFC 8439.
* @param msg - Message bytes to authenticate.
* @param key - 32-byte Poly1305 one-time key.
* @returns 16-byte authentication tag.
* @example
* Authenticates one message with a one-shot Poly1305 call and a fresh key.
*
* ```ts
* import { poly1305 } from '@noble/ciphers/_poly1305.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* poly1305(new Uint8Array(), key);
* ```
*/
export declare const poly1305: TRet<CHash>;
//# sourceMappingURL=_poly1305.d.ts.map

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/**
* Poly1305 ({@link https://cr.yp.to/mac/poly1305-20050329.pdf | PDF},
* {@link https://en.wikipedia.org/wiki/Poly1305 | wiki})
* is a fast and parallel secret-key message-authentication code suitable for
* a wide variety of applications. It was standardized in
* {@link https://www.rfc-editor.org/rfc/rfc8439 | RFC 8439} and is now used in TLS 1.3.
*
* Polynomial MACs are not perfect for every situation:
* they lack Random Key Robustness: the MAC can be forged, and can't be used in PAKE schemes.
* See {@link https://keymaterial.net/2020/09/07/invisible-salamanders-in-aes-gcm-siv/ | the invisible salamanders attack writeup}.
* To combat invisible salamanders, `hash(key)` can be included in ciphertext,
* however, this would violate ciphertext indistinguishability:
* an attacker would know which key was used - so `HKDF(key, i)`
* could be used instead.
*
* Check out the {@link https://cr.yp.to/mac.html | original website}.
* Based on public-domain {@link https://github.com/floodyberry/poly1305-donna | poly1305-donna}.
* @module
*/
// prettier-ignore
import { abytes, aexists, aoutput, bytesToHex, clean, concatBytes, copyBytes, hexToNumber, numberToBytesBE, wrapMacConstructor } from "./utils.js";
// Little-endian 2-byte load used by the Poly1305 limb decomposition.
function u8to16(a, i) {
return (a[i++] & 0xff) | ((a[i++] & 0xff) << 8);
}
function bytesToNumberLE(bytes) {
return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));
}
/** Small version of `poly1305` without loop unrolling. Unused, provided for auditability. */
function poly1305_small(msg, key) {
abytes(msg);
abytes(key, 32, 'key');
const POW_2_130_5 = BigInt(2) ** BigInt(130) - BigInt(5); // 2^130-5
const POW_2_128_1 = BigInt(2) ** BigInt(128) - BigInt(1); // 2^128-1
const CLAMP_R = BigInt('0x0ffffffc0ffffffc0ffffffc0fffffff');
const r = bytesToNumberLE(key.subarray(0, 16)) & CLAMP_R;
const s = bytesToNumberLE(key.subarray(16));
// Process by 16 byte chunks
let acc = BigInt(0);
for (let i = 0; i < msg.length; i += 16) {
const m = msg.subarray(i, i + 16);
// RFC 8439 §2.5.1 / RFC 7539 §2.5.1 append [0x01] to each chunk before multiplying by r.
const n = bytesToNumberLE(m) | (BigInt(1) << BigInt(8 * m.length));
acc = ((acc + n) * r) % POW_2_130_5;
}
const res = (acc + s) & POW_2_128_1;
// RFC 8439 §2.5 / RFC 7539 §2.5 serialize the low 128 bits in little-endian order.
return numberToBytesBE(res, 16).reverse(); // LE
}
// Can be used to replace `computeTag` in chacha.ts. Unused, provided for auditability.
// @ts-expect-error
function poly1305_computeTag_small(authKey,
// AEAD trailer must already be the 16-byte length block:
// 8-byte little-endian AAD length || 8-byte little-endian ciphertext length.
lengths, ciphertext, AAD) {
// RFC 8439 §2.8.1 / RFC 7539 §2.8.1 MAC input is
// AAD || pad16(AAD) || ciphertext || pad16(ciphertext) || lengths.
const res = [];
const updatePadded2 = (msg) => {
res.push(msg);
const leftover = msg.length % 16;
// RFC 8439 §2.8.1 / RFC 7539 §2.8.1: pad16(x) is empty for aligned
// inputs, else 16-(len%16) zero bytes.
if (leftover)
res.push(new Uint8Array(16).slice(leftover));
};
if (AAD)
updatePadded2(AAD);
updatePadded2(ciphertext);
res.push(lengths);
return poly1305_small(concatBytes(...res), authKey);
}
/**
* Incremental Poly1305 MAC state.
* Prefer `poly1305()` for one-shot use.
* @param key - 32-byte Poly1305 one-time key.
* @example
* Feeds one chunk into an incremental Poly1305 state with a fresh one-time key.
*
* ```ts
* import { Poly1305 } from '@noble/ciphers/_poly1305.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const mac = new Poly1305(key);
* mac.update(new Uint8Array([1, 2, 3]));
* mac.digest();
* ```
*/
export class Poly1305 {
blockLen = 16;
outputLen = 16;
buffer = new Uint8Array(16);
r = new Uint16Array(10); // Allocating 1 array with .subarray() here is slower than 3
h = new Uint16Array(10);
pad = new Uint16Array(8);
pos = 0;
finished = false;
destroyed = false;
// Can be speed-up using BigUint64Array, at the cost of complexity
constructor(key) {
key = copyBytes(abytes(key, 32, 'key'));
const t0 = u8to16(key, 0);
const t1 = u8to16(key, 2);
const t2 = u8to16(key, 4);
const t3 = u8to16(key, 6);
const t4 = u8to16(key, 8);
const t5 = u8to16(key, 10);
const t6 = u8to16(key, 12);
const t7 = u8to16(key, 14);
// RFC 8439 §2.5.1 / RFC 7539 §2.5.1 clamp r before multiplication.
// These masks unpack that clamped value into 13-bit limbs, while pad
// keeps the raw s half for finalize().
// {@link https://github.com/floodyberry/poly1305-donna/blob/e6ad6e091d30d7f4ec2d4f978be1fcfcbce72781/poly1305-donna-16.h#L47 | poly1305-donna reference}
this.r[0] = t0 & 0x1fff;
this.r[1] = ((t0 >>> 13) | (t1 << 3)) & 0x1fff;
this.r[2] = ((t1 >>> 10) | (t2 << 6)) & 0x1f03;
this.r[3] = ((t2 >>> 7) | (t3 << 9)) & 0x1fff;
this.r[4] = ((t3 >>> 4) | (t4 << 12)) & 0x00ff;
this.r[5] = (t4 >>> 1) & 0x1ffe;
this.r[6] = ((t4 >>> 14) | (t5 << 2)) & 0x1fff;
this.r[7] = ((t5 >>> 11) | (t6 << 5)) & 0x1f81;
this.r[8] = ((t6 >>> 8) | (t7 << 8)) & 0x1fff;
this.r[9] = (t7 >>> 5) & 0x007f;
for (let i = 0; i < 8; i++)
this.pad[i] = u8to16(key, 16 + 2 * i);
}
process(data, offset, isLast = false) {
// RFC 8439 §2.5 / §2.5.1 and RFC 7539 §2.5 / §2.5.1 add an extra high
// bit to every full 16-byte block. The final partial block gets its
// explicit `1` byte during digestInto(), so `hibit` stays zero there.
const hibit = isLast ? 0 : 1 << 11;
const { h, r } = this;
const r0 = r[0];
const r1 = r[1];
const r2 = r[2];
const r3 = r[3];
const r4 = r[4];
const r5 = r[5];
const r6 = r[6];
const r7 = r[7];
const r8 = r[8];
const r9 = r[9];
const t0 = u8to16(data, offset + 0);
const t1 = u8to16(data, offset + 2);
const t2 = u8to16(data, offset + 4);
const t3 = u8to16(data, offset + 6);
const t4 = u8to16(data, offset + 8);
const t5 = u8to16(data, offset + 10);
const t6 = u8to16(data, offset + 12);
const t7 = u8to16(data, offset + 14);
let h0 = h[0] + (t0 & 0x1fff);
let h1 = h[1] + (((t0 >>> 13) | (t1 << 3)) & 0x1fff);
let h2 = h[2] + (((t1 >>> 10) | (t2 << 6)) & 0x1fff);
let h3 = h[3] + (((t2 >>> 7) | (t3 << 9)) & 0x1fff);
let h4 = h[4] + (((t3 >>> 4) | (t4 << 12)) & 0x1fff);
let h5 = h[5] + ((t4 >>> 1) & 0x1fff);
let h6 = h[6] + (((t4 >>> 14) | (t5 << 2)) & 0x1fff);
let h7 = h[7] + (((t5 >>> 11) | (t6 << 5)) & 0x1fff);
let h8 = h[8] + (((t6 >>> 8) | (t7 << 8)) & 0x1fff);
let h9 = h[9] + ((t7 >>> 5) | hibit);
let c = 0;
let d0 = c + h0 * r0 + h1 * (5 * r9) + h2 * (5 * r8) + h3 * (5 * r7) + h4 * (5 * r6);
c = d0 >>> 13;
d0 &= 0x1fff;
d0 += h5 * (5 * r5) + h6 * (5 * r4) + h7 * (5 * r3) + h8 * (5 * r2) + h9 * (5 * r1);
c += d0 >>> 13;
d0 &= 0x1fff;
let d1 = c + h0 * r1 + h1 * r0 + h2 * (5 * r9) + h3 * (5 * r8) + h4 * (5 * r7);
c = d1 >>> 13;
d1 &= 0x1fff;
d1 += h5 * (5 * r6) + h6 * (5 * r5) + h7 * (5 * r4) + h8 * (5 * r3) + h9 * (5 * r2);
c += d1 >>> 13;
d1 &= 0x1fff;
let d2 = c + h0 * r2 + h1 * r1 + h2 * r0 + h3 * (5 * r9) + h4 * (5 * r8);
c = d2 >>> 13;
d2 &= 0x1fff;
d2 += h5 * (5 * r7) + h6 * (5 * r6) + h7 * (5 * r5) + h8 * (5 * r4) + h9 * (5 * r3);
c += d2 >>> 13;
d2 &= 0x1fff;
let d3 = c + h0 * r3 + h1 * r2 + h2 * r1 + h3 * r0 + h4 * (5 * r9);
c = d3 >>> 13;
d3 &= 0x1fff;
d3 += h5 * (5 * r8) + h6 * (5 * r7) + h7 * (5 * r6) + h8 * (5 * r5) + h9 * (5 * r4);
c += d3 >>> 13;
d3 &= 0x1fff;
let d4 = c + h0 * r4 + h1 * r3 + h2 * r2 + h3 * r1 + h4 * r0;
c = d4 >>> 13;
d4 &= 0x1fff;
d4 += h5 * (5 * r9) + h6 * (5 * r8) + h7 * (5 * r7) + h8 * (5 * r6) + h9 * (5 * r5);
c += d4 >>> 13;
d4 &= 0x1fff;
let d5 = c + h0 * r5 + h1 * r4 + h2 * r3 + h3 * r2 + h4 * r1;
c = d5 >>> 13;
d5 &= 0x1fff;
d5 += h5 * r0 + h6 * (5 * r9) + h7 * (5 * r8) + h8 * (5 * r7) + h9 * (5 * r6);
c += d5 >>> 13;
d5 &= 0x1fff;
let d6 = c + h0 * r6 + h1 * r5 + h2 * r4 + h3 * r3 + h4 * r2;
c = d6 >>> 13;
d6 &= 0x1fff;
d6 += h5 * r1 + h6 * r0 + h7 * (5 * r9) + h8 * (5 * r8) + h9 * (5 * r7);
c += d6 >>> 13;
d6 &= 0x1fff;
let d7 = c + h0 * r7 + h1 * r6 + h2 * r5 + h3 * r4 + h4 * r3;
c = d7 >>> 13;
d7 &= 0x1fff;
d7 += h5 * r2 + h6 * r1 + h7 * r0 + h8 * (5 * r9) + h9 * (5 * r8);
c += d7 >>> 13;
d7 &= 0x1fff;
let d8 = c + h0 * r8 + h1 * r7 + h2 * r6 + h3 * r5 + h4 * r4;
c = d8 >>> 13;
d8 &= 0x1fff;
d8 += h5 * r3 + h6 * r2 + h7 * r1 + h8 * r0 + h9 * (5 * r9);
c += d8 >>> 13;
d8 &= 0x1fff;
let d9 = c + h0 * r9 + h1 * r8 + h2 * r7 + h3 * r6 + h4 * r5;
c = d9 >>> 13;
d9 &= 0x1fff;
d9 += h5 * r4 + h6 * r3 + h7 * r2 + h8 * r1 + h9 * r0;
c += d9 >>> 13;
d9 &= 0x1fff;
c = ((c << 2) + c) | 0;
c = (c + d0) | 0;
d0 = c & 0x1fff;
c = c >>> 13;
d1 += c;
h[0] = d0;
h[1] = d1;
h[2] = d2;
h[3] = d3;
h[4] = d4;
h[5] = d5;
h[6] = d6;
h[7] = d7;
h[8] = d8;
h[9] = d9;
}
finalize() {
const { h, pad } = this;
const g = new Uint16Array(10);
let c = h[1] >>> 13;
h[1] &= 0x1fff;
for (let i = 2; i < 10; i++) {
h[i] += c;
c = h[i] >>> 13;
h[i] &= 0x1fff;
}
h[0] += c * 5;
c = h[0] >>> 13;
h[0] &= 0x1fff;
h[1] += c;
c = h[1] >>> 13;
h[1] &= 0x1fff;
h[2] += c;
// RFC 8439 §2.5 / RFC 7539 §2.5 reduce modulo 2^130-5 before repacking
// to 16-bit words and adding the raw s half.
g[0] = h[0] + 5;
c = g[0] >>> 13;
g[0] &= 0x1fff;
for (let i = 1; i < 10; i++) {
g[i] = h[i] + c;
c = g[i] >>> 13;
g[i] &= 0x1fff;
}
g[9] -= 1 << 13;
let mask = (c ^ 1) - 1;
for (let i = 0; i < 10; i++)
g[i] &= mask;
mask = ~mask;
for (let i = 0; i < 10; i++)
h[i] = (h[i] & mask) | g[i];
h[0] = (h[0] | (h[1] << 13)) & 0xffff;
h[1] = ((h[1] >>> 3) | (h[2] << 10)) & 0xffff;
h[2] = ((h[2] >>> 6) | (h[3] << 7)) & 0xffff;
h[3] = ((h[3] >>> 9) | (h[4] << 4)) & 0xffff;
h[4] = ((h[4] >>> 12) | (h[5] << 1) | (h[6] << 14)) & 0xffff;
h[5] = ((h[6] >>> 2) | (h[7] << 11)) & 0xffff;
h[6] = ((h[7] >>> 5) | (h[8] << 8)) & 0xffff;
h[7] = ((h[8] >>> 8) | (h[9] << 5)) & 0xffff;
let f = h[0] + pad[0];
h[0] = f & 0xffff;
for (let i = 1; i < 8; i++) {
f = (((h[i] + pad[i]) | 0) + (f >>> 16)) | 0;
h[i] = f & 0xffff;
}
clean(g);
}
update(data) {
aexists(this);
abytes(data);
data = copyBytes(data);
const { buffer, blockLen } = this;
const len = data.length;
for (let pos = 0; pos < len;) {
const take = Math.min(blockLen - this.pos, len - pos);
// Fast path: we have at least one block in input
if (take === blockLen) {
for (; blockLen <= len - pos; pos += blockLen)
this.process(data, pos);
continue;
}
buffer.set(data.subarray(pos, pos + take), this.pos);
this.pos += take;
pos += take;
if (this.pos === blockLen) {
this.process(buffer, 0, false);
this.pos = 0;
}
}
return this;
}
destroy() {
// `aexists(this)` guards update/digest paths, so destroy must mark the instance unusable too.
this.destroyed = true;
clean(this.h, this.r, this.buffer, this.pad);
}
digestInto(out) {
aexists(this);
aoutput(out, this);
this.finished = true;
const { buffer, h } = this;
let { pos } = this;
if (pos) {
// RFC 8439 §2.5 / RFC 7539 §2.5: the final short block appends a
// single `0x01` byte and zero-fills the remaining bytes before the
// last multiplication step.
buffer[pos++] = 1;
for (; pos < 16; pos++)
buffer[pos] = 0;
this.process(buffer, 0, true);
}
this.finalize();
let opos = 0;
for (let i = 0; i < 8; i++) {
out[opos++] = h[i] >>> 0;
out[opos++] = h[i] >>> 8;
}
}
digest() {
const { buffer, outputLen } = this;
this.digestInto(buffer);
// Copy out before destroy() zeroes the internal buffer.
const res = buffer.slice(0, outputLen);
this.destroy();
return res;
}
}
/**
* Poly1305 MAC from RFC 8439.
* @param msg - Message bytes to authenticate.
* @param key - 32-byte Poly1305 one-time key.
* @returns 16-byte authentication tag.
* @example
* Authenticates one message with a one-shot Poly1305 call and a fresh key.
*
* ```ts
* import { poly1305 } from '@noble/ciphers/_poly1305.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* poly1305(new Uint8Array(), key);
* ```
*/
export const poly1305 = /* @__PURE__ */ wrapMacConstructor(32, (key) => new Poly1305(key));
//# sourceMappingURL=_poly1305.js.map

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/**
* GHash from AES-GCM and its little-endian "mirror image" Polyval from AES-SIV.
*
* Implemented in terms of GHash with conversion function for keys
* GCM GHASH from
* {@link https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-38d.pdf | NIST SP800-38d},
* SIV from
* {@link https://www.rfc-editor.org/rfc/rfc8452 | RFC 8452}.
*
* GHASH modulo: x^128 + x^7 + x^2 + x + 1
* POLYVAL modulo: x^128 + x^127 + x^126 + x^121 + 1
*
* @module
*/
import { type CMac, type IHash2, type TArg, type TRet } from './utils.ts';
/**
* `mulX_GHASH(ByteReverse(H))` from RFC 8452 Appendix A.
* @param k mutated in place
*/
export declare function _toGHASHKey(k: TArg<Uint8Array>): TRet<Uint8Array>;
type Value = {
s0: number;
s1: number;
s2: number;
s3: number;
};
/**
* Incremental GHASH state for AES-GCM.
* @param key - 16-byte GHASH key.
* @param expectedLength - Expected message length for table sizing.
* Chunking is segment-based, not hash-streaming: every `update()` call is zero-padded
* to the next 16-byte boundary before it is absorbed. This matches the internal AES/GCM
* use where AAD, payload, and length block are separate padded segments.
* @example
* Feeds one ciphertext block into an incremental GHASH state with a fresh hash key.
*
* ```ts
* import { GHASH } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const mac = new GHASH(key);
* mac.update(new Uint8Array(16));
* mac.digest();
* ```
*/
export declare class GHASH implements IHash2 {
readonly blockLen: number;
readonly outputLen: number;
protected s0: number;
protected s1: number;
protected s2: number;
protected s3: number;
protected finished: boolean;
protected destroyed: boolean;
protected t: Value[];
private W;
private windowSize;
constructor(key: TArg<Uint8Array>, expectedLength?: number);
protected _updateBlock(s0: number, s1: number, s2: number, s3: number): void;
update(data: TArg<Uint8Array>): this;
destroy(): void;
digestInto(out: TArg<Uint8Array>): void;
digest(): TRet<Uint8Array>;
}
/**
* Incremental POLYVAL state for AES-SIV.
* @param key - 16-byte POLYVAL key.
* @param expectedLength - Expected message length for table sizing.
* Inherits GHASH's segment-padded `update()` behavior: each call is padded
* independently to a 16-byte boundary before absorption.
* @example
* Feeds one block into an incremental POLYVAL state with a fresh hash key.
*
* ```ts
* import { Polyval } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const mac = new Polyval(key);
* mac.update(new Uint8Array(16));
* mac.digest();
* ```
*/
export declare class Polyval extends GHASH {
constructor(key: TArg<Uint8Array>, expectedLength?: number);
update(data: TArg<Uint8Array>): this;
digestInto(out: TArg<Uint8Array>): void;
}
/**
* GHash MAC for AES-GCM.
* @param msg - Message bytes to authenticate.
* @param key - 16-byte GHASH key.
* @returns 16-byte authentication tag.
* @example
* Authenticates a short message with GHASH and a fresh hash key.
*
* ```ts
* import { ghash } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* ghash(new Uint8Array(), key);
* ```
*/
export declare const ghash: TRet<CMac<GHASH, [expectedLength?: number]>>;
/**
* POLYVAL MAC for AES-SIV.
* @param msg - Message bytes to authenticate.
* @param key - 16-byte POLYVAL key.
* @returns 16-byte authentication tag.
* @example
* Authenticates a short message with POLYVAL and a fresh hash key.
*
* ```ts
* import { polyval } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* polyval(new Uint8Array(), key);
* ```
*/
export declare const polyval: TRet<CMac<Polyval, [expectedLength?: number]>>;
export {};
//# sourceMappingURL=_polyval.d.ts.map

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/**
* GHash from AES-GCM and its little-endian "mirror image" Polyval from AES-SIV.
*
* Implemented in terms of GHash with conversion function for keys
* GCM GHASH from
* {@link https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-38d.pdf | NIST SP800-38d},
* SIV from
* {@link https://www.rfc-editor.org/rfc/rfc8452 | RFC 8452}.
*
* GHASH modulo: x^128 + x^7 + x^2 + x + 1
* POLYVAL modulo: x^128 + x^127 + x^126 + x^121 + 1
*
* @module
*/
import { abytes, aexists, aoutput, clean, copyBytes, createView, swap32IfBE, swap8IfBE, u32, wrapMacConstructor, } from "./utils.js";
const BLOCK_SIZE = 16;
// TODO: rewrite
// temporary padding buffer
// ZEROS32 aliases these bytes, so clean(ZEROS32) also resets this shared tail-padding scratch.
const ZEROS16 = /* @__PURE__ */ new Uint8Array(16);
const ZEROS32 = /* @__PURE__ */ u32(ZEROS16);
// GHASH reduces modulo x^128 + x^7 + x^2 + x + 1, so the low-degree terms
// x^7 + x^2 + x + 1 become bits `11100001` = 0xe1 in R = 0xe1 || 0^120.
const POLY = 0xe1;
// v = 2*v % POLY
// NOTE: because x + x = 0 (add/sub is same), mul2(x) != x+x
// Montgomery ladder can multiply any field element with this doubling step;
// addition stays simple xor.
const mul2 = (s0, s1, s2, s3) => {
const hiBit = s3 & 1;
return {
s3: (s2 << 31) | (s3 >>> 1),
s2: (s1 << 31) | (s2 >>> 1),
s1: (s0 << 31) | (s1 >>> 1),
// NIST SP 800-38D §6.3 applies `V >> 1` and XORs R on carry. In this
// 4x32-bit split, R = 0xe1 || 0^120 lives in the top byte of s0.
s0: (s0 >>> 1) ^ ((POLY << 24) & -(hiBit & 1)), // reduce % poly
};
};
// Per-word part of RFC 8452 `ByteReverse`; callers also reverse the 32-bit word order.
const swapLE = (n) => (((n >>> 0) & 0xff) << 24) |
(((n >>> 8) & 0xff) << 16) |
(((n >>> 16) & 0xff) << 8) |
((n >>> 24) & 0xff) |
0;
// POLYVAL first applies RFC 8452's per-word byte reversal, then re-normalizes
// host-endian u32 loads to the little-endian word value `_updateBlock()` expects.
const swap8IfLE = (n) => swap8IfBE(swapLE(n));
/**
* `mulX_GHASH(ByteReverse(H))` from RFC 8452 Appendix A.
* @param k mutated in place
*/
export function _toGHASHKey(k) {
// The input is the original POLYVAL key H; reverse() materializes
// RFC 8452's `ByteReverse(H)` before the GHASH mulX step.
k.reverse();
const hiBit = k[15] & 1;
// k >>= 1
let carry = 0;
for (let i = 0; i < k.length; i++) {
const t = k[i];
k[i] = (t >>> 1) | carry;
carry = (t & 1) << 7;
}
k[0] ^= -hiBit & 0xe1; // if (hiBit) n ^= 0xe1000000000000000000000000000000;
return k;
}
// Precompute-window heuristic only: larger inputs trade memory for fewer table lookups.
// Any caller-provided length hint still collapses to one of the supported windows {2, 4, 8}.
const estimateWindow = (bytes) => {
if (bytes > 64 * 1024)
return 8;
if (bytes > 1024)
return 4;
return 2;
};
/**
* Incremental GHASH state for AES-GCM.
* @param key - 16-byte GHASH key.
* @param expectedLength - Expected message length for table sizing.
* Chunking is segment-based, not hash-streaming: every `update()` call is zero-padded
* to the next 16-byte boundary before it is absorbed. This matches the internal AES/GCM
* use where AAD, payload, and length block are separate padded segments.
* @example
* Feeds one ciphertext block into an incremental GHASH state with a fresh hash key.
*
* ```ts
* import { GHASH } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const mac = new GHASH(key);
* mac.update(new Uint8Array(16));
* mac.digest();
* ```
*/
export class GHASH {
blockLen = BLOCK_SIZE;
outputLen = BLOCK_SIZE;
s0 = 0;
s1 = 0;
s2 = 0;
s3 = 0;
finished = false;
destroyed = false;
t;
W;
windowSize;
// We select bits per window adaptively based on expectedLength
constructor(key, expectedLength) {
abytes(key, 16, 'key');
key = copyBytes(key);
const kView = createView(key);
let k0 = kView.getUint32(0, false);
let k1 = kView.getUint32(4, false);
let k2 = kView.getUint32(8, false);
let k3 = kView.getUint32(12, false);
// generate table of doubled keys (half of montgomery ladder)
const doubles = [];
for (let i = 0; i < 128; i++) {
doubles.push({ s0: swapLE(k0), s1: swapLE(k1), s2: swapLE(k2), s3: swapLE(k3) });
({ s0: k0, s1: k1, s2: k2, s3: k3 } = mul2(k0, k1, k2, k3));
}
const W = estimateWindow(expectedLength || 1024);
if (![1, 2, 4, 8].includes(W))
throw new Error('ghash: invalid window size, expected 2, 4 or 8');
this.W = W;
const bits = 128; // always 128 bits;
const windows = bits / W;
const windowSize = (this.windowSize = 2 ** W);
const items = [];
// Create precompute table for window of W bits
for (let w = 0; w < windows; w++) {
// truth table: 00, 01, 10, 11
for (let byte = 0; byte < windowSize; byte++) {
// prettier-ignore
let s0 = 0, s1 = 0, s2 = 0, s3 = 0;
for (let j = 0; j < W; j++) {
const bit = (byte >>> (W - j - 1)) & 1;
if (!bit)
continue;
const { s0: d0, s1: d1, s2: d2, s3: d3 } = doubles[W * w + j];
((s0 ^= d0), (s1 ^= d1), (s2 ^= d2), (s3 ^= d3));
}
items.push({ s0, s1, s2, s3 });
}
}
this.t = items;
}
_updateBlock(s0, s1, s2, s3) {
((s0 ^= this.s0), (s1 ^= this.s1), (s2 ^= this.s2), (s3 ^= this.s3));
const { W, t, windowSize } = this;
// prettier-ignore
let o0 = 0, o1 = 0, o2 = 0, o3 = 0;
const mask = (1 << W) - 1; // 2**W will kill performance.
let w = 0;
// NIST SP 800-38D §6.3 interprets blocks as little-endian polynomials,
// so the lookup walk consumes each word byte-by-byte from
// least-significant to most-significant bits.
for (const num of [s0, s1, s2, s3]) {
for (let bytePos = 0; bytePos < 4; bytePos++) {
const byte = (num >>> (8 * bytePos)) & 0xff;
for (let bitPos = 8 / W - 1; bitPos >= 0; bitPos--) {
const bit = (byte >>> (W * bitPos)) & mask;
const { s0: e0, s1: e1, s2: e2, s3: e3 } = t[w * windowSize + bit];
((o0 ^= e0), (o1 ^= e1), (o2 ^= e2), (o3 ^= e3));
w += 1;
}
}
}
this.s0 = o0;
this.s1 = o1;
this.s2 = o2;
this.s3 = o3;
}
update(data) {
aexists(this);
abytes(data);
data = copyBytes(data);
const b32 = u32(data);
const blocks = Math.floor(data.length / BLOCK_SIZE);
const left = data.length % BLOCK_SIZE;
for (let i = 0; i < blocks; i++) {
this._updateBlock(swap8IfBE(b32[i * 4 + 0]), swap8IfBE(b32[i * 4 + 1]), swap8IfBE(b32[i * 4 + 2]), swap8IfBE(b32[i * 4 + 3]));
}
if (left) {
ZEROS16.set(data.subarray(blocks * BLOCK_SIZE));
// Tail blocks go through the shared ZEROS32 scratch, so they need the same host-endian
// normalization as full blocks; otherwise segmented GHASH/POLYVAL updates diverge on BE.
this._updateBlock(swap8IfBE(ZEROS32[0]), swap8IfBE(ZEROS32[1]), swap8IfBE(ZEROS32[2]), swap8IfBE(ZEROS32[3]));
clean(ZEROS32); // clean tmp buffer
}
return this;
}
destroy() {
// `aexists(this)` guards update/digest paths, so destroy must mark the instance unusable too.
this.destroyed = true;
const { t } = this;
// Wipe the key-derived precompute table; scalar accumulator words remain,
// but the destroyed guard blocks further use.
// clean precompute table
for (const elm of t) {
((elm.s0 = 0), (elm.s1 = 0), (elm.s2 = 0), (elm.s3 = 0));
}
}
digestInto(out) {
aexists(this);
// `digestInto(out)` is the no-allocation fast path, so callers must pass a
// 32-bit-aligned buffer before we reinterpret it with `u32(out)`.
aoutput(out, this, true);
this.finished = true;
// NIST SP 800-38D §6.4 returns the final 128-bit block Y_m.
// `digestInto()` follows the relaxed `aoutput()` contract, so only
// out[0..15] may be touched.
const { s0, s1, s2, s3 } = this;
const o32 = u32(out);
o32[0] = s0;
o32[1] = s1;
o32[2] = s2;
o32[3] = s3;
swap32IfBE(o32);
}
digest() {
const res = new Uint8Array(BLOCK_SIZE);
this.digestInto(res);
// `res` is independent of internal state, so it stays valid after destroy() wipes the table.
this.destroy();
return res;
}
}
/**
* Incremental POLYVAL state for AES-SIV.
* @param key - 16-byte POLYVAL key.
* @param expectedLength - Expected message length for table sizing.
* Inherits GHASH's segment-padded `update()` behavior: each call is padded
* independently to a 16-byte boundary before absorption.
* @example
* Feeds one block into an incremental POLYVAL state with a fresh hash key.
*
* ```ts
* import { Polyval } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const mac = new Polyval(key);
* mac.update(new Uint8Array(16));
* mac.digest();
* ```
*/
export class Polyval extends GHASH {
constructor(key, expectedLength) {
abytes(key);
// RFC 8452 Appendix A converts the POLYVAL key with
// `mulX_GHASH(ByteReverse(H))`; copy first because `_toGHASHKey(...)`
// mutates in place.
const ghKey = _toGHASHKey(copyBytes(key));
super(ghKey, expectedLength);
clean(ghKey);
}
update(data) {
aexists(this);
abytes(data);
data = copyBytes(data);
const b32 = u32(data);
const left = data.length % BLOCK_SIZE;
const blocks = Math.floor(data.length / BLOCK_SIZE);
for (let i = 0; i < blocks; i++) {
// RFC 8452 Appendix A feeds `ByteReverse(X_i)` into GHASH, so POLYVAL
// reverses the 32-bit word order in addition to the per-word byte swap.
this._updateBlock(swap8IfLE(b32[i * 4 + 3]), swap8IfLE(b32[i * 4 + 2]), swap8IfLE(b32[i * 4 + 1]), swap8IfLE(b32[i * 4 + 0]));
}
if (left) {
ZEROS16.set(data.subarray(blocks * BLOCK_SIZE));
this._updateBlock(swap8IfLE(ZEROS32[3]), swap8IfLE(ZEROS32[2]), swap8IfLE(ZEROS32[1]), swap8IfLE(ZEROS32[0]));
clean(ZEROS32);
}
return this;
}
digestInto(out) {
aexists(this);
// `digestInto(out)` is the no-allocation fast path, so callers must pass a
// 32-bit-aligned buffer before we reinterpret the output prefix with `u32(view)`.
aoutput(out, this, true);
this.finished = true;
// RFC 8452 Appendix A maps POLYVAL output back through `ByteReverse(...)`.
// `digestInto()` follows the relaxed `aoutput()` contract, so only out[0..15] may be touched.
const view = out.subarray(0, this.outputLen);
const { s0, s1, s2, s3 } = this;
const o32 = u32(view);
o32[0] = s0;
o32[1] = s1;
o32[2] = s2;
o32[3] = s3;
swap32IfBE(o32);
view.reverse();
}
}
/**
* GHash MAC for AES-GCM.
* @param msg - Message bytes to authenticate.
* @param key - 16-byte GHASH key.
* @returns 16-byte authentication tag.
* @example
* Authenticates a short message with GHASH and a fresh hash key.
*
* ```ts
* import { ghash } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* ghash(new Uint8Array(), key);
* ```
*/
export const ghash =
/* @__PURE__ */ wrapMacConstructor(16, (key, expectedLength) => new GHASH(key, expectedLength), (msg) => [msg.length]);
/**
* POLYVAL MAC for AES-SIV.
* @param msg - Message bytes to authenticate.
* @param key - 16-byte POLYVAL key.
* @returns 16-byte authentication tag.
* @example
* Authenticates a short message with POLYVAL and a fresh hash key.
*
* ```ts
* import { polyval } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* polyval(new Uint8Array(), key);
* ```
*/
export const polyval =
/* @__PURE__ */ wrapMacConstructor(16, (key, expectedLength) => new Polyval(key, expectedLength), (msg) => [msg.length]);
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import { type Cipher, type CipherWithOutput, type CMac, type IHash2, type PRG, type TArg, type TRet, type Uint8ArrayBuffer } from './utils.ts';
/**
* Increments a counter block with wrap around.
* AES call sites here currently use the big-endian branch, but the helper supports both layouts.
* NIST SP 800-38A Appendix B.1 and SP 800-38D §6.2 increment the
* least-significant/rightmost bits.
* `isLE=false` matches that standard counter-block layout, while `isLE=true`
* is a generic extension for non-AES callers.
* The implementation keeps a 32-bit bitwise carry path, so `carry` is capped at `0xffffff00`;
* larger values throw instead of silently overflowing before the next-byte propagation step.
*/
declare const incBytes: (data: TArg<Uint8Array>, isLE: boolean, carry?: number) => void;
/** Forward AES key expansion used across ECB/CBC/CTR/GCM/CMAC/KW-style paths. */
declare function expandKeyLE(key: TArg<Uint8Array>): TRet<Uint32Array>;
declare function expandKeyDecLE(key: TArg<Uint8Array>): TRet<Uint32Array>;
declare function encrypt(xk: TArg<Uint32Array>, s0: number, s1: number, s2: number, s3: number): {
s0: number;
s1: number;
s2: number;
s3: number;
};
declare function decrypt(xk: TArg<Uint32Array>, s0: number, s1: number, s2: number, s3: number): {
s0: number;
s1: number;
s2: number;
s3: number;
};
declare function ctrCounter(xk: TArg<Uint32Array>, nonce: TArg<Uint8Array>, src: TArg<Uint8Array>, dst?: TArg<Uint8Array>): TRet<Uint8Array>;
declare function ctr32(xk: TArg<Uint32Array>, isLE: boolean, nonce: TArg<Uint8Array>, src: TArg<Uint8Array>, dst?: TArg<Uint8Array>): TRet<Uint8Array>;
/**
* **CTR** (Counter Mode): turns a block cipher into a stream cipher using a
* full 16-byte counter block.
* Efficient and parallelizable. Requires a unique nonce per encryption. Unauthenticated: needs MAC.
* @param key - AES key bytes.
* @param nonce - 16-byte counter block, incremented as a full AES block.
* @returns Cipher instance with `encrypt()` and `decrypt()`.
* @example
* Encrypts a short payload with a fresh AES key and counter block.
*
* ```ts
* import { ctr } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(16);
* const cipher = ctr(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const ctr: TRet<((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>) => CipherWithOutput) & {
blockSize: number;
nonceLength: number;
}>;
/** Options for ECB and CBC. */
export type BlockOpts = {
/** Disable the library's PKCS#7 padding/unpadding layer and require exact-block inputs. */
disablePadding?: boolean;
};
/**
* **ECB** (Electronic Codebook): Deterministic encryption; identical plaintext blocks yield
* identical ciphertexts. Not secure due to pattern leakage.
* See {@link https://words.filippo.io/the-ecb-penguin/ | the AES Penguin}.
* @param key - AES key bytes.
* @param opts - Padding options. See {@link BlockOpts}.
* @returns Cipher instance with `encrypt()` and `decrypt()`.
* @example
* Shows the basic ECB encrypt call shape with a fresh key; avoid ECB in new designs.
*
* ```ts
* import { ecb } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const cipher = ecb(key);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const ecb: TRet<((key: TArg<Uint8Array>, opts?: BlockOpts) => CipherWithOutput) & {
blockSize: number;
}>;
/**
* **CBC** (Cipher Block Chaining): Each plaintext block is XORed with the
* previous block of ciphertext before encryption.
* Hard to use: requires proper padding and an unpredictable IV. Unauthenticated: needs MAC.
* @param key - AES key bytes.
* @param iv - 16-byte unpredictable initialization vector.
* @param opts - Padding options. See {@link BlockOpts}.
* @returns Cipher instance with `encrypt()` and `decrypt()`.
* @example
* Encrypts a padded message with a fresh key and 16-byte IV.
*
* ```ts
* import { cbc } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const iv = randomBytes(16);
* const cipher = cbc(key, iv);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const cbc: TRet<((key: TArg<Uint8Array>, iv: TArg<Uint8Array>, opts?: BlockOpts) => CipherWithOutput) & {
blockSize: number;
nonceLength: number;
}>;
/**
* CFB (CFB-128): Cipher Feedback Mode with 128-bit segments. The input for the
* block cipher is the previous cipher output.
* Unauthenticated: needs MAC.
* @param key - AES key bytes.
* @param iv - 16-byte unpredictable initialization vector.
* @returns Cipher instance with `encrypt()` and `decrypt()`.
* @example
* Encrypts a short message with feedback mode and a fresh key/IV pair.
*
* ```ts
* import { cfb } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const iv = randomBytes(16);
* const cipher = cfb(key, iv);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const cfb: TRet<((key: TArg<Uint8Array>, iv: TArg<Uint8Array>) => CipherWithOutput) & {
blockSize: number;
nonceLength: number;
}>;
/**
* **GCM** (Galois/Counter Mode): Combines CTR mode with polynomial MAC. Efficient and widely used.
* Not perfect:
* a) conservative key wear-out is `2**32` (4B) msgs.
* b) key wear-out under random nonces is even smaller: `2**23` (8M) messages for `2**-50` chance.
* c) MAC can be forged: see Poly1305 documentation.
* @param key - AES key bytes.
* @param nonce - Nonce bytes (12 recommended, minimum 8; other lengths use GHASH J0 derivation).
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance with a fixed 16-byte tag.
* @example
* Encrypts and authenticates plaintext with a fresh key and 12-byte nonce.
*
* ```ts
* import { gcm } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(12);
* const cipher = gcm(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const gcm: TRet<((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => Cipher) & {
blockSize: number;
nonceLength: number;
tagLength: number;
varSizeNonce: true;
}>;
/**
* **SIV** (Synthetic IV): GCM with nonce-misuse resistance.
* Repeating nonces reveal only the fact plaintexts are identical.
* Also suffers from GCM issues: key wear-out limits & MAC forging.
* See {@link https://www.rfc-editor.org/rfc/rfc8452 | RFC 8452}.
* RFC 8452 defines 16-byte and 32-byte AES keys for this mode.
* This implementation also accepts 24-byte AES-192 keys as a local
* extension; see the inline comment next to `validateKeyLength(key)` below
* for the exact scope note.
* @param key - AES key bytes.
* @param nonce - 12-byte nonce.
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with a fresh key and nonce, while tolerating reuse.
*
* ```ts
* import { gcmsiv } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(12);
* const cipher = gcmsiv(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const gcmsiv: TRet<((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => Cipher) & {
blockSize: number;
nonceLength: number;
tagLength: number;
varSizeNonce: true;
}>;
declare function encryptBlock(xk: TArg<Uint32Array>, block: TArg<Uint8Array>): TRet<Uint8Array>;
declare function decryptBlock(xk: TArg<Uint32Array>, block: TArg<Uint8Array>): TRet<Uint8Array>;
/**
* AES-KW (key-wrap). Injects static IV into plaintext, adds counter, encrypts 6 times.
* Reduces block size from 16 to 8 bytes.
* Plaintext must be a non-empty multiple of 8 bytes with minimum 16 bytes.
* 8-byte inputs use aeskwp.
* Wrapped ciphertext must be a multiple of 8 bytes with minimum 24 bytes.
* For padded version, use aeskwp.
* See {@link https://www.rfc-editor.org/rfc/rfc3394/ | RFC 3394} and
* {@link https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-38F.pdf | NIST SP 800-38F}.
* @param kek - AES key-encryption key.
* @returns Key-wrap cipher instance.
* As with other `wrapCipher(...)` wrappers, `encrypt()` is single-use per
* instance.
* @example
* Wraps a 128-bit content-encryption key with a fresh key-encryption key.
*
* ```ts
* import { aeskw } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const kek = randomBytes(16);
* const cek = randomBytes(16);
* const wrap = aeskw(kek);
* wrap.encrypt(cek);
* ```
*/
export declare const aeskw: TRet<((kek: TArg<Uint8Array>) => Cipher) & {
blockSize: number;
}>;
/**
* AES-KW, but with padding and allows random keys.
* Uses the RFC 5649 alternative initial value; the second u32 stores the
* 32-bit MLI in network order.
* Wrapped ciphertext must be at least 16 bytes; malformed lengths are
* rejected during AIV/padding checks.
* See {@link https://www.rfc-editor.org/rfc/rfc5649 | RFC 5649}.
* @param kek - AES key-encryption key.
* @returns Padded key-wrap cipher instance.
* @example
* Wraps a short key blob using the padded variant and a fresh key-encryption key.
*
* ```ts
* import { aeskwp } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const kek = randomBytes(16);
* const wrap = aeskwp(kek);
* wrap.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const aeskwp: TRet<((kek: TArg<Uint8Array>) => Cipher) & {
blockSize: number;
}>;
declare class _AesCtrDRBG implements PRG {
readonly blockLen: number;
private key;
private nonce;
private state;
private reseedCnt;
constructor(keyLen: number, seed: TArg<Uint8Array>, personalization?: TArg<Uint8Array>);
private update;
addEntropy(seed: TArg<Uint8Array>, info?: TArg<Uint8Array>): void;
randomBytes(len: number, info?: TArg<Uint8Array>): TRet<Uint8Array>;
clean(): void;
}
/**
* Factory for AES-CTR DRBG instances.
* @param seed - Initial entropy input.
* @param personalization - Optional personalization string mixed into the state.
* @returns Seeded AES-CTR DRBG instance.
*/
export type AesCtrDrbg = (seed: TArg<Uint8Array>, personalization?: TArg<Uint8Array>) => TRet<_AesCtrDRBG>;
/**
* AES-CTR DRBG 128-bit - CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* @param seed - Initial 32-byte entropy input.
* @param personalization - Optional personalization string.
* @returns Seeded DRBG instance. The concrete methods also accept optional additional-input bytes.
* @example
* Seeds the test-only AES-CTR DRBG from fresh entropy and reads bytes from it.
*
* ```ts
* import { rngAesCtrDrbg128 } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const prg = rngAesCtrDrbg128(seed);
* prg.randomBytes(8);
* ```
*/
export declare const rngAesCtrDrbg128: TRet<AesCtrDrbg>;
/**
* AES-CTR DRBG 256-bit - CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* @param seed - Initial 48-byte entropy input.
* @param personalization - Optional personalization string.
* @returns Seeded DRBG instance. The concrete methods also accept optional additional-input bytes.
* @example
* Seeds the test-only AES-CTR DRBG from fresh entropy and reads bytes from it.
*
* ```ts
* import { rngAesCtrDrbg256 } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(48);
* const prg = rngAesCtrDrbg256(seed);
* prg.randomBytes(8);
* ```
*/
export declare const rngAesCtrDrbg256: TRet<AesCtrDrbg>;
/**
* Left-shift by one bit and conditionally XOR with 0x87:
* ```
* if MSB(L) is equal to 0
* then K1 := L << 1;
* else K1 := (L << 1) XOR const_Rb;
* ```
*
* Specs:
* {@link https://www.rfc-editor.org/rfc/rfc4493.html#section-2.3 | RFC 4493 Section 2.3},
* {@link https://datatracker.ietf.org/doc/html/rfc5297.html#section-2.3 | RFC 5297 Section 2.3}
*
* @returns modified `block` (for chaining)
*/
declare function dbl<T extends Uint8Array>(block: T): T;
/**
* `a XOR b`, running in-place on `a`.
* @param a left operand and output
* @param b right operand
* @returns `a` (for chaining)
*/
declare function xorBlock<T extends TArg<Uint8Array>>(a: T, b: TArg<Uint8Array>): T;
/**
* xorend as defined in
* {@link https://datatracker.ietf.org/doc/html/rfc5297.html#section-2.1 | RFC 5297 Section 2.1}.
*
* ```
* leftmost(A, len(A)-len(B)) || (rightmost(A, len(B)) xor B)
* ```
*
* Mutates `a` in place so the left prefix stays untouched and only the
* rightmost `len(B)` bytes are xored with `b`.
*/
declare function xorend<T extends TArg<Uint8Array>>(a: T, b: TArg<Uint8Array>): T;
/**
* Internal CMAC class.
*/
declare class _CMAC implements IHash2 {
readonly blockLen: number;
readonly outputLen: number;
private buffer;
private pos;
private finished;
private destroyed;
private k1;
private k2;
private x;
private xk;
constructor(key: TArg<Uint8Array>);
private process;
update(data: TArg<Uint8Array>): this;
digestInto(out: TArg<Uint8Array>): void;
digest(): Uint8ArrayBuffer;
destroy(): void;
}
/**
* AES-CMAC (Cipher-based Message Authentication Code).
* Specs: {@link https://www.rfc-editor.org/rfc/rfc4493.html | RFC 4493}.
* @param msg - Message bytes to authenticate.
* @param key - AES key bytes.
* @returns 16-byte authentication tag. `cmac.create(...)` follows the same incremental MAC shape as
* the other keyed helpers in this repo, including `blockLen`,
* `outputLen`, `digestInto()` and `destroy()`.
* @example
* Authenticates a message with AES-CMAC and a fresh key.
*
* ```ts
* import { cmac } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* cmac(new Uint8Array(), key);
* ```
*/
export declare const cmac: TRet<CMac<_CMAC>>;
/**
* S2V (Synthetic Initialization Vector) function as described in
* {@link https://datatracker.ietf.org/doc/html/rfc5297.html#section-2.4 | RFC 5297 Section 2.4}.
*
* ```
* S2V(K, S1, ..., Sn) {
* if n = 0 then
* return V = AES-CMAC(K, <one>)
* fi
* D = AES-CMAC(K, <zero>)
* for i = 1 to n-1 do
* D = dbl(D) xor AES-CMAC(K, Si)
* done
* if len(Sn) >= 128 then
* T = Sn xorend D
* else
* T = dbl(D) xor pad(Sn)
* fi
* return V = AES-CMAC(K, T)
* }
* ```
*
* S2V takes a key and a vector of strings S1, S2, ..., Sn and returns a 128-bit string.
* The S2V function is used to generate a synthetic IV for AES-SIV.
*
* @param key - AES key (128, 192, or 256 bits)
* @param strings - Array of byte arrays to process
* @returns 128-bit synthetic IV
*/
declare function s2v(key: TArg<Uint8Array>, strings: TArg<Uint8Array[]>): TRet<Uint8Array>;
/**
* Use `gcmsiv` or `aessiv`.
* @returns Never; always throws with the migration hint.
* @throws If called; `siv()` is a removed v1 alias. {@link Error}
* @example
* `siv()` was removed in v2; use `gcmsiv()` for nonce-based SIV instead.
*
* ```ts
* import { gcmsiv } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(12);
* const cipher = gcmsiv(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const siv: () => never;
/**
* **SIV**: Synthetic Initialization Vector (SIV) Authenticated Encryption
* Nonce is derived from the plaintext and AAD using the S2V function.
* Supports at most 126 AAD components. RFC 5297 nonce-based use is expressed by
* passing the nonce as the final AAD component before the plaintext.
* See {@link https://datatracker.ietf.org/doc/html/rfc5297.html | RFC 5297}.
* @param key - 32-byte, 48-byte, or 64-byte key.
* @param AAD - Additional authenticated data chunks (up to 126).
* @returns AEAD cipher instance.
* @example
* Authenticates and encrypts plaintext with a fresh key without requiring unique nonces.
*
* ```ts
* import { aessiv } from '@noble/ciphers/aes.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const cipher = aessiv(key);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const aessiv: TRet<((key: TArg<Uint8Array>, ...AAD: TArg<Uint8Array[]>) => Cipher) & {
blockSize: number;
tagLength: number;
}>;
/**
* Unsafe low-level internal methods. May change at any time.
* Callers are expected to use reviewed expanded-key outputs, pass mutable and
* aligned 16-byte blocks where required, and treat several helpers as in-place
* mutations of their input buffers or counters.
*/
export declare const unsafe: {
expandKeyLE: typeof expandKeyLE;
expandKeyDecLE: typeof expandKeyDecLE;
encrypt: typeof encrypt;
decrypt: typeof decrypt;
encryptBlock: typeof encryptBlock;
decryptBlock: typeof decryptBlock;
ctrCounter: typeof ctrCounter;
ctr32: typeof ctr32;
dbl: typeof dbl;
xorBlock: typeof xorBlock;
xorend: typeof xorend;
s2v: typeof s2v;
};
export declare const __TESTS: {
incBytes: typeof incBytes;
};
export {};
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/**
* ChaCha stream cipher, released
* in 2008. Developed after Salsa20, ChaCha aims to increase diffusion per round.
* It was standardized in
* {@link https://www.rfc-editor.org/rfc/rfc8439 | RFC 8439} and
* is now used in TLS 1.3.
*
* {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | XChaCha20}
* extended-nonce variant is also provided. Similar to XSalsa, it's safe to use with
* randomly-generated nonces.
*
* Check out
* {@link http://cr.yp.to/chacha/chacha-20080128.pdf | PDF},
* {@link https://en.wikipedia.org/wiki/Salsa20 | wiki}, and
* {@link https://cr.yp.to/chacha.html | website}.
*
* @module
*/
import { type XorPRG } from './_arx.ts';
import { type ARXCipher, type CipherWithOutput, type TArg, type TRet, type XorStream } from './utils.ts';
/** Identical to `chachaCore`. Reached only through the test-only `__TESTS` export. */
declare const chachaCore_small: typeof chachaCore;
/** RFC 8439 §2.3 block core for `state = constants | key | counter | nonce`. */
declare function chachaCore(s: TArg<Uint32Array>, k: TArg<Uint32Array>, n: TArg<Uint32Array>, out: TArg<Uint32Array>, cnt: number, rounds?: number): void;
/**
* hchacha hashes key and nonce into key' and nonce' for xchacha20.
* Algorithmically identical to `hchacha_small`, but this exported path
* normalizes word order on big-endian hosts.
* Need to find a way to merge it with `chachaCore` without 25% performance hit.
* @param s - Sigma constants as 32-bit words.
* @param k - Key words.
* @param i - Nonce-prefix words.
* @param out - Output buffer for the derived subkey.
* @example
* Derives the XChaCha subkey from sigma, key, and nonce-prefix words.
*
* ```ts
* const sigma = new Uint32Array(4);
* const key = new Uint32Array(8);
* const nonce = new Uint32Array(4);
* const out = new Uint32Array(8);
* hchacha(sigma, key, nonce, out);
* ```
*/
export declare function hchacha(s: TArg<Uint32Array>, k: TArg<Uint32Array>, i: TArg<Uint32Array>, out: TArg<Uint32Array>): void;
/**
* Original, non-RFC chacha20 from DJB. 8-byte nonce, 8-byte counter.
* The nonce/counter layout still reserves 8 counter bytes internally, but the shared public
* `counter` argument follows noble's strict non-wrapping 32-bit policy. See `src/_arx.ts`
* near `MAX_COUNTER` for the full counter-policy rationale.
* @param key - 16-byte or 32-byte key.
* @param nonce - 8-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the original 8-byte-nonce ChaCha variant and a fresh key/nonce.
*
* ```ts
* import { chacha20orig } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(8);
* chacha20orig(key, nonce, new Uint8Array(4));
* ```
*/
export declare const chacha20orig: TRet<XorStream>;
/**
* ChaCha stream cipher. Conforms to RFC 8439 (IETF, TLS). 12-byte nonce, 4-byte counter.
* With smaller nonce, it's not safe to make it random (CSPRNG), due to collision chance.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the RFC 8439 ChaCha20 stream cipher and a fresh key/nonce.
*
* ```ts
* import { chacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha20(key, nonce, new Uint8Array(4));
* ```
*/
export declare const chacha20: TRet<XorStream>;
/**
* XChaCha eXtended-nonce ChaCha. With 24-byte nonce, it's safe to make it random (CSPRNG).
* See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | the IRTF draft}.
* The nonce/counter layout still reserves 8 counter bytes internally, but the shared public
* `counter` argument follows noble's strict non-wrapping 32-bit policy. See `src/_arx.ts`
* near `MAX_COUNTER` for the full counter-policy rationale.
* @param key - 32-byte key.
* @param nonce - 24-byte extended nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with XChaCha20 using a fresh key and random 24-byte nonce.
*
* ```ts
* import { xchacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* xchacha20(key, nonce, new Uint8Array(4));
* ```
*/
export declare const xchacha20: TRet<XorStream>;
/**
* Reduced 8-round chacha, described in original paper.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Uses the reduced 8-round variant for non-critical workloads with a fresh key/nonce.
*
* ```ts
* import { chacha8 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha8(key, nonce, new Uint8Array(4));
* ```
*/
export declare const chacha8: TRet<XorStream>;
/**
* Reduced 12-round chacha, described in original paper.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Uses the reduced 12-round variant for non-critical workloads with a fresh key/nonce.
*
* ```ts
* import { chacha12 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha12(key, nonce, new Uint8Array(4));
* ```
*/
export declare const chacha12: TRet<XorStream>;
export declare const __TESTS: {
chachaCore_small: typeof chachaCore_small;
chachaCore: typeof chachaCore;
};
/**
* AEAD algorithm from RFC 8439.
* Salsa20 and chacha (RFC 8439) use poly1305 differently.
* We could have composed them, but it's hard because of authKey:
* In salsa20, authKey changes position in salsa stream.
* In chacha, authKey can't be computed inside computeTag, it modifies the counter.
*/
export declare const _poly1305_aead: (xorStream: TArg<XorStream>) => (key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => CipherWithOutput;
/**
* ChaCha20-Poly1305 from RFC 8439.
*
* Unsafe to use random nonces under the same key, due to collision chance.
* Prefer XChaCha instead.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with a fresh key and nonce.
*
* ```ts
* import { chacha20poly1305 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* const cipher = chacha20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const chacha20poly1305: TRet<ARXCipher>;
/**
* XChaCha20-Poly1305 extended-nonce chacha.
*
* Can be safely used with random nonces (CSPRNG).
* See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | the IRTF draft}.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with a fresh key and random 24-byte nonce.
*
* ```ts
* import { xchacha20poly1305 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const cipher = xchacha20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const xchacha20poly1305: TRet<ARXCipher>;
/**
* Chacha20 CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* Compatible with libtomcrypt. It does not have a specification, so unclear how secure it is.
* @param seed - Optional seed bytes mixed into the internal `key || nonce` state. When omitted,
* only 32 random bytes are mixed into the 40-byte state.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
* @example
* Seeds the test-only ChaCha20 DRBG from fresh entropy.
*
* ```ts
* import { rngChacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const prg = rngChacha20(seed);
* prg.randomBytes(8);
* ```
*/
export declare const rngChacha20: TRet<XorPRG>;
/**
* Chacha20/8 CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* Faster than `rngChacha20`.
* @param seed - Optional seed bytes mixed into the internal `key || nonce` state. When omitted,
* only 32 random bytes are mixed into the 44-byte state.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
* @example
* Seeds the faster test-only ChaCha8 DRBG from fresh entropy.
*
* ```ts
* import { rngChacha8 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const prg = rngChacha8(seed);
* prg.randomBytes(8);
* ```
*/
export declare const rngChacha8: TRet<XorPRG>;
export {};
//# sourceMappingURL=chacha.d.ts.map

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/**
* ChaCha stream cipher, released
* in 2008. Developed after Salsa20, ChaCha aims to increase diffusion per round.
* It was standardized in
* {@link https://www.rfc-editor.org/rfc/rfc8439 | RFC 8439} and
* is now used in TLS 1.3.
*
* {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | XChaCha20}
* extended-nonce variant is also provided. Similar to XSalsa, it's safe to use with
* randomly-generated nonces.
*
* Check out
* {@link http://cr.yp.to/chacha/chacha-20080128.pdf | PDF},
* {@link https://en.wikipedia.org/wiki/Salsa20 | wiki}, and
* {@link https://cr.yp.to/chacha.html | website}.
*
* @module
*/
import { createCipher, createPRG, rotl } from "./_arx.js";
import { poly1305 } from "./_poly1305.js";
import { abytes, clean, equalBytes, getOutput, swap8IfBE, swap32IfBE, u64Lengths, wrapCipher, } from "./utils.js";
/**
* ChaCha core function. It is implemented twice:
* 1. Simple loop (chachaCore_small, hchacha_small)
* 2. Unrolled loop (chachaCore, hchacha) - 4x faster, but larger & harder to read
* The specific implementation is selected in `createCipher` below.
*/
/** RFC 8439 §2.1 quarter round on words a, b, c, d. */
// prettier-ignore
function chachaQR(x, a, b, c, d) {
x[a] = (x[a] + x[b]) | 0;
x[d] = rotl(x[d] ^ x[a], 16);
x[c] = (x[c] + x[d]) | 0;
x[b] = rotl(x[b] ^ x[c], 12);
x[a] = (x[a] + x[b]) | 0;
x[d] = rotl(x[d] ^ x[a], 8);
x[c] = (x[c] + x[d]) | 0;
x[b] = rotl(x[b] ^ x[c], 7);
}
/** Repeated ChaCha double rounds; callers are expected to pass an even round count. */
function chachaRound(x, rounds = 20) {
for (let r = 0; r < rounds; r += 2) {
// RFC 8439 §2.3 / §2.3.1 inner_block: four column rounds, then four diagonal rounds.
chachaQR(x, 0, 4, 8, 12);
chachaQR(x, 1, 5, 9, 13);
chachaQR(x, 2, 6, 10, 14);
chachaQR(x, 3, 7, 11, 15);
chachaQR(x, 0, 5, 10, 15);
chachaQR(x, 1, 6, 11, 12);
chachaQR(x, 2, 7, 8, 13);
chachaQR(x, 3, 4, 9, 14);
}
}
// Shared scratch for the auditability-only helper below; only the test-only
// __TESTS.chachaCore_small hook reaches it, so production exports stay reentrant.
const ctmp = /* @__PURE__ */ new Uint32Array(16);
/** Small version of chacha without loop unrolling. Unused, provided for auditability. */
// prettier-ignore
function chacha(s, k, i, out, isHChacha = true, rounds = 20) {
// `i` is either `[counter, nonce0, nonce1, nonce2]` for the ChaCha block
// function or the full 128-bit nonce prefix for the HChaCha subkey path.
// Create initial array using common pattern
const y = Uint32Array.from([
s[0], s[1], s[2], s[3], // "expa" "nd 3" "2-by" "te k"
k[0], k[1], k[2], k[3], // Key Key Key Key
k[4], k[5], k[6], k[7], // Key Key Key Key
i[0], i[1], i[2], i[3], // Counter Counter Nonce Nonce
]);
const x = ctmp;
x.set(y);
chachaRound(x, rounds);
// HChaCha writes words 0..3 and 12..15 after the rounds; the ChaCha
// block path adds the original state word-by-word.
if (isHChacha) {
const xindexes = [0, 1, 2, 3, 12, 13, 14, 15];
for (let i = 0; i < 8; i++)
out[i] = x[xindexes[i]];
}
else {
for (let i = 0; i < 16; i++)
out[i] = (y[i] + x[i]) | 0;
}
}
/** Identical to `chachaCore`. Reached only through the test-only `__TESTS` export. */
// @ts-ignore
const chachaCore_small = (s, k, n, out, cnt, rounds) =>
// Keep the reference wrapper on the same [counter, nonce0, nonce1, nonce2] layout as chacha().
chacha(s, k, Uint32Array.from([cnt, n[0], n[1], n[2]]), out, false, rounds);
/** Identical to `hchacha`. Unused. */
// @ts-ignore
const hchacha_small = chacha;
/** RFC 8439 §2.3 block core for `state = constants | key | counter | nonce`. */
// prettier-ignore
function chachaCore(s, k, n, out, cnt, rounds = 20) {
let y00 = s[0], y01 = s[1], y02 = s[2], y03 = s[3], // "expa" "nd 3" "2-by" "te k"
y04 = k[0], y05 = k[1], y06 = k[2], y07 = k[3], // Key Key Key Key
y08 = k[4], y09 = k[5], y10 = k[6], y11 = k[7], // Key Key Key Key
y12 = cnt, y13 = n[0], y14 = n[1], y15 = n[2]; // Counter Nonce Nonce Nonce
// Save state to temporary variables
let x00 = y00, x01 = y01, x02 = y02, x03 = y03, x04 = y04, x05 = y05, x06 = y06, x07 = y07, x08 = y08, x09 = y09, x10 = y10, x11 = y11, x12 = y12, x13 = y13, x14 = y14, x15 = y15;
for (let r = 0; r < rounds; r += 2) {
x00 = (x00 + x04) | 0;
x12 = rotl(x12 ^ x00, 16);
x08 = (x08 + x12) | 0;
x04 = rotl(x04 ^ x08, 12);
x00 = (x00 + x04) | 0;
x12 = rotl(x12 ^ x00, 8);
x08 = (x08 + x12) | 0;
x04 = rotl(x04 ^ x08, 7);
x01 = (x01 + x05) | 0;
x13 = rotl(x13 ^ x01, 16);
x09 = (x09 + x13) | 0;
x05 = rotl(x05 ^ x09, 12);
x01 = (x01 + x05) | 0;
x13 = rotl(x13 ^ x01, 8);
x09 = (x09 + x13) | 0;
x05 = rotl(x05 ^ x09, 7);
x02 = (x02 + x06) | 0;
x14 = rotl(x14 ^ x02, 16);
x10 = (x10 + x14) | 0;
x06 = rotl(x06 ^ x10, 12);
x02 = (x02 + x06) | 0;
x14 = rotl(x14 ^ x02, 8);
x10 = (x10 + x14) | 0;
x06 = rotl(x06 ^ x10, 7);
x03 = (x03 + x07) | 0;
x15 = rotl(x15 ^ x03, 16);
x11 = (x11 + x15) | 0;
x07 = rotl(x07 ^ x11, 12);
x03 = (x03 + x07) | 0;
x15 = rotl(x15 ^ x03, 8);
x11 = (x11 + x15) | 0;
x07 = rotl(x07 ^ x11, 7);
x00 = (x00 + x05) | 0;
x15 = rotl(x15 ^ x00, 16);
x10 = (x10 + x15) | 0;
x05 = rotl(x05 ^ x10, 12);
x00 = (x00 + x05) | 0;
x15 = rotl(x15 ^ x00, 8);
x10 = (x10 + x15) | 0;
x05 = rotl(x05 ^ x10, 7);
x01 = (x01 + x06) | 0;
x12 = rotl(x12 ^ x01, 16);
x11 = (x11 + x12) | 0;
x06 = rotl(x06 ^ x11, 12);
x01 = (x01 + x06) | 0;
x12 = rotl(x12 ^ x01, 8);
x11 = (x11 + x12) | 0;
x06 = rotl(x06 ^ x11, 7);
x02 = (x02 + x07) | 0;
x13 = rotl(x13 ^ x02, 16);
x08 = (x08 + x13) | 0;
x07 = rotl(x07 ^ x08, 12);
x02 = (x02 + x07) | 0;
x13 = rotl(x13 ^ x02, 8);
x08 = (x08 + x13) | 0;
x07 = rotl(x07 ^ x08, 7);
x03 = (x03 + x04) | 0;
x14 = rotl(x14 ^ x03, 16);
x09 = (x09 + x14) | 0;
x04 = rotl(x04 ^ x09, 12);
x03 = (x03 + x04) | 0;
x14 = rotl(x14 ^ x03, 8);
x09 = (x09 + x14) | 0;
x04 = rotl(x04 ^ x09, 7);
}
// RFC 8439 §2.3 / §2.3.1: add the original state words back in state order.
let oi = 0;
out[oi++] = (y00 + x00) | 0;
out[oi++] = (y01 + x01) | 0;
out[oi++] = (y02 + x02) | 0;
out[oi++] = (y03 + x03) | 0;
out[oi++] = (y04 + x04) | 0;
out[oi++] = (y05 + x05) | 0;
out[oi++] = (y06 + x06) | 0;
out[oi++] = (y07 + x07) | 0;
out[oi++] = (y08 + x08) | 0;
out[oi++] = (y09 + x09) | 0;
out[oi++] = (y10 + x10) | 0;
out[oi++] = (y11 + x11) | 0;
out[oi++] = (y12 + x12) | 0;
out[oi++] = (y13 + x13) | 0;
out[oi++] = (y14 + x14) | 0;
out[oi++] = (y15 + x15) | 0;
}
/**
* hchacha hashes key and nonce into key' and nonce' for xchacha20.
* Algorithmically identical to `hchacha_small`, but this exported path
* normalizes word order on big-endian hosts.
* Need to find a way to merge it with `chachaCore` without 25% performance hit.
* @param s - Sigma constants as 32-bit words.
* @param k - Key words.
* @param i - Nonce-prefix words.
* @param out - Output buffer for the derived subkey.
* @example
* Derives the XChaCha subkey from sigma, key, and nonce-prefix words.
*
* ```ts
* const sigma = new Uint32Array(4);
* const key = new Uint32Array(8);
* const nonce = new Uint32Array(4);
* const out = new Uint32Array(8);
* hchacha(sigma, key, nonce, out);
* ```
*/
// prettier-ignore
export function hchacha(s, k, i, out) {
let x00 = swap8IfBE(s[0]), x01 = swap8IfBE(s[1]), x02 = swap8IfBE(s[2]), x03 = swap8IfBE(s[3]), x04 = swap8IfBE(k[0]), x05 = swap8IfBE(k[1]), x06 = swap8IfBE(k[2]), x07 = swap8IfBE(k[3]), x08 = swap8IfBE(k[4]), x09 = swap8IfBE(k[5]), x10 = swap8IfBE(k[6]), x11 = swap8IfBE(k[7]), x12 = swap8IfBE(i[0]), x13 = swap8IfBE(i[1]), x14 = swap8IfBE(i[2]), x15 = swap8IfBE(i[3]);
for (let r = 0; r < 20; r += 2) {
x00 = (x00 + x04) | 0;
x12 = rotl(x12 ^ x00, 16);
x08 = (x08 + x12) | 0;
x04 = rotl(x04 ^ x08, 12);
x00 = (x00 + x04) | 0;
x12 = rotl(x12 ^ x00, 8);
x08 = (x08 + x12) | 0;
x04 = rotl(x04 ^ x08, 7);
x01 = (x01 + x05) | 0;
x13 = rotl(x13 ^ x01, 16);
x09 = (x09 + x13) | 0;
x05 = rotl(x05 ^ x09, 12);
x01 = (x01 + x05) | 0;
x13 = rotl(x13 ^ x01, 8);
x09 = (x09 + x13) | 0;
x05 = rotl(x05 ^ x09, 7);
x02 = (x02 + x06) | 0;
x14 = rotl(x14 ^ x02, 16);
x10 = (x10 + x14) | 0;
x06 = rotl(x06 ^ x10, 12);
x02 = (x02 + x06) | 0;
x14 = rotl(x14 ^ x02, 8);
x10 = (x10 + x14) | 0;
x06 = rotl(x06 ^ x10, 7);
x03 = (x03 + x07) | 0;
x15 = rotl(x15 ^ x03, 16);
x11 = (x11 + x15) | 0;
x07 = rotl(x07 ^ x11, 12);
x03 = (x03 + x07) | 0;
x15 = rotl(x15 ^ x03, 8);
x11 = (x11 + x15) | 0;
x07 = rotl(x07 ^ x11, 7);
x00 = (x00 + x05) | 0;
x15 = rotl(x15 ^ x00, 16);
x10 = (x10 + x15) | 0;
x05 = rotl(x05 ^ x10, 12);
x00 = (x00 + x05) | 0;
x15 = rotl(x15 ^ x00, 8);
x10 = (x10 + x15) | 0;
x05 = rotl(x05 ^ x10, 7);
x01 = (x01 + x06) | 0;
x12 = rotl(x12 ^ x01, 16);
x11 = (x11 + x12) | 0;
x06 = rotl(x06 ^ x11, 12);
x01 = (x01 + x06) | 0;
x12 = rotl(x12 ^ x01, 8);
x11 = (x11 + x12) | 0;
x06 = rotl(x06 ^ x11, 7);
x02 = (x02 + x07) | 0;
x13 = rotl(x13 ^ x02, 16);
x08 = (x08 + x13) | 0;
x07 = rotl(x07 ^ x08, 12);
x02 = (x02 + x07) | 0;
x13 = rotl(x13 ^ x02, 8);
x08 = (x08 + x13) | 0;
x07 = rotl(x07 ^ x08, 7);
x03 = (x03 + x04) | 0;
x14 = rotl(x14 ^ x03, 16);
x09 = (x09 + x14) | 0;
x04 = rotl(x04 ^ x09, 12);
x03 = (x03 + x04) | 0;
x14 = rotl(x14 ^ x03, 8);
x09 = (x09 + x14) | 0;
x04 = rotl(x04 ^ x09, 7);
}
// HChaCha derives the subkey from state words 0..3 and 12..15 after 20 rounds.
let oi = 0;
out[oi++] = x00;
out[oi++] = x01;
out[oi++] = x02;
out[oi++] = x03;
out[oi++] = x12;
out[oi++] = x13;
out[oi++] = x14;
out[oi++] = x15;
swap32IfBE(out);
}
/**
* Original, non-RFC chacha20 from DJB. 8-byte nonce, 8-byte counter.
* The nonce/counter layout still reserves 8 counter bytes internally, but the shared public
* `counter` argument follows noble's strict non-wrapping 32-bit policy. See `src/_arx.ts`
* near `MAX_COUNTER` for the full counter-policy rationale.
* @param key - 16-byte or 32-byte key.
* @param nonce - 8-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the original 8-byte-nonce ChaCha variant and a fresh key/nonce.
*
* ```ts
* import { chacha20orig } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(8);
* chacha20orig(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha20orig = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 8,
allowShortKeys: true,
});
/**
* ChaCha stream cipher. Conforms to RFC 8439 (IETF, TLS). 12-byte nonce, 4-byte counter.
* With smaller nonce, it's not safe to make it random (CSPRNG), due to collision chance.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the RFC 8439 ChaCha20 stream cipher and a fresh key/nonce.
*
* ```ts
* import { chacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha20(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha20 = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 4,
allowShortKeys: false,
});
/**
* XChaCha eXtended-nonce ChaCha. With 24-byte nonce, it's safe to make it random (CSPRNG).
* See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | the IRTF draft}.
* The nonce/counter layout still reserves 8 counter bytes internally, but the shared public
* `counter` argument follows noble's strict non-wrapping 32-bit policy. See `src/_arx.ts`
* near `MAX_COUNTER` for the full counter-policy rationale.
* @param key - 32-byte key.
* @param nonce - 24-byte extended nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with XChaCha20 using a fresh key and random 24-byte nonce.
*
* ```ts
* import { xchacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* xchacha20(key, nonce, new Uint8Array(4));
* ```
*/
export const xchacha20 = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 8,
extendNonceFn: hchacha,
allowShortKeys: false,
});
/**
* Reduced 8-round chacha, described in original paper.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Uses the reduced 8-round variant for non-critical workloads with a fresh key/nonce.
*
* ```ts
* import { chacha8 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha8(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha8 = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 4,
rounds: 8,
});
/**
* Reduced 12-round chacha, described in original paper.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Uses the reduced 12-round variant for non-critical workloads with a fresh key/nonce.
*
* ```ts
* import { chacha12 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha12(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha12 = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 4,
rounds: 12,
});
// Test-only hooks for keeping the simple/reference core aligned with the unrolled production core.
export const __TESTS = /* @__PURE__ */ Object.freeze({ chachaCore_small, chachaCore });
// RFC 8439 §2.8.1 pad16(x): shared zero block for AAD/ciphertext padding.
const ZEROS16 = /* @__PURE__ */ new Uint8Array(16);
// RFC 8439 §2.8 / §2.8.1: aligned inputs add nothing, otherwise append 16-(len%16) zero bytes.
const updatePadded = (h, msg) => {
h.update(msg);
const leftover = msg.length % 16;
if (leftover)
h.update(ZEROS16.subarray(leftover));
};
// RFC 8439 §2.6.1 poly1305_key_gen returns `block[0..31]`, so AEAD key
// generation only needs 32 zero bytes.
const ZEROS32 = /* @__PURE__ */ new Uint8Array(32);
function computeTag(fn, key, nonce, ciphertext, AAD) {
if (AAD !== undefined)
abytes(AAD, undefined, 'AAD');
// RFC 8439 §2.6 / §2.8: derive the Poly1305 one-time key from counter 0,
// then MAC AAD || pad16(AAD) || ciphertext || pad16(ciphertext) || len(AAD) || len(ciphertext).
const authKey = fn(key, nonce, ZEROS32);
const lengths = u64Lengths(ciphertext.length, AAD ? AAD.length : 0, true);
// Methods below can be replaced with
// return poly1305_computeTag_small(authKey, lengths, ciphertext, AAD)
const h = poly1305.create(authKey);
if (AAD)
updatePadded(h, AAD);
updatePadded(h, ciphertext);
h.update(lengths);
const res = h.digest();
clean(authKey, lengths);
return res;
}
/**
* AEAD algorithm from RFC 8439.
* Salsa20 and chacha (RFC 8439) use poly1305 differently.
* We could have composed them, but it's hard because of authKey:
* In salsa20, authKey changes position in salsa stream.
* In chacha, authKey can't be computed inside computeTag, it modifies the counter.
*/
export const _poly1305_aead = (xorStream) => (key, nonce, AAD) => {
// This borrows caller key/nonce/AAD buffers by reference; mutating them after construction
// changes future encrypt/decrypt results.
const tagLength = 16;
return {
encrypt(plaintext, output) {
const plength = plaintext.length;
output = getOutput(plength + tagLength, output, false);
output.set(plaintext);
const oPlain = output.subarray(0, -tagLength);
// RFC 8439 §2.8: payload encryption starts at counter 1 because counter 0 produced the OTK.
xorStream(key, nonce, oPlain, oPlain, 1);
const tag = computeTag(xorStream, key, nonce, oPlain, AAD);
output.set(tag, plength); // append tag
clean(tag);
return output;
},
decrypt(ciphertext, output) {
output = getOutput(ciphertext.length - tagLength, output, false);
const data = ciphertext.subarray(0, -tagLength);
const passedTag = ciphertext.subarray(-tagLength);
const tag = computeTag(xorStream, key, nonce, data, AAD);
// RFC 8439 §2.8 / §4: authenticate ciphertext before decrypting it, and compare tags with
// the constant-time equalBytes() helper rather than decrypting speculative plaintext first.
if (!equalBytes(passedTag, tag)) {
clean(tag);
throw new Error('invalid tag');
}
output.set(ciphertext.subarray(0, -tagLength));
// Actual decryption
xorStream(key, nonce, output, output, 1); // start stream with i=1
clean(tag);
return output;
},
};
};
/**
* ChaCha20-Poly1305 from RFC 8439.
*
* Unsafe to use random nonces under the same key, due to collision chance.
* Prefer XChaCha instead.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with a fresh key and nonce.
*
* ```ts
* import { chacha20poly1305 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* const cipher = chacha20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const chacha20poly1305 = /* @__PURE__ */ wrapCipher({ blockSize: 64, nonceLength: 12, tagLength: 16 },
/* @__PURE__ */ _poly1305_aead(chacha20));
/**
* XChaCha20-Poly1305 extended-nonce chacha.
*
* Can be safely used with random nonces (CSPRNG).
* See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | the IRTF draft}.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with a fresh key and random 24-byte nonce.
*
* ```ts
* import { xchacha20poly1305 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const cipher = xchacha20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const xchacha20poly1305 = /* @__PURE__ */ wrapCipher({ blockSize: 64, nonceLength: 24, tagLength: 16 },
/* @__PURE__ */ _poly1305_aead(xchacha20));
/**
* Chacha20 CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* Compatible with libtomcrypt. It does not have a specification, so unclear how secure it is.
* @param seed - Optional seed bytes mixed into the internal `key || nonce` state. When omitted,
* only 32 random bytes are mixed into the 40-byte state.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
* @example
* Seeds the test-only ChaCha20 DRBG from fresh entropy.
*
* ```ts
* import { rngChacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const prg = rngChacha20(seed);
* prg.randomBytes(8);
* ```
*/
export const rngChacha20 = /* @__PURE__ */ createPRG(chacha20orig, 64, 32, 8);
/**
* Chacha20/8 CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* Faster than `rngChacha20`.
* @param seed - Optional seed bytes mixed into the internal `key || nonce` state. When omitted,
* only 32 random bytes are mixed into the 44-byte state.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
* @example
* Seeds the faster test-only ChaCha8 DRBG from fresh entropy.
*
* ```ts
* import { rngChacha8 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const prg = rngChacha8(seed);
* prg.randomBytes(8);
* ```
*/
export const rngChacha8 = /* @__PURE__ */ createPRG(chacha8, 64, 32, 12);
//# sourceMappingURL=chacha.js.map

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node_modules/@noble/ciphers/ff1.d.ts generated vendored Normal file
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import { type Cipher, type TArg, type TRet } from './utils.ts';
/**
* FPE-FF1 format-preserving encryption.
* @param radix - Alphabet size for each input digit.
* @param key - AES key bytes.
* @param tweak - Optional tweak bytes.
* @returns Encrypt/decrypt helpers over digit arrays.
* @example
* Encrypts decimal digits without changing their format, using a fresh AES key.
*
* ```ts
* import { FF1 } from '@noble/ciphers/ff1.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const ff1 = FF1(10, key);
* ff1.encrypt([1, 2, 3]);
* ```
*/
export declare function FF1(radix: number, key: TArg<Uint8Array>, tweak?: TArg<Uint8Array>): {
encrypt(x: number[]): number[];
decrypt(x: number[]): number[];
};
/**
* Binary FPE-FF1 wrapper over byte arrays.
* @param key - AES key bytes.
* @param tweak - Optional tweak bytes.
* @returns Encrypt/decrypt helpers over byte arrays.
* @example
* Encrypts raw bytes through FF1's binary alphabet wrapper with a fresh AES key.
*
* ```ts
* import { BinaryFF1 } from '@noble/ciphers/ff1.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const ff1 = BinaryFF1(key);
* ff1.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare function BinaryFF1(key: TArg<Uint8Array>, tweak?: TArg<Uint8Array>): TRet<Cipher>;
//# sourceMappingURL=ff1.d.ts.map

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{"version":3,"file":"ff1.d.ts","sourceRoot":"","sources":["src/ff1.ts"],"names":[],"mappings":"AAMA,OAAO,EAML,KAAK,MAAM,EACX,KAAK,IAAI,EACT,KAAK,IAAI,EACV,MAAM,YAAY,CAAC;AAqGpB;;;;;;;;;;;;;;;;GAgBG;AACH,wBAAgB,GAAG,CACjB,KAAK,EAAE,MAAM,EACb,GAAG,EAAE,IAAI,CAAC,UAAU,CAAC,EACrB,KAAK,GAAE,IAAI,CAAC,UAAU,CAAa,GAClC;IAAE,OAAO,CAAC,CAAC,EAAE,MAAM,EAAE,GAAG,MAAM,EAAE,CAAC;IAAC,OAAO,CAAC,CAAC,EAAE,MAAM,EAAE,GAAG,MAAM,EAAE,CAAA;CAAE,CAkCpE;AAsBD;;;;;;;;;;;;;;;GAeG;AACH,wBAAgB,SAAS,CACvB,GAAG,EAAE,IAAI,CAAC,UAAU,CAAC,EACrB,KAAK,GAAE,IAAI,CAAC,UAAU,CAAa,GAClC,IAAI,CAAC,MAAM,CAAC,CAQd"}

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/**
* FPE-FF1 (Format-preserving encryption algorithm) specified in
* {@link https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-38G.pdf | NIST 800-38G}.
* @module
*/
import { unsafe } from "./aes.js";
import { abytes, anumber, bytesToNumberBE, clean, numberToBytesBE, } from "./utils.js";
// NIST SP 800-38G §4.3 / §5.1 Algorithm 7: FF1's designated CIPH_K here is AES, so this file
// reuses the reviewed AES key schedule and single-block encryption helpers.
// NOTE: no point in inlining encrypt instead of encryptBlock, since BigInt stuff will be slow
const { expandKeyLE, encryptBlock } = unsafe;
// Format-preserving encryption algorithm (FPE-FF1) specified in
// {@link https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-38G.pdf | NIST Special Publication 800-38G}.
const BLOCK_LEN = 16;
function mod(a, b) {
const result = a % b;
return result >= 0 ? result : b + result;
}
function NUMradix(radix, data) {
let res = BigInt(0);
for (let i of data)
res = res * BigInt(radix) + BigInt(i);
return res;
}
function getRound(radix, key, tweak, x) {
if (radix > 2 ** 16 - 1)
throw new Error('invalid radix ' + radix);
// radix**minlen ≥ 100
const minLen = Math.ceil(Math.log(100) / Math.log(radix));
const maxLen = 2 ** 32 - 1;
// 2 ≤ minlen ≤ maxlen < 2**32
if (2 > minLen || minLen > maxLen || maxLen >= 2 ** 32)
throw new Error('Invalid radix: 2 ≤ minlen ≤ maxlen < 2**32');
if (!Array.isArray(x))
throw new Error('invalid X');
if (x.length < minLen || x.length > maxLen)
throw new Error('X is outside minLen..maxLen bounds');
// SP 800-38G defines FF1 over numeral strings in base `radix`; out-of-range digits must fail
// before NUMradix(...) or round splitting can reinterpret them as a different numeral string.
for (const i of x) {
if (!Number.isSafeInteger(i) || i < 0 || i >= radix)
throw new Error('invalid X: digit outside radix');
}
const u = Math.floor(x.length / 2);
const v = x.length - u;
const b = Math.ceil(Math.ceil(v * Math.log2(radix)) / 8);
const d = 4 * Math.ceil(b / 4) + 4;
const padding = mod(-tweak.length - b - 1, 16);
// P = [1]1 || [2]1 || [1]1 || [radix]3 || [10]1 || [u mod 256]1 || [n]4 || [t]4.
const P = Uint8Array.from([1, 2, 1, 0, 0, 0, 10, u, 0, 0, 0, 0, 0, 0, 0, 0]);
const view = new DataView(P.buffer);
// NIST SP 800-38G §5.1 bounds radix <= 2^16, so the 24-bit [radix]3 field is encoded here as
// 0x00 || uint16_be(radix).
view.setUint16(4, radix, false);
view.setUint32(8, x.length, false);
view.setUint32(12, tweak.length, false);
// Q = T || [0](tb1) mod 16 || [i]1 || [NUMradix(B)]b.
const PQ = new Uint8Array(P.length + tweak.length + padding + 1 + b);
PQ.set(P);
clean(P);
PQ.set(tweak, P.length);
const xk = expandKeyLE(key);
const round = (A, B, i, decrypt = false) => {
// Q = ... || [i]1 || [NUMradix(B)]b.
PQ[PQ.length - b - 1] = i;
if (b)
PQ.set(numberToBytesBE(NUMradix(radix, B), b), PQ.length - b);
// NIST SP 800-38G Algorithm 6 PRF: Y_j = CIPH_K(Y_(j-1) xor X_j) starting from Y_0 = 0^128.
let r = new Uint8Array(16);
for (let j = 0; j < PQ.length / BLOCK_LEN; j++) {
for (let i = 0; i < BLOCK_LEN; i++)
r[i] ^= PQ[j * BLOCK_LEN + i];
encryptBlock(xk, r);
}
// Let S be the first d bytes of the following string of ⎡d/16⎤ blocks:
// R || CIPHK(R ⊕[1]16) || CIPHK(R ⊕[2]16) ...CIPHK(R ⊕[⎡d / 16⎤ 1]16).
let s = Array.from(r);
for (let j = 1; s.length < d; j++) {
const block = numberToBytesBE(BigInt(j), 16);
for (let k = 0; k < BLOCK_LEN; k++)
block[k] ^= r[k];
s.push(...Array.from(encryptBlock(xk, block)));
}
let y = bytesToNumberBE(Uint8Array.from(s.slice(0, d)));
s.fill(0);
if (decrypt)
y = -y;
const m = i % 2 === 0 ? u : v;
let c = mod(NUMradix(radix, A) + y, BigInt(radix) ** BigInt(m));
// STR(radix, m, c)
const C = Array(m).fill(0);
for (let i = 0; i < m; i++, c /= BigInt(radix))
C[m - 1 - i] = Number(c % BigInt(radix));
A.fill(0);
A = B;
B = C;
return [A, B];
};
const destroy = () => {
clean(xk, PQ);
};
return { u, round, destroy };
}
const EMPTY_BUF = /* @__PURE__ */ Uint8Array.of();
/**
* FPE-FF1 format-preserving encryption.
* @param radix - Alphabet size for each input digit.
* @param key - AES key bytes.
* @param tweak - Optional tweak bytes.
* @returns Encrypt/decrypt helpers over digit arrays.
* @example
* Encrypts decimal digits without changing their format, using a fresh AES key.
*
* ```ts
* import { FF1 } from '@noble/ciphers/ff1.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const ff1 = FF1(10, key);
* ff1.encrypt([1, 2, 3]);
* ```
*/
export function FF1(radix, key, tweak = EMPTY_BUF) {
anumber(radix);
abytes(key);
abytes(tweak);
// This borrows caller key/tweak buffers by reference through the bound closure; mutating them
// after construction changes later encrypt/decrypt outputs.
const PQ = getRound.bind(null, radix, key, tweak);
return {
encrypt(x) {
const { u, round, destroy } = PQ(x);
let [A, B] = [x.slice(0, u), x.slice(u)];
for (let i = 0; i < 10; i++)
[A, B] = round(A, B, i);
destroy();
const res = A.concat(B);
A.fill(0);
B.fill(0);
return res;
},
decrypt(x) {
const { u, round, destroy } = PQ(x);
// The FF1.Decrypt algorithm is similar to the FF1.Encrypt algorithm;
// the differences are in Step 6, where:
// 1) the order of the indices is reversed,
// 2) the roles of A and B are swapped
// 3) modular addition is replaced by modular subtraction, in Step 6vi.
let [B, A] = [x.slice(0, u), x.slice(u)];
for (let i = 9; i >= 0; i--)
[A, B] = round(A, B, i, true);
destroy();
const res = B.concat(A);
A.fill(0);
B.fill(0);
return res;
},
};
}
// Binary wrapper uses little-endian bit order within each byte so bit 0 stays
// in the first numeral slot for this library-defined byte-array surface.
const binLE = {
encode(bytes) {
const x = [];
for (let i = 0; i < bytes.length; i++) {
for (let j = 0, tmp = bytes[i]; j < 8; j++, tmp >>= 1)
x.push(tmp & 1);
}
return x;
},
decode(b) {
if (!Array.isArray(b) || b.length % 8)
throw new Error('Invalid binary string');
const res = new Uint8Array(b.length / 8);
for (let i = 0, j = 0; i < res.length; i++) {
res[i] = b[j++] | (b[j++] << 1) | (b[j++] << 2) | (b[j++] << 3);
res[i] |= (b[j++] << 4) | (b[j++] << 5) | (b[j++] << 6) | (b[j++] << 7);
}
return res;
},
};
/**
* Binary FPE-FF1 wrapper over byte arrays.
* @param key - AES key bytes.
* @param tweak - Optional tweak bytes.
* @returns Encrypt/decrypt helpers over byte arrays.
* @example
* Encrypts raw bytes through FF1's binary alphabet wrapper with a fresh AES key.
*
* ```ts
* import { BinaryFF1 } from '@noble/ciphers/ff1.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const ff1 = BinaryFF1(key);
* ff1.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export function BinaryFF1(key, tweak = EMPTY_BUF) {
const ff1 = FF1(2, key, tweak);
return {
encrypt: (x) => binLE.decode(ff1.encrypt(binLE.encode(x))),
decrypt: (x) => binLE.decode(ff1.decrypt(binLE.encode(x))),
};
}
//# sourceMappingURL=ff1.js.map

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export {};
//# sourceMappingURL=index.d.ts.map

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{"version":3,"file":"index.d.ts","sourceRoot":"","sources":["src/index.ts"],"names":[],"mappings":""}

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/**
* Audited & minimal JS implementation of Salsa20, ChaCha and AES. Check out individual modules.
* @example
```js
import { gcm, aessiv } from '@noble/ciphers/aes.js';
import { xsalsa20poly1305 } from '@noble/ciphers/salsa.js';
import { secretbox } from '@noble/ciphers/salsa.js'; // == xsalsa20poly1305
import { chacha20poly1305, xchacha20poly1305 } from '@noble/ciphers/chacha.js';
// Unauthenticated encryption: make sure to use HMAC or similar
import { ctr, cfb, cbc, ecb } from '@noble/ciphers/aes.js';
import { salsa20, xsalsa20 } from '@noble/ciphers/salsa.js';
import { chacha20, xchacha20, chacha8, chacha12 } from '@noble/ciphers/chacha.js';
// KW
import { aeskw, aeskwp } from '@noble/ciphers/aes.js';
// Utilities
import { managedNonce, randomBytes, bytesToHex, hexToBytes } from '@noble/ciphers/utils.js';
import { poly1305 } from '@noble/ciphers/_poly1305.js';
import { ghash, polyval } from '@noble/ciphers/_polyval.js';
```
* @module
*/
throw new Error('root module cannot be imported: import submodules instead. Check out README');
export {};
//# sourceMappingURL=index.js.map

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{"version":3,"file":"index.js","sourceRoot":"","sources":["src/index.ts"],"names":[],"mappings":"AAAA;;;;;;;;;;;;;;;;;;;;;;;GAuBG;AACH,MAAM,IAAI,KAAK,CAAC,6EAA6E,CAAC,CAAC"}

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{
"name": "@noble/ciphers",
"version": "2.2.0",
"description": "Audited & minimal JS implementation of Salsa20, ChaCha and AES",
"files": [
"src",
"*.js",
"*.js.map",
"*.d.ts",
"*.d.ts.map"
],
"devDependencies": {
"@paulmillr/jsbt": "0.5.0",
"@scure/base": "2.0.0",
"@types/node": "25.3.0",
"fast-check": "4.2.0",
"prettier": "3.6.2",
"typescript": "6.0.2"
},
"scripts": {
"bench": "node test/benchmark/noble.ts",
"bench:compare": "cd test/benchmark; npm install; node compare.ts",
"build": "tsc",
"build:release": "npx --no @paulmillr/jsbt esbuild test/build",
"check": "npm run check:readme && npm run check:treeshake && npm run check:jsdoc",
"check:readme": "npx --no @paulmillr/jsbt readme package.json",
"check:treeshake": "npx --no @paulmillr/jsbt treeshake package.json test/build/out-treeshake",
"check:jsdoc": "npx --no @paulmillr/jsbt tsdoc package.json",
"build:clean": "rm *.{js,js.map,d.ts,d.ts.map} 2> /dev/null",
"format": "prettier --write 'src/**/*.{js,ts}' 'test/**/*.{js,ts,mjs}'",
"test": "node test/index.ts",
"test:bun": "bun test/index.ts",
"test:deno": "deno --allow-env --allow-read test/index.ts",
"test:node20": "cd test; npx tsc; node compiled/test/index.js",
"test:slow": "node test/crosstest.test.ts slow"
},
"exports": {
".": "./index.js",
"./_arx.js": "./_arx.js",
"./_poly1305.js": "./_poly1305.js",
"./_polyval.js": "./_polyval.js",
"./aes.js": "./aes.js",
"./chacha.js": "./chacha.js",
"./ff1.js": "./ff1.js",
"./salsa.js": "./salsa.js",
"./utils.js": "./utils.js",
"./webcrypto.js": "./webcrypto.js"
},
"engines": {
"node": ">= 20.19.0"
},
"keywords": [
"salsa20",
"chacha",
"aes",
"cryptography",
"crypto",
"noble",
"cipher",
"ciphers",
"xsalsa20",
"xchacha20",
"poly1305",
"xsalsa20poly1305",
"chacha20poly1305",
"xchacha20poly1305",
"secretbox",
"rijndael",
"siv",
"ff1"
],
"homepage": "https://paulmillr.com/noble/",
"funding": "https://paulmillr.com/funding/",
"repository": {
"type": "git",
"url": "git+https://github.com/paulmillr/noble-ciphers.git"
},
"type": "module",
"main": "index.js",
"module": "index.js",
"types": "index.d.ts",
"sideEffects": false,
"author": "Paul Miller (https://paulmillr.com)",
"license": "MIT"
}

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import { type ARXCipher, type TArg, type TRet, type XorStream } from './utils.ts';
/**
* hsalsa hashes key and nonce-prefix words into the 32-byte subkey used by XSalsa20.
* Identical to `hsalsa_small`.
* Need to find a way to merge it with `salsaCore` without 25% performance hit.
* @param s - Sigma constants as 32-bit words.
* @param k - Key words.
* @param i - Nonce-prefix words.
* @param out - Output buffer for the derived subkey.
* @example
* Derives the XSalsa20 subkey from sigma, key, and nonce-prefix words.
*
* ```ts
* const sigma = new Uint32Array(4);
* const key = new Uint32Array(8);
* const nonce = new Uint32Array(4);
* const out = new Uint32Array(8);
* hsalsa(sigma, key, nonce, out);
* ```
*/
export declare function hsalsa(s: TArg<Uint32Array>, k: TArg<Uint32Array>, i: TArg<Uint32Array>, out: TArg<Uint32Array>): void;
/**
* Salsa20 from original paper. 8-byte nonce.
* With smaller nonce, it's not safe to make it random (CSPRNG), due to collision chance.
* @param key - 16-byte or 32-byte key.
* @param nonce - 8-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* Only the low 32 bits of Salsa20's 64-bit counter state are exposed here;
* the high word stays zero and the implementation still caps the public
* value to 32 bits.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the original 8-byte-nonce Salsa20 stream cipher.
*
* ```ts
* import { salsa20 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(8);
* salsa20(key, nonce, new Uint8Array([1, 2, 3, 4]));
* ```
*/
export declare const salsa20: TRet<XorStream>;
/**
* XSalsa20 extended-nonce salsa.
* With 24-byte nonce, it's safe to make it random (CSPRNG).
* @param key - 32-byte key.
* This XSalsa20 wrapper does not enable Salsa20's 16-byte legacy key mode.
* @param nonce - 24-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with XSalsa20 and a random 24-byte nonce.
*
* ```ts
* import { xsalsa20 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* xsalsa20(key, nonce, new Uint8Array([1, 2, 3, 4]));
* ```
*/
export declare const xsalsa20: TRet<XorStream>;
/**
* xsalsa20-poly1305 eXtended-nonce (24 bytes) salsa.
* With 24-byte nonce, it's safe to make it random (CSPRNG).
* Also known as `secretbox` from libsodium / nacl.
* No AAD input is supported here. Caller-provided `output` buffers for
* `encrypt()` / `decrypt()` must be `input.length + 32` bytes because the
* implementation uses a 32-byte leading scratch area before returning `+16`.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @param AAD - Must be omitted; XSalsa20-Poly1305 secretbox does not support associated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with XSalsa20-Poly1305.
*
* ```ts
* import { xsalsa20poly1305 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const cipher = xsalsa20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const xsalsa20poly1305: TRet<ARXCipher>;
/**
* Alias to `xsalsa20poly1305`, for compatibility with libsodium / nacl.
* Check out {@link https://github.com/serenity-kit/noble-sodium | noble-sodium}
* for `crypto_box`.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @returns Wrapper with `seal()` and `open()` helpers.
* @example
* Uses the libsodium-style `seal()` and `open()` wrapper.
*
* ```ts
* import { secretbox } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const box = secretbox(key, nonce);
* box.seal(new Uint8Array([1, 2, 3]));
* ```
*/
export declare function secretbox(key: TArg<Uint8Array>, nonce: TArg<Uint8Array>): TRet<{
seal: (plaintext: TArg<Uint8Array>, output?: TArg<Uint8Array>) => TRet<Uint8Array>;
open: (ciphertext: TArg<Uint8Array>, output?: TArg<Uint8Array>) => TRet<Uint8Array>;
}>;
//# sourceMappingURL=salsa.d.ts.map

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/**
* Salsa20 stream cipher, released in 2005.
* Salsa's goal was to implement AES replacement that does not rely on S-Boxes,
* which are hard to implement in a constant-time manner.
* Salsa20 is usually faster than AES, a big deal on slow, budget mobile phones.
*
* - {@link https://cr.yp.to/snuffle/xsalsa-20110204.pdf | XSalsa20},
* extended-nonce
* variant was released in 2008. It extends Salsa20's 64-bit nonce to 192 bits,
* and became safe to be picked at random.
* - Nacl / Libsodium popularized term "secretbox", - which is just xsalsa20poly1305.
* We provide the alias and corresponding seal / open methods.
* "crypto_box" and "sealedbox" are available in package
* {@link https://github.com/serenity-kit/noble-sodium | noble-sodium}.
* - Check out
* {@link https://cr.yp.to/snuffle/salsafamily-20071225.pdf | PDF}
* and {@link https://cr.yp.to/snuffle.html | website}.
* @module
*/
import { createCipher, rotl } from "./_arx.js";
import { poly1305 } from "./_poly1305.js";
import { abytes, clean, equalBytes, getOutput, swap32IfBE, swap8IfBE, wrapCipher, } from "./utils.js";
/**
* Salsa20 core function. It is implemented twice:
* 1. Simple loop (salsaCore_small, hsalsa_small)
* 2. Unrolled loop (salsaCore, hsalsa) - 4x faster, but larger & harder to read
* The specific implementation is selected in `createCipher` below.
* Performance numbers for 1MB inputs:
* * default x 779 ops/sec @ 1ms/op
* * if salsa+hsalsa are merged x 459 ops/sec @ 2ms/op
* * small x 132 ops/sec @ 7ms/op
*/
/** RFC 7914 §3 Salsa20/8 core quarter-round on words a, b, c, d. */
function salsaQR(x, a, b, c, d) {
x[b] ^= rotl((x[a] + x[d]) | 0, 7);
x[c] ^= rotl((x[b] + x[a]) | 0, 9);
x[d] ^= rotl((x[c] + x[b]) | 0, 13);
x[a] ^= rotl((x[d] + x[c]) | 0, 18);
}
/** RFC 7914 §3 double-round schedule: four column rounds, then four row rounds. */
function salsaRound(x, rounds = 20) {
for (let r = 0; r < rounds; r += 2) {
salsaQR(x, 0, 4, 8, 12);
salsaQR(x, 5, 9, 13, 1);
salsaQR(x, 10, 14, 2, 6);
salsaQR(x, 15, 3, 7, 11);
salsaQR(x, 0, 1, 2, 3);
salsaQR(x, 5, 6, 7, 4);
salsaQR(x, 10, 11, 8, 9);
salsaQR(x, 15, 12, 13, 14);
}
}
// Shared scratch for the unused auditability helper below; it would be
// non-reentrant under overlapping/nested calls, but current code doesn't invoke it.
const stmp = /* @__PURE__ */ new Uint32Array(16);
/** Small version of salsa without loop unrolling. Unused, provided for auditability. */
// prettier-ignore
function salsa(s, k, i, out, isHSalsa = true, rounds = 20) {
// Create initial array using common pattern
const y = Uint32Array.from([
s[0], k[0], k[1], k[2], // "expa" Key Key Key
k[3], s[1], i[0], i[1], // Key "nd 3" Nonce Nonce
i[2], i[3], s[2], k[4], // Pos. Pos. "2-by" Key
k[5], k[6], k[7], s[3], // Key Key Key "te k"
]);
const x = stmp;
x.set(y);
// const x = y.slice();
salsaRound(x, rounds);
// hsalsa extracts 8 specific words for the 32-byte subkey; salsa adds the original state.
if (isHSalsa) {
const xindexes = [0, 5, 10, 15, 6, 7, 8, 9];
for (let i = 0; i < 8; i++)
out[i] = x[xindexes[i]];
}
else {
for (let i = 0; i < 16; i++)
out[i] = (y[i] + x[i]) | 0;
}
}
/** Identical to `salsaCore`. Unused. */
// @ts-ignore
const salsaCore_small = (s, k, n, out, cnt, rounds) => salsa(s, k, Uint32Array.from([n[0], n[1], cnt, 0]), out, false, rounds);
/** Identical to `hsalsa`. Unused. */
// @ts-ignore
const hsalsa_small = salsa;
/** Identical to `salsaCore_small`. Uses only the low 32 bits of Salsa20's 64-bit counter state. */
// prettier-ignore
function salsaCore(s, k, n, out, cnt, rounds = 20) {
// Public wrappers expose only the low 32 bits of Salsa20's 64-bit counter; y09 stays zero.
// Based on {@link https://cr.yp.to/salsa20.html | the Salsa20 reference page}.
let y00 = s[0], y01 = k[0], y02 = k[1], y03 = k[2], // "expa" Key Key Key
y04 = k[3], y05 = s[1], y06 = n[0], y07 = n[1], // Key "nd 3" Nonce Nonce
y08 = cnt, y09 = 0, y10 = s[2], y11 = k[4], // Pos. Pos. "2-by" Key
y12 = k[5], y13 = k[6], y14 = k[7], y15 = s[3]; // Key Key Key "te k"
// Save state to temporary variables
let x00 = y00, x01 = y01, x02 = y02, x03 = y03, x04 = y04, x05 = y05, x06 = y06, x07 = y07, x08 = y08, x09 = y09, x10 = y10, x11 = y11, x12 = y12, x13 = y13, x14 = y14, x15 = y15;
for (let r = 0; r < rounds; r += 2) {
x04 ^= rotl(x00 + x12 | 0, 7);
x08 ^= rotl(x04 + x00 | 0, 9);
x12 ^= rotl(x08 + x04 | 0, 13);
x00 ^= rotl(x12 + x08 | 0, 18);
x09 ^= rotl(x05 + x01 | 0, 7);
x13 ^= rotl(x09 + x05 | 0, 9);
x01 ^= rotl(x13 + x09 | 0, 13);
x05 ^= rotl(x01 + x13 | 0, 18);
x14 ^= rotl(x10 + x06 | 0, 7);
x02 ^= rotl(x14 + x10 | 0, 9);
x06 ^= rotl(x02 + x14 | 0, 13);
x10 ^= rotl(x06 + x02 | 0, 18);
x03 ^= rotl(x15 + x11 | 0, 7);
x07 ^= rotl(x03 + x15 | 0, 9);
x11 ^= rotl(x07 + x03 | 0, 13);
x15 ^= rotl(x11 + x07 | 0, 18);
x01 ^= rotl(x00 + x03 | 0, 7);
x02 ^= rotl(x01 + x00 | 0, 9);
x03 ^= rotl(x02 + x01 | 0, 13);
x00 ^= rotl(x03 + x02 | 0, 18);
x06 ^= rotl(x05 + x04 | 0, 7);
x07 ^= rotl(x06 + x05 | 0, 9);
x04 ^= rotl(x07 + x06 | 0, 13);
x05 ^= rotl(x04 + x07 | 0, 18);
x11 ^= rotl(x10 + x09 | 0, 7);
x08 ^= rotl(x11 + x10 | 0, 9);
x09 ^= rotl(x08 + x11 | 0, 13);
x10 ^= rotl(x09 + x08 | 0, 18);
x12 ^= rotl(x15 + x14 | 0, 7);
x13 ^= rotl(x12 + x15 | 0, 9);
x14 ^= rotl(x13 + x12 | 0, 13);
x15 ^= rotl(x14 + x13 | 0, 18);
}
// Write output
let oi = 0;
out[oi++] = (y00 + x00) | 0;
out[oi++] = (y01 + x01) | 0;
out[oi++] = (y02 + x02) | 0;
out[oi++] = (y03 + x03) | 0;
out[oi++] = (y04 + x04) | 0;
out[oi++] = (y05 + x05) | 0;
out[oi++] = (y06 + x06) | 0;
out[oi++] = (y07 + x07) | 0;
out[oi++] = (y08 + x08) | 0;
out[oi++] = (y09 + x09) | 0;
out[oi++] = (y10 + x10) | 0;
out[oi++] = (y11 + x11) | 0;
out[oi++] = (y12 + x12) | 0;
out[oi++] = (y13 + x13) | 0;
out[oi++] = (y14 + x14) | 0;
out[oi++] = (y15 + x15) | 0;
}
/**
* hsalsa hashes key and nonce-prefix words into the 32-byte subkey used by XSalsa20.
* Identical to `hsalsa_small`.
* Need to find a way to merge it with `salsaCore` without 25% performance hit.
* @param s - Sigma constants as 32-bit words.
* @param k - Key words.
* @param i - Nonce-prefix words.
* @param out - Output buffer for the derived subkey.
* @example
* Derives the XSalsa20 subkey from sigma, key, and nonce-prefix words.
*
* ```ts
* const sigma = new Uint32Array(4);
* const key = new Uint32Array(8);
* const nonce = new Uint32Array(4);
* const out = new Uint32Array(8);
* hsalsa(sigma, key, nonce, out);
* ```
*/
// prettier-ignore
export function hsalsa(s, k, i, out) {
let x00 = swap8IfBE(s[0]), x01 = swap8IfBE(k[0]), x02 = swap8IfBE(k[1]), x03 = swap8IfBE(k[2]), x04 = swap8IfBE(k[3]), x05 = swap8IfBE(s[1]), x06 = swap8IfBE(i[0]), x07 = swap8IfBE(i[1]), x08 = swap8IfBE(i[2]), x09 = swap8IfBE(i[3]), x10 = swap8IfBE(s[2]), x11 = swap8IfBE(k[4]), x12 = swap8IfBE(k[5]), x13 = swap8IfBE(k[6]), x14 = swap8IfBE(k[7]), x15 = swap8IfBE(s[3]);
for (let r = 0; r < 20; r += 2) {
x04 ^= rotl(x00 + x12 | 0, 7);
x08 ^= rotl(x04 + x00 | 0, 9);
x12 ^= rotl(x08 + x04 | 0, 13);
x00 ^= rotl(x12 + x08 | 0, 18);
x09 ^= rotl(x05 + x01 | 0, 7);
x13 ^= rotl(x09 + x05 | 0, 9);
x01 ^= rotl(x13 + x09 | 0, 13);
x05 ^= rotl(x01 + x13 | 0, 18);
x14 ^= rotl(x10 + x06 | 0, 7);
x02 ^= rotl(x14 + x10 | 0, 9);
x06 ^= rotl(x02 + x14 | 0, 13);
x10 ^= rotl(x06 + x02 | 0, 18);
x03 ^= rotl(x15 + x11 | 0, 7);
x07 ^= rotl(x03 + x15 | 0, 9);
x11 ^= rotl(x07 + x03 | 0, 13);
x15 ^= rotl(x11 + x07 | 0, 18);
x01 ^= rotl(x00 + x03 | 0, 7);
x02 ^= rotl(x01 + x00 | 0, 9);
x03 ^= rotl(x02 + x01 | 0, 13);
x00 ^= rotl(x03 + x02 | 0, 18);
x06 ^= rotl(x05 + x04 | 0, 7);
x07 ^= rotl(x06 + x05 | 0, 9);
x04 ^= rotl(x07 + x06 | 0, 13);
x05 ^= rotl(x04 + x07 | 0, 18);
x11 ^= rotl(x10 + x09 | 0, 7);
x08 ^= rotl(x11 + x10 | 0, 9);
x09 ^= rotl(x08 + x11 | 0, 13);
x10 ^= rotl(x09 + x08 | 0, 18);
x12 ^= rotl(x15 + x14 | 0, 7);
x13 ^= rotl(x12 + x15 | 0, 9);
x14 ^= rotl(x13 + x12 | 0, 13);
x15 ^= rotl(x14 + x13 | 0, 18);
}
let oi = 0;
// XSalsa20 takes words 0,5,10,15 and 6,7,8,9 as the 32-byte subkey material.
out[oi++] = x00;
out[oi++] = x05;
out[oi++] = x10;
out[oi++] = x15;
out[oi++] = x06;
out[oi++] = x07;
out[oi++] = x08;
out[oi++] = x09;
swap32IfBE(out);
}
/**
* Salsa20 from original paper. 8-byte nonce.
* With smaller nonce, it's not safe to make it random (CSPRNG), due to collision chance.
* @param key - 16-byte or 32-byte key.
* @param nonce - 8-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* Only the low 32 bits of Salsa20's 64-bit counter state are exposed here;
* the high word stays zero and the implementation still caps the public
* value to 32 bits.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the original 8-byte-nonce Salsa20 stream cipher.
*
* ```ts
* import { salsa20 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(8);
* salsa20(key, nonce, new Uint8Array([1, 2, 3, 4]));
* ```
*/
export const salsa20 = /* @__PURE__ */ createCipher(salsaCore, {
allowShortKeys: true,
counterRight: true,
});
/**
* XSalsa20 extended-nonce salsa.
* With 24-byte nonce, it's safe to make it random (CSPRNG).
* @param key - 32-byte key.
* This XSalsa20 wrapper does not enable Salsa20's 16-byte legacy key mode.
* @param nonce - 24-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with XSalsa20 and a random 24-byte nonce.
*
* ```ts
* import { xsalsa20 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* xsalsa20(key, nonce, new Uint8Array([1, 2, 3, 4]));
* ```
*/
export const xsalsa20 = /* @__PURE__ */ createCipher(salsaCore, {
counterRight: true,
extendNonceFn: hsalsa,
});
/**
* xsalsa20-poly1305 eXtended-nonce (24 bytes) salsa.
* With 24-byte nonce, it's safe to make it random (CSPRNG).
* Also known as `secretbox` from libsodium / nacl.
* No AAD input is supported here. Caller-provided `output` buffers for
* `encrypt()` / `decrypt()` must be `input.length + 32` bytes because the
* implementation uses a 32-byte leading scratch area before returning `+16`.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @param AAD - Must be omitted; XSalsa20-Poly1305 secretbox does not support associated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with XSalsa20-Poly1305.
*
* ```ts
* import { xsalsa20poly1305 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const cipher = xsalsa20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const xsalsa20poly1305 = /* @__PURE__ */ wrapCipher({ blockSize: 64, nonceLength: 24, tagLength: 16 }, (key, nonce) => {
// This borrows caller key/nonce buffers by reference; mutating them after construction changes
// later encrypt/decrypt outputs.
return {
encrypt(plaintext, output) {
// xsalsa20poly1305 optimizes by calculating auth key during the same call as encryption.
// Unfortunately, makes it hard to separate tag calculation & encryption itself,
// because 32 bytes is half-block of 64-byte salsa.
// Need 32 extra bytes up front for the auth-key scratch area described above.
output = getOutput(plaintext.length + 32, output, false);
// output[0..32] = Poly1305 auth key, output[32..] = plaintext then ciphertext.
const authKey = output.subarray(0, 32);
const ciphPlaintext = output.subarray(32);
output.set(plaintext, 32);
// authKey is produced by xoring the first 32 bytes with zeros.
clean(authKey);
// output = stream ^ output; authKey = stream ^ zeros(32)
xsalsa20(key, nonce, output, output);
const tag = poly1305(ciphPlaintext, authKey);
output.set(tag, 16);
// Clean up auth-key remnants and the temporary tag copy.
clean(output.subarray(0, 16), tag);
// Return output[16..].
return output.subarray(16);
},
decrypt(ciphertext, output) {
// tmp part passed tag ciphertext
// [0..32] [32..48] [48..]
// Authenticate the ciphertext before decrypting it; on tag failure the scratch/output
// buffer may already contain copied ciphertext and derived auth-key material.
abytes(ciphertext);
output = getOutput(ciphertext.length + 32, output, false);
// output[0..32] is auth-key scratch, output[32..48] is passed tag,
// output[48..] is ciphertext then plaintext.
const tmp = output.subarray(0, 32);
const passedTag = output.subarray(32, 48);
const ciphPlaintext = output.subarray(48);
output.set(ciphertext, 32);
// authKey is produced by xoring the scratch area with zeros.
clean(tmp);
const authKey = xsalsa20(key, nonce, tmp, tmp);
const tag = poly1305(ciphPlaintext, authKey);
if (!equalBytes(passedTag, tag)) {
clean(output);
throw new Error('invalid tag');
}
// output = stream ^ output[16..]
xsalsa20(key, nonce, output.subarray(16), output.subarray(16));
clean(tmp, passedTag, tag);
// Return output[48..], skipping zeroized output[0..48].
return ciphPlaintext;
},
};
});
/**
* Alias to `xsalsa20poly1305`, for compatibility with libsodium / nacl.
* Check out {@link https://github.com/serenity-kit/noble-sodium | noble-sodium}
* for `crypto_box`.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @returns Wrapper with `seal()` and `open()` helpers.
* @example
* Uses the libsodium-style `seal()` and `open()` wrapper.
*
* ```ts
* import { secretbox } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const box = secretbox(key, nonce);
* box.seal(new Uint8Array([1, 2, 3]));
* ```
*/
export function secretbox(key, nonce) {
const xs = xsalsa20poly1305(key, nonce);
return { seal: xs.encrypt, open: xs.decrypt };
}
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/**
* Basic utils for ARX (add-rotate-xor) salsa and chacha ciphers.
RFC8439 requires multi-step cipher stream, where
authKey starts with counter: 0, actual msg with counter: 1.
For this, we need a way to re-use nonce / counter:
const counter = new Uint8Array(4);
chacha(..., counter, ...); // counter is now 1
chacha(..., counter, ...); // counter is now 2
This is complicated:
- 32-bit counters are enough, no need for 64-bit: max ArrayBuffer size in JS is 4GB
- Original papers don't allow mutating counters
- Counter overflow is undefined [^1]
- Idea A: allow providing (nonce | counter) instead of just nonce, re-use it
- Caveat: Cannot be re-used through all cases:
- * chacha has (counter | nonce)
- * xchacha has (nonce16 | counter | nonce16)
- Idea B: separate nonce / counter and provide separate API for counter re-use
- Caveat: there are different counter sizes depending on an algorithm.
- salsa & chacha also differ in structures of key & sigma:
salsa20: s[0] | k(4) | s[1] | nonce(2) | cnt(2) | s[2] | k(4) | s[3]
chacha: s(4) | k(8) | cnt(1) | nonce(3)
chacha20orig: s(4) | k(8) | cnt(2) | nonce(2)
- Idea C: helper method such as `setSalsaState(key, nonce, sigma, data)`
- Caveat: we can't re-use counter array
xchacha uses the subkey and remaining 8 byte nonce with ChaCha20 as normal
(prefixed by 4 NUL bytes, since RFC8439 specifies a 12-byte nonce).
Counter overflow is undefined; see {@link https://mailarchive.ietf.org/arch/msg/cfrg/gsOnTJzcbgG6OqD8Sc0GO5aR_tU/ | the CFRG thread}.
Current noble policy is strict non-wrap for the shared 32-bit counter path:
exported ARX ciphers reject initial `0xffffffff` and stop before any implicit
wrap back to zero.
See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha#appendix-A.2 | the XChaCha appendix} for the extended-nonce construction.
* @module
*/
import {
type PRG,
type TArg,
type TRet,
type XorStream,
abool,
abytes,
anumber,
checkOpts,
clean,
copyBytes,
getOutput,
isAligned32,
isLE,
randomBytes,
swap32IfBE,
u32,
} from './utils.ts';
// Replaces `TextEncoder` for ASCII literals, which is enough for sigma constants.
// Non-ASCII input would not match UTF-8 `TextEncoder` output.
const encodeStr = (str: string) => Uint8Array.from(str.split(''), (c) => c.charCodeAt(0));
// Raw `createCipher(...)` exports consume these native-endian `u32(...)` views directly.
// Public `wrapCipher(...)` APIs reject non-little-endian platforms before reaching this path.
// RFC 8439 §2.3 / RFC 7539 §2.3 only define the 256-bit-key constants; this 16-byte sigma is
// kept for legacy allowShortKeys Salsa/ChaCha variants.
const sigma16_32 = /* @__PURE__ */ (() => swap32IfBE(u32(encodeStr('expand 16-byte k'))))();
// RFC 8439 §2.3 / RFC 7539 §2.3 define words 0-3 as
// `0x61707865 0x3320646e 0x79622d32 0x6b206574`, i.e. `expand 32-byte k`.
const sigma32_32 = /* @__PURE__ */ (() => swap32IfBE(u32(encodeStr('expand 32-byte k'))))();
/**
* Rotates a 32-bit word left.
* @param a - Input word.
* @param b - Rotation count in bits.
* @returns Rotated 32-bit word.
* @example
* Moves the top byte of `0x12345678` into the low byte position.
* ```ts
* rotl(0x12345678, 8);
* ```
*/
export function rotl(a: number, b: number): number {
return (a << b) | (a >>> (32 - b));
}
/**
* ARX core function operating on 32-bit words. Ciphers must use u32 for efficiency.
* @param sigma - Sigma constants for the selected cipher layout.
* @param key - Expanded key words.
* @param nonce - Nonce and counter words prepared for the round function.
* @param output - Output block written in place.
* @param counter - Block counter value.
* @param rounds - Optional round count override.
*/
export type CipherCoreFn = (
sigma: TArg<Uint32Array>,
key: TArg<Uint32Array>,
nonce: TArg<Uint32Array>,
output: TArg<Uint32Array>,
counter: number,
rounds?: number
) => void;
/**
* Nonce-extension function used by XChaCha and XSalsa.
* @param sigma - Sigma constants for the selected cipher layout.
* @param key - Expanded key words.
* @param input - Input nonce words used for subkey derivation.
* @param output - Output buffer written with the derived nonce words.
*/
export type ExtendNonceFn = (
sigma: TArg<Uint32Array>,
key: TArg<Uint32Array>,
input: TArg<Uint32Array>,
output: TArg<Uint32Array>
) => void;
/** ARX cipher options.
* * `allowShortKeys` for 16-byte keys
* * `counterLength` in bytes
* * `counterRight`: right: `nonce|counter`; left: `counter|nonce`
* */
export type CipherOpts = {
/** Whether 16-byte keys are accepted for legacy Salsa and ChaCha variants. */
allowShortKeys?: boolean;
/** Optional nonce-expansion hook used by extended-nonce variants. */
extendNonceFn?: ExtendNonceFn;
/** Counter length in bytes inside the nonce/counter layout. */
counterLength?: number;
/** Whether the layout is `nonce|counter` instead of `counter|nonce`. */
counterRight?: boolean;
/** Number of core rounds to execute. */
rounds?: number;
};
// Salsa and Chacha block length is always 512-bit
const BLOCK_LEN = 64;
// RFC 8439 §2.2 / RFC 7539 §2.2: the ChaCha state has 16 32-bit words.
const BLOCK_LEN32 = 16;
// Counter policy for the shared public `counter` argument:
// - RFC/IETF ChaCha20 uses a 32-bit counter.
// - OpenSSL/Node `chacha20` instead treat the full 16-byte IV as a 128-bit
// counter state and carry into the next word.
// - Raw `chacha20orig`, `salsa20`, `xsalsa20`, and `xchacha20` use 64-bit counters in libsodium
// and libtomcrypt, while some libs (for example libtomcrypt's RFC/IETF path) reject the max
// boundary instead of carrying.
// - AEAD wrappers diverge too: libsodium `xchacha20poly1305` uses the IETF payload counter from
// block 1, while `secretstream_xchacha20poly1305` is a different protocol with rekey/reset.
// Noble intentionally throws instead of silently picking one wrap model for users. In the default
// path, even a 32-bit boundary would take 2^32 blocks * 64 bytes = 256 GiB, which is practically
// unreachable for normal JS callers; advanced users who pass `counter` explicitly can implement
// whatever wider carry / wrap policy they need on top.
const MAX_COUNTER = /* @__PURE__ */ (() => 2 ** 32 - 1)();
const U32_EMPTY = /* @__PURE__ */ Uint32Array.of();
function runCipher(
core: TArg<CipherCoreFn>,
sigma: TArg<Uint32Array>,
key: TArg<Uint32Array>,
nonce: TArg<Uint32Array>,
data: TArg<Uint8Array>,
output: TArg<Uint8Array>,
counter: number,
rounds: number
): void {
const len = data.length;
const block = new Uint8Array(BLOCK_LEN);
const b32 = u32(block);
// Make sure that buffers aligned to 4 bytes
const isAligned = isLE && isAligned32(data) && isAligned32(output);
const d32 = isAligned ? u32(data) : U32_EMPTY;
const o32 = isAligned ? u32(output) : U32_EMPTY;
// RFC 8439 §2.4.1 / RFC 7539 §2.4.1 allow XORing one keystream block at a time and
// truncating the final partial block instead of materializing the whole keystream.
if (!isLE) {
for (let pos = 0; pos < len; counter++) {
core(
sigma as TRet<Uint32Array>,
key as TRet<Uint32Array>,
nonce as TRet<Uint32Array>,
b32,
counter,
rounds
);
// RFC 8439 §2.4 / RFC 7539 §2.4 serialize keystream words in little-endian order.
swap32IfBE(b32);
if (counter >= MAX_COUNTER) throw new Error('arx: counter overflow');
const take = Math.min(BLOCK_LEN, len - pos);
for (let j = 0, posj; j < take; j++) {
posj = pos + j;
output[posj] = data[posj] ^ block[j];
}
pos += take;
}
return;
}
for (let pos = 0; pos < len; counter++) {
core(
sigma as TRet<Uint32Array>,
key as TRet<Uint32Array>,
nonce as TRet<Uint32Array>,
b32,
counter,
rounds
);
// See MAX_COUNTER policy note above: never silently wrap the shared public counter.
if (counter >= MAX_COUNTER) throw new Error('arx: counter overflow');
const take = Math.min(BLOCK_LEN, len - pos);
// aligned to 4 bytes
if (isAligned && take === BLOCK_LEN) {
const pos32 = pos / 4;
if (pos % 4 !== 0) throw new Error('arx: invalid block position');
for (let j = 0, posj: number; j < BLOCK_LEN32; j++) {
posj = pos32 + j;
o32[posj] = d32[posj] ^ b32[j];
}
pos += BLOCK_LEN;
continue;
}
for (let j = 0, posj; j < take; j++) {
posj = pos + j;
output[posj] = data[posj] ^ block[j];
}
pos += take;
}
}
/**
* Creates an ARX stream cipher from a 32-bit core permutation.
* Used internally to build the exported Salsa and ChaCha stream ciphers.
* @param core - Core function that fills one keystream block.
* @param opts - Cipher layout and nonce-extension options. See {@link CipherOpts}.
* @returns Stream cipher function over byte arrays.
* @throws If the core callback, key size, counter, or output sizing is invalid. {@link Error}
*/
export function createCipher(core: TArg<CipherCoreFn>, opts: TArg<CipherOpts>): TRet<XorStream> {
const { allowShortKeys, extendNonceFn, counterLength, counterRight, rounds } = checkOpts(
{ allowShortKeys: false, counterLength: 8, counterRight: false, rounds: 20 },
opts
);
if (typeof core !== 'function') throw new Error('core must be a function');
anumber(counterLength);
anumber(rounds);
abool(counterRight);
abool(allowShortKeys);
return (
key: TArg<Uint8Array>,
nonce: TArg<Uint8Array>,
data: TArg<Uint8Array>,
output?: TArg<Uint8Array>,
counter = 0
): TRet<Uint8Array> => {
abytes(key, undefined, 'key');
abytes(nonce, undefined, 'nonce');
abytes(data, undefined, 'data');
const len = data.length;
// Raw XorStream APIs return ciphertext/plaintext bytes directly, so caller-provided outputs
// must match the logical result length exactly instead of returning an oversized workspace.
output = getOutput(len, output, false);
anumber(counter);
// See MAX_COUNTER policy note above: reject advanced explicit-counter requests before any wrap.
if (counter < 0 || counter >= MAX_COUNTER) throw new Error('arx: counter overflow');
const toClean = [];
// Key & sigma
// key=16 -> sigma16, k=key|key
// key=32 -> sigma32, k=key
let l = key.length;
let k: Uint8Array;
let sigma: Uint32Array;
if (l === 32) {
// Copy caller keys too: big-endian normalization, extended-nonce subkey derivation, and
// final clean(...) all mutate or wipe the temporary buffer in place.
toClean.push((k = copyBytes(key)));
sigma = sigma32_32;
} else if (l === 16 && allowShortKeys) {
k = new Uint8Array(32);
k.set(key);
k.set(key, 16);
sigma = sigma16_32;
toClean.push(k);
} else {
abytes(key, 32, 'arx key');
throw new Error('invalid key size');
// throw new Error(`"arx key" expected Uint8Array of length 32, got length=${l}`);
}
// Nonce
// salsa20: 8 (8-byte counter)
// chacha20orig: 8 (8-byte counter)
// chacha20: 12 (4-byte counter)
// xsalsa20: 24 (16 -> hsalsa, 8 -> old nonce)
// xchacha20: 24 (16 -> hchacha, 8 -> old nonce)
// Copy before taking u32(...) views on misaligned inputs, and on big-endian so later
// swap32IfBE(...) never mutates caller nonce bytes in place.
if (!isLE || !isAligned32(nonce)) toClean.push((nonce = copyBytes(nonce)));
let k32 = u32(k);
// hsalsa & hchacha: handle extended nonce
if (extendNonceFn) {
if (nonce.length !== 24) throw new Error(`arx: extended nonce must be 24 bytes`);
const n16 = nonce.subarray(0, 16);
if (isLE) extendNonceFn(sigma as TRet<Uint32Array>, k32, u32(n16), k32);
else {
const sigmaRaw = swap32IfBE(Uint32Array.from(sigma));
extendNonceFn(sigmaRaw, k32, u32(n16), k32);
clean(sigmaRaw);
swap32IfBE(k32);
}
nonce = nonce.subarray(16);
} else if (!isLE) swap32IfBE(k32);
// Handle nonce counter
const nonceNcLen = 16 - counterLength;
if (nonceNcLen !== nonce.length)
throw new Error(`arx: nonce must be ${nonceNcLen} or 16 bytes`);
// Normalize 64-bit-nonce layouts to the 12-byte core input: ChaCha/XChaCha prefix 4 zero
// counter bytes, while Salsa/XSalsa append them after the nonce words.
if (nonceNcLen !== 12) {
const nc = new Uint8Array(12);
nc.set(nonce, counterRight ? 0 : 12 - nonce.length);
nonce = nc;
toClean.push(nonce);
}
const n32 = swap32IfBE(u32(nonce));
// Ensure temporary key/nonce copies are wiped even if the remaining
// runtime guard in runCipher(...) throws on counter overflow.
try {
runCipher(core, sigma, k32, n32, data, output, counter, rounds);
return output as TRet<Uint8Array>;
} finally {
clean(...toClean);
}
};
}
/** Internal class which wraps chacha20 or chacha8 to create CSPRNG. */
export class _XorStreamPRG implements PRG {
readonly blockLen: number;
readonly keyLen: number;
readonly nonceLen: number;
private state: TRet<Uint8Array>;
private buf: TRet<Uint8Array>;
private key: TRet<Uint8Array>;
private nonce: TRet<Uint8Array>;
private pos: number;
private ctr: number;
private cipher: TArg<XorStream>;
constructor(
cipher: TArg<XorStream>,
blockLen: number,
keyLen: number,
nonceLen: number,
seed: TArg<Uint8Array>
) {
this.cipher = cipher;
this.blockLen = blockLen;
this.keyLen = keyLen;
this.nonceLen = nonceLen;
this.state = new Uint8Array(this.keyLen + this.nonceLen) as TRet<Uint8Array>;
this.reseed(seed);
this.ctr = 0;
this.pos = this.blockLen;
this.buf = new Uint8Array(this.blockLen) as TRet<Uint8Array>;
// Keep a single key||nonce backing buffer so reseed/addEntropy/clean update the live cipher
// inputs in place through these subarray views.
this.key = this.state.subarray(0, this.keyLen) as TRet<Uint8Array>;
this.nonce = this.state.subarray(this.keyLen) as TRet<Uint8Array>;
}
private reseed(seed: TArg<Uint8Array>) {
abytes(seed);
if (!seed || seed.length === 0) throw new Error('entropy required');
// Mix variable-length entropy cyclically across the whole key||nonce state, then restart the
// keystream so buffered leftovers from the previous state are never reused.
for (let i = 0; i < seed.length; i++) this.state[i % this.state.length] ^= seed[i];
this.ctr = 0;
this.pos = this.blockLen;
}
addEntropy(seed: TArg<Uint8Array>): void {
// Reject empty entropy before re-keying, otherwise a throwing call would still advance state.
abytes(seed);
if (seed.length === 0) throw new Error('entropy required');
// Re-key from the current stream first, then mix external entropy into the fresh key||nonce
// state through reseed() so stale buffered bytes are discarded.
this.state.set(this.randomBytes(this.state.length));
this.reseed(seed);
}
randomBytes(len: number): TRet<Uint8Array> {
anumber(len);
if (len === 0) return new Uint8Array(0) as TRet<Uint8Array>;
const avail = this.pos < this.blockLen ? this.blockLen - this.pos : 0;
const blocks = Math.ceil(Math.max(0, len - avail) / this.blockLen);
// Preflight overflow so failed reads don't partially consume keystream
// and leave the PRG repeating blocks.
if (blocks > 0 && this.ctr > MAX_COUNTER - blocks) throw new Error('arx: counter overflow');
const out = new Uint8Array(len);
let outPos = 0;
// `out` starts zero-filled, and `buf.fill(0)` below does the same for leftovers: XOR-stream
// ciphers then emit raw keystream bytes directly into those buffers.
// Serve buffered leftovers first so split reads stay identical to one larger read.
if (this.pos < this.blockLen) {
const take = Math.min(len, this.blockLen - this.pos);
out.set(this.buf.subarray(this.pos, this.pos + take), 0);
this.pos += take;
outPos += take;
if (outPos === len) return out as TRet<Uint8Array>; // fast path
}
// Full blocks directly to out
const full = Math.floor((len - outPos) / this.blockLen);
if (full > 0) {
const blockBytes = full * this.blockLen;
const b = out.subarray(outPos, outPos + blockBytes);
this.cipher(this.key, this.nonce, b as TRet<Uint8Array>, b as TRet<Uint8Array>, this.ctr);
this.ctr += full;
outPos += blockBytes;
}
// Save leftovers
const left = len - outPos;
if (left > 0) {
this.buf.fill(0);
// NOTE: cipher will handle overflow
this.cipher(
this.key,
this.nonce,
this.buf as TRet<Uint8Array>,
this.buf as TRet<Uint8Array>,
this.ctr++
);
out.set(this.buf.subarray(0, left), outPos);
this.pos = left;
}
return out as TRet<Uint8Array>;
}
// Clone seeds the new instance from this stream, so the source PRG advances too.
clone(): _XorStreamPRG {
return new _XorStreamPRG(
this.cipher,
this.blockLen,
this.keyLen,
this.nonceLen,
this.randomBytes(this.state.length)
);
}
// Zeroes the current state and leftover buffer, but does not make the instance unusable:
// Later reads first drain zeros from the cleared buffer and then continue
// from zero key||nonce state.
clean(): void {
this.pos = 0;
this.ctr = 0;
this.buf.fill(0);
this.state.fill(0);
}
}
/**
* PRG constructor backed by an ARX stream cipher.
* @param seed - Optional seed bytes mixed into the initial state. When omitted, exactly 32
* random bytes are mixed in by default: larger states keep a zero tail, while smaller states
* wrap those bytes through `reseed()`'s XOR schedule.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
*/
export type XorPRG = (seed?: TArg<Uint8Array>) => TRet<_XorStreamPRG>;
/**
* Creates a PRG constructor from a stream cipher.
* @param cipher - Stream cipher used to fill output blocks.
* @param blockLen - Keystream block length in bytes.
* @param keyLen - Internal key length in bytes.
* @param nonceLen - Internal nonce length in bytes.
* @returns PRG factory for seeded concrete `_XorStreamPRG` instances.
* @example
* Builds a PRG from XChaCha20 and reads bytes from a randomly seeded instance.
* ```ts
* import { xchacha20 } from '@noble/ciphers/chacha.js';
* import { createPRG } from '@noble/ciphers/_arx.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const init = createPRG(xchacha20, 64, 32, 24);
* const prg = init(seed);
* prg.randomBytes(8);
* ```
*/
export const createPRG = (
cipher: TArg<XorStream>,
blockLen: number,
keyLen: number,
nonceLen: number
): TRet<XorPRG> => {
return ((seed: TArg<Uint8Array> = randomBytes(32)): TRet<_XorStreamPRG> =>
new _XorStreamPRG(
cipher,
blockLen,
keyLen,
nonceLen,
seed
) as TRet<_XorStreamPRG>) as TRet<XorPRG>;
};

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node_modules/@noble/ciphers/src/_poly1305.ts generated vendored Normal file
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/**
* Poly1305 ({@link https://cr.yp.to/mac/poly1305-20050329.pdf | PDF},
* {@link https://en.wikipedia.org/wiki/Poly1305 | wiki})
* is a fast and parallel secret-key message-authentication code suitable for
* a wide variety of applications. It was standardized in
* {@link https://www.rfc-editor.org/rfc/rfc8439 | RFC 8439} and is now used in TLS 1.3.
*
* Polynomial MACs are not perfect for every situation:
* they lack Random Key Robustness: the MAC can be forged, and can't be used in PAKE schemes.
* See {@link https://keymaterial.net/2020/09/07/invisible-salamanders-in-aes-gcm-siv/ | the invisible salamanders attack writeup}.
* To combat invisible salamanders, `hash(key)` can be included in ciphertext,
* however, this would violate ciphertext indistinguishability:
* an attacker would know which key was used - so `HKDF(key, i)`
* could be used instead.
*
* Check out the {@link https://cr.yp.to/mac.html | original website}.
* Based on public-domain {@link https://github.com/floodyberry/poly1305-donna | poly1305-donna}.
* @module
*/
// prettier-ignore
import {
abytes, aexists, aoutput, bytesToHex,
clean, concatBytes, copyBytes, hexToNumber, numberToBytesBE,
wrapMacConstructor, type CMac, type IHash2, type TArg, type TRet
} from './utils.ts';
// Little-endian 2-byte load used by the Poly1305 limb decomposition.
function u8to16(a: TArg<Uint8Array>, i: number) {
return (a[i++] & 0xff) | ((a[i++] & 0xff) << 8);
}
function bytesToNumberLE(bytes: TArg<Uint8Array>): bigint {
return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));
}
/** Small version of `poly1305` without loop unrolling. Unused, provided for auditability. */
function poly1305_small(msg: TArg<Uint8Array>, key: TArg<Uint8Array>): TRet<Uint8Array> {
abytes(msg);
abytes(key, 32, 'key');
const POW_2_130_5 = BigInt(2) ** BigInt(130) - BigInt(5); // 2^130-5
const POW_2_128_1 = BigInt(2) ** BigInt(128) - BigInt(1); // 2^128-1
const CLAMP_R = BigInt('0x0ffffffc0ffffffc0ffffffc0fffffff');
const r = bytesToNumberLE(key.subarray(0, 16)) & CLAMP_R;
const s = bytesToNumberLE(key.subarray(16));
// Process by 16 byte chunks
let acc = BigInt(0);
for (let i = 0; i < msg.length; i += 16) {
const m = msg.subarray(i, i + 16);
// RFC 8439 §2.5.1 / RFC 7539 §2.5.1 append [0x01] to each chunk before multiplying by r.
const n = bytesToNumberLE(m) | (BigInt(1) << BigInt(8 * m.length));
acc = ((acc + n) * r) % POW_2_130_5;
}
const res = (acc + s) & POW_2_128_1;
// RFC 8439 §2.5 / RFC 7539 §2.5 serialize the low 128 bits in little-endian order.
return numberToBytesBE(res, 16).reverse() as TRet<Uint8Array>; // LE
}
// Can be used to replace `computeTag` in chacha.ts. Unused, provided for auditability.
// @ts-expect-error
function poly1305_computeTag_small(
authKey: TArg<Uint8Array>,
// AEAD trailer must already be the 16-byte length block:
// 8-byte little-endian AAD length || 8-byte little-endian ciphertext length.
lengths: TArg<Uint8Array>,
ciphertext: TArg<Uint8Array>,
AAD?: TArg<Uint8Array>
): TRet<Uint8Array> {
// RFC 8439 §2.8.1 / RFC 7539 §2.8.1 MAC input is
// AAD || pad16(AAD) || ciphertext || pad16(ciphertext) || lengths.
const res = [];
const updatePadded2 = (msg: TArg<Uint8Array>) => {
res.push(msg);
const leftover = msg.length % 16;
// RFC 8439 §2.8.1 / RFC 7539 §2.8.1: pad16(x) is empty for aligned
// inputs, else 16-(len%16) zero bytes.
if (leftover) res.push(new Uint8Array(16).slice(leftover));
};
if (AAD) updatePadded2(AAD);
updatePadded2(ciphertext);
res.push(lengths);
return poly1305_small(concatBytes(...res), authKey);
}
/**
* Incremental Poly1305 MAC state.
* Prefer `poly1305()` for one-shot use.
* @param key - 32-byte Poly1305 one-time key.
* @example
* Feeds one chunk into an incremental Poly1305 state with a fresh one-time key.
*
* ```ts
* import { Poly1305 } from '@noble/ciphers/_poly1305.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const mac = new Poly1305(key);
* mac.update(new Uint8Array([1, 2, 3]));
* mac.digest();
* ```
*/
export class Poly1305 implements IHash2 {
readonly blockLen = 16;
readonly outputLen = 16;
private buffer = new Uint8Array(16);
private r = new Uint16Array(10); // Allocating 1 array with .subarray() here is slower than 3
private h = new Uint16Array(10);
private pad = new Uint16Array(8);
private pos = 0;
protected finished = false;
protected destroyed = false;
// Can be speed-up using BigUint64Array, at the cost of complexity
constructor(key: TArg<Uint8Array>) {
key = copyBytes(abytes(key, 32, 'key'));
const t0 = u8to16(key, 0);
const t1 = u8to16(key, 2);
const t2 = u8to16(key, 4);
const t3 = u8to16(key, 6);
const t4 = u8to16(key, 8);
const t5 = u8to16(key, 10);
const t6 = u8to16(key, 12);
const t7 = u8to16(key, 14);
// RFC 8439 §2.5.1 / RFC 7539 §2.5.1 clamp r before multiplication.
// These masks unpack that clamped value into 13-bit limbs, while pad
// keeps the raw s half for finalize().
// {@link https://github.com/floodyberry/poly1305-donna/blob/e6ad6e091d30d7f4ec2d4f978be1fcfcbce72781/poly1305-donna-16.h#L47 | poly1305-donna reference}
this.r[0] = t0 & 0x1fff;
this.r[1] = ((t0 >>> 13) | (t1 << 3)) & 0x1fff;
this.r[2] = ((t1 >>> 10) | (t2 << 6)) & 0x1f03;
this.r[3] = ((t2 >>> 7) | (t3 << 9)) & 0x1fff;
this.r[4] = ((t3 >>> 4) | (t4 << 12)) & 0x00ff;
this.r[5] = (t4 >>> 1) & 0x1ffe;
this.r[6] = ((t4 >>> 14) | (t5 << 2)) & 0x1fff;
this.r[7] = ((t5 >>> 11) | (t6 << 5)) & 0x1f81;
this.r[8] = ((t6 >>> 8) | (t7 << 8)) & 0x1fff;
this.r[9] = (t7 >>> 5) & 0x007f;
for (let i = 0; i < 8; i++) this.pad[i] = u8to16(key, 16 + 2 * i);
}
private process(data: TArg<Uint8Array>, offset: number, isLast = false) {
// RFC 8439 §2.5 / §2.5.1 and RFC 7539 §2.5 / §2.5.1 add an extra high
// bit to every full 16-byte block. The final partial block gets its
// explicit `1` byte during digestInto(), so `hibit` stays zero there.
const hibit = isLast ? 0 : 1 << 11;
const { h, r } = this;
const r0 = r[0];
const r1 = r[1];
const r2 = r[2];
const r3 = r[3];
const r4 = r[4];
const r5 = r[5];
const r6 = r[6];
const r7 = r[7];
const r8 = r[8];
const r9 = r[9];
const t0 = u8to16(data, offset + 0);
const t1 = u8to16(data, offset + 2);
const t2 = u8to16(data, offset + 4);
const t3 = u8to16(data, offset + 6);
const t4 = u8to16(data, offset + 8);
const t5 = u8to16(data, offset + 10);
const t6 = u8to16(data, offset + 12);
const t7 = u8to16(data, offset + 14);
let h0 = h[0] + (t0 & 0x1fff);
let h1 = h[1] + (((t0 >>> 13) | (t1 << 3)) & 0x1fff);
let h2 = h[2] + (((t1 >>> 10) | (t2 << 6)) & 0x1fff);
let h3 = h[3] + (((t2 >>> 7) | (t3 << 9)) & 0x1fff);
let h4 = h[4] + (((t3 >>> 4) | (t4 << 12)) & 0x1fff);
let h5 = h[5] + ((t4 >>> 1) & 0x1fff);
let h6 = h[6] + (((t4 >>> 14) | (t5 << 2)) & 0x1fff);
let h7 = h[7] + (((t5 >>> 11) | (t6 << 5)) & 0x1fff);
let h8 = h[8] + (((t6 >>> 8) | (t7 << 8)) & 0x1fff);
let h9 = h[9] + ((t7 >>> 5) | hibit);
let c = 0;
let d0 = c + h0 * r0 + h1 * (5 * r9) + h2 * (5 * r8) + h3 * (5 * r7) + h4 * (5 * r6);
c = d0 >>> 13;
d0 &= 0x1fff;
d0 += h5 * (5 * r5) + h6 * (5 * r4) + h7 * (5 * r3) + h8 * (5 * r2) + h9 * (5 * r1);
c += d0 >>> 13;
d0 &= 0x1fff;
let d1 = c + h0 * r1 + h1 * r0 + h2 * (5 * r9) + h3 * (5 * r8) + h4 * (5 * r7);
c = d1 >>> 13;
d1 &= 0x1fff;
d1 += h5 * (5 * r6) + h6 * (5 * r5) + h7 * (5 * r4) + h8 * (5 * r3) + h9 * (5 * r2);
c += d1 >>> 13;
d1 &= 0x1fff;
let d2 = c + h0 * r2 + h1 * r1 + h2 * r0 + h3 * (5 * r9) + h4 * (5 * r8);
c = d2 >>> 13;
d2 &= 0x1fff;
d2 += h5 * (5 * r7) + h6 * (5 * r6) + h7 * (5 * r5) + h8 * (5 * r4) + h9 * (5 * r3);
c += d2 >>> 13;
d2 &= 0x1fff;
let d3 = c + h0 * r3 + h1 * r2 + h2 * r1 + h3 * r0 + h4 * (5 * r9);
c = d3 >>> 13;
d3 &= 0x1fff;
d3 += h5 * (5 * r8) + h6 * (5 * r7) + h7 * (5 * r6) + h8 * (5 * r5) + h9 * (5 * r4);
c += d3 >>> 13;
d3 &= 0x1fff;
let d4 = c + h0 * r4 + h1 * r3 + h2 * r2 + h3 * r1 + h4 * r0;
c = d4 >>> 13;
d4 &= 0x1fff;
d4 += h5 * (5 * r9) + h6 * (5 * r8) + h7 * (5 * r7) + h8 * (5 * r6) + h9 * (5 * r5);
c += d4 >>> 13;
d4 &= 0x1fff;
let d5 = c + h0 * r5 + h1 * r4 + h2 * r3 + h3 * r2 + h4 * r1;
c = d5 >>> 13;
d5 &= 0x1fff;
d5 += h5 * r0 + h6 * (5 * r9) + h7 * (5 * r8) + h8 * (5 * r7) + h9 * (5 * r6);
c += d5 >>> 13;
d5 &= 0x1fff;
let d6 = c + h0 * r6 + h1 * r5 + h2 * r4 + h3 * r3 + h4 * r2;
c = d6 >>> 13;
d6 &= 0x1fff;
d6 += h5 * r1 + h6 * r0 + h7 * (5 * r9) + h8 * (5 * r8) + h9 * (5 * r7);
c += d6 >>> 13;
d6 &= 0x1fff;
let d7 = c + h0 * r7 + h1 * r6 + h2 * r5 + h3 * r4 + h4 * r3;
c = d7 >>> 13;
d7 &= 0x1fff;
d7 += h5 * r2 + h6 * r1 + h7 * r0 + h8 * (5 * r9) + h9 * (5 * r8);
c += d7 >>> 13;
d7 &= 0x1fff;
let d8 = c + h0 * r8 + h1 * r7 + h2 * r6 + h3 * r5 + h4 * r4;
c = d8 >>> 13;
d8 &= 0x1fff;
d8 += h5 * r3 + h6 * r2 + h7 * r1 + h8 * r0 + h9 * (5 * r9);
c += d8 >>> 13;
d8 &= 0x1fff;
let d9 = c + h0 * r9 + h1 * r8 + h2 * r7 + h3 * r6 + h4 * r5;
c = d9 >>> 13;
d9 &= 0x1fff;
d9 += h5 * r4 + h6 * r3 + h7 * r2 + h8 * r1 + h9 * r0;
c += d9 >>> 13;
d9 &= 0x1fff;
c = ((c << 2) + c) | 0;
c = (c + d0) | 0;
d0 = c & 0x1fff;
c = c >>> 13;
d1 += c;
h[0] = d0;
h[1] = d1;
h[2] = d2;
h[3] = d3;
h[4] = d4;
h[5] = d5;
h[6] = d6;
h[7] = d7;
h[8] = d8;
h[9] = d9;
}
private finalize() {
const { h, pad } = this;
const g = new Uint16Array(10);
let c = h[1] >>> 13;
h[1] &= 0x1fff;
for (let i = 2; i < 10; i++) {
h[i] += c;
c = h[i] >>> 13;
h[i] &= 0x1fff;
}
h[0] += c * 5;
c = h[0] >>> 13;
h[0] &= 0x1fff;
h[1] += c;
c = h[1] >>> 13;
h[1] &= 0x1fff;
h[2] += c;
// RFC 8439 §2.5 / RFC 7539 §2.5 reduce modulo 2^130-5 before repacking
// to 16-bit words and adding the raw s half.
g[0] = h[0] + 5;
c = g[0] >>> 13;
g[0] &= 0x1fff;
for (let i = 1; i < 10; i++) {
g[i] = h[i] + c;
c = g[i] >>> 13;
g[i] &= 0x1fff;
}
g[9] -= 1 << 13;
let mask = (c ^ 1) - 1;
for (let i = 0; i < 10; i++) g[i] &= mask;
mask = ~mask;
for (let i = 0; i < 10; i++) h[i] = (h[i] & mask) | g[i];
h[0] = (h[0] | (h[1] << 13)) & 0xffff;
h[1] = ((h[1] >>> 3) | (h[2] << 10)) & 0xffff;
h[2] = ((h[2] >>> 6) | (h[3] << 7)) & 0xffff;
h[3] = ((h[3] >>> 9) | (h[4] << 4)) & 0xffff;
h[4] = ((h[4] >>> 12) | (h[5] << 1) | (h[6] << 14)) & 0xffff;
h[5] = ((h[6] >>> 2) | (h[7] << 11)) & 0xffff;
h[6] = ((h[7] >>> 5) | (h[8] << 8)) & 0xffff;
h[7] = ((h[8] >>> 8) | (h[9] << 5)) & 0xffff;
let f = h[0] + pad[0];
h[0] = f & 0xffff;
for (let i = 1; i < 8; i++) {
f = (((h[i] + pad[i]) | 0) + (f >>> 16)) | 0;
h[i] = f & 0xffff;
}
clean(g);
}
update(data: TArg<Uint8Array>): this {
aexists(this);
abytes(data);
data = copyBytes(data);
const { buffer, blockLen } = this;
const len = data.length;
for (let pos = 0; pos < len; ) {
const take = Math.min(blockLen - this.pos, len - pos);
// Fast path: we have at least one block in input
if (take === blockLen) {
for (; blockLen <= len - pos; pos += blockLen) this.process(data, pos);
continue;
}
buffer.set(data.subarray(pos, pos + take), this.pos);
this.pos += take;
pos += take;
if (this.pos === blockLen) {
this.process(buffer, 0, false);
this.pos = 0;
}
}
return this;
}
destroy(): void {
// `aexists(this)` guards update/digest paths, so destroy must mark the instance unusable too.
this.destroyed = true;
clean(this.h, this.r, this.buffer, this.pad);
}
digestInto(out: TArg<Uint8Array>): void {
aexists(this);
aoutput(out, this);
this.finished = true;
const { buffer, h } = this;
let { pos } = this;
if (pos) {
// RFC 8439 §2.5 / RFC 7539 §2.5: the final short block appends a
// single `0x01` byte and zero-fills the remaining bytes before the
// last multiplication step.
buffer[pos++] = 1;
for (; pos < 16; pos++) buffer[pos] = 0;
this.process(buffer, 0, true);
}
this.finalize();
let opos = 0;
for (let i = 0; i < 8; i++) {
out[opos++] = h[i] >>> 0;
out[opos++] = h[i] >>> 8;
}
}
digest(): TRet<Uint8Array> {
const { buffer, outputLen } = this;
this.digestInto(buffer);
// Copy out before destroy() zeroes the internal buffer.
const res = buffer.slice(0, outputLen);
this.destroy();
return res as TRet<Uint8Array>;
}
}
/** One-shot keyed hash helper with `.create()`. */
export type CHash = CMac<Poly1305>;
/**
* Poly1305 MAC from RFC 8439.
* @param msg - Message bytes to authenticate.
* @param key - 32-byte Poly1305 one-time key.
* @returns 16-byte authentication tag.
* @example
* Authenticates one message with a one-shot Poly1305 call and a fresh key.
*
* ```ts
* import { poly1305 } from '@noble/ciphers/_poly1305.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* poly1305(new Uint8Array(), key);
* ```
*/
export const poly1305: TRet<CHash> = /* @__PURE__ */ wrapMacConstructor(
32,
(key: TArg<Uint8Array>) => new Poly1305(key)
);

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/**
* GHash from AES-GCM and its little-endian "mirror image" Polyval from AES-SIV.
*
* Implemented in terms of GHash with conversion function for keys
* GCM GHASH from
* {@link https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-38d.pdf | NIST SP800-38d},
* SIV from
* {@link https://www.rfc-editor.org/rfc/rfc8452 | RFC 8452}.
*
* GHASH modulo: x^128 + x^7 + x^2 + x + 1
* POLYVAL modulo: x^128 + x^127 + x^126 + x^121 + 1
*
* @module
*/
import {
abytes,
aexists,
aoutput,
clean,
copyBytes,
createView,
swap32IfBE,
swap8IfBE,
u32,
wrapMacConstructor,
type CMac,
type IHash2,
type TArg,
type TRet,
} from './utils.ts';
const BLOCK_SIZE = 16;
// TODO: rewrite
// temporary padding buffer
// ZEROS32 aliases these bytes, so clean(ZEROS32) also resets this shared tail-padding scratch.
const ZEROS16 = /* @__PURE__ */ new Uint8Array(16);
const ZEROS32 = /* @__PURE__ */ u32(ZEROS16);
// GHASH reduces modulo x^128 + x^7 + x^2 + x + 1, so the low-degree terms
// x^7 + x^2 + x + 1 become bits `11100001` = 0xe1 in R = 0xe1 || 0^120.
const POLY = 0xe1;
// v = 2*v % POLY
// NOTE: because x + x = 0 (add/sub is same), mul2(x) != x+x
// Montgomery ladder can multiply any field element with this doubling step;
// addition stays simple xor.
const mul2 = (s0: number, s1: number, s2: number, s3: number) => {
const hiBit = s3 & 1;
return {
s3: (s2 << 31) | (s3 >>> 1),
s2: (s1 << 31) | (s2 >>> 1),
s1: (s0 << 31) | (s1 >>> 1),
// NIST SP 800-38D §6.3 applies `V >> 1` and XORs R on carry. In this
// 4x32-bit split, R = 0xe1 || 0^120 lives in the top byte of s0.
s0: (s0 >>> 1) ^ ((POLY << 24) & -(hiBit & 1)), // reduce % poly
};
};
// Per-word part of RFC 8452 `ByteReverse`; callers also reverse the 32-bit word order.
const swapLE = (n: number) =>
(((n >>> 0) & 0xff) << 24) |
(((n >>> 8) & 0xff) << 16) |
(((n >>> 16) & 0xff) << 8) |
((n >>> 24) & 0xff) |
0;
// POLYVAL first applies RFC 8452's per-word byte reversal, then re-normalizes
// host-endian u32 loads to the little-endian word value `_updateBlock()` expects.
const swap8IfLE = (n: number) => swap8IfBE(swapLE(n));
/**
* `mulX_GHASH(ByteReverse(H))` from RFC 8452 Appendix A.
* @param k mutated in place
*/
export function _toGHASHKey(k: TArg<Uint8Array>): TRet<Uint8Array> {
// The input is the original POLYVAL key H; reverse() materializes
// RFC 8452's `ByteReverse(H)` before the GHASH mulX step.
k.reverse();
const hiBit = k[15] & 1;
// k >>= 1
let carry = 0;
for (let i = 0; i < k.length; i++) {
const t = k[i];
k[i] = (t >>> 1) | carry;
carry = (t & 1) << 7;
}
k[0] ^= -hiBit & 0xe1; // if (hiBit) n ^= 0xe1000000000000000000000000000000;
return k as TRet<Uint8Array>;
}
type Value = { s0: number; s1: number; s2: number; s3: number };
// Precompute-window heuristic only: larger inputs trade memory for fewer table lookups.
// Any caller-provided length hint still collapses to one of the supported windows {2, 4, 8}.
const estimateWindow = (bytes: number) => {
if (bytes > 64 * 1024) return 8;
if (bytes > 1024) return 4;
return 2;
};
/**
* Incremental GHASH state for AES-GCM.
* @param key - 16-byte GHASH key.
* @param expectedLength - Expected message length for table sizing.
* Chunking is segment-based, not hash-streaming: every `update()` call is zero-padded
* to the next 16-byte boundary before it is absorbed. This matches the internal AES/GCM
* use where AAD, payload, and length block are separate padded segments.
* @example
* Feeds one ciphertext block into an incremental GHASH state with a fresh hash key.
*
* ```ts
* import { GHASH } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const mac = new GHASH(key);
* mac.update(new Uint8Array(16));
* mac.digest();
* ```
*/
export class GHASH implements IHash2 {
readonly blockLen: number = BLOCK_SIZE;
readonly outputLen: number = BLOCK_SIZE;
protected s0 = 0;
protected s1 = 0;
protected s2 = 0;
protected s3 = 0;
protected finished = false;
protected destroyed = false;
protected t: Value[];
private W: number;
private windowSize: number;
// We select bits per window adaptively based on expectedLength
constructor(key: TArg<Uint8Array>, expectedLength?: number) {
abytes(key, 16, 'key');
key = copyBytes(key);
const kView = createView(key);
let k0 = kView.getUint32(0, false);
let k1 = kView.getUint32(4, false);
let k2 = kView.getUint32(8, false);
let k3 = kView.getUint32(12, false);
// generate table of doubled keys (half of montgomery ladder)
const doubles: Value[] = [];
for (let i = 0; i < 128; i++) {
doubles.push({ s0: swapLE(k0), s1: swapLE(k1), s2: swapLE(k2), s3: swapLE(k3) });
({ s0: k0, s1: k1, s2: k2, s3: k3 } = mul2(k0, k1, k2, k3));
}
const W = estimateWindow(expectedLength || 1024);
if (![1, 2, 4, 8].includes(W))
throw new Error('ghash: invalid window size, expected 2, 4 or 8');
this.W = W;
const bits = 128; // always 128 bits;
const windows = bits / W;
const windowSize = (this.windowSize = 2 ** W);
const items: Value[] = [];
// Create precompute table for window of W bits
for (let w = 0; w < windows; w++) {
// truth table: 00, 01, 10, 11
for (let byte = 0; byte < windowSize; byte++) {
// prettier-ignore
let s0 = 0, s1 = 0, s2 = 0, s3 = 0;
for (let j = 0; j < W; j++) {
const bit = (byte >>> (W - j - 1)) & 1;
if (!bit) continue;
const { s0: d0, s1: d1, s2: d2, s3: d3 } = doubles[W * w + j];
((s0 ^= d0), (s1 ^= d1), (s2 ^= d2), (s3 ^= d3));
}
items.push({ s0, s1, s2, s3 });
}
}
this.t = items;
}
protected _updateBlock(s0: number, s1: number, s2: number, s3: number): void {
((s0 ^= this.s0), (s1 ^= this.s1), (s2 ^= this.s2), (s3 ^= this.s3));
const { W, t, windowSize } = this;
// prettier-ignore
let o0 = 0, o1 = 0, o2 = 0, o3 = 0;
const mask = (1 << W) - 1; // 2**W will kill performance.
let w = 0;
// NIST SP 800-38D §6.3 interprets blocks as little-endian polynomials,
// so the lookup walk consumes each word byte-by-byte from
// least-significant to most-significant bits.
for (const num of [s0, s1, s2, s3]) {
for (let bytePos = 0; bytePos < 4; bytePos++) {
const byte = (num >>> (8 * bytePos)) & 0xff;
for (let bitPos = 8 / W - 1; bitPos >= 0; bitPos--) {
const bit = (byte >>> (W * bitPos)) & mask;
const { s0: e0, s1: e1, s2: e2, s3: e3 } = t[w * windowSize + bit];
((o0 ^= e0), (o1 ^= e1), (o2 ^= e2), (o3 ^= e3));
w += 1;
}
}
}
this.s0 = o0;
this.s1 = o1;
this.s2 = o2;
this.s3 = o3;
}
update(data: TArg<Uint8Array>): this {
aexists(this);
abytes(data);
data = copyBytes(data);
const b32 = u32(data);
const blocks = Math.floor(data.length / BLOCK_SIZE);
const left = data.length % BLOCK_SIZE;
for (let i = 0; i < blocks; i++) {
this._updateBlock(
swap8IfBE(b32[i * 4 + 0]),
swap8IfBE(b32[i * 4 + 1]),
swap8IfBE(b32[i * 4 + 2]),
swap8IfBE(b32[i * 4 + 3])
);
}
if (left) {
ZEROS16.set(data.subarray(blocks * BLOCK_SIZE));
// Tail blocks go through the shared ZEROS32 scratch, so they need the same host-endian
// normalization as full blocks; otherwise segmented GHASH/POLYVAL updates diverge on BE.
this._updateBlock(
swap8IfBE(ZEROS32[0]),
swap8IfBE(ZEROS32[1]),
swap8IfBE(ZEROS32[2]),
swap8IfBE(ZEROS32[3])
);
clean(ZEROS32); // clean tmp buffer
}
return this;
}
destroy(): void {
// `aexists(this)` guards update/digest paths, so destroy must mark the instance unusable too.
this.destroyed = true;
const { t } = this;
// Wipe the key-derived precompute table; scalar accumulator words remain,
// but the destroyed guard blocks further use.
// clean precompute table
for (const elm of t) {
((elm.s0 = 0), (elm.s1 = 0), (elm.s2 = 0), (elm.s3 = 0));
}
}
digestInto(out: TArg<Uint8Array>): void {
aexists(this);
// `digestInto(out)` is the no-allocation fast path, so callers must pass a
// 32-bit-aligned buffer before we reinterpret it with `u32(out)`.
aoutput(out, this, true);
this.finished = true;
// NIST SP 800-38D §6.4 returns the final 128-bit block Y_m.
// `digestInto()` follows the relaxed `aoutput()` contract, so only
// out[0..15] may be touched.
const { s0, s1, s2, s3 } = this;
const o32 = u32(out);
o32[0] = s0;
o32[1] = s1;
o32[2] = s2;
o32[3] = s3;
swap32IfBE(o32);
}
digest(): TRet<Uint8Array> {
const res = new Uint8Array(BLOCK_SIZE);
this.digestInto(res);
// `res` is independent of internal state, so it stays valid after destroy() wipes the table.
this.destroy();
return res as TRet<Uint8Array>;
}
}
/**
* Incremental POLYVAL state for AES-SIV.
* @param key - 16-byte POLYVAL key.
* @param expectedLength - Expected message length for table sizing.
* Inherits GHASH's segment-padded `update()` behavior: each call is padded
* independently to a 16-byte boundary before absorption.
* @example
* Feeds one block into an incremental POLYVAL state with a fresh hash key.
*
* ```ts
* import { Polyval } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const mac = new Polyval(key);
* mac.update(new Uint8Array(16));
* mac.digest();
* ```
*/
export class Polyval extends GHASH {
constructor(key: TArg<Uint8Array>, expectedLength?: number) {
abytes(key);
// RFC 8452 Appendix A converts the POLYVAL key with
// `mulX_GHASH(ByteReverse(H))`; copy first because `_toGHASHKey(...)`
// mutates in place.
const ghKey = _toGHASHKey(copyBytes(key));
super(ghKey, expectedLength);
clean(ghKey);
}
update(data: TArg<Uint8Array>): this {
aexists(this);
abytes(data);
data = copyBytes(data);
const b32 = u32(data);
const left = data.length % BLOCK_SIZE;
const blocks = Math.floor(data.length / BLOCK_SIZE);
for (let i = 0; i < blocks; i++) {
// RFC 8452 Appendix A feeds `ByteReverse(X_i)` into GHASH, so POLYVAL
// reverses the 32-bit word order in addition to the per-word byte swap.
this._updateBlock(
swap8IfLE(b32[i * 4 + 3]),
swap8IfLE(b32[i * 4 + 2]),
swap8IfLE(b32[i * 4 + 1]),
swap8IfLE(b32[i * 4 + 0])
);
}
if (left) {
ZEROS16.set(data.subarray(blocks * BLOCK_SIZE));
this._updateBlock(
swap8IfLE(ZEROS32[3]),
swap8IfLE(ZEROS32[2]),
swap8IfLE(ZEROS32[1]),
swap8IfLE(ZEROS32[0])
);
clean(ZEROS32);
}
return this;
}
digestInto(out: TArg<Uint8Array>): void {
aexists(this);
// `digestInto(out)` is the no-allocation fast path, so callers must pass a
// 32-bit-aligned buffer before we reinterpret the output prefix with `u32(view)`.
aoutput(out, this, true);
this.finished = true;
// RFC 8452 Appendix A maps POLYVAL output back through `ByteReverse(...)`.
// `digestInto()` follows the relaxed `aoutput()` contract, so only out[0..15] may be touched.
const view = out.subarray(0, this.outputLen);
const { s0, s1, s2, s3 } = this;
const o32 = u32(view);
o32[0] = s0;
o32[1] = s1;
o32[2] = s2;
o32[3] = s3;
swap32IfBE(o32);
view.reverse();
}
}
/**
* GHash MAC for AES-GCM.
* @param msg - Message bytes to authenticate.
* @param key - 16-byte GHASH key.
* @returns 16-byte authentication tag.
* @example
* Authenticates a short message with GHASH and a fresh hash key.
*
* ```ts
* import { ghash } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* ghash(new Uint8Array(), key);
* ```
*/
export const ghash: TRet<CMac<GHASH, [expectedLength?: number]>> =
/* @__PURE__ */ wrapMacConstructor(
16,
(key: TArg<Uint8Array>, expectedLength?: number) => new GHASH(key, expectedLength),
(msg: TArg<Uint8Array>): [expectedLength?: number] => [msg.length]
);
/**
* POLYVAL MAC for AES-SIV.
* @param msg - Message bytes to authenticate.
* @param key - 16-byte POLYVAL key.
* @returns 16-byte authentication tag.
* @example
* Authenticates a short message with POLYVAL and a fresh hash key.
*
* ```ts
* import { polyval } from '@noble/ciphers/_polyval.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* polyval(new Uint8Array(), key);
* ```
*/
export const polyval: TRet<CMac<Polyval, [expectedLength?: number]>> =
/* @__PURE__ */ wrapMacConstructor(
16,
(key: TArg<Uint8Array>, expectedLength?: number) => new Polyval(key, expectedLength),
(msg: TArg<Uint8Array>): [expectedLength?: number] => [msg.length]
);

2018
node_modules/@noble/ciphers/src/aes.ts generated vendored Normal file

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node_modules/@noble/ciphers/src/chacha.ts generated vendored Normal file
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/**
* ChaCha stream cipher, released
* in 2008. Developed after Salsa20, ChaCha aims to increase diffusion per round.
* It was standardized in
* {@link https://www.rfc-editor.org/rfc/rfc8439 | RFC 8439} and
* is now used in TLS 1.3.
*
* {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | XChaCha20}
* extended-nonce variant is also provided. Similar to XSalsa, it's safe to use with
* randomly-generated nonces.
*
* Check out
* {@link http://cr.yp.to/chacha/chacha-20080128.pdf | PDF},
* {@link https://en.wikipedia.org/wiki/Salsa20 | wiki}, and
* {@link https://cr.yp.to/chacha.html | website}.
*
* @module
*/
import { type XorPRG, createCipher, createPRG, rotl } from './_arx.ts';
import { poly1305 } from './_poly1305.ts';
import {
type ARXCipher,
type CipherWithOutput,
type TArg,
type TRet,
type XorStream,
abytes,
clean,
equalBytes,
getOutput,
swap8IfBE,
swap32IfBE,
u64Lengths,
wrapCipher,
} from './utils.ts';
/**
* ChaCha core function. It is implemented twice:
* 1. Simple loop (chachaCore_small, hchacha_small)
* 2. Unrolled loop (chachaCore, hchacha) - 4x faster, but larger & harder to read
* The specific implementation is selected in `createCipher` below.
*/
/** RFC 8439 §2.1 quarter round on words a, b, c, d. */
// prettier-ignore
function chachaQR(x: TArg<Uint32Array>, a: number, b: number, c: number, d: number) {
x[a] = (x[a] + x[b]) | 0; x[d] = rotl(x[d] ^ x[a], 16);
x[c] = (x[c] + x[d]) | 0; x[b] = rotl(x[b] ^ x[c], 12);
x[a] = (x[a] + x[b]) | 0; x[d] = rotl(x[d] ^ x[a], 8);
x[c] = (x[c] + x[d]) | 0; x[b] = rotl(x[b] ^ x[c], 7);
}
/** Repeated ChaCha double rounds; callers are expected to pass an even round count. */
function chachaRound(x: TArg<Uint32Array>, rounds = 20) {
for (let r = 0; r < rounds; r += 2) {
// RFC 8439 §2.3 / §2.3.1 inner_block: four column rounds, then four diagonal rounds.
chachaQR(x, 0, 4, 8, 12);
chachaQR(x, 1, 5, 9, 13);
chachaQR(x, 2, 6, 10, 14);
chachaQR(x, 3, 7, 11, 15);
chachaQR(x, 0, 5, 10, 15);
chachaQR(x, 1, 6, 11, 12);
chachaQR(x, 2, 7, 8, 13);
chachaQR(x, 3, 4, 9, 14);
}
}
// Shared scratch for the auditability-only helper below; only the test-only
// __TESTS.chachaCore_small hook reaches it, so production exports stay reentrant.
const ctmp = /* @__PURE__ */ new Uint32Array(16);
/** Small version of chacha without loop unrolling. Unused, provided for auditability. */
// prettier-ignore
function chacha(
s: TArg<Uint32Array>, k: TArg<Uint32Array>, i: TArg<Uint32Array>, out: TArg<Uint32Array>,
isHChacha: boolean = true, rounds: number = 20
): void {
// `i` is either `[counter, nonce0, nonce1, nonce2]` for the ChaCha block
// function or the full 128-bit nonce prefix for the HChaCha subkey path.
// Create initial array using common pattern
const y = Uint32Array.from([
s[0], s[1], s[2], s[3], // "expa" "nd 3" "2-by" "te k"
k[0], k[1], k[2], k[3], // Key Key Key Key
k[4], k[5], k[6], k[7], // Key Key Key Key
i[0], i[1], i[2], i[3], // Counter Counter Nonce Nonce
]);
const x = ctmp;
x.set(y);
chachaRound(x, rounds);
// HChaCha writes words 0..3 and 12..15 after the rounds; the ChaCha
// block path adds the original state word-by-word.
if (isHChacha) {
const xindexes = [0, 1, 2, 3, 12, 13, 14, 15];
for (let i = 0; i < 8; i++) out[i] = x[xindexes[i]];
} else {
for (let i = 0; i < 16; i++) out[i] = (y[i] + x[i]) | 0;
}
}
/** Identical to `chachaCore`. Reached only through the test-only `__TESTS` export. */
// @ts-ignore
const chachaCore_small: typeof chachaCore = (s, k, n, out, cnt, rounds) =>
// Keep the reference wrapper on the same [counter, nonce0, nonce1, nonce2] layout as chacha().
chacha(s, k, Uint32Array.from([cnt, n[0], n[1], n[2]]), out, false, rounds);
/** Identical to `hchacha`. Unused. */
// @ts-ignore
const hchacha_small: typeof hchacha = chacha;
/** RFC 8439 §2.3 block core for `state = constants | key | counter | nonce`. */
// prettier-ignore
function chachaCore(
s: TArg<Uint32Array>, k: TArg<Uint32Array>, n: TArg<Uint32Array>, out: TArg<Uint32Array>, cnt: number, rounds = 20
): void {
let y00 = s[0], y01 = s[1], y02 = s[2], y03 = s[3], // "expa" "nd 3" "2-by" "te k"
y04 = k[0], y05 = k[1], y06 = k[2], y07 = k[3], // Key Key Key Key
y08 = k[4], y09 = k[5], y10 = k[6], y11 = k[7], // Key Key Key Key
y12 = cnt, y13 = n[0], y14 = n[1], y15 = n[2]; // Counter Nonce Nonce Nonce
// Save state to temporary variables
let x00 = y00, x01 = y01, x02 = y02, x03 = y03,
x04 = y04, x05 = y05, x06 = y06, x07 = y07,
x08 = y08, x09 = y09, x10 = y10, x11 = y11,
x12 = y12, x13 = y13, x14 = y14, x15 = y15;
for (let r = 0; r < rounds; r += 2) {
x00 = (x00 + x04) | 0; x12 = rotl(x12 ^ x00, 16);
x08 = (x08 + x12) | 0; x04 = rotl(x04 ^ x08, 12);
x00 = (x00 + x04) | 0; x12 = rotl(x12 ^ x00, 8);
x08 = (x08 + x12) | 0; x04 = rotl(x04 ^ x08, 7);
x01 = (x01 + x05) | 0; x13 = rotl(x13 ^ x01, 16);
x09 = (x09 + x13) | 0; x05 = rotl(x05 ^ x09, 12);
x01 = (x01 + x05) | 0; x13 = rotl(x13 ^ x01, 8);
x09 = (x09 + x13) | 0; x05 = rotl(x05 ^ x09, 7);
x02 = (x02 + x06) | 0; x14 = rotl(x14 ^ x02, 16);
x10 = (x10 + x14) | 0; x06 = rotl(x06 ^ x10, 12);
x02 = (x02 + x06) | 0; x14 = rotl(x14 ^ x02, 8);
x10 = (x10 + x14) | 0; x06 = rotl(x06 ^ x10, 7);
x03 = (x03 + x07) | 0; x15 = rotl(x15 ^ x03, 16);
x11 = (x11 + x15) | 0; x07 = rotl(x07 ^ x11, 12);
x03 = (x03 + x07) | 0; x15 = rotl(x15 ^ x03, 8)
x11 = (x11 + x15) | 0; x07 = rotl(x07 ^ x11, 7);
x00 = (x00 + x05) | 0; x15 = rotl(x15 ^ x00, 16);
x10 = (x10 + x15) | 0; x05 = rotl(x05 ^ x10, 12);
x00 = (x00 + x05) | 0; x15 = rotl(x15 ^ x00, 8);
x10 = (x10 + x15) | 0; x05 = rotl(x05 ^ x10, 7);
x01 = (x01 + x06) | 0; x12 = rotl(x12 ^ x01, 16);
x11 = (x11 + x12) | 0; x06 = rotl(x06 ^ x11, 12);
x01 = (x01 + x06) | 0; x12 = rotl(x12 ^ x01, 8);
x11 = (x11 + x12) | 0; x06 = rotl(x06 ^ x11, 7);
x02 = (x02 + x07) | 0; x13 = rotl(x13 ^ x02, 16);
x08 = (x08 + x13) | 0; x07 = rotl(x07 ^ x08, 12);
x02 = (x02 + x07) | 0; x13 = rotl(x13 ^ x02, 8);
x08 = (x08 + x13) | 0; x07 = rotl(x07 ^ x08, 7);
x03 = (x03 + x04) | 0; x14 = rotl(x14 ^ x03, 16)
x09 = (x09 + x14) | 0; x04 = rotl(x04 ^ x09, 12);
x03 = (x03 + x04) | 0; x14 = rotl(x14 ^ x03, 8);
x09 = (x09 + x14) | 0; x04 = rotl(x04 ^ x09, 7);
}
// RFC 8439 §2.3 / §2.3.1: add the original state words back in state order.
let oi = 0;
out[oi++] = (y00 + x00) | 0; out[oi++] = (y01 + x01) | 0;
out[oi++] = (y02 + x02) | 0; out[oi++] = (y03 + x03) | 0;
out[oi++] = (y04 + x04) | 0; out[oi++] = (y05 + x05) | 0;
out[oi++] = (y06 + x06) | 0; out[oi++] = (y07 + x07) | 0;
out[oi++] = (y08 + x08) | 0; out[oi++] = (y09 + x09) | 0;
out[oi++] = (y10 + x10) | 0; out[oi++] = (y11 + x11) | 0;
out[oi++] = (y12 + x12) | 0; out[oi++] = (y13 + x13) | 0;
out[oi++] = (y14 + x14) | 0; out[oi++] = (y15 + x15) | 0;
}
/**
* hchacha hashes key and nonce into key' and nonce' for xchacha20.
* Algorithmically identical to `hchacha_small`, but this exported path
* normalizes word order on big-endian hosts.
* Need to find a way to merge it with `chachaCore` without 25% performance hit.
* @param s - Sigma constants as 32-bit words.
* @param k - Key words.
* @param i - Nonce-prefix words.
* @param out - Output buffer for the derived subkey.
* @example
* Derives the XChaCha subkey from sigma, key, and nonce-prefix words.
*
* ```ts
* const sigma = new Uint32Array(4);
* const key = new Uint32Array(8);
* const nonce = new Uint32Array(4);
* const out = new Uint32Array(8);
* hchacha(sigma, key, nonce, out);
* ```
*/
// prettier-ignore
export function hchacha(
s: TArg<Uint32Array>, k: TArg<Uint32Array>, i: TArg<Uint32Array>, out: TArg<Uint32Array>
): void {
let x00 = swap8IfBE(s[0]), x01 = swap8IfBE(s[1]), x02 = swap8IfBE(s[2]), x03 = swap8IfBE(s[3]),
x04 = swap8IfBE(k[0]), x05 = swap8IfBE(k[1]), x06 = swap8IfBE(k[2]), x07 = swap8IfBE(k[3]),
x08 = swap8IfBE(k[4]), x09 = swap8IfBE(k[5]), x10 = swap8IfBE(k[6]), x11 = swap8IfBE(k[7]),
x12 = swap8IfBE(i[0]), x13 = swap8IfBE(i[1]), x14 = swap8IfBE(i[2]), x15 = swap8IfBE(i[3]);
for (let r = 0; r < 20; r += 2) {
x00 = (x00 + x04) | 0; x12 = rotl(x12 ^ x00, 16);
x08 = (x08 + x12) | 0; x04 = rotl(x04 ^ x08, 12);
x00 = (x00 + x04) | 0; x12 = rotl(x12 ^ x00, 8);
x08 = (x08 + x12) | 0; x04 = rotl(x04 ^ x08, 7);
x01 = (x01 + x05) | 0; x13 = rotl(x13 ^ x01, 16);
x09 = (x09 + x13) | 0; x05 = rotl(x05 ^ x09, 12);
x01 = (x01 + x05) | 0; x13 = rotl(x13 ^ x01, 8);
x09 = (x09 + x13) | 0; x05 = rotl(x05 ^ x09, 7);
x02 = (x02 + x06) | 0; x14 = rotl(x14 ^ x02, 16);
x10 = (x10 + x14) | 0; x06 = rotl(x06 ^ x10, 12);
x02 = (x02 + x06) | 0; x14 = rotl(x14 ^ x02, 8);
x10 = (x10 + x14) | 0; x06 = rotl(x06 ^ x10, 7);
x03 = (x03 + x07) | 0; x15 = rotl(x15 ^ x03, 16);
x11 = (x11 + x15) | 0; x07 = rotl(x07 ^ x11, 12);
x03 = (x03 + x07) | 0; x15 = rotl(x15 ^ x03, 8)
x11 = (x11 + x15) | 0; x07 = rotl(x07 ^ x11, 7);
x00 = (x00 + x05) | 0; x15 = rotl(x15 ^ x00, 16);
x10 = (x10 + x15) | 0; x05 = rotl(x05 ^ x10, 12);
x00 = (x00 + x05) | 0; x15 = rotl(x15 ^ x00, 8);
x10 = (x10 + x15) | 0; x05 = rotl(x05 ^ x10, 7);
x01 = (x01 + x06) | 0; x12 = rotl(x12 ^ x01, 16);
x11 = (x11 + x12) | 0; x06 = rotl(x06 ^ x11, 12);
x01 = (x01 + x06) | 0; x12 = rotl(x12 ^ x01, 8);
x11 = (x11 + x12) | 0; x06 = rotl(x06 ^ x11, 7);
x02 = (x02 + x07) | 0; x13 = rotl(x13 ^ x02, 16);
x08 = (x08 + x13) | 0; x07 = rotl(x07 ^ x08, 12);
x02 = (x02 + x07) | 0; x13 = rotl(x13 ^ x02, 8);
x08 = (x08 + x13) | 0; x07 = rotl(x07 ^ x08, 7);
x03 = (x03 + x04) | 0; x14 = rotl(x14 ^ x03, 16)
x09 = (x09 + x14) | 0; x04 = rotl(x04 ^ x09, 12);
x03 = (x03 + x04) | 0; x14 = rotl(x14 ^ x03, 8);
x09 = (x09 + x14) | 0; x04 = rotl(x04 ^ x09, 7);
}
// HChaCha derives the subkey from state words 0..3 and 12..15 after 20 rounds.
let oi = 0;
out[oi++] = x00; out[oi++] = x01;
out[oi++] = x02; out[oi++] = x03;
out[oi++] = x12; out[oi++] = x13;
out[oi++] = x14; out[oi++] = x15;
swap32IfBE(out);
}
/**
* Original, non-RFC chacha20 from DJB. 8-byte nonce, 8-byte counter.
* The nonce/counter layout still reserves 8 counter bytes internally, but the shared public
* `counter` argument follows noble's strict non-wrapping 32-bit policy. See `src/_arx.ts`
* near `MAX_COUNTER` for the full counter-policy rationale.
* @param key - 16-byte or 32-byte key.
* @param nonce - 8-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the original 8-byte-nonce ChaCha variant and a fresh key/nonce.
*
* ```ts
* import { chacha20orig } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(8);
* chacha20orig(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha20orig: TRet<XorStream> = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 8,
allowShortKeys: true,
});
/**
* ChaCha stream cipher. Conforms to RFC 8439 (IETF, TLS). 12-byte nonce, 4-byte counter.
* With smaller nonce, it's not safe to make it random (CSPRNG), due to collision chance.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the RFC 8439 ChaCha20 stream cipher and a fresh key/nonce.
*
* ```ts
* import { chacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha20(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha20: TRet<XorStream> = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 4,
allowShortKeys: false,
});
/**
* XChaCha eXtended-nonce ChaCha. With 24-byte nonce, it's safe to make it random (CSPRNG).
* See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | the IRTF draft}.
* The nonce/counter layout still reserves 8 counter bytes internally, but the shared public
* `counter` argument follows noble's strict non-wrapping 32-bit policy. See `src/_arx.ts`
* near `MAX_COUNTER` for the full counter-policy rationale.
* @param key - 32-byte key.
* @param nonce - 24-byte extended nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with XChaCha20 using a fresh key and random 24-byte nonce.
*
* ```ts
* import { xchacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* xchacha20(key, nonce, new Uint8Array(4));
* ```
*/
export const xchacha20: TRet<XorStream> = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 8,
extendNonceFn: hchacha,
allowShortKeys: false,
});
/**
* Reduced 8-round chacha, described in original paper.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Uses the reduced 8-round variant for non-critical workloads with a fresh key/nonce.
*
* ```ts
* import { chacha8 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha8(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha8: TRet<XorStream> = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 4,
rounds: 8,
});
/**
* Reduced 12-round chacha, described in original paper.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Uses the reduced 12-round variant for non-critical workloads with a fresh key/nonce.
*
* ```ts
* import { chacha12 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* chacha12(key, nonce, new Uint8Array(4));
* ```
*/
export const chacha12: TRet<XorStream> = /* @__PURE__ */ createCipher(chachaCore, {
counterRight: false,
counterLength: 4,
rounds: 12,
});
// Test-only hooks for keeping the simple/reference core aligned with the unrolled production core.
export const __TESTS: {
chachaCore_small: typeof chachaCore_small;
chachaCore: typeof chachaCore;
} = /* @__PURE__ */ Object.freeze({ chachaCore_small, chachaCore });
// RFC 8439 §2.8.1 pad16(x): shared zero block for AAD/ciphertext padding.
const ZEROS16 = /* @__PURE__ */ new Uint8Array(16);
// RFC 8439 §2.8 / §2.8.1: aligned inputs add nothing, otherwise append 16-(len%16) zero bytes.
const updatePadded = (h: ReturnType<typeof poly1305.create>, msg: TArg<Uint8Array>) => {
h.update(msg);
const leftover = msg.length % 16;
if (leftover) h.update(ZEROS16.subarray(leftover));
};
// RFC 8439 §2.6.1 poly1305_key_gen returns `block[0..31]`, so AEAD key
// generation only needs 32 zero bytes.
const ZEROS32 = /* @__PURE__ */ new Uint8Array(32);
function computeTag(
fn: TArg<XorStream>,
key: TArg<Uint8Array>,
nonce: TArg<Uint8Array>,
ciphertext: TArg<Uint8Array>,
AAD?: TArg<Uint8Array>
): TRet<Uint8Array> {
if (AAD !== undefined) abytes(AAD, undefined, 'AAD');
// RFC 8439 §2.6 / §2.8: derive the Poly1305 one-time key from counter 0,
// then MAC AAD || pad16(AAD) || ciphertext || pad16(ciphertext) || len(AAD) || len(ciphertext).
const authKey = fn(
key as TRet<Uint8Array>,
nonce as TRet<Uint8Array>,
ZEROS32 as TRet<Uint8Array>
);
const lengths = u64Lengths(ciphertext.length, AAD ? AAD.length : 0, true);
// Methods below can be replaced with
// return poly1305_computeTag_small(authKey, lengths, ciphertext, AAD)
const h = poly1305.create(authKey);
if (AAD) updatePadded(h, AAD);
updatePadded(h, ciphertext);
h.update(lengths);
const res = h.digest();
clean(authKey, lengths);
return res;
}
/**
* AEAD algorithm from RFC 8439.
* Salsa20 and chacha (RFC 8439) use poly1305 differently.
* We could have composed them, but it's hard because of authKey:
* In salsa20, authKey changes position in salsa stream.
* In chacha, authKey can't be computed inside computeTag, it modifies the counter.
*/
export const _poly1305_aead =
(xorStream: TArg<XorStream>) =>
(key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>): CipherWithOutput => {
// This borrows caller key/nonce/AAD buffers by reference; mutating them after construction
// changes future encrypt/decrypt results.
const tagLength = 16;
return {
encrypt(plaintext: TArg<Uint8Array>, output?: TArg<Uint8Array>): TRet<Uint8Array> {
const plength = plaintext.length;
output = getOutput(plength + tagLength, output, false);
output.set(plaintext);
const oPlain = output.subarray(0, -tagLength);
// RFC 8439 §2.8: payload encryption starts at counter 1 because counter 0 produced the OTK.
xorStream(
key as TRet<Uint8Array>,
nonce as TRet<Uint8Array>,
oPlain as TRet<Uint8Array>,
oPlain as TRet<Uint8Array>,
1
);
const tag = computeTag(xorStream, key, nonce, oPlain, AAD);
output.set(tag, plength); // append tag
clean(tag);
return output as TRet<Uint8Array>;
},
decrypt(ciphertext: TArg<Uint8Array>, output?: TArg<Uint8Array>): TRet<Uint8Array> {
output = getOutput(ciphertext.length - tagLength, output, false);
const data = ciphertext.subarray(0, -tagLength);
const passedTag = ciphertext.subarray(-tagLength);
const tag = computeTag(xorStream, key, nonce, data, AAD);
// RFC 8439 §2.8 / §4: authenticate ciphertext before decrypting it, and compare tags with
// the constant-time equalBytes() helper rather than decrypting speculative plaintext first.
if (!equalBytes(passedTag, tag)) {
clean(tag);
throw new Error('invalid tag');
}
output.set(ciphertext.subarray(0, -tagLength));
// Actual decryption
xorStream(
key as TRet<Uint8Array>,
nonce as TRet<Uint8Array>,
output as TRet<Uint8Array>,
output as TRet<Uint8Array>,
1
); // start stream with i=1
clean(tag);
return output as TRet<Uint8Array>;
},
};
};
/**
* ChaCha20-Poly1305 from RFC 8439.
*
* Unsafe to use random nonces under the same key, due to collision chance.
* Prefer XChaCha instead.
* @param key - 32-byte key.
* @param nonce - 12-byte nonce.
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with a fresh key and nonce.
*
* ```ts
* import { chacha20poly1305 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(12);
* const cipher = chacha20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const chacha20poly1305: TRet<ARXCipher> = /* @__PURE__ */ wrapCipher(
{ blockSize: 64, nonceLength: 12, tagLength: 16 },
/* @__PURE__ */ _poly1305_aead(chacha20)
);
/**
* XChaCha20-Poly1305 extended-nonce chacha.
*
* Can be safely used with random nonces (CSPRNG).
* See {@link https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-xchacha | the IRTF draft}.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @param AAD - Additional authenticated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with a fresh key and random 24-byte nonce.
*
* ```ts
* import { xchacha20poly1305 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const cipher = xchacha20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const xchacha20poly1305: TRet<ARXCipher> = /* @__PURE__ */ wrapCipher(
{ blockSize: 64, nonceLength: 24, tagLength: 16 },
/* @__PURE__ */ _poly1305_aead(xchacha20)
);
/**
* Chacha20 CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* Compatible with libtomcrypt. It does not have a specification, so unclear how secure it is.
* @param seed - Optional seed bytes mixed into the internal `key || nonce` state. When omitted,
* only 32 random bytes are mixed into the 40-byte state.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
* @example
* Seeds the test-only ChaCha20 DRBG from fresh entropy.
*
* ```ts
* import { rngChacha20 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const prg = rngChacha20(seed);
* prg.randomBytes(8);
* ```
*/
export const rngChacha20: TRet<XorPRG> = /* @__PURE__ */ createPRG(chacha20orig, 64, 32, 8);
/**
* Chacha20/8 CSPRNG (cryptographically secure pseudorandom number generator).
* It's best to limit usage to non-production, non-critical cases: for example, test-only.
* Faster than `rngChacha20`.
* @param seed - Optional seed bytes mixed into the internal `key || nonce` state. When omitted,
* only 32 random bytes are mixed into the 44-byte state.
* @returns Seeded concrete `_XorStreamPRG` instance, including `clone()`.
* @example
* Seeds the faster test-only ChaCha8 DRBG from fresh entropy.
*
* ```ts
* import { rngChacha8 } from '@noble/ciphers/chacha.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const seed = randomBytes(32);
* const prg = rngChacha8(seed);
* prg.randomBytes(8);
* ```
*/
export const rngChacha8: TRet<XorPRG> = /* @__PURE__ */ createPRG(chacha8, 64, 32, 12);

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node_modules/@noble/ciphers/src/ff1.ts generated vendored Normal file
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/**
* FPE-FF1 (Format-preserving encryption algorithm) specified in
* {@link https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-38G.pdf | NIST 800-38G}.
* @module
*/
import { unsafe } from './aes.ts';
import {
abytes,
anumber,
bytesToNumberBE,
clean,
numberToBytesBE,
type Cipher,
type TArg,
type TRet,
} from './utils.ts';
// NIST SP 800-38G §4.3 / §5.1 Algorithm 7: FF1's designated CIPH_K here is AES, so this file
// reuses the reviewed AES key schedule and single-block encryption helpers.
// NOTE: no point in inlining encrypt instead of encryptBlock, since BigInt stuff will be slow
const { expandKeyLE, encryptBlock } = unsafe;
// Format-preserving encryption algorithm (FPE-FF1) specified in
// {@link https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-38G.pdf | NIST Special Publication 800-38G}.
const BLOCK_LEN = 16;
// FF1 step 6vi needs mathematical modulo in [0, b); JS `%` is remainder, so decrypt rounds must
// map negative intermediate values back into that range.
function mod(a: number, b: number): number;
function mod(a: bigint, b: bigint): bigint;
function mod(a: any, b: any): number | bigint {
const result = a % b;
return result >= 0 ? result : b + result;
}
function NUMradix(radix: number, data: number[]): bigint {
let res = BigInt(0);
for (let i of data) res = res * BigInt(radix) + BigInt(i);
return res;
}
function getRound(radix: number, key: TArg<Uint8Array>, tweak: TArg<Uint8Array>, x: number[]) {
if (radix > 2 ** 16 - 1) throw new Error('invalid radix ' + radix);
// radix**minlen ≥ 100
const minLen = Math.ceil(Math.log(100) / Math.log(radix));
const maxLen = 2 ** 32 - 1;
// 2 ≤ minlen ≤ maxlen < 2**32
if (2 > minLen || minLen > maxLen || maxLen >= 2 ** 32)
throw new Error('Invalid radix: 2 ≤ minlen ≤ maxlen < 2**32');
if (!Array.isArray(x)) throw new Error('invalid X');
if (x.length < minLen || x.length > maxLen) throw new Error('X is outside minLen..maxLen bounds');
// SP 800-38G defines FF1 over numeral strings in base `radix`; out-of-range digits must fail
// before NUMradix(...) or round splitting can reinterpret them as a different numeral string.
for (const i of x) {
if (!Number.isSafeInteger(i) || i < 0 || i >= radix)
throw new Error('invalid X: digit outside radix');
}
const u = Math.floor(x.length / 2);
const v = x.length - u;
const b = Math.ceil(Math.ceil(v * Math.log2(radix)) / 8);
const d = 4 * Math.ceil(b / 4) + 4;
const padding = mod(-tweak.length - b - 1, 16);
// P = [1]1 || [2]1 || [1]1 || [radix]3 || [10]1 || [u mod 256]1 || [n]4 || [t]4.
const P = Uint8Array.from([1, 2, 1, 0, 0, 0, 10, u, 0, 0, 0, 0, 0, 0, 0, 0]);
const view = new DataView(P.buffer);
// NIST SP 800-38G §5.1 bounds radix <= 2^16, so the 24-bit [radix]3 field is encoded here as
// 0x00 || uint16_be(radix).
view.setUint16(4, radix, false);
view.setUint32(8, x.length, false);
view.setUint32(12, tweak.length, false);
// Q = T || [0](tb1) mod 16 || [i]1 || [NUMradix(B)]b.
const PQ = new Uint8Array(P.length + tweak.length + padding + 1 + b);
PQ.set(P);
clean(P);
PQ.set(tweak, P.length);
const xk = expandKeyLE(key);
const round = (A: number[], B: number[], i: number, decrypt = false) => {
// Q = ... || [i]1 || [NUMradix(B)]b.
PQ[PQ.length - b - 1] = i;
if (b) PQ.set(numberToBytesBE(NUMradix(radix, B), b), PQ.length - b);
// NIST SP 800-38G Algorithm 6 PRF: Y_j = CIPH_K(Y_(j-1) xor X_j) starting from Y_0 = 0^128.
let r = new Uint8Array(16);
for (let j = 0; j < PQ.length / BLOCK_LEN; j++) {
for (let i = 0; i < BLOCK_LEN; i++) r[i] ^= PQ[j * BLOCK_LEN + i];
encryptBlock(xk, r);
}
// Let S be the first d bytes of the following string of ⎡d/16⎤ blocks:
// R || CIPHK(R ⊕[1]16) || CIPHK(R ⊕[2]16) ...CIPHK(R ⊕[⎡d / 16⎤ 1]16).
let s = Array.from(r);
for (let j = 1; s.length < d; j++) {
const block = numberToBytesBE(BigInt(j), 16);
for (let k = 0; k < BLOCK_LEN; k++) block[k] ^= r[k];
s.push(...Array.from(encryptBlock(xk, block)));
}
let y = bytesToNumberBE(Uint8Array.from(s.slice(0, d)));
s.fill(0);
if (decrypt) y = -y;
const m = i % 2 === 0 ? u : v;
let c = mod(NUMradix(radix, A) + y, BigInt(radix) ** BigInt(m));
// STR(radix, m, c)
const C = Array(m).fill(0);
for (let i = 0; i < m; i++, c /= BigInt(radix)) C[m - 1 - i] = Number(c % BigInt(radix));
A.fill(0);
A = B;
B = C;
return [A, B];
};
const destroy = () => {
clean(xk, PQ);
};
return { u, round, destroy };
}
const EMPTY_BUF = /* @__PURE__ */ Uint8Array.of();
/**
* FPE-FF1 format-preserving encryption.
* @param radix - Alphabet size for each input digit.
* @param key - AES key bytes.
* @param tweak - Optional tweak bytes.
* @returns Encrypt/decrypt helpers over digit arrays.
* @example
* Encrypts decimal digits without changing their format, using a fresh AES key.
*
* ```ts
* import { FF1 } from '@noble/ciphers/ff1.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const ff1 = FF1(10, key);
* ff1.encrypt([1, 2, 3]);
* ```
*/
export function FF1(
radix: number,
key: TArg<Uint8Array>,
tweak: TArg<Uint8Array> = EMPTY_BUF
): { encrypt(x: number[]): number[]; decrypt(x: number[]): number[] } {
anumber(radix);
abytes(key);
abytes(tweak);
// This borrows caller key/tweak buffers by reference through the bound closure; mutating them
// after construction changes later encrypt/decrypt outputs.
const PQ = getRound.bind(null, radix, key, tweak);
return {
encrypt(x: number[]): number[] {
const { u, round, destroy } = PQ(x);
let [A, B] = [x.slice(0, u), x.slice(u)];
for (let i = 0; i < 10; i++) [A, B] = round(A, B, i);
destroy();
const res = A.concat(B);
A.fill(0);
B.fill(0);
return res;
},
decrypt(x: number[]): number[] {
const { u, round, destroy } = PQ(x);
// The FF1.Decrypt algorithm is similar to the FF1.Encrypt algorithm;
// the differences are in Step 6, where:
// 1) the order of the indices is reversed,
// 2) the roles of A and B are swapped
// 3) modular addition is replaced by modular subtraction, in Step 6vi.
let [B, A] = [x.slice(0, u), x.slice(u)];
for (let i = 9; i >= 0; i--) [A, B] = round(A, B, i, true);
destroy();
const res = B.concat(A);
A.fill(0);
B.fill(0);
return res;
},
};
}
// Binary wrapper uses little-endian bit order within each byte so bit 0 stays
// in the first numeral slot for this library-defined byte-array surface.
const binLE = {
encode(bytes: TArg<Uint8Array>): number[] {
const x = [];
for (let i = 0; i < bytes.length; i++) {
for (let j = 0, tmp = bytes[i]; j < 8; j++, tmp >>= 1) x.push(tmp & 1);
}
return x;
},
decode(b: number[]): TRet<Uint8Array> {
if (!Array.isArray(b) || b.length % 8) throw new Error('Invalid binary string');
const res = new Uint8Array(b.length / 8);
for (let i = 0, j = 0; i < res.length; i++) {
res[i] = b[j++] | (b[j++] << 1) | (b[j++] << 2) | (b[j++] << 3);
res[i] |= (b[j++] << 4) | (b[j++] << 5) | (b[j++] << 6) | (b[j++] << 7);
}
return res as TRet<Uint8Array>;
},
};
/**
* Binary FPE-FF1 wrapper over byte arrays.
* @param key - AES key bytes.
* @param tweak - Optional tweak bytes.
* @returns Encrypt/decrypt helpers over byte arrays.
* @example
* Encrypts raw bytes through FF1's binary alphabet wrapper with a fresh AES key.
*
* ```ts
* import { BinaryFF1 } from '@noble/ciphers/ff1.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const ff1 = BinaryFF1(key);
* ff1.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export function BinaryFF1(
key: TArg<Uint8Array>,
tweak: TArg<Uint8Array> = EMPTY_BUF
): TRet<Cipher> {
const ff1 = FF1(2, key, tweak);
return {
encrypt: (x: TArg<Uint8Array>): TRet<Uint8Array> =>
binLE.decode(ff1.encrypt(binLE.encode(x))) as TRet<Uint8Array>,
decrypt: (x: TArg<Uint8Array>): TRet<Uint8Array> =>
binLE.decode(ff1.decrypt(binLE.encode(x))) as TRet<Uint8Array>,
} as TRet<Cipher>;
}

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/**
* Audited & minimal JS implementation of Salsa20, ChaCha and AES. Check out individual modules.
* @example
```js
import { gcm, aessiv } from '@noble/ciphers/aes.js';
import { xsalsa20poly1305 } from '@noble/ciphers/salsa.js';
import { secretbox } from '@noble/ciphers/salsa.js'; // == xsalsa20poly1305
import { chacha20poly1305, xchacha20poly1305 } from '@noble/ciphers/chacha.js';
// Unauthenticated encryption: make sure to use HMAC or similar
import { ctr, cfb, cbc, ecb } from '@noble/ciphers/aes.js';
import { salsa20, xsalsa20 } from '@noble/ciphers/salsa.js';
import { chacha20, xchacha20, chacha8, chacha12 } from '@noble/ciphers/chacha.js';
// KW
import { aeskw, aeskwp } from '@noble/ciphers/aes.js';
// Utilities
import { managedNonce, randomBytes, bytesToHex, hexToBytes } from '@noble/ciphers/utils.js';
import { poly1305 } from '@noble/ciphers/_poly1305.js';
import { ghash, polyval } from '@noble/ciphers/_polyval.js';
```
* @module
*/
throw new Error('root module cannot be imported: import submodules instead. Check out README');

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/**
* Salsa20 stream cipher, released in 2005.
* Salsa's goal was to implement AES replacement that does not rely on S-Boxes,
* which are hard to implement in a constant-time manner.
* Salsa20 is usually faster than AES, a big deal on slow, budget mobile phones.
*
* - {@link https://cr.yp.to/snuffle/xsalsa-20110204.pdf | XSalsa20},
* extended-nonce
* variant was released in 2008. It extends Salsa20's 64-bit nonce to 192 bits,
* and became safe to be picked at random.
* - Nacl / Libsodium popularized term "secretbox", - which is just xsalsa20poly1305.
* We provide the alias and corresponding seal / open methods.
* "crypto_box" and "sealedbox" are available in package
* {@link https://github.com/serenity-kit/noble-sodium | noble-sodium}.
* - Check out
* {@link https://cr.yp.to/snuffle/salsafamily-20071225.pdf | PDF}
* and {@link https://cr.yp.to/snuffle.html | website}.
* @module
*/
import { createCipher, rotl } from './_arx.ts';
import { poly1305 } from './_poly1305.ts';
import {
abytes,
clean,
equalBytes,
getOutput,
swap32IfBE,
swap8IfBE,
wrapCipher,
type ARXCipher,
type CipherWithOutput,
type TArg,
type TRet,
type XorStream,
} from './utils.ts';
/**
* Salsa20 core function. It is implemented twice:
* 1. Simple loop (salsaCore_small, hsalsa_small)
* 2. Unrolled loop (salsaCore, hsalsa) - 4x faster, but larger & harder to read
* The specific implementation is selected in `createCipher` below.
* Performance numbers for 1MB inputs:
* * default x 779 ops/sec @ 1ms/op
* * if salsa+hsalsa are merged x 459 ops/sec @ 2ms/op
* * small x 132 ops/sec @ 7ms/op
*/
/** RFC 7914 §3 Salsa20/8 core quarter-round on words a, b, c, d. */
function salsaQR(x: TArg<Uint32Array>, a: number, b: number, c: number, d: number) {
x[b] ^= rotl((x[a] + x[d]) | 0, 7);
x[c] ^= rotl((x[b] + x[a]) | 0, 9);
x[d] ^= rotl((x[c] + x[b]) | 0, 13);
x[a] ^= rotl((x[d] + x[c]) | 0, 18);
}
/** RFC 7914 §3 double-round schedule: four column rounds, then four row rounds. */
function salsaRound(x: TArg<Uint32Array>, rounds = 20) {
for (let r = 0; r < rounds; r += 2) {
salsaQR(x, 0, 4, 8, 12);
salsaQR(x, 5, 9, 13, 1);
salsaQR(x, 10, 14, 2, 6);
salsaQR(x, 15, 3, 7, 11);
salsaQR(x, 0, 1, 2, 3);
salsaQR(x, 5, 6, 7, 4);
salsaQR(x, 10, 11, 8, 9);
salsaQR(x, 15, 12, 13, 14);
}
}
// Shared scratch for the unused auditability helper below; it would be
// non-reentrant under overlapping/nested calls, but current code doesn't invoke it.
const stmp = /* @__PURE__ */ new Uint32Array(16);
/** Small version of salsa without loop unrolling. Unused, provided for auditability. */
// prettier-ignore
function salsa(
s: TArg<Uint32Array>, k: TArg<Uint32Array>, i: TArg<Uint32Array>, out: TArg<Uint32Array>,
isHSalsa: boolean = true, rounds: number = 20
): void {
// Create initial array using common pattern
const y = Uint32Array.from([
s[0], k[0], k[1], k[2], // "expa" Key Key Key
k[3], s[1], i[0], i[1], // Key "nd 3" Nonce Nonce
i[2], i[3], s[2], k[4], // Pos. Pos. "2-by" Key
k[5], k[6], k[7], s[3], // Key Key Key "te k"
]);
const x = stmp;
x.set(y);
// const x = y.slice();
salsaRound(x, rounds);
// hsalsa extracts 8 specific words for the 32-byte subkey; salsa adds the original state.
if (isHSalsa) {
const xindexes = [0, 5, 10, 15, 6, 7, 8, 9];
for (let i = 0; i < 8; i++) out[i] = x[xindexes[i]];
} else {
for (let i = 0; i < 16; i++) out[i] = (y[i] + x[i]) | 0;
}
}
/** Identical to `salsaCore`. Unused. */
// @ts-ignore
const salsaCore_small: typeof salsaCore = (s, k, n, out, cnt, rounds) =>
salsa(s, k, Uint32Array.from([n[0], n[1], cnt, 0]), out, false, rounds);
/** Identical to `hsalsa`. Unused. */
// @ts-ignore
const hsalsa_small: typeof hsalsa = salsa;
/** Identical to `salsaCore_small`. Uses only the low 32 bits of Salsa20's 64-bit counter state. */
// prettier-ignore
function salsaCore(
s: TArg<Uint32Array>, k: TArg<Uint32Array>, n: TArg<Uint32Array>, out: TArg<Uint32Array>, cnt: number, rounds = 20
): void {
// Public wrappers expose only the low 32 bits of Salsa20's 64-bit counter; y09 stays zero.
// Based on {@link https://cr.yp.to/salsa20.html | the Salsa20 reference page}.
let y00 = s[0], y01 = k[0], y02 = k[1], y03 = k[2], // "expa" Key Key Key
y04 = k[3], y05 = s[1], y06 = n[0], y07 = n[1], // Key "nd 3" Nonce Nonce
y08 = cnt, y09 = 0, y10 = s[2], y11 = k[4], // Pos. Pos. "2-by" Key
y12 = k[5], y13 = k[6], y14 = k[7], y15 = s[3]; // Key Key Key "te k"
// Save state to temporary variables
let x00 = y00, x01 = y01, x02 = y02, x03 = y03,
x04 = y04, x05 = y05, x06 = y06, x07 = y07,
x08 = y08, x09 = y09, x10 = y10, x11 = y11,
x12 = y12, x13 = y13, x14 = y14, x15 = y15;
for (let r = 0; r < rounds; r += 2) {
x04 ^= rotl(x00 + x12 | 0, 7); x08 ^= rotl(x04 + x00 | 0, 9);
x12 ^= rotl(x08 + x04 | 0, 13); x00 ^= rotl(x12 + x08 | 0, 18);
x09 ^= rotl(x05 + x01 | 0, 7); x13 ^= rotl(x09 + x05 | 0, 9);
x01 ^= rotl(x13 + x09 | 0, 13); x05 ^= rotl(x01 + x13 | 0, 18);
x14 ^= rotl(x10 + x06 | 0, 7); x02 ^= rotl(x14 + x10 | 0, 9);
x06 ^= rotl(x02 + x14 | 0, 13); x10 ^= rotl(x06 + x02 | 0, 18);
x03 ^= rotl(x15 + x11 | 0, 7); x07 ^= rotl(x03 + x15 | 0, 9);
x11 ^= rotl(x07 + x03 | 0, 13); x15 ^= rotl(x11 + x07 | 0, 18);
x01 ^= rotl(x00 + x03 | 0, 7); x02 ^= rotl(x01 + x00 | 0, 9);
x03 ^= rotl(x02 + x01 | 0, 13); x00 ^= rotl(x03 + x02 | 0, 18);
x06 ^= rotl(x05 + x04 | 0, 7); x07 ^= rotl(x06 + x05 | 0, 9);
x04 ^= rotl(x07 + x06 | 0, 13); x05 ^= rotl(x04 + x07 | 0, 18);
x11 ^= rotl(x10 + x09 | 0, 7); x08 ^= rotl(x11 + x10 | 0, 9);
x09 ^= rotl(x08 + x11 | 0, 13); x10 ^= rotl(x09 + x08 | 0, 18);
x12 ^= rotl(x15 + x14 | 0, 7); x13 ^= rotl(x12 + x15 | 0, 9);
x14 ^= rotl(x13 + x12 | 0, 13); x15 ^= rotl(x14 + x13 | 0, 18);
}
// Write output
let oi = 0;
out[oi++] = (y00 + x00) | 0; out[oi++] = (y01 + x01) | 0;
out[oi++] = (y02 + x02) | 0; out[oi++] = (y03 + x03) | 0;
out[oi++] = (y04 + x04) | 0; out[oi++] = (y05 + x05) | 0;
out[oi++] = (y06 + x06) | 0; out[oi++] = (y07 + x07) | 0;
out[oi++] = (y08 + x08) | 0; out[oi++] = (y09 + x09) | 0;
out[oi++] = (y10 + x10) | 0; out[oi++] = (y11 + x11) | 0;
out[oi++] = (y12 + x12) | 0; out[oi++] = (y13 + x13) | 0;
out[oi++] = (y14 + x14) | 0; out[oi++] = (y15 + x15) | 0;
}
/**
* hsalsa hashes key and nonce-prefix words into the 32-byte subkey used by XSalsa20.
* Identical to `hsalsa_small`.
* Need to find a way to merge it with `salsaCore` without 25% performance hit.
* @param s - Sigma constants as 32-bit words.
* @param k - Key words.
* @param i - Nonce-prefix words.
* @param out - Output buffer for the derived subkey.
* @example
* Derives the XSalsa20 subkey from sigma, key, and nonce-prefix words.
*
* ```ts
* const sigma = new Uint32Array(4);
* const key = new Uint32Array(8);
* const nonce = new Uint32Array(4);
* const out = new Uint32Array(8);
* hsalsa(sigma, key, nonce, out);
* ```
*/
// prettier-ignore
export function hsalsa(
s: TArg<Uint32Array>, k: TArg<Uint32Array>, i: TArg<Uint32Array>, out: TArg<Uint32Array>
): void {
let x00 = swap8IfBE(s[0]), x01 = swap8IfBE(k[0]), x02 = swap8IfBE(k[1]), x03 = swap8IfBE(k[2]),
x04 = swap8IfBE(k[3]), x05 = swap8IfBE(s[1]), x06 = swap8IfBE(i[0]), x07 = swap8IfBE(i[1]),
x08 = swap8IfBE(i[2]), x09 = swap8IfBE(i[3]), x10 = swap8IfBE(s[2]), x11 = swap8IfBE(k[4]),
x12 = swap8IfBE(k[5]), x13 = swap8IfBE(k[6]), x14 = swap8IfBE(k[7]), x15 = swap8IfBE(s[3]);
for (let r = 0; r < 20; r += 2) {
x04 ^= rotl(x00 + x12 | 0, 7); x08 ^= rotl(x04 + x00 | 0, 9);
x12 ^= rotl(x08 + x04 | 0, 13); x00 ^= rotl(x12 + x08 | 0, 18);
x09 ^= rotl(x05 + x01 | 0, 7); x13 ^= rotl(x09 + x05 | 0, 9);
x01 ^= rotl(x13 + x09 | 0, 13); x05 ^= rotl(x01 + x13 | 0, 18);
x14 ^= rotl(x10 + x06 | 0, 7); x02 ^= rotl(x14 + x10 | 0, 9);
x06 ^= rotl(x02 + x14 | 0, 13); x10 ^= rotl(x06 + x02 | 0, 18);
x03 ^= rotl(x15 + x11 | 0, 7); x07 ^= rotl(x03 + x15 | 0, 9);
x11 ^= rotl(x07 + x03 | 0, 13); x15 ^= rotl(x11 + x07 | 0, 18);
x01 ^= rotl(x00 + x03 | 0, 7); x02 ^= rotl(x01 + x00 | 0, 9);
x03 ^= rotl(x02 + x01 | 0, 13); x00 ^= rotl(x03 + x02 | 0, 18);
x06 ^= rotl(x05 + x04 | 0, 7); x07 ^= rotl(x06 + x05 | 0, 9);
x04 ^= rotl(x07 + x06 | 0, 13); x05 ^= rotl(x04 + x07 | 0, 18);
x11 ^= rotl(x10 + x09 | 0, 7); x08 ^= rotl(x11 + x10 | 0, 9);
x09 ^= rotl(x08 + x11 | 0, 13); x10 ^= rotl(x09 + x08 | 0, 18);
x12 ^= rotl(x15 + x14 | 0, 7); x13 ^= rotl(x12 + x15 | 0, 9);
x14 ^= rotl(x13 + x12 | 0, 13); x15 ^= rotl(x14 + x13 | 0, 18);
}
let oi = 0;
// XSalsa20 takes words 0,5,10,15 and 6,7,8,9 as the 32-byte subkey material.
out[oi++] = x00; out[oi++] = x05;
out[oi++] = x10; out[oi++] = x15;
out[oi++] = x06; out[oi++] = x07;
out[oi++] = x08; out[oi++] = x09;
swap32IfBE(out);
}
/**
* Salsa20 from original paper. 8-byte nonce.
* With smaller nonce, it's not safe to make it random (CSPRNG), due to collision chance.
* @param key - 16-byte or 32-byte key.
* @param nonce - 8-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* Only the low 32 bits of Salsa20's 64-bit counter state are exposed here;
* the high word stays zero and the implementation still caps the public
* value to 32 bits.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with the original 8-byte-nonce Salsa20 stream cipher.
*
* ```ts
* import { salsa20 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(8);
* salsa20(key, nonce, new Uint8Array([1, 2, 3, 4]));
* ```
*/
export const salsa20: TRet<XorStream> = /* @__PURE__ */ createCipher(salsaCore, {
allowShortKeys: true,
counterRight: true,
});
/**
* XSalsa20 extended-nonce salsa.
* With 24-byte nonce, it's safe to make it random (CSPRNG).
* @param key - 32-byte key.
* This XSalsa20 wrapper does not enable Salsa20's 16-byte legacy key mode.
* @param nonce - 24-byte nonce.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Initial block counter.
* @returns Encrypted or decrypted bytes.
* @example
* Encrypts bytes with XSalsa20 and a random 24-byte nonce.
*
* ```ts
* import { xsalsa20 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* xsalsa20(key, nonce, new Uint8Array([1, 2, 3, 4]));
* ```
*/
export const xsalsa20: TRet<XorStream> = /* @__PURE__ */ createCipher(salsaCore, {
counterRight: true,
extendNonceFn: hsalsa,
});
/**
* xsalsa20-poly1305 eXtended-nonce (24 bytes) salsa.
* With 24-byte nonce, it's safe to make it random (CSPRNG).
* Also known as `secretbox` from libsodium / nacl.
* No AAD input is supported here. Caller-provided `output` buffers for
* `encrypt()` / `decrypt()` must be `input.length + 32` bytes because the
* implementation uses a 32-byte leading scratch area before returning `+16`.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @param AAD - Must be omitted; XSalsa20-Poly1305 secretbox does not support associated data.
* @returns AEAD cipher instance.
* @example
* Encrypts and authenticates plaintext with XSalsa20-Poly1305.
*
* ```ts
* import { xsalsa20poly1305 } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const cipher = xsalsa20poly1305(key, nonce);
* cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const xsalsa20poly1305: TRet<ARXCipher> = /* @__PURE__ */ wrapCipher(
{ blockSize: 64, nonceLength: 24, tagLength: 16 },
(key: TArg<Uint8Array>, nonce: TArg<Uint8Array>): TRet<CipherWithOutput> => {
// This borrows caller key/nonce buffers by reference; mutating them after construction changes
// later encrypt/decrypt outputs.
return {
encrypt(plaintext: TArg<Uint8Array>, output?: TArg<Uint8Array>): TRet<Uint8Array> {
// xsalsa20poly1305 optimizes by calculating auth key during the same call as encryption.
// Unfortunately, makes it hard to separate tag calculation & encryption itself,
// because 32 bytes is half-block of 64-byte salsa.
// Need 32 extra bytes up front for the auth-key scratch area described above.
output = getOutput(plaintext.length + 32, output, false);
// output[0..32] = Poly1305 auth key, output[32..] = plaintext then ciphertext.
const authKey = output.subarray(0, 32);
const ciphPlaintext = output.subarray(32);
output.set(plaintext, 32);
// authKey is produced by xoring the first 32 bytes with zeros.
clean(authKey);
// output = stream ^ output; authKey = stream ^ zeros(32)
xsalsa20(key, nonce, output, output);
const tag = poly1305(ciphPlaintext, authKey);
output.set(tag, 16);
// Clean up auth-key remnants and the temporary tag copy.
clean(output.subarray(0, 16), tag);
// Return output[16..].
return output.subarray(16) as TRet<Uint8Array>;
},
decrypt(ciphertext: TArg<Uint8Array>, output?: TArg<Uint8Array>): TRet<Uint8Array> {
// tmp part passed tag ciphertext
// [0..32] [32..48] [48..]
// Authenticate the ciphertext before decrypting it; on tag failure the scratch/output
// buffer may already contain copied ciphertext and derived auth-key material.
abytes(ciphertext);
output = getOutput(ciphertext.length + 32, output, false);
// output[0..32] is auth-key scratch, output[32..48] is passed tag,
// output[48..] is ciphertext then plaintext.
const tmp = output.subarray(0, 32);
const passedTag = output.subarray(32, 48);
const ciphPlaintext = output.subarray(48);
output.set(ciphertext, 32);
// authKey is produced by xoring the scratch area with zeros.
clean(tmp);
const authKey = xsalsa20(key, nonce, tmp, tmp);
const tag = poly1305(ciphPlaintext, authKey);
if (!equalBytes(passedTag, tag)) {
clean(output);
throw new Error('invalid tag');
}
// output = stream ^ output[16..]
xsalsa20(key, nonce, output.subarray(16), output.subarray(16));
clean(tmp, passedTag, tag);
// Return output[48..], skipping zeroized output[0..48].
return ciphPlaintext as TRet<Uint8Array>;
},
} as TRet<CipherWithOutput>;
}
);
/**
* Alias to `xsalsa20poly1305`, for compatibility with libsodium / nacl.
* Check out {@link https://github.com/serenity-kit/noble-sodium | noble-sodium}
* for `crypto_box`.
* @param key - 32-byte key.
* @param nonce - 24-byte nonce.
* @returns Wrapper with `seal()` and `open()` helpers.
* @example
* Uses the libsodium-style `seal()` and `open()` wrapper.
*
* ```ts
* import { secretbox } from '@noble/ciphers/salsa.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(32);
* const nonce = randomBytes(24);
* const box = secretbox(key, nonce);
* box.seal(new Uint8Array([1, 2, 3]));
* ```
*/
export function secretbox(
key: TArg<Uint8Array>,
nonce: TArg<Uint8Array>
): TRet<{
seal: (plaintext: TArg<Uint8Array>, output?: TArg<Uint8Array>) => TRet<Uint8Array>;
open: (ciphertext: TArg<Uint8Array>, output?: TArg<Uint8Array>) => TRet<Uint8Array>;
}> {
const xs = xsalsa20poly1305(key, nonce);
return { seal: xs.encrypt, open: xs.decrypt } as TRet<{
seal: (plaintext: TArg<Uint8Array>, output?: TArg<Uint8Array>) => TRet<Uint8Array>;
open: (ciphertext: TArg<Uint8Array>, output?: TArg<Uint8Array>) => TRet<Uint8Array>;
}>;
}

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/**
* WebCrypto-based AES gcm/ctr/cbc, `managedNonce` and `randomBytes`.
* We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.
* @module
*/
import { abytes, anumber, type AsyncCipher, type TArg, type TRet } from './utils.ts';
function getWebcryptoSubtle(): any {
const cr = typeof globalThis !== 'undefined' && (globalThis as any).crypto;
if (cr && typeof cr.subtle === 'object' && cr.subtle != null) return cr.subtle;
throw new Error('crypto.subtle must be defined');
}
type WebcryptoUtils = {
encrypt(
key: TArg<Uint8Array>,
keyParams: unknown,
cryptParams: unknown,
plaintext: TArg<Uint8Array>
): Promise<TRet<Uint8Array>>;
decrypt(
key: TArg<Uint8Array>,
keyParams: unknown,
cryptParams: unknown,
ciphertext: TArg<Uint8Array>
): Promise<TRet<Uint8Array>>;
};
/**
* Internal webcrypto utils. Can be overridden if crypto.subtle is not present,
* for example in React Native.
* Raw keys are re-imported on every call; this wrapper intentionally does not
* cache `CryptoKey` objects between operations.
*/
export const utils: TRet<WebcryptoUtils> = {
async encrypt(
key: TArg<Uint8Array>,
keyParams: any,
cryptParams: any,
plaintext: TArg<Uint8Array>
): Promise<TRet<Uint8Array>> {
const cr = getWebcryptoSubtle();
const iKey = await cr.importKey('raw', key, keyParams, true, ['encrypt']);
const ciphertext = await cr.encrypt(cryptParams, iKey, plaintext);
return new Uint8Array(ciphertext) as TRet<Uint8Array>;
},
async decrypt(
key: TArg<Uint8Array>,
keyParams: any,
cryptParams: any,
ciphertext: TArg<Uint8Array>
): Promise<TRet<Uint8Array>> {
const cr = getWebcryptoSubtle();
const iKey = await cr.importKey('raw', key, keyParams, true, ['decrypt']);
const plaintext = await cr.decrypt(cryptParams, iKey, ciphertext);
return new Uint8Array(plaintext) as TRet<Uint8Array>;
},
};
const mode = {
CBC: 'AES-CBC',
CTR: 'AES-CTR',
GCM: 'AES-GCM',
} as const;
type BlockMode = (typeof mode)[keyof typeof mode];
function getCryptParams(algo: BlockMode, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) {
if (algo === mode.CBC) return { name: mode.CBC, iv: nonce };
// WebCrypto allows 1..128 counter bits; use the full block to match sync ctr() / Node CTR wrap.
if (algo === mode.CTR) return { name: mode.CTR, counter: nonce, length: 128 };
if (algo === mode.GCM) {
// Rely on the backend default tag length (128 bits) instead of setting it explicitly.
if (AAD) return { name: mode.GCM, iv: nonce, additionalData: AAD };
else return { name: mode.GCM, iv: nonce };
}
throw new Error('unknown aes block mode');
}
function generate(
algo: BlockMode,
nonceLength: number
): TRet<
((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}
> {
anumber(nonceLength);
const res = (
key: TArg<Uint8Array>,
nonce: TArg<Uint8Array>,
AAD?: TArg<Uint8Array>
): TRet<AsyncCipher> => {
abytes(key);
abytes(nonce);
// Reject falsy non-byte AAD locally; otherwise false/0/''/null silently become "no AAD".
if (AAD !== undefined) abytes(AAD, undefined, 'AAD');
// Exact nonce-length enforcement and WebCrypto-specific AAD normalization are
// delegated to the backend; locally we only require byte-array inputs here.
// Keep caller key/nonce/AAD by reference; mutating them after
// construction changes later operations.
const keyParams = { name: algo, length: key.length * 8 };
const cryptParams = getCryptParams(algo, nonce, AAD);
let consumed = false;
return {
// keyLength,
encrypt(plaintext: TArg<Uint8Array>): Promise<TRet<Uint8Array>> {
abytes(plaintext);
if (consumed) throw new Error('Cannot encrypt() twice with same key / nonce');
consumed = true;
return utils.encrypt(key, keyParams, cryptParams, plaintext);
},
decrypt(ciphertext: TArg<Uint8Array>): Promise<TRet<Uint8Array>> {
abytes(ciphertext);
return utils.decrypt(key, keyParams, cryptParams, ciphertext);
},
} as TRet<AsyncCipher>;
};
res.nonceLength = nonceLength;
res.blockSize = 16; // always for AES
return res as TRet<
((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}
>;
}
/**
* AES-CBC implemented with WebCrypto.
* Uses WebCrypto's built-in PKCS padding behavior; exact IV-length checks are
* delegated to the backend instead of local `abytes(..., 16)` validation.
* @param key - AES key bytes.
* @param iv - 16-byte initialization vector.
* @returns Async cipher instance.
* @example
* Encrypts a block with the browser or Node WebCrypto backend.
*
* ```ts
* import { cbc } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const iv = randomBytes(16);
* const cipher = cbc(key, iv);
* await cipher.encrypt(new Uint8Array(16));
* ```
*/
export const cbc: TRet<
((key: TArg<Uint8Array>, iv: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}
> = /* @__PURE__ */ (() => generate(mode.CBC, 16))();
/**
* AES-CTR implemented with WebCrypto.
* Uses WebCrypto's full 128-bit counter-length setting so the whole
* 16-byte counter block is incremented, matching sync `aes.ts:ctr`.
* @param key - AES key bytes.
* @param nonce - 16-byte counter block incremented as a full big-endian AES counter block.
* @returns Async cipher instance.
* @example
* Encrypts a short payload with WebCrypto AES-CTR.
*
* ```ts
* import { ctr } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(16);
* const cipher = ctr(key, nonce);
* await cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const ctr: TRet<
((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}
> = /* @__PURE__ */ (() => generate(mode.CTR, 16))();
/**
* AES-GCM implemented with WebCrypto.
* AAD type normalization and nonce-shape enforcement beyond raw bytes are left
* to the backend WebCrypto implementation.
* @param key - AES key bytes.
* @param nonce - Nonce bytes.
* @param AAD - Additional authenticated data.
* @returns Async cipher instance.
* @example
* Encrypts and authenticates plaintext with WebCrypto AES-GCM.
*
* ```ts
* import { gcm } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(12);
* const cipher = gcm(key, nonce);
* await cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const gcm: TRet<
((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}
> = /* @__PURE__ */ (() => generate(mode.GCM, 12))();
// // Type tests
// import { siv, gcm, ctr, ecb, cbc } from '../aes.ts';
// import { xsalsa20poly1305 } from '../salsa.ts';
// import { chacha20poly1305, xchacha20poly1305 } from '../chacha.ts';
// const wsiv = managedNonce(siv);
// const wgcm = managedNonce(gcm);
// const wctr = managedNonce(ctr);
// const wcbc = managedNonce(cbc);
// const wsalsapoly = managedNonce(xsalsa20poly1305);
// const wchacha = managedNonce(chacha20poly1305);
// const wxchacha = managedNonce(xchacha20poly1305);
// // should fail
// const wcbc2 = managedNonce(managedNonce(cbc));
// const wctr = managedNonce(ctr);
// import { gcm as gcmSync } from '../aes.ts';
// const x1 = managedNonce(gcmSync);
// // const x1: (key: Uint8Array, AAD?: Uint8Array | undefined) => Cipher
// const x2 = managedNonce(gcm);
// // const x2: (key: Uint8Array, AAD?: Uint8Array | undefined) => AsyncCipher

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node_modules/@noble/ciphers/utils.d.ts generated vendored Normal file
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@@ -0,0 +1,717 @@
/**
* Utilities for hex, bytes, CSPRNG.
* @module
*/
/*! noble-ciphers - MIT License (c) 2023 Paul Miller (paulmillr.com) */
/**
* Bytes API type helpers for old + new TypeScript.
*
* TS 5.6 has `Uint8Array`, while TS 5.9+ made it generic `Uint8Array<ArrayBuffer>`.
* We can't use specific return type, because TS 5.6 will error.
* We can't use generic return type, because most TS 5.9 software will expect specific type.
*
* Maps typed-array input leaves to broad forms.
* These are compatibility adapters, not ownership guarantees.
*
* - `TArg` keeps byte inputs broad.
* - `TRet` marks byte outputs for TS 5.6 and TS 5.9+ compatibility.
*/
export type TypedArg<T> = T extends BigInt64Array ? BigInt64Array : T extends BigUint64Array ? BigUint64Array : T extends Float32Array ? Float32Array : T extends Float64Array ? Float64Array : T extends Int16Array ? Int16Array : T extends Int32Array ? Int32Array : T extends Int8Array ? Int8Array : T extends Uint16Array ? Uint16Array : T extends Uint32Array ? Uint32Array : T extends Uint8ClampedArray ? Uint8ClampedArray : T extends Uint8Array ? Uint8Array : never;
/** Maps typed-array output leaves to narrow TS-compatible forms. */
export type TypedRet<T> = T extends BigInt64Array ? ReturnType<typeof BigInt64Array.of> : T extends BigUint64Array ? ReturnType<typeof BigUint64Array.of> : T extends Float32Array ? ReturnType<typeof Float32Array.of> : T extends Float64Array ? ReturnType<typeof Float64Array.of> : T extends Int16Array ? ReturnType<typeof Int16Array.of> : T extends Int32Array ? ReturnType<typeof Int32Array.of> : T extends Int8Array ? ReturnType<typeof Int8Array.of> : T extends Uint16Array ? ReturnType<typeof Uint16Array.of> : T extends Uint32Array ? ReturnType<typeof Uint32Array.of> : T extends Uint8ClampedArray ? ReturnType<typeof Uint8ClampedArray.of> : T extends Uint8Array ? ReturnType<typeof Uint8Array.of> : never;
/** Recursively adapts byte-carrying API input types. See {@link TypedArg}. */
export type TArg<T> = T | ([TypedArg<T>] extends [never] ? T extends (...args: infer A) => infer R ? ((...args: {
[K in keyof A]: TRet<A[K]>;
}) => TArg<R>) & {
[K in keyof T]: T[K] extends (...args: any) => any ? T[K] : TArg<T[K]>;
} : T extends [infer A, ...infer R] ? [TArg<A>, ...{
[K in keyof R]: TArg<R[K]>;
}] : T extends readonly [infer A, ...infer R] ? readonly [TArg<A>, ...{
[K in keyof R]: TArg<R[K]>;
}] : T extends (infer A)[] ? TArg<A>[] : T extends readonly (infer A)[] ? readonly TArg<A>[] : T extends Promise<infer A> ? Promise<TArg<A>> : T extends object ? {
[K in keyof T]: TArg<T[K]>;
} : T : TypedArg<T>);
/** Recursively adapts byte-carrying API output types. See {@link TypedArg}. */
export type TRet<T> = T extends unknown ? T & ([TypedRet<T>] extends [never] ? T extends (...args: infer A) => infer R ? ((...args: {
[K in keyof A]: TArg<A[K]>;
}) => TRet<R>) & {
[K in keyof T]: T[K] extends (...args: any) => any ? T[K] : TRet<T[K]>;
} : T extends [infer A, ...infer R] ? [TRet<A>, ...{
[K in keyof R]: TRet<R[K]>;
}] : T extends readonly [infer A, ...infer R] ? readonly [TRet<A>, ...{
[K in keyof R]: TRet<R[K]>;
}] : T extends (infer A)[] ? TRet<A>[] : T extends readonly (infer A)[] ? readonly TRet<A>[] : T extends Promise<infer A> ? Promise<TRet<A>> : T extends object ? {
[K in keyof T]: TRet<T[K]>;
} : T : TypedRet<T>) : never;
/**
* Checks if something is Uint8Array. Be careful: nodejs Buffer will return true.
* @param a - Value to inspect.
* @returns `true` when the value is a Uint8Array view, including Node's `Buffer`.
* @example
* Guards a value before treating it as raw key material.
*
* ```ts
* isBytes(new Uint8Array());
* ```
*/
export declare function isBytes(a: unknown): a is Uint8Array;
/**
* Asserts something is boolean.
* @param b - Value to validate.
* @throws On wrong argument types. {@link TypeError}
* @example
* Validates a boolean option before branching on it.
*
* ```ts
* abool(true);
* ```
*/
export declare function abool(b: boolean): void;
/**
* Asserts something is a non-negative safe integer.
* @param n - Value to validate.
* @throws On wrong argument types. {@link TypeError}
* @throws On wrong argument ranges or values. {@link RangeError}
* @example
* Validates a non-negative length or counter.
*
* ```ts
* anumber(1);
* ```
*/
export declare function anumber(n: number): void;
/**
* Asserts something is Uint8Array.
* @param value - Value to validate.
* @param length - Expected byte length.
* @param title - Optional label used in error messages.
* @returns The validated byte array.
* On Node, `Buffer` is accepted too because it is a Uint8Array view.
* @throws On wrong argument types. {@link TypeError}
* @throws On wrong argument lengths. {@link RangeError}
* @example
* Validates a fixed-length nonce or key buffer.
*
* ```ts
* abytes(new Uint8Array([1, 2]), 2);
* ```
*/
export declare function abytes(value: TArg<Uint8Array>, length?: number, title?: string): TRet<Uint8Array>;
/**
* Asserts a hash- or MAC-like instance has not been destroyed or finished.
* @param instance - Stateful instance to validate.
* @param checkFinished - Whether to reject finished instances.
* When `false`, only `destroyed` is checked.
* @throws If the hash instance has already been destroyed or finalized. {@link Error}
* @example
* Guards against calling `update()` or `digest()` on a finished hash.
*
* ```ts
* aexists({ destroyed: false, finished: false });
* ```
*/
export declare function aexists(instance: any, checkFinished?: boolean): void;
/**
* Asserts output is a properly-sized byte array.
* @param out - Output buffer to validate.
* @param instance - Hash-like instance providing `outputLen`.
* This is the relaxed `digestInto()`-style contract: output must be at least `outputLen`,
* unlike one-shot cipher helpers elsewhere in the repo that often require exact lengths.
* @throws On wrong argument types. {@link TypeError}
* @param onlyAligned - Whether `out` must be 4-byte aligned for zero-allocation word views.
* @throws On wrong output buffer lengths. {@link RangeError}
* @throws On wrong output buffer alignment. {@link Error}
* @example
* Verifies that a caller-provided output buffer is large enough.
*
* ```ts
* aoutput(new Uint8Array(16), { outputLen: 16 });
* ```
*/
export declare function aoutput(out: any, instance: any, onlyAligned?: boolean): void;
/** One-shot hash helper with `.create()`. */
export type IHash = {
(data: string | TArg<Uint8Array>): TRet<Uint8Array>;
/** Input block size in bytes. */
blockLen: number;
/** Digest size in bytes. */
outputLen: number;
/** Creates a fresh incremental hash instance of the same algorithm. */
create: any;
};
/** One-shot MAC helper with `.create()`. */
export type CMac<H extends IHash2 = IHash2, A extends any[] = []> = {
(msg: TArg<Uint8Array>, key: TArg<Uint8Array>): TRet<Uint8Array>;
/** Input block size in bytes. */
blockLen: number;
/** Digest size in bytes. */
outputLen: number;
/**
* Creates a fresh incremental MAC instance of the same algorithm.
* @param key - MAC key bytes.
* @param args - Additional constructor arguments, when the MAC wrapper needs them.
* @returns Fresh incremental MAC instance.
*/
create(key: TArg<Uint8Array>, ...args: A): H;
};
/** Generic type encompassing 8/16/32-bit typed arrays, but not 64-bit. */
export type TypedArray = Int8Array | Uint8ClampedArray | Uint8Array | Uint16Array | Int16Array | Uint32Array | Int32Array;
/**
* Casts a typed-array view to Uint8Array.
* @param arr - Typed-array view to reinterpret.
* @returns Uint8Array view over the same bytes.
* @example
* Views 32-bit words as raw bytes without copying.
*
* ```ts
* u8(new Uint32Array([1]));
* ```
*/
export declare function u8(arr: TArg<TypedArray>): TRet<Uint8Array>;
/**
* Casts a typed-array view to Uint32Array.
* @param arr - Typed-array view to reinterpret.
* @returns Uint32Array view over the same bytes. Callers are expected to provide a
* 4-byte-aligned offset; trailing `1..3` bytes are silently dropped.
* @example
* Views a byte buffer as 32-bit words for block processing.
*
* ```ts
* u32(new Uint8Array(4));
* ```
*/
export declare function u32(arr: TArg<TypedArray>): TRet<Uint32Array>;
/**
* Zeroizes typed arrays in place.
* Warning: JS provides no guarantees.
* @param arrays - Arrays to wipe.
* @example
* Wipes a temporary key buffer after use.
*
* ```ts
* const bytes = new Uint8Array([1]);
* clean(bytes);
* ```
*/
export declare function clean(...arrays: TArg<TypedArray[]>): void;
/**
* Creates a DataView for byte-level manipulation.
* @param arr - Typed-array view to wrap.
* @returns DataView over the same bytes.
* @example
* Creates an endian-aware view for length encoding.
*
* ```ts
* createView(new Uint8Array(4));
* ```
*/
export declare function createView(arr: TArg<TypedArray>): DataView;
/**
* Whether the current platform is little-endian.
* Most are; some IBM systems are not.
*/
export declare const isLE: boolean;
/**
* Reverses byte order of one 32-bit word.
* @param word - Unsigned 32-bit word to swap.
* @returns The same word with bytes reversed.
* @example
* Swaps a big-endian word into little-endian byte order.
*
* ```ts
* byteSwap(0x11223344);
* ```
*/
export declare const byteSwap: (word: number) => number;
/**
* Normalizes one 32-bit word to the little-endian representation expected by cipher cores.
* @param n - Unsigned 32-bit word to normalize.
* @returns Little-endian normalized word on big-endian hosts, else the input word unchanged.
* @example
* Normalizes a host-endian word before passing it into an ARX/AES core.
*
* ```ts
* swap8IfBE(0x11223344);
* ```
*/
export declare const swap8IfBE: (n: number) => number;
/**
* Byte-swaps every word of a Uint32Array in place.
* @param arr - Uint32Array whose words should be swapped.
* @returns The same array after in-place byte swapping.
* @example
* Swaps every 32-bit word in a word-view buffer.
*
* ```ts
* byteSwap32(new Uint32Array([0x11223344]));
* ```
*/
export declare const byteSwap32: (arr: TArg<Uint32Array>) => TRet<Uint32Array>;
/**
* Normalizes a Uint32Array view to the little-endian representation expected by cipher cores.
* @param u - Word view to normalize in place.
* @returns Little-endian normalized word view.
* @example
* Normalizes a word-view buffer before block processing.
*
* ```ts
* swap32IfBE(new Uint32Array([0x11223344]));
* ```
*/
export declare const swap32IfBE: (u: TArg<Uint32Array>) => TRet<Uint32Array>;
/**
* Convert byte array to hex string. Uses built-in function, when available.
* @param bytes - Bytes to encode.
* @returns Lowercase hexadecimal string.
* @throws On wrong argument types. {@link TypeError}
* @example
* Formats ciphertext bytes for logs or test vectors.
*
* ```ts
* bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])); // 'cafe0123'
* ```
*/
export declare function bytesToHex(bytes: TArg<Uint8Array>): string;
/**
* Convert hex string to byte array. Uses built-in function, when available.
* @param hex - Hexadecimal string to decode.
* @returns Decoded bytes.
* @throws On wrong argument types. {@link TypeError}
* @throws On malformed hexadecimal input. {@link RangeError}
* @example
* Parses a hex test vector into bytes.
*
* ```ts
* hexToBytes('cafe0123'); // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])
* ```
*/
export declare function hexToBytes(hex: string): TRet<Uint8Array>;
/**
* Converts a big-endian hex string into bigint.
* @param hex - Hexadecimal string without `0x`.
* @returns Parsed bigint value. The empty string is treated as `0n`.
* @throws On wrong argument types. {@link TypeError}
* @example
* Parses a big-endian field element or counter from hex.
*
* ```ts
* hexToNumber('ff');
* ```
*/
export declare function hexToNumber(hex: string): bigint;
/**
* Converts big-endian bytes into bigint.
* @param bytes - Big-endian bytes.
* @returns Parsed bigint value. Empty input is treated as `0n`.
* @throws On invalid byte input passed to the internal hex conversion. {@link TypeError}
* @example
* Reads a big-endian integer from serialized bytes.
*
* ```ts
* bytesToNumberBE(new Uint8Array([1, 0]));
* ```
*/
export declare function bytesToNumberBE(bytes: TArg<Uint8Array>): bigint;
/**
* Converts a number into big-endian bytes of fixed length.
* @param n - Number to encode.
* @param len - Output length in bytes.
* @returns Big-endian bytes padded to `len`.
* Validation is indirect through `hexToBytes(...)`, so negative values, `len = 0`,
* and values that do not fit surface through the downstream hex parser instead of a
* dedicated range guard here.
* @throws On wrong argument types. {@link TypeError}
* @throws If the requested output length cannot represent the encoded value. {@link RangeError}
* @example
* Encodes a counter as fixed-width big-endian bytes.
*
* ```ts
* numberToBytesBE(1, 2);
* ```
*/
export declare function numberToBytesBE(n: number | bigint, len: number): TRet<Uint8Array>;
/**
* Converts string to bytes using UTF8 encoding.
* @param str - String to encode.
* @returns UTF-8 bytes in a detached fresh Uint8Array copy.
* @throws On wrong argument types. {@link TypeError}
* @example
* Encodes application text before encryption or MACing.
*
* ```ts
* utf8ToBytes('abc'); // new Uint8Array([97, 98, 99])
* ```
*/
export declare function utf8ToBytes(str: string): TRet<Uint8Array>;
/**
* Converts bytes to string using UTF8 encoding.
* @param bytes - UTF-8 bytes.
* @returns Decoded string. Input validation is delegated to `TextDecoder`, and malformed
* UTF-8 is replacement-decoded instead of rejected.
* @example
* Decodes UTF-8 plaintext back into a string.
*
* ```ts
* bytesToUtf8(new Uint8Array([97, 98, 99])); // 'abc'
* ```
*/
export declare function bytesToUtf8(bytes: TArg<Uint8Array>): string;
/**
* Checks if two U8A use same underlying buffer and overlaps.
* This is invalid and can corrupt data.
* @param a - First byte view.
* @param b - Second byte view.
* @returns `true` when the views overlap in memory.
* @example
* Detects whether two slices alias the same backing buffer.
*
* ```ts
* overlapBytes(new Uint8Array(4), new Uint8Array(4));
* ```
*/
export declare function overlapBytes(a: TArg<Uint8Array>, b: TArg<Uint8Array>): boolean;
/**
* If input and output overlap and input starts before output, we will overwrite end of input before
* we start processing it, so this is not supported for most ciphers
* (except chacha/salsa, which were designed for this)
* @param input - Input bytes.
* @param output - Output bytes.
* @throws If the output view would overwrite unread input bytes. {@link Error}
* @example
* Rejects an in-place layout that would overwrite unread input bytes.
*
* ```ts
* complexOverlapBytes(new Uint8Array(4), new Uint8Array(4));
* ```
*/
export declare function complexOverlapBytes(input: TArg<Uint8Array>, output: TArg<Uint8Array>): void;
/**
* Copies several Uint8Arrays into one.
* @param arrays - Byte arrays to concatenate.
* @returns Combined byte array.
* @throws On wrong argument types inside the byte-array list. {@link TypeError}
* @example
* Builds a `nonce || ciphertext` style buffer.
*
* ```ts
* concatBytes(new Uint8Array([1]), new Uint8Array([2]));
* ```
*/
export declare function concatBytes(...arrays: TArg<Uint8Array[]>): TRet<Uint8Array>;
type EmptyObj = {};
/**
* Merges user options into defaults.
* @param defaults - Default option values.
* @param opts - User-provided overrides.
* @returns Combined options object.
* The merge mutates `defaults` in place and returns the same object.
* @throws If options are missing or not an object. {@link Error}
* @example
* Applies user overrides to the default cipher options.
*
* ```ts
* checkOpts({ rounds: 20 }, { rounds: 8 });
* ```
*/
export declare function checkOpts<T1 extends EmptyObj, T2 extends EmptyObj>(defaults: T1, opts: T2): T1 & T2;
/**
* Compares two byte arrays in kinda constant time once lengths already match.
* @param a - First byte array.
* @param b - Second byte array.
* @returns `true` when the arrays contain the same bytes. Different lengths still return early.
* @example
* Compares an expected authentication tag with the received one.
*
* ```ts
* equalBytes(new Uint8Array([1]), new Uint8Array([1]));
* ```
*/
export declare function equalBytes(a: TArg<Uint8Array>, b: TArg<Uint8Array>): boolean;
/** Incremental hash interface used internally. */
export interface IHash2 {
/** Bytes processed per compression block. */
blockLen: number;
/** Bytes produced by the final digest. */
outputLen: number;
/**
* Absorbs one more chunk into the hash state.
* @param buf - Data chunk to hash.
* @returns The same hash instance for chaining.
*/
update(buf: string | TArg<Uint8Array>): this;
/**
* Writes the final digest into a caller-provided buffer.
* @param buf - Destination buffer for the digest bytes.
* @returns Nothing. Implementations write into `buf` in place.
*/
digestInto(buf: TArg<Uint8Array>): void;
/**
* Finalizes the hash and returns a fresh digest buffer.
* @returns Digest bytes.
*/
digest(): TRet<Uint8Array>;
/**
* Resets internal state. Makes Hash instance unusable.
* Reset is impossible for keyed hashes if key is consumed into state. If digest is not consumed
* by user, they will need to manually call `destroy()` when zeroing is necessary.
*/
destroy(): void;
}
/**
* Wraps a keyed MAC constructor into a one-shot helper with `.create()`.
* @param keyLen - Valid probe-key length used to read static metadata once.
* The probe key is only used for `outputLen` / `blockLen`, so callers with several valid key sizes
* can pass any representative size as long as those values stay fixed.
* @param macCons - Keyed MAC constructor or factory.
* @param fromMsg - Optional adapter that derives extra constructor args from the one-shot message.
* @returns Callable MAC helper with `.create()`.
*/
export declare function wrapMacConstructor<H extends IHash2, A extends any[] = []>(keyLen: number, macCons: TArg<(key: Uint8Array, ...args: A) => H>, fromMsg?: TArg<(msg: Uint8Array) => A>): TRet<CMac<H, A>>;
/** Sync cipher: takes byte array and returns byte array. */
export type Cipher = {
/**
* Encrypts plaintext bytes.
* @param plaintext - Data to encrypt.
* @returns Ciphertext bytes.
*/
encrypt(plaintext: TArg<Uint8Array>): TRet<Uint8Array>;
/**
* Decrypts ciphertext bytes.
* @param ciphertext - Data to decrypt.
* @returns Plaintext bytes.
*/
decrypt(ciphertext: TArg<Uint8Array>): TRet<Uint8Array>;
};
/** Async cipher e.g. from built-in WebCrypto. */
export type AsyncCipher = {
/**
* Encrypts plaintext bytes.
* @param plaintext - Data to encrypt.
* @returns Promise resolving to ciphertext bytes.
*/
encrypt(plaintext: TArg<Uint8Array>): Promise<TRet<Uint8Array>>;
/**
* Decrypts ciphertext bytes.
* @param ciphertext - Data to decrypt.
* @returns Promise resolving to plaintext bytes.
*/
decrypt(ciphertext: TArg<Uint8Array>): Promise<TRet<Uint8Array>>;
};
/** Cipher with `output` argument which can optimize by doing 1 less allocation. */
export type CipherWithOutput = Cipher & {
/**
* Encrypts plaintext bytes into an optional caller-provided buffer.
* @param plaintext - Data to encrypt.
* @param output - Optional destination buffer.
* @returns Ciphertext bytes.
*/
encrypt(plaintext: TArg<Uint8Array>, output?: TArg<Uint8Array>): TRet<Uint8Array>;
/**
* Decrypts ciphertext bytes into an optional caller-provided buffer.
* @param ciphertext - Data to decrypt.
* @param output - Optional destination buffer.
* @returns Plaintext bytes.
*/
decrypt(ciphertext: TArg<Uint8Array>, output?: TArg<Uint8Array>): TRet<Uint8Array>;
};
/**
* Params are outside of return type, so it is accessible before calling constructor.
* If function support multiple nonceLength's, we return the best one.
*/
export type CipherParams = {
/** Cipher block size in bytes. */
blockSize: number;
/** Nonce length in bytes when the cipher uses a fixed nonce size. */
nonceLength?: number;
/** Authentication-tag length in bytes for AEAD modes. */
tagLength?: number;
/** Whether nonce length is variable at runtime. */
varSizeNonce?: boolean;
};
/**
* ARX AEAD cipher, like salsa or chacha.
* @param key - Secret key bytes.
* @param nonce - Nonce bytes.
* @param AAD - Optional associated data.
* @returns Cipher instance with caller-managed output buffers.
*/
export type ARXCipher = ((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => CipherWithOutput) & {
blockSize: number;
nonceLength: number;
tagLength: number;
};
/**
* Cipher constructor signature.
* @param key - Secret key bytes.
* @param args - Additional constructor arguments, such as nonce or IV.
* @returns Cipher instance.
*/
export type CipherCons<T extends any[]> = (key: TArg<Uint8Array>, ...args: T) => Cipher;
/**
* Wraps a cipher: validates args, ensures encrypt() can only be called once.
* Used internally by the exported cipher constructors.
* Output-buffer support is inferred from the wrapped `encrypt` / `decrypt`
* arity (`fn.length === 2`), and tag-bearing constructors are expected to use
* `args[1]` for optional AAD.
* @__NO_SIDE_EFFECTS__
* @param params - Static cipher metadata. See {@link CipherParams}.
* @param constructor - Cipher constructor.
* @returns Wrapped constructor with validation.
*/
export declare const wrapCipher: <C extends CipherCons<any>, P extends CipherParams>(params: P, constructor: C) => C & P;
/**
* Represents a Salsa or ChaCha xor stream.
* @param key - Secret key bytes.
* @param nonce - Nonce bytes.
* @param data - Input bytes to xor with the keystream.
* @param output - Optional destination buffer.
* @param counter - Optional starting block counter.
* @returns Output bytes.
*/
export type XorStream = (key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, data: TArg<Uint8Array>, output?: TArg<Uint8Array>, counter?: number) => TRet<Uint8Array>;
/**
* By default, returns u8a of length.
* When out is available, it checks it for validity and uses it.
* @param expectedLength - Required output length.
* @param out - Optional destination buffer.
* @param onlyAligned - Whether `out` must be 4-byte aligned.
* @returns Output buffer ready for writing.
* @throws On wrong argument types. {@link TypeError}
* @throws If the provided output buffer has the wrong size or alignment. {@link Error}
* @example
* Reuses a caller-provided output buffer when lengths match.
*
* ```ts
* getOutput(16, new Uint8Array(16));
* ```
*/
export declare function getOutput(expectedLength: number, out?: TArg<Uint8Array>, onlyAligned?: boolean): TRet<Uint8Array>;
/**
* Encodes data and AAD bit lengths into a 16-byte buffer.
* @param dataLength - Data length in bits.
* @param aadLength - AAD length in bits.
* The serialized block is still `aadLength || dataLength`, matching GCM/Poly1305
* conventions even though the helper parameter order is `(dataLength, aadLength)`.
* @param isLE - Whether to encode lengths as little-endian.
* @returns 16-byte length block.
* @throws On wrong argument types passed to the endian validator. {@link TypeError}
* @throws On wrong argument ranges or values. {@link RangeError}
* @example
* Builds the length block appended by GCM and Poly1305.
*
* ```ts
* u64Lengths(16, 8, true);
* ```
*/
export declare function u64Lengths(dataLength: number, aadLength: number, isLE: boolean): TRet<Uint8Array>;
/**
* Checks whether a byte array is aligned to a 4-byte offset.
* @param bytes - Byte array to inspect.
* @returns `true` when the view is 4-byte aligned.
* @example
* Checks whether a buffer can be safely viewed as Uint32Array.
*
* ```ts
* isAligned32(new Uint8Array(4));
* ```
*/
export declare function isAligned32(bytes: TArg<Uint8Array>): boolean;
/**
* Copies bytes into a new Uint8Array.
* @param bytes - Bytes to copy.
* @returns Copied byte array.
* @throws On wrong argument types. {@link TypeError}
* @example
* Copies input into an aligned Uint8Array before block processing.
*
* ```ts
* copyBytes(new Uint8Array([1, 2]));
* ```
*/
export declare function copyBytes(bytes: TArg<Uint8Array>): TRet<Uint8Array>;
/**
* Cryptographically secure PRNG.
* Uses internal OS-level `crypto.getRandomValues`.
* @param bytesLength - Number of bytes to produce.
* Validation is delegated to `Uint8Array(bytesLength)` and `getRandomValues`, so
* non-integers, negative lengths, and oversize requests surface backend/runtime errors.
* @returns Random byte array.
* @throws On wrong argument types. {@link TypeError}
* @throws On wrong argument ranges or values. {@link RangeError}
* @throws If the runtime does not expose `crypto.getRandomValues`. {@link Error}
* @example
* Generates a fresh nonce or key.
*
* ```ts
* randomBytes(16);
* ```
*/
export declare function randomBytes(bytesLength?: number): TRet<Uint8Array>;
/**
* The pseudorandom number generator doesn't wipe current state:
* instead, it generates new one based on previous state + entropy.
* Not reseed/rekey, since AES CTR DRBG does rekey on each randomBytes,
* which is in fact `reseed`, since it changes counter too.
*/
export interface PRG {
/**
* Mixes fresh entropy into the current generator state.
* @param seed - Entropy bytes to absorb.
*/
addEntropy(seed: TArg<Uint8Array>): void;
/**
* Produces a requested number of pseudorandom bytes.
* @param bytesLength - Number of bytes to generate.
* @returns Random byte array.
*/
randomBytes(bytesLength: number): TRet<Uint8Array>;
/** Destroys the generator state. */
clean(): void;
}
/** Removes the nonce argument from a cipher constructor type. */
export type RemoveNonce<T extends (...args: any) => any> = T extends (arg0: any, arg1: any, ...rest: infer R) => infer Ret ? (key: TArg<Uint8Array>, ...args: R) => Ret : never;
/**
* Cipher constructor that requires a nonce argument.
* @param key - Secret key bytes.
* @param nonce - Nonce bytes.
* @param args - Additional cipher-specific arguments.
* @returns Cipher instance.
*/
export type CipherWithNonce = ((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, ...args: any[]) => Cipher | AsyncCipher) & {
nonceLength: number;
};
/**
* Uses CSPRNG for nonce, nonce injected in ciphertext.
* For `encrypt`, a `nonceBytes`-length buffer is fetched from CSPRNG and
* prepended to encrypted ciphertext. For `decrypt`, first `nonceBytes` of ciphertext
* are treated as nonce. The wrapper always allocates a fresh `nonce || ciphertext`
* buffer on encrypt and intentionally does not support caller-provided destination buffers.
* Too-short decrypt inputs are split into short/empty nonce views and then delegated
* to the wrapped cipher instead of being rejected here first.
*
* NOTE: Under the same key, using random nonces (e.g. `managedNonce`) with AES-GCM and ChaCha
* should be limited to `2**23` (8M) messages to get a collision chance of
* `2**-50`. Stretching to `2**32` (4B) messages would raise that chance to
* `2**-33`, still negligible but creeping up.
* @param fn - Cipher constructor that expects a nonce.
* @param randomBytes_ - Random-byte source used for nonce generation.
* @returns Cipher constructor that prepends the nonce to ciphertext.
* @throws On wrong argument types. {@link TypeError}
* @throws On invalid nonce lengths observed at wrapper construction or use. {@link RangeError}
* @example
* Prepends a fresh random nonce to every ciphertext.
*
* ```ts
* import { gcm } from '@noble/ciphers/aes.js';
* import { managedNonce, randomBytes } from '@noble/ciphers/utils.js';
* const wrapped = managedNonce(gcm);
* const key = randomBytes(16);
* const ciphertext = wrapped(key).encrypt(new Uint8Array([1, 2, 3]));
* wrapped(key).decrypt(ciphertext);
* ```
*/
export declare function managedNonce<T extends CipherWithNonce>(fn: T, randomBytes_?: typeof randomBytes): TRet<RemoveNonce<T>>;
/** `Uint8Array.of()` return type helper for TS 5.9. */
export type Uint8ArrayBuffer = TRet<Uint8Array>;
export {};
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/**
* Utilities for hex, bytes, CSPRNG.
* @module
*/
/*! noble-ciphers - MIT License (c) 2023 Paul Miller (paulmillr.com) */
/**
* Checks if something is Uint8Array. Be careful: nodejs Buffer will return true.
* @param a - Value to inspect.
* @returns `true` when the value is a Uint8Array view, including Node's `Buffer`.
* @example
* Guards a value before treating it as raw key material.
*
* ```ts
* isBytes(new Uint8Array());
* ```
*/
export function isBytes(a) {
// Plain `instanceof Uint8Array` is too strict for some Buffer / proxy /
// cross-realm cases. The fallback still requires a real ArrayBuffer view
// so plain JSON-deserialized `{ constructor: ... }`
// spoofing is rejected, and `BYTES_PER_ELEMENT === 1` keeps the fallback on byte-oriented views.
return (a instanceof Uint8Array ||
(ArrayBuffer.isView(a) &&
a.constructor.name === 'Uint8Array' &&
'BYTES_PER_ELEMENT' in a &&
a.BYTES_PER_ELEMENT === 1));
}
/**
* Asserts something is boolean.
* @param b - Value to validate.
* @throws On wrong argument types. {@link TypeError}
* @example
* Validates a boolean option before branching on it.
*
* ```ts
* abool(true);
* ```
*/
export function abool(b) {
if (typeof b !== 'boolean')
throw new TypeError(`boolean expected, not ${b}`);
}
/**
* Asserts something is a non-negative safe integer.
* @param n - Value to validate.
* @throws On wrong argument types. {@link TypeError}
* @throws On wrong argument ranges or values. {@link RangeError}
* @example
* Validates a non-negative length or counter.
*
* ```ts
* anumber(1);
* ```
*/
export function anumber(n) {
if (typeof n !== 'number')
throw new TypeError('number expected, got ' + typeof n);
if (!Number.isSafeInteger(n) || n < 0)
throw new RangeError('positive integer expected, got ' + n);
}
/**
* Asserts something is Uint8Array.
* @param value - Value to validate.
* @param length - Expected byte length.
* @param title - Optional label used in error messages.
* @returns The validated byte array.
* On Node, `Buffer` is accepted too because it is a Uint8Array view.
* @throws On wrong argument types. {@link TypeError}
* @throws On wrong argument lengths. {@link RangeError}
* @example
* Validates a fixed-length nonce or key buffer.
*
* ```ts
* abytes(new Uint8Array([1, 2]), 2);
* ```
*/
export function abytes(value, length, title = '') {
const bytes = isBytes(value);
const len = value?.length;
const needsLen = length !== undefined;
if (!bytes || (needsLen && len !== length)) {
const prefix = title && `"${title}" `;
const ofLen = needsLen ? ` of length ${length}` : '';
const got = bytes ? `length=${len}` : `type=${typeof value}`;
const message = prefix + 'expected Uint8Array' + ofLen + ', got ' + got;
if (!bytes)
throw new TypeError(message);
throw new RangeError(message);
}
return value;
}
/**
* Asserts a hash- or MAC-like instance has not been destroyed or finished.
* @param instance - Stateful instance to validate.
* @param checkFinished - Whether to reject finished instances.
* When `false`, only `destroyed` is checked.
* @throws If the hash instance has already been destroyed or finalized. {@link Error}
* @example
* Guards against calling `update()` or `digest()` on a finished hash.
*
* ```ts
* aexists({ destroyed: false, finished: false });
* ```
*/
export function aexists(instance, checkFinished = true) {
if (instance.destroyed)
throw new Error('Hash instance has been destroyed');
if (checkFinished && instance.finished)
throw new Error('Hash#digest() has already been called');
}
/**
* Asserts output is a properly-sized byte array.
* @param out - Output buffer to validate.
* @param instance - Hash-like instance providing `outputLen`.
* This is the relaxed `digestInto()`-style contract: output must be at least `outputLen`,
* unlike one-shot cipher helpers elsewhere in the repo that often require exact lengths.
* @throws On wrong argument types. {@link TypeError}
* @param onlyAligned - Whether `out` must be 4-byte aligned for zero-allocation word views.
* @throws On wrong output buffer lengths. {@link RangeError}
* @throws On wrong output buffer alignment. {@link Error}
* @example
* Verifies that a caller-provided output buffer is large enough.
*
* ```ts
* aoutput(new Uint8Array(16), { outputLen: 16 });
* ```
*/
export function aoutput(out, instance, onlyAligned = false) {
abytes(out, undefined, 'output');
const min = instance.outputLen;
if (out.length < min) {
throw new RangeError('digestInto() expects output buffer of length at least ' + min);
}
if (onlyAligned && !isAligned32(out))
throw new Error('invalid output, must be aligned');
}
/**
* Casts a typed-array view to Uint8Array.
* @param arr - Typed-array view to reinterpret.
* @returns Uint8Array view over the same bytes.
* @example
* Views 32-bit words as raw bytes without copying.
*
* ```ts
* u8(new Uint32Array([1]));
* ```
*/
export function u8(arr) {
return new Uint8Array(arr.buffer, arr.byteOffset, arr.byteLength);
}
/**
* Casts a typed-array view to Uint32Array.
* @param arr - Typed-array view to reinterpret.
* @returns Uint32Array view over the same bytes. Callers are expected to provide a
* 4-byte-aligned offset; trailing `1..3` bytes are silently dropped.
* @example
* Views a byte buffer as 32-bit words for block processing.
*
* ```ts
* u32(new Uint8Array(4));
* ```
*/
export function u32(arr) {
return new Uint32Array(arr.buffer, arr.byteOffset, Math.floor(arr.byteLength / 4));
}
/**
* Zeroizes typed arrays in place.
* Warning: JS provides no guarantees.
* @param arrays - Arrays to wipe.
* @example
* Wipes a temporary key buffer after use.
*
* ```ts
* const bytes = new Uint8Array([1]);
* clean(bytes);
* ```
*/
export function clean(...arrays) {
for (let i = 0; i < arrays.length; i++) {
arrays[i].fill(0);
}
}
/**
* Creates a DataView for byte-level manipulation.
* @param arr - Typed-array view to wrap.
* @returns DataView over the same bytes.
* @example
* Creates an endian-aware view for length encoding.
*
* ```ts
* createView(new Uint8Array(4));
* ```
*/
export function createView(arr) {
return new DataView(arr.buffer, arr.byteOffset, arr.byteLength);
}
/**
* Whether the current platform is little-endian.
* Most are; some IBM systems are not.
*/
export const isLE = /* @__PURE__ */ (() => new Uint8Array(new Uint32Array([0x11223344]).buffer)[0] === 0x44)();
/**
* Reverses byte order of one 32-bit word.
* @param word - Unsigned 32-bit word to swap.
* @returns The same word with bytes reversed.
* @example
* Swaps a big-endian word into little-endian byte order.
*
* ```ts
* byteSwap(0x11223344);
* ```
*/
export const byteSwap = (word) => ((word << 24) & 0xff000000) |
((word << 8) & 0xff0000) |
((word >>> 8) & 0xff00) |
((word >>> 24) & 0xff);
/**
* Normalizes one 32-bit word to the little-endian representation expected by cipher cores.
* @param n - Unsigned 32-bit word to normalize.
* @returns Little-endian normalized word on big-endian hosts, else the input word unchanged.
* @example
* Normalizes a host-endian word before passing it into an ARX/AES core.
*
* ```ts
* swap8IfBE(0x11223344);
* ```
*/
export const swap8IfBE = isLE
? (n) => n
: (n) => byteSwap(n) >>> 0;
/**
* Byte-swaps every word of a Uint32Array in place.
* @param arr - Uint32Array whose words should be swapped.
* @returns The same array after in-place byte swapping.
* @example
* Swaps every 32-bit word in a word-view buffer.
*
* ```ts
* byteSwap32(new Uint32Array([0x11223344]));
* ```
*/
export const byteSwap32 = (arr) => {
for (let i = 0; i < arr.length; i++)
arr[i] = byteSwap(arr[i]);
return arr;
};
/**
* Normalizes a Uint32Array view to the little-endian representation expected by cipher cores.
* @param u - Word view to normalize in place.
* @returns Little-endian normalized word view.
* @example
* Normalizes a word-view buffer before block processing.
*
* ```ts
* swap32IfBE(new Uint32Array([0x11223344]));
* ```
*/
export const swap32IfBE = isLE
? (u) => u
: byteSwap32;
// Built-in hex conversion:
// {@link https://caniuse.com/mdn-javascript_builtins_uint8array_fromhex | caniuse entry}
const hasHexBuiltin = /* @__PURE__ */ (() =>
// @ts-ignore
typeof Uint8Array.from([]).toHex === 'function' && typeof Uint8Array.fromHex === 'function')();
// Array where index 0xf0 (240) is mapped to string 'f0'
const hexes = /* @__PURE__ */ Array.from({ length: 256 }, (_, i) => i.toString(16).padStart(2, '0'));
/**
* Convert byte array to hex string. Uses built-in function, when available.
* @param bytes - Bytes to encode.
* @returns Lowercase hexadecimal string.
* @throws On wrong argument types. {@link TypeError}
* @example
* Formats ciphertext bytes for logs or test vectors.
*
* ```ts
* bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])); // 'cafe0123'
* ```
*/
export function bytesToHex(bytes) {
abytes(bytes);
// @ts-ignore
if (hasHexBuiltin)
return bytes.toHex();
// pre-caching improves the speed 6x
let hex = '';
for (let i = 0; i < bytes.length; i++) {
hex += hexes[bytes[i]];
}
return hex;
}
// We use optimized technique to convert hex string to byte array
const asciis = { _0: 48, _9: 57, A: 65, F: 70, a: 97, f: 102 };
function asciiToBase16(ch) {
if (ch >= asciis._0 && ch <= asciis._9)
return ch - asciis._0; // '2' => 50-48
if (ch >= asciis.A && ch <= asciis.F)
return ch - (asciis.A - 10); // 'B' => 66-(65-10)
if (ch >= asciis.a && ch <= asciis.f)
return ch - (asciis.a - 10); // 'b' => 98-(97-10)
return;
}
/**
* Convert hex string to byte array. Uses built-in function, when available.
* @param hex - Hexadecimal string to decode.
* @returns Decoded bytes.
* @throws On wrong argument types. {@link TypeError}
* @throws On malformed hexadecimal input. {@link RangeError}
* @example
* Parses a hex test vector into bytes.
*
* ```ts
* hexToBytes('cafe0123'); // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])
* ```
*/
export function hexToBytes(hex) {
if (typeof hex !== 'string')
throw new TypeError('hex string expected, got ' + typeof hex);
if (hasHexBuiltin) {
try {
return Uint8Array.fromHex(hex);
}
catch (error) {
if (error instanceof SyntaxError)
throw new RangeError(error.message);
throw error;
}
}
const hl = hex.length;
const al = hl / 2;
if (hl % 2)
throw new RangeError('hex string expected, got unpadded hex of length ' + hl);
const array = new Uint8Array(al);
for (let ai = 0, hi = 0; ai < al; ai++, hi += 2) {
const n1 = asciiToBase16(hex.charCodeAt(hi));
const n2 = asciiToBase16(hex.charCodeAt(hi + 1));
if (n1 === undefined || n2 === undefined) {
const char = hex[hi] + hex[hi + 1];
throw new RangeError('hex string expected, got non-hex character "' + char + '" at index ' + hi);
}
array[ai] = n1 * 16 + n2; // multiply first octet, e.g. 'a3' => 10*16+3 => 160 + 3 => 163
}
return array;
}
// Used in micro
/**
* Converts a big-endian hex string into bigint.
* @param hex - Hexadecimal string without `0x`.
* @returns Parsed bigint value. The empty string is treated as `0n`.
* @throws On wrong argument types. {@link TypeError}
* @example
* Parses a big-endian field element or counter from hex.
*
* ```ts
* hexToNumber('ff');
* ```
*/
export function hexToNumber(hex) {
if (typeof hex !== 'string')
throw new TypeError('hex string expected, got ' + typeof hex);
return BigInt(hex === '' ? '0' : '0x' + hex); // Big Endian
}
// Used in ff1
// BE: Big Endian, LE: Little Endian
/**
* Converts big-endian bytes into bigint.
* @param bytes - Big-endian bytes.
* @returns Parsed bigint value. Empty input is treated as `0n`.
* @throws On invalid byte input passed to the internal hex conversion. {@link TypeError}
* @example
* Reads a big-endian integer from serialized bytes.
*
* ```ts
* bytesToNumberBE(new Uint8Array([1, 0]));
* ```
*/
export function bytesToNumberBE(bytes) {
return hexToNumber(bytesToHex(bytes));
}
// Used in micro, ff1
/**
* Converts a number into big-endian bytes of fixed length.
* @param n - Number to encode.
* @param len - Output length in bytes.
* @returns Big-endian bytes padded to `len`.
* Validation is indirect through `hexToBytes(...)`, so negative values, `len = 0`,
* and values that do not fit surface through the downstream hex parser instead of a
* dedicated range guard here.
* @throws On wrong argument types. {@link TypeError}
* @throws If the requested output length cannot represent the encoded value. {@link RangeError}
* @example
* Encodes a counter as fixed-width big-endian bytes.
*
* ```ts
* numberToBytesBE(1, 2);
* ```
*/
export function numberToBytesBE(n, len) {
// Reject coercible non-numeric inputs before string/hex conversion changes behavior.
if (typeof n === 'number')
anumber(n);
else if (typeof n !== 'bigint')
throw new TypeError(`number or bigint expected, got ${typeof n}`);
anumber(len);
return hexToBytes(n.toString(16).padStart(len * 2, '0'));
}
/**
* Converts string to bytes using UTF8 encoding.
* @param str - String to encode.
* @returns UTF-8 bytes in a detached fresh Uint8Array copy.
* @throws On wrong argument types. {@link TypeError}
* @example
* Encodes application text before encryption or MACing.
*
* ```ts
* utf8ToBytes('abc'); // new Uint8Array([97, 98, 99])
* ```
*/
export function utf8ToBytes(str) {
if (typeof str !== 'string')
throw new TypeError('string expected');
return new Uint8Array(new TextEncoder().encode(str)); // {@link https://bugzil.la/1681809 | Firefox bug 1681809}
}
/**
* Converts bytes to string using UTF8 encoding.
* @param bytes - UTF-8 bytes.
* @returns Decoded string. Input validation is delegated to `TextDecoder`, and malformed
* UTF-8 is replacement-decoded instead of rejected.
* @example
* Decodes UTF-8 plaintext back into a string.
*
* ```ts
* bytesToUtf8(new Uint8Array([97, 98, 99])); // 'abc'
* ```
*/
export function bytesToUtf8(bytes) {
return new TextDecoder().decode(bytes);
}
/**
* Checks if two U8A use same underlying buffer and overlaps.
* This is invalid and can corrupt data.
* @param a - First byte view.
* @param b - Second byte view.
* @returns `true` when the views overlap in memory.
* @example
* Detects whether two slices alias the same backing buffer.
*
* ```ts
* overlapBytes(new Uint8Array(4), new Uint8Array(4));
* ```
*/
export function overlapBytes(a, b) {
// Zero-length views cannot overwrite anything, even if their offset sits inside another range.
if (!a.byteLength || !b.byteLength)
return false;
return (a.buffer === b.buffer && // best we can do, may fail with an obscure Proxy
a.byteOffset < b.byteOffset + b.byteLength && // a starts before b end
b.byteOffset < a.byteOffset + a.byteLength // b starts before a end
);
}
/**
* If input and output overlap and input starts before output, we will overwrite end of input before
* we start processing it, so this is not supported for most ciphers
* (except chacha/salsa, which were designed for this)
* @param input - Input bytes.
* @param output - Output bytes.
* @throws If the output view would overwrite unread input bytes. {@link Error}
* @example
* Rejects an in-place layout that would overwrite unread input bytes.
*
* ```ts
* complexOverlapBytes(new Uint8Array(4), new Uint8Array(4));
* ```
*/
export function complexOverlapBytes(input, output) {
// This is very cursed. It works somehow, but I'm completely unsure,
// reasoning about overlapping aligned windows is very hard.
if (overlapBytes(input, output) && input.byteOffset < output.byteOffset)
throw new Error('complex overlap of input and output is not supported');
}
/**
* Copies several Uint8Arrays into one.
* @param arrays - Byte arrays to concatenate.
* @returns Combined byte array.
* @throws On wrong argument types inside the byte-array list. {@link TypeError}
* @example
* Builds a `nonce || ciphertext` style buffer.
*
* ```ts
* concatBytes(new Uint8Array([1]), new Uint8Array([2]));
* ```
*/
export function concatBytes(...arrays) {
let sum = 0;
for (let i = 0; i < arrays.length; i++) {
const a = arrays[i];
abytes(a);
sum += a.length;
}
const res = new Uint8Array(sum);
for (let i = 0, pad = 0; i < arrays.length; i++) {
const a = arrays[i];
res.set(a, pad);
pad += a.length;
}
return res;
}
/**
* Merges user options into defaults.
* @param defaults - Default option values.
* @param opts - User-provided overrides.
* @returns Combined options object.
* The merge mutates `defaults` in place and returns the same object.
* @throws If options are missing or not an object. {@link Error}
* @example
* Applies user overrides to the default cipher options.
*
* ```ts
* checkOpts({ rounds: 20 }, { rounds: 8 });
* ```
*/
export function checkOpts(defaults, opts) {
if (opts == null || typeof opts !== 'object')
throw new Error('options must be defined');
const merged = Object.assign(defaults, opts);
return merged;
}
/**
* Compares two byte arrays in kinda constant time once lengths already match.
* @param a - First byte array.
* @param b - Second byte array.
* @returns `true` when the arrays contain the same bytes. Different lengths still return early.
* @example
* Compares an expected authentication tag with the received one.
*
* ```ts
* equalBytes(new Uint8Array([1]), new Uint8Array([1]));
* ```
*/
export function equalBytes(a, b) {
if (a.length !== b.length)
return false;
let diff = 0;
for (let i = 0; i < a.length; i++)
diff |= a[i] ^ b[i];
return diff === 0;
}
/**
* Wraps a keyed MAC constructor into a one-shot helper with `.create()`.
* @param keyLen - Valid probe-key length used to read static metadata once.
* The probe key is only used for `outputLen` / `blockLen`, so callers with several valid key sizes
* can pass any representative size as long as those values stay fixed.
* @param macCons - Keyed MAC constructor or factory.
* @param fromMsg - Optional adapter that derives extra constructor args from the one-shot message.
* @returns Callable MAC helper with `.create()`.
*/
export function wrapMacConstructor(keyLen, macCons, fromMsg) {
const mac = macCons;
const getArgs = (fromMsg || (() => []));
const macC = (msg, key) => mac(key, ...getArgs(msg))
.update(msg)
.digest();
const tmp = mac(new Uint8Array(keyLen), ...getArgs(new Uint8Array(0)));
macC.outputLen = tmp.outputLen;
macC.blockLen = tmp.blockLen;
macC.create = (key, ...args) => mac(key, ...args);
return macC;
}
/**
* Wraps a cipher: validates args, ensures encrypt() can only be called once.
* Used internally by the exported cipher constructors.
* Output-buffer support is inferred from the wrapped `encrypt` / `decrypt`
* arity (`fn.length === 2`), and tag-bearing constructors are expected to use
* `args[1]` for optional AAD.
* @__NO_SIDE_EFFECTS__
* @param params - Static cipher metadata. See {@link CipherParams}.
* @param constructor - Cipher constructor.
* @returns Wrapped constructor with validation.
*/
export const wrapCipher = (params, constructor) => {
function wrappedCipher(key, ...args) {
// Validate key
abytes(key, undefined, 'key');
// Validate nonce if nonceLength is present
if (params.nonceLength !== undefined) {
const nonce = args[0];
abytes(nonce, params.varSizeNonce ? undefined : params.nonceLength, 'nonce');
}
// Validate AAD if tagLength present
const tagl = params.tagLength;
if (tagl && args[1] !== undefined)
abytes(args[1], undefined, 'AAD');
const cipher = constructor(key, ...args);
const checkOutput = (fnLength, output) => {
if (output !== undefined) {
if (fnLength !== 2)
throw new Error('cipher output not supported');
abytes(output, undefined, 'output');
}
};
// Create wrapped cipher with validation and single-use encryption
let called = false;
const wrCipher = {
encrypt(data, output) {
if (called)
throw new Error('cannot encrypt() twice with same key + nonce');
called = true;
abytes(data);
checkOutput(cipher.encrypt.length, output);
return cipher.encrypt(data, output);
},
decrypt(data, output) {
abytes(data);
if (tagl && data.length < tagl)
throw new Error('"ciphertext" expected length bigger than tagLength=' + tagl);
checkOutput(cipher.decrypt.length, output);
return cipher.decrypt(data, output);
},
};
return wrCipher;
}
Object.assign(wrappedCipher, params);
return wrappedCipher;
};
/**
* By default, returns u8a of length.
* When out is available, it checks it for validity and uses it.
* @param expectedLength - Required output length.
* @param out - Optional destination buffer.
* @param onlyAligned - Whether `out` must be 4-byte aligned.
* @returns Output buffer ready for writing.
* @throws On wrong argument types. {@link TypeError}
* @throws If the provided output buffer has the wrong size or alignment. {@link Error}
* @example
* Reuses a caller-provided output buffer when lengths match.
*
* ```ts
* getOutput(16, new Uint8Array(16));
* ```
*/
export function getOutput(expectedLength, out, onlyAligned = true) {
if (out === undefined)
return new Uint8Array(expectedLength);
// Keep Buffer/cross-realm Uint8Array support here instead of trusting a shape-compatible object.
abytes(out, undefined, 'output');
if (out.length !== expectedLength)
throw new Error('"output" expected Uint8Array of length ' + expectedLength + ', got: ' + out.length);
if (onlyAligned && !isAligned32(out))
throw new Error('invalid output, must be aligned');
return out;
}
/**
* Encodes data and AAD bit lengths into a 16-byte buffer.
* @param dataLength - Data length in bits.
* @param aadLength - AAD length in bits.
* The serialized block is still `aadLength || dataLength`, matching GCM/Poly1305
* conventions even though the helper parameter order is `(dataLength, aadLength)`.
* @param isLE - Whether to encode lengths as little-endian.
* @returns 16-byte length block.
* @throws On wrong argument types passed to the endian validator. {@link TypeError}
* @throws On wrong argument ranges or values. {@link RangeError}
* @example
* Builds the length block appended by GCM and Poly1305.
*
* ```ts
* u64Lengths(16, 8, true);
* ```
*/
export function u64Lengths(dataLength, aadLength, isLE) {
// Reject coercible non-number lengths like '10' and true before BigInt(...) accepts them.
anumber(dataLength);
anumber(aadLength);
abool(isLE);
const num = new Uint8Array(16);
const view = createView(num);
view.setBigUint64(0, BigInt(aadLength), isLE);
view.setBigUint64(8, BigInt(dataLength), isLE);
return num;
}
/**
* Checks whether a byte array is aligned to a 4-byte offset.
* @param bytes - Byte array to inspect.
* @returns `true` when the view is 4-byte aligned.
* @example
* Checks whether a buffer can be safely viewed as Uint32Array.
*
* ```ts
* isAligned32(new Uint8Array(4));
* ```
*/
export function isAligned32(bytes) {
return bytes.byteOffset % 4 === 0;
}
/**
* Copies bytes into a new Uint8Array.
* @param bytes - Bytes to copy.
* @returns Copied byte array.
* @throws On wrong argument types. {@link TypeError}
* @example
* Copies input into an aligned Uint8Array before block processing.
*
* ```ts
* copyBytes(new Uint8Array([1, 2]));
* ```
*/
export function copyBytes(bytes) {
// `Uint8Array.from(...)` would also accept arrays / other typed arrays. Keep this helper strict
// because callers use it at byte-validation boundaries before mutating the detached copy.
return Uint8Array.from(abytes(bytes));
}
/**
* Cryptographically secure PRNG.
* Uses internal OS-level `crypto.getRandomValues`.
* @param bytesLength - Number of bytes to produce.
* Validation is delegated to `Uint8Array(bytesLength)` and `getRandomValues`, so
* non-integers, negative lengths, and oversize requests surface backend/runtime errors.
* @returns Random byte array.
* @throws On wrong argument types. {@link TypeError}
* @throws On wrong argument ranges or values. {@link RangeError}
* @throws If the runtime does not expose `crypto.getRandomValues`. {@link Error}
* @example
* Generates a fresh nonce or key.
*
* ```ts
* randomBytes(16);
* ```
*/
export function randomBytes(bytesLength = 32) {
// Validate upfront so fractional / coercible lengths do not silently
// truncate through Uint8Array().
anumber(bytesLength);
const cr = typeof globalThis === 'object' ? globalThis.crypto : null;
if (typeof cr?.getRandomValues !== 'function')
throw new Error('crypto.getRandomValues must be defined');
return cr.getRandomValues(new Uint8Array(bytesLength));
}
/**
* Uses CSPRNG for nonce, nonce injected in ciphertext.
* For `encrypt`, a `nonceBytes`-length buffer is fetched from CSPRNG and
* prepended to encrypted ciphertext. For `decrypt`, first `nonceBytes` of ciphertext
* are treated as nonce. The wrapper always allocates a fresh `nonce || ciphertext`
* buffer on encrypt and intentionally does not support caller-provided destination buffers.
* Too-short decrypt inputs are split into short/empty nonce views and then delegated
* to the wrapped cipher instead of being rejected here first.
*
* NOTE: Under the same key, using random nonces (e.g. `managedNonce`) with AES-GCM and ChaCha
* should be limited to `2**23` (8M) messages to get a collision chance of
* `2**-50`. Stretching to `2**32` (4B) messages would raise that chance to
* `2**-33`, still negligible but creeping up.
* @param fn - Cipher constructor that expects a nonce.
* @param randomBytes_ - Random-byte source used for nonce generation.
* @returns Cipher constructor that prepends the nonce to ciphertext.
* @throws On wrong argument types. {@link TypeError}
* @throws On invalid nonce lengths observed at wrapper construction or use. {@link RangeError}
* @example
* Prepends a fresh random nonce to every ciphertext.
*
* ```ts
* import { gcm } from '@noble/ciphers/aes.js';
* import { managedNonce, randomBytes } from '@noble/ciphers/utils.js';
* const wrapped = managedNonce(gcm);
* const key = randomBytes(16);
* const ciphertext = wrapped(key).encrypt(new Uint8Array([1, 2, 3]));
* wrapped(key).decrypt(ciphertext);
* ```
*/
export function managedNonce(fn, randomBytes_ = randomBytes) {
const { nonceLength } = fn;
anumber(nonceLength);
const addNonce = (nonce, ciphertext, plaintext) => {
const out = concatBytes(nonce, ciphertext);
// Wrapped ciphers may alias caller plaintext on encrypt(); never zero
// caller-owned buffers here.
if (!overlapBytes(plaintext, ciphertext))
ciphertext.fill(0);
return out;
};
// NOTE: we cannot support DST here, it would be mistake:
// - we don't know how much dst length cipher requires
// - nonce may unalign dst and break everything
// - we create new u8a anyway (concatBytes)
// - previously we passed all args to cipher, but that was mistake!
const res = ((key, ...args) => ({
encrypt(plaintext) {
abytes(plaintext);
const nonce = randomBytes_(nonceLength);
const encrypted = fn(key, nonce, ...args).encrypt(plaintext);
// @ts-ignore
if (encrypted instanceof Promise)
return encrypted.then((ct) => addNonce(nonce, ct, plaintext));
return addNonce(nonce, encrypted, plaintext);
},
decrypt(ciphertext) {
abytes(ciphertext);
const nonce = ciphertext.subarray(0, nonceLength);
const decrypted = ciphertext.subarray(nonceLength);
return fn(key, nonce, ...args).decrypt(decrypted);
},
}));
// Auto-nonce wrappers still preserve the wrapped payload geometry.
if ('blockSize' in fn)
res.blockSize = fn.blockSize;
if ('tagLength' in fn)
res.tagLength = fn.tagLength;
return res;
}
//# sourceMappingURL=utils.js.map

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/**
* WebCrypto-based AES gcm/ctr/cbc, `managedNonce` and `randomBytes`.
* We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.
* @module
*/
import { type AsyncCipher, type TArg, type TRet } from './utils.ts';
type WebcryptoUtils = {
encrypt(key: TArg<Uint8Array>, keyParams: unknown, cryptParams: unknown, plaintext: TArg<Uint8Array>): Promise<TRet<Uint8Array>>;
decrypt(key: TArg<Uint8Array>, keyParams: unknown, cryptParams: unknown, ciphertext: TArg<Uint8Array>): Promise<TRet<Uint8Array>>;
};
/**
* Internal webcrypto utils. Can be overridden if crypto.subtle is not present,
* for example in React Native.
* Raw keys are re-imported on every call; this wrapper intentionally does not
* cache `CryptoKey` objects between operations.
*/
export declare const utils: TRet<WebcryptoUtils>;
/**
* AES-CBC implemented with WebCrypto.
* Uses WebCrypto's built-in PKCS padding behavior; exact IV-length checks are
* delegated to the backend instead of local `abytes(..., 16)` validation.
* @param key - AES key bytes.
* @param iv - 16-byte initialization vector.
* @returns Async cipher instance.
* @example
* Encrypts a block with the browser or Node WebCrypto backend.
*
* ```ts
* import { cbc } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const iv = randomBytes(16);
* const cipher = cbc(key, iv);
* await cipher.encrypt(new Uint8Array(16));
* ```
*/
export declare const cbc: TRet<((key: TArg<Uint8Array>, iv: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}>;
/**
* AES-CTR implemented with WebCrypto.
* Uses WebCrypto's full 128-bit counter-length setting so the whole
* 16-byte counter block is incremented, matching sync `aes.ts:ctr`.
* @param key - AES key bytes.
* @param nonce - 16-byte counter block incremented as a full big-endian AES counter block.
* @returns Async cipher instance.
* @example
* Encrypts a short payload with WebCrypto AES-CTR.
*
* ```ts
* import { ctr } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(16);
* const cipher = ctr(key, nonce);
* await cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const ctr: TRet<((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}>;
/**
* AES-GCM implemented with WebCrypto.
* AAD type normalization and nonce-shape enforcement beyond raw bytes are left
* to the backend WebCrypto implementation.
* @param key - AES key bytes.
* @param nonce - Nonce bytes.
* @param AAD - Additional authenticated data.
* @returns Async cipher instance.
* @example
* Encrypts and authenticates plaintext with WebCrypto AES-GCM.
*
* ```ts
* import { gcm } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(12);
* const cipher = gcm(key, nonce);
* await cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export declare const gcm: TRet<((key: TArg<Uint8Array>, nonce: TArg<Uint8Array>, AAD?: TArg<Uint8Array>) => AsyncCipher) & {
blockSize: number;
nonceLength: number;
}>;
export {};
//# sourceMappingURL=webcrypto.d.ts.map

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/**
* WebCrypto-based AES gcm/ctr/cbc, `managedNonce` and `randomBytes`.
* We use WebCrypto aka globalThis.crypto, which exists in browsers and node.js 16+.
* @module
*/
import { abytes, anumber } from "./utils.js";
function getWebcryptoSubtle() {
const cr = typeof globalThis !== 'undefined' && globalThis.crypto;
if (cr && typeof cr.subtle === 'object' && cr.subtle != null)
return cr.subtle;
throw new Error('crypto.subtle must be defined');
}
/**
* Internal webcrypto utils. Can be overridden if crypto.subtle is not present,
* for example in React Native.
* Raw keys are re-imported on every call; this wrapper intentionally does not
* cache `CryptoKey` objects between operations.
*/
export const utils = {
async encrypt(key, keyParams, cryptParams, plaintext) {
const cr = getWebcryptoSubtle();
const iKey = await cr.importKey('raw', key, keyParams, true, ['encrypt']);
const ciphertext = await cr.encrypt(cryptParams, iKey, plaintext);
return new Uint8Array(ciphertext);
},
async decrypt(key, keyParams, cryptParams, ciphertext) {
const cr = getWebcryptoSubtle();
const iKey = await cr.importKey('raw', key, keyParams, true, ['decrypt']);
const plaintext = await cr.decrypt(cryptParams, iKey, ciphertext);
return new Uint8Array(plaintext);
},
};
const mode = {
CBC: 'AES-CBC',
CTR: 'AES-CTR',
GCM: 'AES-GCM',
};
function getCryptParams(algo, nonce, AAD) {
if (algo === mode.CBC)
return { name: mode.CBC, iv: nonce };
// WebCrypto allows 1..128 counter bits; use the full block to match sync ctr() / Node CTR wrap.
if (algo === mode.CTR)
return { name: mode.CTR, counter: nonce, length: 128 };
if (algo === mode.GCM) {
// Rely on the backend default tag length (128 bits) instead of setting it explicitly.
if (AAD)
return { name: mode.GCM, iv: nonce, additionalData: AAD };
else
return { name: mode.GCM, iv: nonce };
}
throw new Error('unknown aes block mode');
}
function generate(algo, nonceLength) {
anumber(nonceLength);
const res = (key, nonce, AAD) => {
abytes(key);
abytes(nonce);
// Reject falsy non-byte AAD locally; otherwise false/0/''/null silently become "no AAD".
if (AAD !== undefined)
abytes(AAD, undefined, 'AAD');
// Exact nonce-length enforcement and WebCrypto-specific AAD normalization are
// delegated to the backend; locally we only require byte-array inputs here.
// Keep caller key/nonce/AAD by reference; mutating them after
// construction changes later operations.
const keyParams = { name: algo, length: key.length * 8 };
const cryptParams = getCryptParams(algo, nonce, AAD);
let consumed = false;
return {
// keyLength,
encrypt(plaintext) {
abytes(plaintext);
if (consumed)
throw new Error('Cannot encrypt() twice with same key / nonce');
consumed = true;
return utils.encrypt(key, keyParams, cryptParams, plaintext);
},
decrypt(ciphertext) {
abytes(ciphertext);
return utils.decrypt(key, keyParams, cryptParams, ciphertext);
},
};
};
res.nonceLength = nonceLength;
res.blockSize = 16; // always for AES
return res;
}
/**
* AES-CBC implemented with WebCrypto.
* Uses WebCrypto's built-in PKCS padding behavior; exact IV-length checks are
* delegated to the backend instead of local `abytes(..., 16)` validation.
* @param key - AES key bytes.
* @param iv - 16-byte initialization vector.
* @returns Async cipher instance.
* @example
* Encrypts a block with the browser or Node WebCrypto backend.
*
* ```ts
* import { cbc } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const iv = randomBytes(16);
* const cipher = cbc(key, iv);
* await cipher.encrypt(new Uint8Array(16));
* ```
*/
export const cbc = /* @__PURE__ */ (() => generate(mode.CBC, 16))();
/**
* AES-CTR implemented with WebCrypto.
* Uses WebCrypto's full 128-bit counter-length setting so the whole
* 16-byte counter block is incremented, matching sync `aes.ts:ctr`.
* @param key - AES key bytes.
* @param nonce - 16-byte counter block incremented as a full big-endian AES counter block.
* @returns Async cipher instance.
* @example
* Encrypts a short payload with WebCrypto AES-CTR.
*
* ```ts
* import { ctr } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(16);
* const cipher = ctr(key, nonce);
* await cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const ctr = /* @__PURE__ */ (() => generate(mode.CTR, 16))();
/**
* AES-GCM implemented with WebCrypto.
* AAD type normalization and nonce-shape enforcement beyond raw bytes are left
* to the backend WebCrypto implementation.
* @param key - AES key bytes.
* @param nonce - Nonce bytes.
* @param AAD - Additional authenticated data.
* @returns Async cipher instance.
* @example
* Encrypts and authenticates plaintext with WebCrypto AES-GCM.
*
* ```ts
* import { gcm } from '@noble/ciphers/webcrypto.js';
* import { randomBytes } from '@noble/ciphers/utils.js';
* const key = randomBytes(16);
* const nonce = randomBytes(12);
* const cipher = gcm(key, nonce);
* await cipher.encrypt(new Uint8Array([1, 2, 3]));
* ```
*/
export const gcm = /* @__PURE__ */ (() => generate(mode.GCM, 12))();
// // Type tests
// import { siv, gcm, ctr, ecb, cbc } from '../aes.ts';
// import { xsalsa20poly1305 } from '../salsa.ts';
// import { chacha20poly1305, xchacha20poly1305 } from '../chacha.ts';
// const wsiv = managedNonce(siv);
// const wgcm = managedNonce(gcm);
// const wctr = managedNonce(ctr);
// const wcbc = managedNonce(cbc);
// const wsalsapoly = managedNonce(xsalsa20poly1305);
// const wchacha = managedNonce(chacha20poly1305);
// const wxchacha = managedNonce(xchacha20poly1305);
// // should fail
// const wcbc2 = managedNonce(managedNonce(cbc));
// const wctr = managedNonce(ctr);
// import { gcm as gcmSync } from '../aes.ts';
// const x1 = managedNonce(gcmSync);
// // const x1: (key: Uint8Array, AAD?: Uint8Array | undefined) => Cipher
// const x2 = managedNonce(gcm);
// // const x2: (key: Uint8Array, AAD?: Uint8Array | undefined) => AsyncCipher
//# sourceMappingURL=webcrypto.js.map

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The MIT License (MIT)
Copyright (c) 2022 Paul Miller (https://paulmillr.com)
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.

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/**
* BLS != BLS.
* The file implements BLS (Boneh-Lynn-Shacham) signatures.
* Used in both BLS (Barreto-Lynn-Scott) and BN (Barreto-Naehrig)
* families of pairing-friendly curves.
* Consists of two curves: G1 and G2:
* - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4.
* - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1
* - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in
* Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not.
* Pairing is used to aggregate and verify signatures.
* There are two modes of operation:
* - Long signatures: X-byte keys + 2X-byte sigs (G1 keys + G2 sigs).
* - Short signatures: 2X-byte keys + X-byte sigs (G2 keys + G1 sigs).
* @module
**/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type TArg, type TRet } from '../utils.ts';
import { type CurveLengths } from './curve.ts';
import { type H2CHasher, type H2COpts, type MapToCurve } from './hash-to-curve.ts';
import { type IField } from './modular.ts';
import type { Fp12, Fp12Bls, Fp2, Fp2Bls, Fp6Bls } from './tower.ts';
import { type WeierstrassPoint, type WeierstrassPointCons } from './weierstrass.ts';
type Fp = bigint;
/**
* Twist convention used by the pairing formulas for a concrete curve family.
* BLS12-381 uses a multiplicative twist, while BN254 uses a divisive one.
*/
export type BlsTwistType = 'multiplicative' | 'divisive';
/**
* Codec exposed as `curve.shortSignatures.Signature`.
* Use it to parse or serialize G1 signatures in short-signature mode.
* In this mode, public keys live in G2.
*/
export type BlsShortSignatureCoder<Fp> = {
/**
* Parse a compressed signature from raw bytes.
* @param bytes - Compressed signature bytes.
* @returns Parsed signature point.
*/
fromBytes(bytes: TArg<Uint8Array>): WeierstrassPoint<Fp>;
/**
* Parse a compressed signature from a hex string.
* @param hex - Compressed signature hex string.
* @returns Parsed signature point.
*/
fromHex(hex: string): WeierstrassPoint<Fp>;
/**
* Encode a signature point into compressed bytes.
* @param point - Signature point.
* @returns Compressed signature bytes.
*/
toBytes(point: WeierstrassPoint<Fp>): TRet<Uint8Array>;
/**
* Encode a signature point into a hex string.
* @param point - Signature point.
* @returns Compressed signature hex.
*/
toHex(point: WeierstrassPoint<Fp>): string;
};
/**
* Codec exposed as `curve.longSignatures.Signature`.
* Use it to parse or serialize G2 signatures in long-signature mode.
* In this mode, public keys live in G1.
*/
export type BlsLongSignatureCoder<Fp> = {
/**
* Parse a compressed signature from raw bytes.
* @param bytes - Compressed signature bytes.
* @returns Parsed signature point.
*/
fromBytes(bytes: TArg<Uint8Array>): WeierstrassPoint<Fp>;
/**
* Parse a compressed signature from a hex string.
* @param hex - Compressed signature hex string.
* @returns Parsed signature point.
*/
fromHex(hex: string): WeierstrassPoint<Fp>;
/**
* Encode a signature point into compressed bytes.
* @param point - Signature point.
* @returns Compressed signature bytes.
*/
toBytes(point: WeierstrassPoint<Fp>): TRet<Uint8Array>;
/**
* Encode a signature point into a hex string.
* @param point - Signature point.
* @returns Compressed signature hex.
*/
toHex(point: WeierstrassPoint<Fp>): string;
};
/** Tower fields needed by pairing code, hash-to-curve, and subgroup arithmetic. */
export type BlsFields = {
/** Base field of G1 coordinates. */
Fp: IField<Fp>;
/** Scalar field used for secret scalars and subgroup order arithmetic. */
Fr: IField<bigint>;
/** Quadratic extension field used by G2. */
Fp2: Fp2Bls;
/** Sextic extension field used inside pairing arithmetic. */
Fp6: Fp6Bls;
/** Degree-12 extension field that contains the GT target group. */
Fp12: Fp12Bls;
};
/**
* Callback used by pairing post-processing hooks to add one more G2 point to the Miller-loop state.
* @param Rx - Current projective X coordinate.
* @param Ry - Current projective Y coordinate.
* @param Rz - Current projective Z coordinate.
* @param Qx - G2 affine x coordinate.
* @param Qy - G2 affine y coordinate.
* @returns Updated projective accumulator coordinates.
*/
export type BlsPostPrecomputePointAddFn = (Rx: Fp2, Ry: Fp2, Rz: Fp2, Qx: Fp2, Qy: Fp2) => {
Rx: Fp2;
Ry: Fp2;
Rz: Fp2;
};
/**
* Hook for curve-specific pairing cleanup after the Miller loop precomputes are built.
* @param Rx - Current projective X coordinate.
* @param Ry - Current projective Y coordinate.
* @param Rz - Current projective Z coordinate.
* @param Qx - G2 affine x coordinate.
* @param Qy - G2 affine y coordinate.
* @param pointAdd - Callback used to fold one more point into the accumulator.
*/
export type BlsPostPrecomputeFn = (Rx: Fp2, Ry: Fp2, Rz: Fp2, Qx: Fp2, Qy: Fp2, pointAdd: BlsPostPrecomputePointAddFn) => void;
/** Low-level pairing helpers shared by BLS curve bundles. */
export type BlsPairing = {
/** Byte lengths for keys and signatures exposed by this pairing family. */
lengths: CurveLengths;
/** Scalar field used by the pairing and signing helpers. */
Fr: IField<bigint>;
/** Target field used for the GT result of pairings. */
Fp12: Fp12Bls;
/**
* Build Miller-loop precomputes for one G2 point.
* @param p - G2 point to precompute.
* @returns Pairing precompute table.
*/
calcPairingPrecomputes: (p: WeierstrassPoint<Fp2>) => Precompute;
/**
* Evaluate a batch of Miller loops from precomputed line coefficients.
* @param pairs - Precomputed Miller-loop inputs.
* @returns Accumulated GT value before or after final exponentiation.
*/
millerLoopBatch: (pairs: [Precompute, Fp, Fp][]) => Fp12;
/**
* Pair one G1 point with one G2 point.
* @param P - G1 point.
* @param Q - G2 point.
* @param withFinalExponent - Whether to apply the final exponentiation step.
* @returns GT pairing result.
* @throws If either point is the point at infinity. {@link Error}
*/
pairing: (P: WeierstrassPoint<Fp>, Q: WeierstrassPoint<Fp2>, withFinalExponent?: boolean) => Fp12;
/**
* Pair many G1/G2 pairs in one batch.
* @param pairs - Point pairs to accumulate.
* @param withFinalExponent - Whether to apply the final exponentiation step.
* @returns GT pairing result. Empty input returns the multiplicative identity in GT.
*/
pairingBatch: (pairs: {
g1: WeierstrassPoint<Fp>;
g2: WeierstrassPoint<Fp2>;
}[], withFinalExponent?: boolean) => Fp12;
/**
* Generate a random secret key for this pairing family.
* @param seed - Optional seed material.
* @returns Secret key bytes.
*/
randomSecretKey: (seed?: TArg<Uint8Array>) => TRet<Uint8Array>;
};
/**
* Parameters that define the Miller-loop shape and twist handling
* for a concrete pairing family.
*/
export type BlsPairingParams = {
/** Signed loop parameter used by the Miller loop. */
ateLoopSize: bigint;
/** Whether the signed Miller-loop parameter is negative. */
xNegative: boolean;
/**
* Twist convention used by the pairing formulas.
* BLS12-381 is multiplicative; BN254 is divisive.
*/
twistType: BlsTwistType;
/**
* Optional RNG override used by helper constructors.
* Receives the requested byte length and returns random bytes.
*/
randomBytes?: (len?: number) => TRet<Uint8Array>;
/**
* Optional hook for curve-specific untwisting after precomputation.
* Used by BN254 after the Miller loop.
*/
postPrecompute?: BlsPostPrecomputeFn;
};
/** Hash-to-curve settings shared by the G1 and G2 hashers inside a BLS curve bundle. */
export type BlsHasherParams = {
/**
* Optional map-to-curve override for G1.
* Receives the hash-to-field tuple and returns one affine G1 point.
*/
mapToG1?: MapToCurve<Fp>;
/**
* Optional map-to-curve override for G2.
* Receives the hash-to-field tuple and returns one affine G2 point.
*/
mapToG2?: MapToCurve<Fp2>;
/** Shared baseline hash-to-curve options. */
hasherOpts: H2COpts;
/** G1-specific hash-to-curve options merged on top of `hasherOpts`. */
hasherOptsG1: H2COpts;
/** G2-specific hash-to-curve options merged on top of `hasherOpts`. */
hasherOptsG2: H2COpts;
};
type PrecomputeSingle = [Fp2, Fp2, Fp2][];
type Precompute = PrecomputeSingle[];
/**
* BLS consists of two curves: G1 and G2:
* - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4.
* - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1
*/
export interface BlsCurvePair {
/** Byte lengths for keys and signatures exposed by this curve family. */
lengths: CurveLengths;
/**
* Shared Miller-loop batch evaluator.
* @param pairs - Precomputed Miller-loop inputs.
* @returns Accumulated GT value.
*/
millerLoopBatch: BlsPairing['millerLoopBatch'];
/**
* Pair one G1 point with one G2 point.
* @param P - G1 point.
* @param Q - G2 point.
* @param withFinalExponent - Whether to apply the final exponentiation step.
* @returns GT pairing result.
* @throws If either point is the point at infinity. {@link Error}
*/
pairing: BlsPairing['pairing'];
/**
* Pair many G1/G2 pairs in one batch.
* @param pairs - Point pairs to accumulate.
* @param withFinalExponent - Whether to apply the final exponentiation step.
* @returns GT pairing result. Empty input returns the multiplicative identity in GT.
*/
pairingBatch: BlsPairing['pairingBatch'];
/** G1 point constructor for the base field subgroup. */
G1: {
Point: WeierstrassPointCons<Fp>;
};
/** G2 point constructor for the twist subgroup. */
G2: {
Point: WeierstrassPointCons<Fp2>;
};
/** Tower fields exposed by the pairing implementation. */
fields: {
Fp: IField<Fp>;
Fp2: Fp2Bls;
Fp6: Fp6Bls;
Fp12: Fp12Bls;
Fr: IField<bigint>;
};
/** Utility helpers shared by hashers and signers. */
utils: {
randomSecretKey: (seed?: TArg<Uint8Array>) => TRet<Uint8Array>;
calcPairingPrecomputes: BlsPairing['calcPairingPrecomputes'];
};
/** Public pairing parameters exposed for introspection. */
params: {
ateLoopSize: bigint;
twistType: BlsTwistType;
};
}
/** BLS curve bundle extended with hash-to-curve helpers for G1 and G2. */
export interface BlsCurvePairWithHashers extends BlsCurvePair {
/** G1 hasher bundle with RFC 9380 helpers. */
G1: H2CHasher<WeierstrassPointCons<Fp>>;
/** G2 hasher bundle with RFC 9380 helpers. */
G2: H2CHasher<WeierstrassPointCons<Fp2>>;
}
/** BLS curve bundle extended with both hashers and signature helpers. */
export interface BlsCurvePairWithSignatures extends BlsCurvePairWithHashers {
/** Long-signature mode: G1 public keys and G2 signatures. */
longSignatures: BlsSigs<bigint, Fp2>;
/** Short-signature mode: G2 public keys and G1 signatures. */
shortSignatures: BlsSigs<Fp2, bigint>;
}
type BLSInput = TArg<Uint8Array>;
/** BLS signer helpers for one signature mode. */
export interface BlsSigs<P, S> {
/** Byte lengths for secret keys, public keys, and signatures. */
lengths: CurveLengths;
/**
* Generate a secret/public key pair for this signature mode.
* @param seed - Optional seed material.
* @returns Secret and public key pair.
*/
keygen(seed?: TArg<Uint8Array>): {
secretKey: TRet<Uint8Array>;
publicKey: WeierstrassPoint<P>;
};
/**
* Derive the public key from a secret key.
* @param secretKey - Secret key bytes.
* @returns Public-key point.
*/
getPublicKey(secretKey: TArg<Uint8Array>): WeierstrassPoint<P>;
/**
* Sign a message already hashed onto the signature subgroup.
* @param hashedMessage - Message mapped to the signature subgroup.
* @param secretKey - Secret key bytes.
* @returns Signature point.
*/
sign(hashedMessage: WeierstrassPoint<S>, secretKey: TArg<Uint8Array>): WeierstrassPoint<S>;
/**
* Verify one signature against one public key and hashed message.
* @param signature - Signature point or encoded signature.
* @param message - Hashed message point.
* @param publicKey - Public-key point or encoded key.
* @returns Whether the signature is valid.
*/
verify(signature: WeierstrassPoint<S> | BLSInput, message: WeierstrassPoint<S>, publicKey: WeierstrassPoint<P> | BLSInput): boolean;
/**
* Verify one aggregated signature against many `(message, publicKey)` pairs.
* @param signature - Aggregated signature.
* @param items - Message/public-key pairs.
* @returns Whether the aggregated signature is valid. Same-message aggregate verification still
* requires proof of possession or another rogue-key defense from the caller.
*/
verifyBatch: (signature: WeierstrassPoint<S> | BLSInput, items: {
message: WeierstrassPoint<S>;
publicKey: WeierstrassPoint<P> | BLSInput;
}[]) => boolean;
/**
* Add many public keys into one aggregate point.
* @param publicKeys - Public keys to aggregate.
* @returns Aggregated public-key point. This is raw point addition and does not add proof of
* possession or rogue-key protection on its own.
*/
aggregatePublicKeys(publicKeys: (WeierstrassPoint<P> | BLSInput)[]): WeierstrassPoint<P>;
/**
* Add many signatures into one aggregate point.
* @param signatures - Signatures to aggregate.
* @returns Aggregated signature point. This is raw point addition and does not change the proof
* of possession requirements of the aggregate-verification scheme.
*/
aggregateSignatures(signatures: (WeierstrassPoint<S> | BLSInput)[]): WeierstrassPoint<S>;
/**
* Hash an arbitrary message onto the signature subgroup.
* @param message - Message bytes.
* @param DST - Optional domain separation tag.
* @returns Curve point on the signature subgroup.
*/
hash(message: TArg<Uint8Array>, DST?: TArg<string | Uint8Array>): WeierstrassPoint<S>;
/** Signature codec for this mode. */
Signature: BlsLongSignatureCoder<S>;
}
type BlsSignatureCoders = Partial<{
LongSignature: BlsLongSignatureCoder<Fp2>;
ShortSignature: BlsShortSignatureCoder<Fp>;
}>;
/**
* @param fields - Tower field implementations.
* @param G1_Point - G1 point constructor.
* @param G2_Point - G2 point constructor.
* @param params - Pairing parameters. See {@link BlsPairingParams}.
* @returns Pairing-only BLS helpers. The returned pairing surface rejects infinity inputs, while
* empty `pairingBatch(...)` calls return the multiplicative identity in GT. This keeps the
* low-level pairing API fail-closed for BLS-style callers, where identity points usually signal
* broken hash / wiring instead of an intentionally neutral pairing term. This also eagerly
* precomputes the G1 base-point table as a performance side effect.
* @throws If the pairing parameters or underlying curve helpers are inconsistent. {@link Error}
* @example
* ```ts
* import { blsBasic } from '@noble/curves/abstract/bls.js';
* import { bn254 } from '@noble/curves/bn254.js';
* // Pair a G1 point with a G2 point without the higher-level signer helpers.
* const gt = bn254.pairing(bn254.G1.Point.BASE, bn254.G2.Point.BASE);
* ```
*/
export declare function blsBasic(fields: TArg<BlsFields>, G1_Point: WeierstrassPointCons<Fp>, G2_Point: WeierstrassPointCons<Fp2>, params: TArg<BlsPairingParams>): BlsCurvePair;
/**
* @param fields - Tower field implementations.
* @param G1_Point - G1 point constructor.
* @param G2_Point - G2 point constructor.
* @param params - Pairing parameters. See {@link BlsPairingParams}.
* @param hasherParams - Hash-to-curve configuration. See {@link BlsHasherParams}.
* @param signatureCoders - Signature codecs.
* @returns BLS helpers with signers. The inherited pairing surface still rejects infinity inputs,
* and empty `pairingBatch(...)` calls still return the multiplicative identity in GT. Aggregate
* verification still requires proof of possession or another rogue-key defense from the caller.
* @throws If the pairing, hashing, or signature helpers are configured inconsistently. {@link Error}
* @example
* ```ts
* import { bls } from '@noble/curves/abstract/bls.js';
* import { bls12_381 } from '@noble/curves/bls12-381.js';
* const sigs = bls12_381.longSignatures;
* // Use the full BLS helper set when you need hashing, keygen, signing, and verification.
* const { secretKey, publicKey } = sigs.keygen();
* const msg = sigs.hash(new TextEncoder().encode('hello noble'));
* const sig = sigs.sign(msg, secretKey);
* const isValid = sigs.verify(sig, msg, publicKey);
* ```
*/
export declare function bls(fields: TArg<BlsFields>, G1_Point: WeierstrassPointCons<Fp>, G2_Point: WeierstrassPointCons<Fp2>, params: TArg<BlsPairingParams>, hasherParams: TArg<BlsHasherParams>, signatureCoders: BlsSignatureCoders): BlsCurvePairWithSignatures;
export {};
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/**
* BLS != BLS.
* The file implements BLS (Boneh-Lynn-Shacham) signatures.
* Used in both BLS (Barreto-Lynn-Scott) and BN (Barreto-Naehrig)
* families of pairing-friendly curves.
* Consists of two curves: G1 and G2:
* - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4.
* - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1
* - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in
* Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not.
* Pairing is used to aggregate and verify signatures.
* There are two modes of operation:
* - Long signatures: X-byte keys + 2X-byte sigs (G1 keys + G2 sigs).
* - Short signatures: 2X-byte keys + X-byte sigs (G2 keys + G1 sigs).
* @module
**/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { abytes, notImplemented, randomBytes } from "../utils.js";
import {} from "./curve.js";
import { createHasher, } from "./hash-to-curve.js";
import { getMinHashLength, mapHashToField } from "./modular.js";
import {} from "./weierstrass.js";
// prettier-ignore
const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
// Signed non-adjacent decomposition of the spec-defined Miller-loop parameter.
// BN254 benefits most because `6x+2` has multiple adjacent `11` runs, but BLS12-381's
// stored `|x|` still starts with `11`, so the Miller loop must also handle one `-1` digit there.
function NAfDecomposition(a) {
const res = [];
// a>1 because of marker bit
for (; a > _1n; a >>= _1n) {
if ((a & _1n) === _0n)
res.unshift(0);
else if ((a & _3n) === _3n) {
res.unshift(-1);
a += _1n;
}
else
res.unshift(1);
}
return res;
}
function aNonEmpty(arr) {
// Aggregate helpers use this to reject empty variable-length inputs consistently.
// Without the guard, each caller would fall through into a different empty-input / identity
// case and hide missing inputs behind outputs that still look structurally valid.
if (!Array.isArray(arr) || arr.length === 0)
throw new Error('expected non-empty array');
}
// This should be enough for bn254, no need to export full stuff?
function createBlsPairing(fields, G1, G2, params) {
const { Fr, Fp2, Fp12 } = fields;
const { twistType, ateLoopSize, xNegative, postPrecompute } = params;
// Applies sparse multiplication as line function
let lineFunction;
if (twistType === 'multiplicative') {
lineFunction = (c0, c1, c2, f, Px, Py) => Fp12.mul014(f, c0, Fp2.mul(c1, Px), Fp2.mul(c2, Py));
}
else if (twistType === 'divisive') {
// NOTE: it should be [c0, c1, c2], but we use different order here to reduce complexity of
// precompute calculations.
lineFunction = (c0, c1, c2, f, Px, Py) => Fp12.mul034(f, Fp2.mul(c2, Py), Fp2.mul(c1, Px), c0);
}
else
throw new Error('bls: unknown twist type');
const Fp2div2 = Fp2.div(Fp2.ONE, Fp2.mul(Fp2.ONE, _2n));
function pointDouble(ell, Rx, Ry, Rz) {
const t0 = Fp2.sqr(Ry); // Ry²
const t1 = Fp2.sqr(Rz); // Rz²
const t2 = Fp2.mulByB(Fp2.mul(t1, _3n)); // 3 * T1 * B
const t3 = Fp2.mul(t2, _3n); // 3 * T2
const t4 = Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0
const c0 = Fp2.sub(t2, t0); // T2 - T0 (i)
const c1 = Fp2.mul(Fp2.sqr(Rx), _3n); // 3 * Rx²
const c2 = Fp2.neg(t4); // -T4 (-h)
ell.push([c0, c1, c2]);
Rx = Fp2.mul(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), Fp2div2); // ((T0 - T3) * Rx * Ry) / 2
// ((T0 + T3) / 2)² - 3 * T2²
Ry = Fp2.sub(Fp2.sqr(Fp2.mul(Fp2.add(t0, t3), Fp2div2)), Fp2.mul(Fp2.sqr(t2), _3n));
Rz = Fp2.mul(t0, t4); // T0 * T4
return { Rx, Ry, Rz };
}
function pointAdd(ell, Rx, Ry, Rz, Qx, Qy) {
// Addition
const t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz
const t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz
const c0 = Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)); // T0 * Qx - T1 * Qy == Ry * Qx - Rx * Qy
const c1 = Fp2.neg(t0); // -T0 == Qy * Rz - Ry
const c2 = t1; // == Rx - Qx * Rz
ell.push([c0, c1, c2]);
const t2 = Fp2.sqr(t1); // T1²
const t3 = Fp2.mul(t2, t1); // T2 * T1
const t4 = Fp2.mul(t2, Rx); // T2 * Rx
// T3 - 2 * T4 + T0² * Rz
const t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, _2n)), Fp2.mul(Fp2.sqr(t0), Rz));
Rx = Fp2.mul(t1, t5); // T1 * T5
Ry = Fp2.sub(Fp2.mul(Fp2.sub(t4, t5), t0), Fp2.mul(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry
Rz = Fp2.mul(Rz, t3); // Rz * T3
return { Rx, Ry, Rz };
}
// Pre-compute coefficients for sparse multiplication
// Point addition and point double calculations is reused for coefficients
// pointAdd happens only if bit set, so wNAF is reasonable. Unfortunately we cannot combine
// add + double in windowed precomputes here, otherwise it would be single op (since X is static)
const ATE_NAF = NAfDecomposition(ateLoopSize);
const calcPairingPrecomputes = (point) => {
const p = point;
const { x, y } = p.toAffine();
// prettier-ignore
const Qx = x, Qy = y, negQy = Fp2.neg(y);
// prettier-ignore
let Rx = Qx, Ry = Qy, Rz = Fp2.ONE;
const ell = [];
for (const bit of ATE_NAF) {
const cur = [];
({ Rx, Ry, Rz } = pointDouble(cur, Rx, Ry, Rz));
if (bit)
({ Rx, Ry, Rz } = pointAdd(cur, Rx, Ry, Rz, Qx, bit === -1 ? negQy : Qy));
ell.push(cur);
}
if (postPrecompute) {
const last = ell[ell.length - 1];
postPrecompute(Rx, Ry, Rz, Qx, Qy, pointAdd.bind(null, last));
}
return ell;
};
function millerLoopBatch(pairs, withFinalExponent = false) {
let f12 = Fp12.ONE;
if (pairs.length) {
const ellLen = pairs[0][0].length;
for (let i = 0; i < ellLen; i++) {
f12 = Fp12.sqr(f12); // This allows us to do sqr only one time for all pairings
// NOTE: we apply multiple pairings in parallel here
for (const [ell, Px, Py] of pairs) {
for (const [c0, c1, c2] of ell[i])
f12 = lineFunction(c0, c1, c2, f12, Px, Py);
}
}
}
if (xNegative)
f12 = Fp12.conjugate(f12);
return withFinalExponent ? Fp12.finalExponentiate(f12) : f12;
}
// Calculates product of multiple pairings
// This up to x2 faster than just `map(({g1, g2})=>pairing({g1,g2}))`
function pairingBatch(pairs, withFinalExponent = true) {
const res = [];
for (const { g1, g2 } of pairs) {
// Mathematically, a zero pairing term contributes GT.ONE. We still reject it here because
// this API mainly backs BLS verification, where ZERO inputs usually mean broken hash /
// wiring. Silently skipping them would turn those failures into a neutral pairing product.
// Callers that want the algebraic neutral-element behavior can filter ZERO terms first.
if (g1.is0() || g2.is0())
throw new Error('pairing is not available for ZERO point');
// This uses toAffine inside
g1.assertValidity();
g2.assertValidity();
const Qa = g1.toAffine();
res.push([calcPairingPrecomputes(g2), Qa.x, Qa.y]);
}
return millerLoopBatch(res, withFinalExponent);
}
// Calculates bilinear pairing
function pairing(Q, P, withFinalExponent = true) {
return pairingBatch([{ g1: Q, g2: P }], withFinalExponent);
}
const lengths = {
seed: getMinHashLength(Fr.ORDER),
};
const rand = params.randomBytes === undefined ? randomBytes : params.randomBytes;
// Seeded calls deterministically reduce exactly `lengths.seed` bytes into `1..Fr.ORDER-1`;
// omitting `seed` just fills that input buffer from the configured RNG first.
const randomSecretKey = (seed) => {
seed = seed === undefined ? rand(lengths.seed) : seed;
abytes(seed, lengths.seed, 'seed');
return mapHashToField(seed, Fr.ORDER);
};
Object.freeze(lengths);
return {
lengths,
Fr,
Fp12, // NOTE: we re-export Fp12 here because pairing results are Fp12!
millerLoopBatch,
pairing,
pairingBatch,
calcPairingPrecomputes,
randomSecretKey,
};
}
function createBlsSig(blsPairing, PubPoint, SigPoint, isSigG1, hashToSigCurve, SignatureCoder) {
const { Fr, Fp12, pairingBatch, randomSecretKey, lengths } = blsPairing;
if (!SignatureCoder) {
SignatureCoder = {
fromBytes: notImplemented,
fromHex: notImplemented,
toBytes: notImplemented,
toHex: notImplemented,
};
}
function normPub(point) {
return point instanceof PubPoint ? point : PubPoint.fromBytes(point);
}
function normSig(point) {
return point instanceof SigPoint ? point : SigPoint.fromBytes(point);
}
// Sign/verify here take points already hashed onto the signature subgroup.
// Raw bytes and points from the other subgroup must fail this constructor-brand
// check before later validity checks run.
function amsg(m) {
if (!(m instanceof SigPoint))
throw new Error(`expected valid message hashed to ${!isSigG1 ? 'G2' : 'G1'} curve`);
return m;
}
// What matters here is what point pairing API accepts as G1 or G2, not actual size or names
const pair = !isSigG1
? (a, b) => ({ g1: a, g2: b })
: (a, b) => ({ g1: b, g2: a });
return Object.freeze({
lengths: Object.freeze({ ...lengths, secretKey: Fr.BYTES }),
keygen(seed) {
const secretKey = randomSecretKey(seed);
const publicKey = this.getPublicKey(secretKey);
return { secretKey, publicKey };
},
// P = pk x G
getPublicKey(secretKey) {
let sec;
try {
sec = PubPoint.Fn.fromBytes(secretKey);
}
catch (error) {
// @ts-ignore
throw new Error('invalid private key: ' + typeof secretKey, { cause: error });
}
return PubPoint.BASE.multiply(sec);
},
// S = pk x H(m)
sign(message, secretKey, unusedArg) {
if (unusedArg != null)
throw new Error('sign() expects 2 arguments');
const sec = PubPoint.Fn.fromBytes(secretKey);
amsg(message).assertValidity();
return message.multiply(sec);
},
// Checks if pairing of public key & hash is equal to pairing of generator & signature.
// e(P, H(m)) == e(G, S)
// e(S, G) == e(H(m), P)
verify(signature, message, publicKey, unusedArg) {
if (unusedArg != null)
throw new Error('verify() expects 3 arguments');
signature = normSig(signature);
publicKey = normPub(publicKey);
const P = publicKey.negate();
const G = PubPoint.BASE;
const Hm = amsg(message);
const S = signature;
// This code was changed in 1.9.x:
// Before it was G.negate() in G2, now it's always pubKey.negate
// e(P, -Q)===e(-P, Q)==e(P, Q)^-1. Negate can be done anywhere (as long it is done once per pair).
// We just moving sign, but since pairing is multiplicative, we doing X * X^-1 = 1
try {
const exp = pairingBatch([pair(P, Hm), pair(G, S)]);
return Fp12.eql(exp, Fp12.ONE);
}
catch {
return false;
}
},
// https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407
// e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))
// TODO: maybe `{message: G2Hex, publicKey: G1Hex}[]` instead?
verifyBatch(signature, items) {
aNonEmpty(items);
const sig = normSig(signature);
const nMessages = items.map((i) => i.message);
const nPublicKeys = items.map((i) => normPub(i.publicKey));
// NOTE: this works only for exact same object
const messagePubKeyMap = new Map();
for (let i = 0; i < nPublicKeys.length; i++) {
const pub = nPublicKeys[i];
const msg = nMessages[i];
let keys = messagePubKeyMap.get(msg);
if (keys === undefined) {
keys = [];
messagePubKeyMap.set(msg, keys);
}
keys.push(pub);
}
const paired = [];
const G = PubPoint.BASE;
try {
for (const [msg, keys] of messagePubKeyMap) {
const groupPublicKey = keys.reduce((acc, msg) => acc.add(msg));
paired.push(pair(groupPublicKey, msg));
}
paired.push(pair(G.negate(), sig));
return Fp12.eql(pairingBatch(paired), Fp12.ONE);
}
catch {
return false;
}
},
// Adds a bunch of public key points together.
// pk1 + pk2 + pk3 = pkA
aggregatePublicKeys(publicKeys) {
aNonEmpty(publicKeys);
publicKeys = publicKeys.map((pub) => normPub(pub));
const agg = publicKeys.reduce((sum, p) => sum.add(p), PubPoint.ZERO);
agg.assertValidity();
return agg;
},
// Adds a bunch of signature points together.
// pk1 + pk2 + pk3 = pkA
aggregateSignatures(signatures) {
aNonEmpty(signatures);
signatures = signatures.map((sig) => normSig(sig));
const agg = signatures.reduce((sum, s) => sum.add(s), SigPoint.ZERO);
agg.assertValidity();
return agg;
},
hash(messageBytes, DST) {
abytes(messageBytes);
const opts = DST ? { DST } : undefined;
return hashToSigCurve(messageBytes, opts);
},
Signature: Object.freeze({ ...SignatureCoder }),
}) /*satisfies Signer */;
}
// NOTE: separate function instead of function override, so we don't depend on hasher in bn254.
/**
* @param fields - Tower field implementations.
* @param G1_Point - G1 point constructor.
* @param G2_Point - G2 point constructor.
* @param params - Pairing parameters. See {@link BlsPairingParams}.
* @returns Pairing-only BLS helpers. The returned pairing surface rejects infinity inputs, while
* empty `pairingBatch(...)` calls return the multiplicative identity in GT. This keeps the
* low-level pairing API fail-closed for BLS-style callers, where identity points usually signal
* broken hash / wiring instead of an intentionally neutral pairing term. This also eagerly
* precomputes the G1 base-point table as a performance side effect.
* @throws If the pairing parameters or underlying curve helpers are inconsistent. {@link Error}
* @example
* ```ts
* import { blsBasic } from '@noble/curves/abstract/bls.js';
* import { bn254 } from '@noble/curves/bn254.js';
* // Pair a G1 point with a G2 point without the higher-level signer helpers.
* const gt = bn254.pairing(bn254.G1.Point.BASE, bn254.G2.Point.BASE);
* ```
*/
export function blsBasic(fields, G1_Point, G2_Point, params) {
// Fields are specific for curve, so for now we'll need to pass them with opts
const { Fp, Fr, Fp2, Fp6, Fp12 } = fields;
// Point on G1 curve: (x, y)
// const G1_Point = weierstrass(CURVE.G1, { Fn: Fr });
const G1 = { Point: G1_Point };
// Point on G2 curve (complex numbers): (x₁, x₂+i), (y₁, y₂+i)
const G2 = { Point: G2_Point };
const pairingRes = createBlsPairing(fields, G1_Point, G2_Point, params);
const { millerLoopBatch, pairing, pairingBatch, calcPairingPrecomputes, randomSecretKey, lengths, } = pairingRes;
G1.Point.BASE.precompute(4);
Object.freeze(G1);
Object.freeze(G2);
return Object.freeze({
lengths: Object.freeze(lengths),
millerLoopBatch,
pairing,
pairingBatch,
G1,
G2,
fields: Object.freeze({ Fr, Fp, Fp2, Fp6, Fp12 }),
params: Object.freeze({
ateLoopSize: params.ateLoopSize,
twistType: params.twistType,
}),
utils: Object.freeze({
randomSecretKey,
calcPairingPrecomputes,
}),
});
}
// We can export this too, but seems there is not much reasons for now? If user wants hasher, they can just create hasher.
function blsHashers(fields, G1_Point, G2_Point, params, hasherParams) {
const base = blsBasic(fields, G1_Point, G2_Point, params);
// Missing map hooks intentionally fail closed via notImplemented on first hash use.
const G1Hasher = createHasher(G1_Point, hasherParams.mapToG1 === undefined ? notImplemented : hasherParams.mapToG1, {
...hasherParams.hasherOpts,
...hasherParams.hasherOptsG1,
});
const G2Hasher = createHasher(G2_Point, hasherParams.mapToG2 === undefined ? notImplemented : hasherParams.mapToG2, {
...hasherParams.hasherOpts,
...hasherParams.hasherOptsG2,
});
return Object.freeze({ ...base, G1: G1Hasher, G2: G2Hasher });
}
// G1_Point: ProjConstructor<bigint>, G2_Point: ProjConstructor<Fp2>,
// Rename to blsSignatures?
/**
* @param fields - Tower field implementations.
* @param G1_Point - G1 point constructor.
* @param G2_Point - G2 point constructor.
* @param params - Pairing parameters. See {@link BlsPairingParams}.
* @param hasherParams - Hash-to-curve configuration. See {@link BlsHasherParams}.
* @param signatureCoders - Signature codecs.
* @returns BLS helpers with signers. The inherited pairing surface still rejects infinity inputs,
* and empty `pairingBatch(...)` calls still return the multiplicative identity in GT. Aggregate
* verification still requires proof of possession or another rogue-key defense from the caller.
* @throws If the pairing, hashing, or signature helpers are configured inconsistently. {@link Error}
* @example
* ```ts
* import { bls } from '@noble/curves/abstract/bls.js';
* import { bls12_381 } from '@noble/curves/bls12-381.js';
* const sigs = bls12_381.longSignatures;
* // Use the full BLS helper set when you need hashing, keygen, signing, and verification.
* const { secretKey, publicKey } = sigs.keygen();
* const msg = sigs.hash(new TextEncoder().encode('hello noble'));
* const sig = sigs.sign(msg, secretKey);
* const isValid = sigs.verify(sig, msg, publicKey);
* ```
*/
export function bls(fields, G1_Point, G2_Point, params, hasherParams, signatureCoders) {
const base = blsHashers(fields, G1_Point, G2_Point, params, hasherParams);
const pairingRes = {
...base,
Fr: base.fields.Fr,
Fp12: base.fields.Fp12,
calcPairingPrecomputes: base.utils.calcPairingPrecomputes,
randomSecretKey: base.utils.randomSecretKey,
};
const longSignatures = createBlsSig(pairingRes, G1_Point, G2_Point, false, base.G2.hashToCurve, signatureCoders?.LongSignature);
const shortSignatures = createBlsSig(pairingRes, G2_Point, G1_Point, true, base.G1.hashToCurve, signatureCoders?.ShortSignature);
return Object.freeze({ ...base, longSignatures, shortSignatures });
}
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/**
* Methods for elliptic curve multiplication by scalars.
* Contains wNAF, pippenger.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type Signer, type TArg, type TRet } from '../utils.ts';
import { type IField } from './modular.ts';
/** Affine point coordinates without projective fields. */
export type AffinePoint<T> = {
/** Affine x coordinate. */
x: T;
/** Affine y coordinate. */
y: T;
} & {
Z?: never;
};
/** Base interface for all elliptic-curve point instances. */
export interface CurvePoint<F, P extends CurvePoint<F, P>> {
/** Affine x coordinate. Different from projective / extended X coordinate. */
x: F;
/** Affine y coordinate. Different from projective / extended Y coordinate. */
y: F;
/** Projective Z coordinate when the point keeps projective state. */
Z?: F;
/**
* Double the point.
* @returns Doubled point.
*/
double(): P;
/**
* Negate the point.
* @returns Negated point.
*/
negate(): P;
/**
* Add another point from the same curve.
* @param other - Point to add.
* @returns Sum point.
*/
add(other: P): P;
/**
* Subtract another point from the same curve.
* @param other - Point to subtract.
* @returns Difference point.
*/
subtract(other: P): P;
/**
* Compare two points for equality.
* @param other - Point to compare.
* @returns Whether the points are equal.
*/
equals(other: P): boolean;
/**
* Multiply the point by a scalar in constant time.
* Implementations keep the subgroup-scalar contract strict and may reject
* `0` instead of returning the identity point.
* @param scalar - Scalar multiplier.
* @returns Product point.
*/
multiply(scalar: bigint): P;
/** Assert that the point satisfies the curve equation and subgroup checks. */
assertValidity(): void;
/**
* Map the point into the prime-order subgroup when the curve requires it.
* @returns Prime-order point.
*/
clearCofactor(): P;
/**
* Check whether the point is the point at infinity.
* @returns Whether the point is zero.
*/
is0(): boolean;
/**
* Check whether the point belongs to the prime-order subgroup.
* @returns Whether the point is torsion-free.
*/
isTorsionFree(): boolean;
/**
* Check whether the point lies in a small torsion subgroup.
* @returns Whether the point has small order.
*/
isSmallOrder(): boolean;
/**
* Multiply the point by a scalar without constant-time guarantees.
* Public-scalar callers that need `0` should use this method instead of
* relying on `multiply(...)` to return the identity point.
* @param scalar - Scalar multiplier.
* @returns Product point.
*/
multiplyUnsafe(scalar: bigint): P;
/**
* Massively speeds up `p.multiply(n)` by using precompute tables (caching). See {@link wNAF}.
* Cache state lives in internal WeakMaps keyed by point identity, not on the point object.
* Repeating `precompute(...)` for the same point identity replaces the remembered window size
* and forces table regeneration for that point.
* @param windowSize - Precompute window size.
* @param isLazy - calculate cache now. Default (true) ensures it's deferred to first `multiply()`
* @returns Same point instance with precompute tables attached.
*/
precompute(windowSize?: number, isLazy?: boolean): P;
/**
* Converts point to 2D xy affine coordinates.
* @param invertedZ - Optional inverted Z coordinate for batch normalization.
* @returns Affine x/y coordinates.
*/
toAffine(invertedZ?: F): AffinePoint<F>;
/**
* Encode the point into the curve's canonical byte form.
* @returns Encoded point bytes.
*/
toBytes(): Uint8Array;
/**
* Encode the point into the curve's canonical hex form.
* @returns Encoded point hex.
*/
toHex(): string;
}
/** Base interface for elliptic-curve point constructors. */
export interface CurvePointCons<P extends CurvePoint<any, P>> {
/**
* Runtime brand check for points created by this constructor.
* @param item - Value to test.
* @returns Whether the value is a point from this constructor.
*/
[Symbol.hasInstance]: (item: unknown) => boolean;
/** Canonical subgroup generator. */
BASE: P;
/** Point at infinity. */
ZERO: P;
/** Field for basic curve math */
Fp: IField<P_F<P>>;
/** Scalar field, for scalars in multiply and others */
Fn: IField<bigint>;
/**
* Create one point from affine coordinates.
* Does NOT validate curve, subgroup, or wrapper invariants.
* Use `.assertValidity()` on adversarial inputs.
* @param p - Affine point coordinates.
* @returns Point instance.
*/
fromAffine(p: AffinePoint<P_F<P>>): P;
/**
* Decode a point from the canonical byte encoding.
* @param bytes - Encoded point bytes.
* Implementations MUST treat `bytes` as read-only.
* @returns Point instance.
*/
fromBytes(bytes: Uint8Array): P;
/**
* Decode a point from the canonical hex encoding.
* @param hex - Encoded point hex.
* @returns Point instance.
*/
fromHex(hex: string): P;
}
/** Returns the affine field type for a point instance (`P_F<P> == P.F`). */
export type P_F<P extends CurvePoint<any, P>> = P extends CurvePoint<infer F, P> ? F : never;
/** Returns the affine field type for a point constructor (`PC_F<PC> == PC.P.F`). */
export type PC_F<PC extends CurvePointCons<CurvePoint<any, any>>> = PC['Fp']['ZERO'];
/** Returns the point instance type for a point constructor (`PC_P<PC> == PC.P`). */
export type PC_P<PC extends CurvePointCons<CurvePoint<any, any>>> = PC['ZERO'];
/** Wide point-constructor type used when the concrete curve is not important. */
export type PC_ANY = CurvePointCons<CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, CurvePoint<any, any>>>>>>>>>>>;
/**
* Validates the static surface of a point constructor.
* This is only a cheap sanity check for the constructor hooks and fields consumed by generic
* factories; it does not certify `BASE`/`ZERO` semantics or prove the curve implementation itself.
* @param Point - Runtime point constructor.
* @throws On missing constructor hooks or malformed field metadata. {@link TypeError}
* @example
* Check that one point constructor exposes the static hooks generic helpers need.
*
* ```ts
* import { ed25519 } from '@noble/curves/ed25519.js';
* import { validatePointCons } from '@noble/curves/abstract/curve.js';
* validatePointCons(ed25519.Point);
* ```
*/
export declare function validatePointCons<P extends CurvePoint<any, P>>(Point: CurvePointCons<P>): void;
/** Byte lengths used by one curve implementation. */
export interface CurveLengths {
/** Secret-key length in bytes. */
secretKey?: number;
/** Compressed public-key length in bytes. */
publicKey?: number;
/** Uncompressed public-key length in bytes. */
publicKeyUncompressed?: number;
/** Whether public-key encodings include a format prefix byte. */
publicKeyHasPrefix?: boolean;
/** Signature length in bytes. */
signature?: number;
/** Seed length in bytes when the curve exposes deterministic keygen from seed. */
seed?: number;
}
/** Reorders or otherwise remaps a batch while preserving its element type. */
export type Mapper<T> = (i: T[]) => T[];
/**
* Computes both candidates first, but the final selection still branches on `condition`, so this
* is not a strict constant-time CMOV primitive.
* @param condition - Whether to negate the point.
* @param item - Point-like value.
* @returns Original or negated value.
* @example
* Keep the point or return its negation based on one boolean branch.
*
* ```ts
* import { negateCt } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const maybeNegated = negateCt(true, p256.Point.BASE);
* ```
*/
export declare function negateCt<T extends {
negate: () => T;
}>(condition: boolean, item: T): T;
/**
* Takes a bunch of Projective Points but executes only one
* inversion on all of them. Inversion is very slow operation,
* so this improves performance massively.
* Optimization: converts a list of projective points to a list of identical points with Z=1.
* Input points are left unchanged; the normalized points are returned as fresh instances.
* @param c - Point constructor.
* @param points - Projective points.
* @returns Fresh projective points reconstructed from normalized affine coordinates.
* @example
* Batch-normalize projective points with a single shared inversion.
*
* ```ts
* import { normalizeZ } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const points = normalizeZ(p256.Point, [p256.Point.BASE, p256.Point.BASE.double()]);
* ```
*/
export declare function normalizeZ<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(c: PC, points: P[]): P[];
/**
* Elliptic curve multiplication of Point by scalar. Fragile.
* Table generation takes **30MB of ram and 10ms on high-end CPU**,
* but may take much longer on slow devices. Actual generation will happen on
* first call of `multiply()`. By default, `BASE` point is precomputed.
*
* Scalars should always be less than curve order: this should be checked inside of a curve itself.
* Creates precomputation tables for fast multiplication:
* - private scalar is split by fixed size windows of W bits
* - every window point is collected from window's table & added to accumulator
* - since windows are different, same point inside tables won't be accessed more than once per calc
* - each multiplication is 'Math.ceil(CURVE_ORDER / 𝑊) + 1' point additions (fixed for any scalar)
* - +1 window is neccessary for wNAF
* - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication
*
* TODO: research returning a 2d JS array of windows instead of a single window.
* This would allow windows to be in different memory locations.
* @param Point - Point constructor.
* @param bits - Scalar bit length.
* @example
* Elliptic curve multiplication of Point by scalar.
*
* ```ts
* import { wNAF } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const ladder = new wNAF(p256.Point, p256.Point.Fn.BITS);
* ```
*/
export declare class wNAF<PC extends PC_ANY> {
private readonly BASE;
private readonly ZERO;
private readonly Fn;
readonly bits: number;
constructor(Point: PC, bits: number);
_unsafeLadder(elm: PC_P<PC>, n: bigint, p?: PC_P<PC>): PC_P<PC>;
/**
* Creates a wNAF precomputation window. Used for caching.
* Default window size is set by `utils.precompute()` and is equal to 8.
* Number of precomputed points depends on the curve size:
* 2^(𝑊1) * (Math.ceil(𝑛 / 𝑊) + 1), where:
* - 𝑊 is the window size
* - 𝑛 is the bitlength of the curve order.
* For a 256-bit curve and window size 8, the number of precomputed points is 128 * 33 = 4224.
* @param point - Point instance
* @param W - window size
* @returns precomputed point tables flattened to a single array
*/
private precomputeWindow;
/**
* Implements ec multiplication using precomputed tables and w-ary non-adjacent form.
* More compact implementation:
* https://github.com/paulmillr/noble-secp256k1/blob/47cb1669b6e506ad66b35fe7d76132ae97465da2/index.ts#L502-L541
* @returns real and fake (for const-time) points
*/
private wNAF;
/**
* Implements unsafe EC multiplication using precomputed tables
* and w-ary non-adjacent form.
* @param acc - accumulator point to add result of multiplication
* @returns point
*/
private wNAFUnsafe;
private getPrecomputes;
cached(point: PC_P<PC>, scalar: bigint, transform?: Mapper<PC_P<PC>>): {
p: PC_P<PC>;
f: PC_P<PC>;
};
unsafe(point: PC_P<PC>, scalar: bigint, transform?: Mapper<PC_P<PC>>, prev?: PC_P<PC>): PC_P<PC>;
createCache(P: PC_P<PC>, W: number): void;
hasCache(elm: PC_P<PC>): boolean;
}
/**
* Endomorphism-specific multiplication for Koblitz curves.
* Cost: 128 dbl, 0-256 adds.
* @param Point - Point constructor.
* @param point - Input point.
* @param k1 - First non-negative absolute scalar chunk.
* @param k2 - Second non-negative absolute scalar chunk.
* @returns Partial multiplication results.
* @example
* Endomorphism-specific multiplication for Koblitz curves.
*
* ```ts
* import { mulEndoUnsafe } from '@noble/curves/abstract/curve.js';
* import { secp256k1 } from '@noble/curves/secp256k1.js';
* const parts = mulEndoUnsafe(secp256k1.Point, secp256k1.Point.BASE, 3n, 5n);
* ```
*/
export declare function mulEndoUnsafe<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(Point: PC, point: P, k1: bigint, k2: bigint): {
p1: P;
p2: P;
};
/**
* Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
* 30x faster vs naive addition on L=4096, 10x faster than precomputes.
* For N=254bit, L=1, it does: 1024 ADD + 254 DBL. For L=5: 1536 ADD + 254 DBL.
* Algorithmically constant-time (for same L), even when 1 point + scalar, or when scalar = 0.
* @param c - Curve Point constructor
* @param points - array of L curve points
* @param scalars - array of L scalars (aka secret keys / bigints)
* @returns MSM result point. Empty input is accepted and returns the identity.
* @throws If the point set, scalar set, or MSM sizing is invalid. {@link Error}
* @example
* Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
*
* ```ts
* import { pippenger } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const point = pippenger(p256.Point, [p256.Point.BASE, p256.Point.BASE.double()], [2n, 3n]);
* ```
*/
export declare function pippenger<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(c: PC, points: P[], scalars: bigint[]): P;
/**
* Precomputed multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
* @param c - Curve Point constructor
* @param points - array of L curve points
* @param windowSize - Precompute window size.
* @returns Function which multiplies points with scalars. The closure accepts
* `scalars.length <= points.length`, and omitted trailing scalars are treated as zero.
* @throws If the point set or precompute window is invalid. {@link Error}
* @example
* Precomputed multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
*
* ```ts
* import { precomputeMSMUnsafe } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const msm = precomputeMSMUnsafe(p256.Point, [p256.Point.BASE], 4);
* const point = msm([3n]);
* ```
*/
export declare function precomputeMSMUnsafe<P extends CurvePoint<any, P>, PC extends CurvePointCons<P>>(c: PC, points: P[], windowSize: number): (scalars: bigint[]) => P;
/** Minimal curve parameters needed to construct a Weierstrass or Edwards curve. */
export type ValidCurveParams<T> = {
/** Base-field modulus. */
p: bigint;
/** Prime subgroup order. */
n: bigint;
/** Cofactor. */
h: bigint;
/** Curve parameter `a`. */
a: T;
/** Weierstrass curve parameter `b`. */
b?: T;
/** Edwards curve parameter `d`. */
d?: T;
/** Generator x coordinate. */
Gx: T;
/** Generator y coordinate. */
Gy: T;
};
/** Pair of fields used by curve constructors. */
export type FpFn<T> = {
/** Base field used for curve coordinates. */
Fp: IField<T>;
/** Scalar field used for secret scalars and subgroup arithmetic. */
Fn: IField<bigint>;
};
/**
* Validates basic CURVE shape and field membership, then creates fields.
* This does not prove that the generator is on-curve, that subgroup/order data are consistent, or
* that the curve equation itself is otherwise sane.
* @param type - Curve family.
* @param CURVE - Curve parameters.
* @param curveOpts - Optional field overrides:
* - `Fp` (optional): Optional base-field override.
* - `Fn` (optional): Optional scalar-field override.
* @param FpFnLE - Whether field encoding is little-endian.
* @returns Frozen curve parameters and fields.
* @throws If the curve parameters or field overrides are invalid. {@link Error}
* @example
* Build curve fields from raw constants before constructing a curve instance.
*
* ```ts
* const curve = createCurveFields('weierstrass', {
* p: 17n,
* n: 19n,
* h: 1n,
* a: 2n,
* b: 2n,
* Gx: 5n,
* Gy: 1n,
* });
* ```
*/
export declare function createCurveFields<T>(type: 'weierstrass' | 'edwards', CURVE: ValidCurveParams<T>, curveOpts?: TArg<Partial<FpFn<T>>>, FpFnLE?: boolean): TRet<FpFn<T> & {
CURVE: ValidCurveParams<T>;
}>;
type KeygenFn = (seed?: Uint8Array, isCompressed?: boolean) => {
secretKey: Uint8Array;
publicKey: Uint8Array;
};
/**
* @param randomSecretKey - Secret-key generator.
* @param getPublicKey - Public-key derivation helper.
* @returns Keypair generator.
* @example
* Build a `keygen()` helper from existing secret-key and public-key primitives.
*
* ```ts
* import { createKeygen } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const keygen = createKeygen(p256.utils.randomSecretKey, p256.getPublicKey);
* const pair = keygen();
* ```
*/
export declare function createKeygen(randomSecretKey: Function, getPublicKey: TArg<Signer['getPublicKey']>): TRet<KeygenFn>;
export {};
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/**
* Methods for elliptic curve multiplication by scalars.
* Contains wNAF, pippenger.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { bitLen, bitMask, validateObject } from "../utils.js";
import { Field, FpInvertBatch, validateField } from "./modular.js";
const _0n = /* @__PURE__ */ BigInt(0);
const _1n = /* @__PURE__ */ BigInt(1);
/**
* Validates the static surface of a point constructor.
* This is only a cheap sanity check for the constructor hooks and fields consumed by generic
* factories; it does not certify `BASE`/`ZERO` semantics or prove the curve implementation itself.
* @param Point - Runtime point constructor.
* @throws On missing constructor hooks or malformed field metadata. {@link TypeError}
* @example
* Check that one point constructor exposes the static hooks generic helpers need.
*
* ```ts
* import { ed25519 } from '@noble/curves/ed25519.js';
* import { validatePointCons } from '@noble/curves/abstract/curve.js';
* validatePointCons(ed25519.Point);
* ```
*/
export function validatePointCons(Point) {
const pc = Point;
if (typeof pc !== 'function')
throw new TypeError('Point must be a constructor');
// validateObject only accepts plain objects, so copy the constructor statics into one bag first.
validateObject({
Fp: pc.Fp,
Fn: pc.Fn,
fromAffine: pc.fromAffine,
fromBytes: pc.fromBytes,
fromHex: pc.fromHex,
}, {
Fp: 'object',
Fn: 'object',
fromAffine: 'function',
fromBytes: 'function',
fromHex: 'function',
});
validateField(pc.Fp);
validateField(pc.Fn);
}
/**
* Computes both candidates first, but the final selection still branches on `condition`, so this
* is not a strict constant-time CMOV primitive.
* @param condition - Whether to negate the point.
* @param item - Point-like value.
* @returns Original or negated value.
* @example
* Keep the point or return its negation based on one boolean branch.
*
* ```ts
* import { negateCt } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const maybeNegated = negateCt(true, p256.Point.BASE);
* ```
*/
export function negateCt(condition, item) {
const neg = item.negate();
return condition ? neg : item;
}
/**
* Takes a bunch of Projective Points but executes only one
* inversion on all of them. Inversion is very slow operation,
* so this improves performance massively.
* Optimization: converts a list of projective points to a list of identical points with Z=1.
* Input points are left unchanged; the normalized points are returned as fresh instances.
* @param c - Point constructor.
* @param points - Projective points.
* @returns Fresh projective points reconstructed from normalized affine coordinates.
* @example
* Batch-normalize projective points with a single shared inversion.
*
* ```ts
* import { normalizeZ } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const points = normalizeZ(p256.Point, [p256.Point.BASE, p256.Point.BASE.double()]);
* ```
*/
export function normalizeZ(c, points) {
const invertedZs = FpInvertBatch(c.Fp, points.map((p) => p.Z));
return points.map((p, i) => c.fromAffine(p.toAffine(invertedZs[i])));
}
function validateW(W, bits) {
if (!Number.isSafeInteger(W) || W <= 0 || W > bits)
throw new Error('invalid window size, expected [1..' + bits + '], got W=' + W);
}
function calcWOpts(W, scalarBits) {
validateW(W, scalarBits);
const windows = Math.ceil(scalarBits / W) + 1; // W=8 33. Not 32, because we skip zero
const windowSize = 2 ** (W - 1); // W=8 128. Not 256, because we skip zero
const maxNumber = 2 ** W; // W=8 256
const mask = bitMask(W); // W=8 255 == mask 0b11111111
const shiftBy = BigInt(W); // W=8 8
return { windows, windowSize, mask, maxNumber, shiftBy };
}
function calcOffsets(n, window, wOpts) {
const { windowSize, mask, maxNumber, shiftBy } = wOpts;
let wbits = Number(n & mask); // extract W bits.
let nextN = n >> shiftBy; // shift number by W bits.
// What actually happens here:
// const highestBit = Number(mask ^ (mask >> 1n));
// let wbits2 = wbits - 1; // skip zero
// if (wbits2 & highestBit) { wbits2 ^= Number(mask); // (~);
// split if bits > max: +224 => 256-32
if (wbits > windowSize) {
// we skip zero, which means instead of `>= size-1`, we do `> size`
wbits -= maxNumber; // -32, can be maxNumber - wbits, but then we need to set isNeg here.
nextN += _1n; // +256 (carry)
}
const offsetStart = window * windowSize;
const offset = offsetStart + Math.abs(wbits) - 1; // -1 because we skip zero; ignore when isZero
const isZero = wbits === 0; // is current window slice a 0?
const isNeg = wbits < 0; // is current window slice negative?
const isNegF = window % 2 !== 0; // fake branch noise only
const offsetF = offsetStart; // fake branch noise only
return { nextN, offset, isZero, isNeg, isNegF, offsetF };
}
function validateMSMPoints(points, c) {
if (!Array.isArray(points))
throw new Error('array expected');
points.forEach((p, i) => {
if (!(p instanceof c))
throw new Error('invalid point at index ' + i);
});
}
function validateMSMScalars(scalars, field) {
if (!Array.isArray(scalars))
throw new Error('array of scalars expected');
scalars.forEach((s, i) => {
if (!field.isValid(s))
throw new Error('invalid scalar at index ' + i);
});
}
// Since points in different groups cannot be equal (different object constructor),
// we can have single place to store precomputes.
// Allows to make points frozen / immutable.
const pointPrecomputes = new WeakMap();
const pointWindowSizes = new WeakMap();
function getW(P) {
// To disable precomputes:
// return 1;
// `1` is also the uncached sentinel: use the ladder / non-precomputed path.
return pointWindowSizes.get(P) || 1;
}
function assert0(n) {
// Internal invariant: a non-zero remainder here means the wNAF window decomposition or loop
// count is inconsistent, not that the original caller provided a bad scalar.
if (n !== _0n)
throw new Error('invalid wNAF');
}
/**
* Elliptic curve multiplication of Point by scalar. Fragile.
* Table generation takes **30MB of ram and 10ms on high-end CPU**,
* but may take much longer on slow devices. Actual generation will happen on
* first call of `multiply()`. By default, `BASE` point is precomputed.
*
* Scalars should always be less than curve order: this should be checked inside of a curve itself.
* Creates precomputation tables for fast multiplication:
* - private scalar is split by fixed size windows of W bits
* - every window point is collected from window's table & added to accumulator
* - since windows are different, same point inside tables won't be accessed more than once per calc
* - each multiplication is 'Math.ceil(CURVE_ORDER / 𝑊) + 1' point additions (fixed for any scalar)
* - +1 window is neccessary for wNAF
* - wNAF reduces table size: 2x less memory + 2x faster generation, but 10% slower multiplication
*
* TODO: research returning a 2d JS array of windows instead of a single window.
* This would allow windows to be in different memory locations.
* @param Point - Point constructor.
* @param bits - Scalar bit length.
* @example
* Elliptic curve multiplication of Point by scalar.
*
* ```ts
* import { wNAF } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const ladder = new wNAF(p256.Point, p256.Point.Fn.BITS);
* ```
*/
export class wNAF {
BASE;
ZERO;
Fn;
bits;
// Parametrized with a given Point class (not individual point)
constructor(Point, bits) {
this.BASE = Point.BASE;
this.ZERO = Point.ZERO;
this.Fn = Point.Fn;
this.bits = bits;
}
// non-const time multiplication ladder
_unsafeLadder(elm, n, p = this.ZERO) {
let d = elm;
while (n > _0n) {
if (n & _1n)
p = p.add(d);
d = d.double();
n >>= _1n;
}
return p;
}
/**
* Creates a wNAF precomputation window. Used for caching.
* Default window size is set by `utils.precompute()` and is equal to 8.
* Number of precomputed points depends on the curve size:
* 2^(𝑊1) * (Math.ceil(𝑛 / 𝑊) + 1), where:
* - 𝑊 is the window size
* - 𝑛 is the bitlength of the curve order.
* For a 256-bit curve and window size 8, the number of precomputed points is 128 * 33 = 4224.
* @param point - Point instance
* @param W - window size
* @returns precomputed point tables flattened to a single array
*/
precomputeWindow(point, W) {
const { windows, windowSize } = calcWOpts(W, this.bits);
const points = [];
let p = point;
let base = p;
for (let window = 0; window < windows; window++) {
base = p;
points.push(base);
// i=1, bc we skip 0
for (let i = 1; i < windowSize; i++) {
base = base.add(p);
points.push(base);
}
p = base.double();
}
return points;
}
/**
* Implements ec multiplication using precomputed tables and w-ary non-adjacent form.
* More compact implementation:
* https://github.com/paulmillr/noble-secp256k1/blob/47cb1669b6e506ad66b35fe7d76132ae97465da2/index.ts#L502-L541
* @returns real and fake (for const-time) points
*/
wNAF(W, precomputes, n) {
// Scalar should be smaller than field order
if (!this.Fn.isValid(n))
throw new Error('invalid scalar');
// Accumulators
let p = this.ZERO;
let f = this.BASE;
// This code was first written with assumption that 'f' and 'p' will never be infinity point:
// since each addition is multiplied by 2 ** W, it cannot cancel each other. However,
// there is negate now: it is possible that negated element from low value
// would be the same as high element, which will create carry into next window.
// It's not obvious how this can fail, but still worth investigating later.
const wo = calcWOpts(W, this.bits);
for (let window = 0; window < wo.windows; window++) {
// (n === _0n) is handled and not early-exited. isEven and offsetF are used for noise
const { nextN, offset, isZero, isNeg, isNegF, offsetF } = calcOffsets(n, window, wo);
n = nextN;
if (isZero) {
// bits are 0: add garbage to fake point
// Important part for const-time getPublicKey: add random "noise" point to f.
f = f.add(negateCt(isNegF, precomputes[offsetF]));
}
else {
// bits are 1: add to result point
p = p.add(negateCt(isNeg, precomputes[offset]));
}
}
assert0(n);
// Return both real and fake points so JIT keeps the noise path alive.
// Known caveat: negate/carry interactions can still drive `f` to infinity even when `p` is not,
// which weakens the noise path and leaves this only "less const-time" by about one bigint mul.
return { p, f };
}
/**
* Implements unsafe EC multiplication using precomputed tables
* and w-ary non-adjacent form.
* @param acc - accumulator point to add result of multiplication
* @returns point
*/
wNAFUnsafe(W, precomputes, n, acc = this.ZERO) {
const wo = calcWOpts(W, this.bits);
for (let window = 0; window < wo.windows; window++) {
if (n === _0n)
break; // Early-exit, skip 0 value
const { nextN, offset, isZero, isNeg } = calcOffsets(n, window, wo);
n = nextN;
if (isZero) {
// Window bits are 0: skip processing.
// Move to next window.
continue;
}
else {
const item = precomputes[offset];
acc = acc.add(isNeg ? item.negate() : item); // Re-using acc allows to save adds in MSM
}
}
assert0(n);
return acc;
}
getPrecomputes(W, point, transform) {
// Cache key is only point identity plus the remembered window size; callers must not reuse the
// same point with incompatible `transform(...)` layouts and expect a separate cache entry.
let comp = pointPrecomputes.get(point);
if (!comp) {
comp = this.precomputeWindow(point, W);
if (W !== 1) {
// Doing transform outside of if brings 15% perf hit
if (typeof transform === 'function')
comp = transform(comp);
pointPrecomputes.set(point, comp);
}
}
return comp;
}
cached(point, scalar, transform) {
const W = getW(point);
return this.wNAF(W, this.getPrecomputes(W, point, transform), scalar);
}
unsafe(point, scalar, transform, prev) {
const W = getW(point);
if (W === 1)
return this._unsafeLadder(point, scalar, prev); // For W=1 ladder is ~x2 faster
return this.wNAFUnsafe(W, this.getPrecomputes(W, point, transform), scalar, prev);
}
// We calculate precomputes for elliptic curve point multiplication
// using windowed method. This specifies window size and
// stores precomputed values. Usually only base point would be precomputed.
createCache(P, W) {
validateW(W, this.bits);
pointWindowSizes.set(P, W);
pointPrecomputes.delete(P);
}
hasCache(elm) {
return getW(elm) !== 1;
}
}
/**
* Endomorphism-specific multiplication for Koblitz curves.
* Cost: 128 dbl, 0-256 adds.
* @param Point - Point constructor.
* @param point - Input point.
* @param k1 - First non-negative absolute scalar chunk.
* @param k2 - Second non-negative absolute scalar chunk.
* @returns Partial multiplication results.
* @example
* Endomorphism-specific multiplication for Koblitz curves.
*
* ```ts
* import { mulEndoUnsafe } from '@noble/curves/abstract/curve.js';
* import { secp256k1 } from '@noble/curves/secp256k1.js';
* const parts = mulEndoUnsafe(secp256k1.Point, secp256k1.Point.BASE, 3n, 5n);
* ```
*/
export function mulEndoUnsafe(Point, point, k1, k2) {
let acc = point;
let p1 = Point.ZERO;
let p2 = Point.ZERO;
while (k1 > _0n || k2 > _0n) {
if (k1 & _1n)
p1 = p1.add(acc);
if (k2 & _1n)
p2 = p2.add(acc);
acc = acc.double();
k1 >>= _1n;
k2 >>= _1n;
}
return { p1, p2 };
}
/**
* Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
* 30x faster vs naive addition on L=4096, 10x faster than precomputes.
* For N=254bit, L=1, it does: 1024 ADD + 254 DBL. For L=5: 1536 ADD + 254 DBL.
* Algorithmically constant-time (for same L), even when 1 point + scalar, or when scalar = 0.
* @param c - Curve Point constructor
* @param points - array of L curve points
* @param scalars - array of L scalars (aka secret keys / bigints)
* @returns MSM result point. Empty input is accepted and returns the identity.
* @throws If the point set, scalar set, or MSM sizing is invalid. {@link Error}
* @example
* Pippenger algorithm for multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
*
* ```ts
* import { pippenger } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const point = pippenger(p256.Point, [p256.Point.BASE, p256.Point.BASE.double()], [2n, 3n]);
* ```
*/
export function pippenger(c, points, scalars) {
// If we split scalars by some window (let's say 8 bits), every chunk will only
// take 256 buckets even if there are 4096 scalars, also re-uses double.
// TODO:
// - https://eprint.iacr.org/2024/750.pdf
// - https://tches.iacr.org/index.php/TCHES/article/view/10287
// 0 is accepted in scalars
const fieldN = c.Fn;
validateMSMPoints(points, c);
validateMSMScalars(scalars, fieldN);
const plength = points.length;
const slength = scalars.length;
if (plength !== slength)
throw new Error('arrays of points and scalars must have equal length');
// if (plength === 0) throw new Error('array must be of length >= 2');
const zero = c.ZERO;
const wbits = bitLen(BigInt(plength));
let windowSize = 1; // bits
if (wbits > 12)
windowSize = wbits - 3;
else if (wbits > 4)
windowSize = wbits - 2;
else if (wbits > 0)
windowSize = 2;
const MASK = bitMask(windowSize);
const buckets = new Array(Number(MASK) + 1).fill(zero); // +1 for zero array
const lastBits = Math.floor((fieldN.BITS - 1) / windowSize) * windowSize;
let sum = zero;
for (let i = lastBits; i >= 0; i -= windowSize) {
buckets.fill(zero);
for (let j = 0; j < slength; j++) {
const scalar = scalars[j];
const wbits = Number((scalar >> BigInt(i)) & MASK);
buckets[wbits] = buckets[wbits].add(points[j]);
}
let resI = zero; // not using this will do small speed-up, but will lose ct
// Skip first bucket, because it is zero
for (let j = buckets.length - 1, sumI = zero; j > 0; j--) {
sumI = sumI.add(buckets[j]);
resI = resI.add(sumI);
}
sum = sum.add(resI);
if (i !== 0)
for (let j = 0; j < windowSize; j++)
sum = sum.double();
}
return sum;
}
/**
* Precomputed multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
* @param c - Curve Point constructor
* @param points - array of L curve points
* @param windowSize - Precompute window size.
* @returns Function which multiplies points with scalars. The closure accepts
* `scalars.length <= points.length`, and omitted trailing scalars are treated as zero.
* @throws If the point set or precompute window is invalid. {@link Error}
* @example
* Precomputed multi-scalar multiplication (MSM, Pa + Qb + Rc + ...).
*
* ```ts
* import { precomputeMSMUnsafe } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const msm = precomputeMSMUnsafe(p256.Point, [p256.Point.BASE], 4);
* const point = msm([3n]);
* ```
*/
export function precomputeMSMUnsafe(c, points, windowSize) {
/**
* Performance Analysis of Window-based Precomputation
*
* Base Case (256-bit scalar, 8-bit window):
* - Standard precomputation requires:
* - 31 additions per scalar × 256 scalars = 7,936 ops
* - Plus 255 summary additions = 8,191 total ops
* Note: Summary additions can be optimized via accumulator
*
* Chunked Precomputation Analysis:
* - Using 32 chunks requires:
* - 255 additions per chunk
* - 256 doublings
* - Total: (255 × 32) + 256 = 8,416 ops
*
* Memory Usage Comparison:
* Window Size | Standard Points | Chunked Points
* ------------|-----------------|---------------
* 4-bit | 520 | 15
* 8-bit | 4,224 | 255
* 10-bit | 13,824 | 1,023
* 16-bit | 557,056 | 65,535
*
* Key Advantages:
* 1. Enables larger window sizes due to reduced memory overhead
* 2. More efficient for smaller scalar counts:
* - 16 chunks: (16 × 255) + 256 = 4,336 ops
* - ~2x faster than standard 8,191 ops
*
* Limitations:
* - Not suitable for plain precomputes (requires 256 constant doublings)
* - Performance degrades with larger scalar counts:
* - Optimal for ~256 scalars
* - Less efficient for 4096+ scalars (Pippenger preferred)
*/
const fieldN = c.Fn;
validateW(windowSize, fieldN.BITS);
validateMSMPoints(points, c);
const zero = c.ZERO;
const tableSize = 2 ** windowSize - 1; // table size (without zero)
const chunks = Math.ceil(fieldN.BITS / windowSize); // chunks of item
const MASK = bitMask(windowSize);
const tables = points.map((p) => {
const res = [];
for (let i = 0, acc = p; i < tableSize; i++) {
res.push(acc);
acc = acc.add(p);
}
return res;
});
return (scalars) => {
validateMSMScalars(scalars, fieldN);
if (scalars.length > points.length)
throw new Error('array of scalars must be smaller than array of points');
let res = zero;
for (let i = 0; i < chunks; i++) {
// No need to double if accumulator is still zero.
if (res !== zero)
for (let j = 0; j < windowSize; j++)
res = res.double();
const shiftBy = BigInt(chunks * windowSize - (i + 1) * windowSize);
for (let j = 0; j < scalars.length; j++) {
const n = scalars[j];
const curr = Number((n >> shiftBy) & MASK);
if (!curr)
continue; // skip zero scalars chunks
res = res.add(tables[j][curr - 1]);
}
}
return res;
};
}
function createField(order, field, isLE) {
if (field) {
// Reuse supplied field overrides as-is; `isLE` only affects freshly constructed fallback
// fields, and validateField() below only checks the arithmetic subset, not full byte/cmov
// behavior.
if (field.ORDER !== order)
throw new Error('Field.ORDER must match order: Fp == p, Fn == n');
validateField(field);
return field;
}
else {
return Field(order, { isLE });
}
}
/**
* Validates basic CURVE shape and field membership, then creates fields.
* This does not prove that the generator is on-curve, that subgroup/order data are consistent, or
* that the curve equation itself is otherwise sane.
* @param type - Curve family.
* @param CURVE - Curve parameters.
* @param curveOpts - Optional field overrides:
* - `Fp` (optional): Optional base-field override.
* - `Fn` (optional): Optional scalar-field override.
* @param FpFnLE - Whether field encoding is little-endian.
* @returns Frozen curve parameters and fields.
* @throws If the curve parameters or field overrides are invalid. {@link Error}
* @example
* Build curve fields from raw constants before constructing a curve instance.
*
* ```ts
* const curve = createCurveFields('weierstrass', {
* p: 17n,
* n: 19n,
* h: 1n,
* a: 2n,
* b: 2n,
* Gx: 5n,
* Gy: 1n,
* });
* ```
*/
export function createCurveFields(type, CURVE, curveOpts = {}, FpFnLE) {
if (FpFnLE === undefined)
FpFnLE = type === 'edwards';
if (!CURVE || typeof CURVE !== 'object')
throw new Error(`expected valid ${type} CURVE object`);
for (const p of ['p', 'n', 'h']) {
const val = CURVE[p];
if (!(typeof val === 'bigint' && val > _0n))
throw new Error(`CURVE.${p} must be positive bigint`);
}
const Fp = createField(CURVE.p, curveOpts.Fp, FpFnLE);
const Fn = createField(CURVE.n, curveOpts.Fn, FpFnLE);
const _b = type === 'weierstrass' ? 'b' : 'd';
const params = ['Gx', 'Gy', 'a', _b];
for (const p of params) {
// @ts-ignore
if (!Fp.isValid(CURVE[p]))
throw new Error(`CURVE.${p} must be valid field element of CURVE.Fp`);
}
CURVE = Object.freeze(Object.assign({}, CURVE));
return { CURVE, Fp, Fn };
}
/**
* @param randomSecretKey - Secret-key generator.
* @param getPublicKey - Public-key derivation helper.
* @returns Keypair generator.
* @example
* Build a `keygen()` helper from existing secret-key and public-key primitives.
*
* ```ts
* import { createKeygen } from '@noble/curves/abstract/curve.js';
* import { p256 } from '@noble/curves/nist.js';
* const keygen = createKeygen(p256.utils.randomSecretKey, p256.getPublicKey);
* const pair = keygen();
* ```
*/
export function createKeygen(randomSecretKey, getPublicKey) {
return function keygen(seed) {
const secretKey = randomSecretKey(seed);
return { secretKey, publicKey: getPublicKey(secretKey) };
};
}
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/**
* Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y².
* For design rationale of types / exports, see weierstrass module documentation.
* Untwisted Edwards curves exist, but they aren't used in real-world protocols.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type FHash, type TArg, type TRet } from '../utils.ts';
import { type AffinePoint, type CurveLengths, type CurvePoint, type CurvePointCons } from './curve.ts';
import { type IField } from './modular.ts';
/** Extended Edwards point with X/Y/Z/T coordinates. */
export interface EdwardsPoint extends CurvePoint<bigint, EdwardsPoint> {
/** extended X coordinate. Different from affine x. */
readonly X: bigint;
/** extended Y coordinate. Different from affine y. */
readonly Y: bigint;
/** extended Z coordinate */
readonly Z: bigint;
/** extended T coordinate */
readonly T: bigint;
}
/** Constructor and decoding helpers for extended Edwards points. */
export interface EdwardsPointCons extends CurvePointCons<EdwardsPoint> {
/** Create a point from extended X/Y/Z/T coordinates without validation. */
new (X: bigint, Y: bigint, Z: bigint, T: bigint): EdwardsPoint;
/**
* Return the curve parameters used by this point constructor.
* @returns Curve parameters.
*/
CURVE(): EdwardsOpts;
/**
* Decode a point from bytes, optionally using ZIP-215 rules.
* @param bytes - Encoded point bytes.
* @param zip215 - Whether to accept ZIP-215 encodings.
* @returns Decoded Edwards point.
*/
fromBytes(bytes: Uint8Array, zip215?: boolean): EdwardsPoint;
/**
* Decode a point from hex, optionally using ZIP-215 rules.
* @param hex - Encoded point hex.
* @param zip215 - Whether to accept ZIP-215 encodings.
* @returns Decoded Edwards point.
*/
fromHex(hex: string, zip215?: boolean): EdwardsPoint;
}
/**
* Twisted Edwards curve options.
*
* * a: formula param
* * d: formula param
* * p: prime characteristic (order) of finite field, in which arithmetics is done
* * n: order of prime subgroup a.k.a total amount of valid curve points
* * h: cofactor. h*n is group order; n is subgroup order
* * Gx: x coordinate of generator point a.k.a. base point
* * Gy: y coordinate of generator point
*/
export type EdwardsOpts = Readonly<{
/** Base-field modulus. */
p: bigint;
/** Prime subgroup order. */
n: bigint;
/** Curve cofactor. */
h: bigint;
/** Edwards curve parameter `a`. */
a: bigint;
/** Edwards curve parameter `d`. */
d: bigint;
/** Generator x coordinate. */
Gx: bigint;
/** Generator y coordinate. */
Gy: bigint;
}>;
/**
* Extra curve options for Twisted Edwards.
*
* * Fp: redefined Field over curve.p
* * Fn: redefined Field over curve.n
* * uvRatio: helper function for decompression, calculating √(u/v)
*/
export type EdwardsExtraOpts = Partial<{
/** Optional base-field override. */
Fp: IField<bigint>;
/** Optional scalar-field override. */
Fn: IField<bigint>;
/** Whether field encodings are little-endian. */
FpFnLE: boolean;
/** Square-root ratio helper used during point decompression. */
uvRatio: (u: bigint, v: bigint) => {
isValid: boolean;
value: bigint;
};
}>;
/**
* EdDSA (Edwards Digital Signature algorithm) options.
*
* * hash: hash function used to hash secret keys and messages
* * adjustScalarBytes: clears bits to get valid field element
* * domain: Used for hashing
* * mapToCurve: for hash-to-curve standard
* * prehash: RFC 8032 pre-hashing of messages to sign() / verify()
* * randomBytes: function generating random bytes, used for randomSecretKey
*/
export type EdDSAOpts = Partial<{
/** Clamp or otherwise normalize secret-scalar bytes before reducing mod `n`. */
adjustScalarBytes: (bytes: TArg<Uint8Array>) => TRet<Uint8Array>;
/** Domain-separation helper for contexts and prehash mode. */
domain: (data: TArg<Uint8Array>, ctx: TArg<Uint8Array>, phflag: boolean) => TRet<Uint8Array>;
/** Optional hash-to-curve mapper for protocols like Ristretto hash-to-group. */
mapToCurve: (scalar: bigint[]) => AffinePoint<bigint>;
/** Optional prehash function used before signing or verifying messages. */
prehash: FHash;
/** Default verification decoding policy. ZIP-215 is more permissive than RFC 8032 / NIST. */
zip215: boolean;
/** RNG override used by helper constructors. */
randomBytes: (bytesLength?: number) => TRet<Uint8Array>;
}>;
/**
* EdDSA (Edwards Digital Signature algorithm) helper namespace.
* Allows creating and verifying signatures, and deriving public keys.
*/
export interface EdDSA {
/**
* Generate a secret/public key pair.
* @param seed - Optional seed material.
* @returns Secret/public key pair.
*/
keygen: (seed?: TArg<Uint8Array>) => {
secretKey: TRet<Uint8Array>;
publicKey: TRet<Uint8Array>;
};
/**
* Derive the public key from a secret key.
* @param secretKey - Secret key bytes.
* @returns Encoded public key.
*/
getPublicKey: (secretKey: TArg<Uint8Array>) => TRet<Uint8Array>;
/**
* Sign a message with an EdDSA secret key.
* @param message - Message bytes.
* @param secretKey - Secret key bytes.
* @param options - Optional signature tweaks:
* - `context` (optional): Domain-separation context for Ed25519ctx/Ed448.
* @returns Encoded signature bytes.
*/
sign: (message: TArg<Uint8Array>, secretKey: TArg<Uint8Array>, options?: TArg<{
context?: Uint8Array;
}>) => TRet<Uint8Array>;
/**
* Verify a signature against a message and public key.
* @param sig - Encoded signature bytes.
* @param message - Message bytes.
* @param publicKey - Encoded public key.
* @param options - Optional verification tweaks:
* - `context` (optional): Domain-separation context for Ed25519ctx/Ed448.
* - `zip215` (optional): Whether to accept ZIP-215 encodings.
* @returns Whether the signature is valid.
*/
verify: (sig: TArg<Uint8Array>, message: TArg<Uint8Array>, publicKey: TArg<Uint8Array>, options?: TArg<{
context?: Uint8Array;
zip215?: boolean;
}>) => boolean;
/** Point constructor used by this signature scheme. */
Point: EdwardsPointCons;
/** Helper utilities for key validation and Montgomery conversion. */
utils: {
/**
* Generate a valid random secret key.
* Optional seed bytes are only length-checked and returned unchanged.
*/
randomSecretKey: (seed?: TArg<Uint8Array>) => TRet<Uint8Array>;
/** Check whether a secret key has the expected encoding. */
isValidSecretKey: (secretKey: TArg<Uint8Array>) => boolean;
/** Check whether a public key decodes to a valid point. */
isValidPublicKey: (publicKey: TArg<Uint8Array>, zip215?: boolean) => boolean;
/**
* Converts ed public key to x public key.
*
* There is NO `fromMontgomery`:
* - There are 2 valid ed25519 points for every x25519, with flipped coordinate
* - Sometimes there are 0 valid ed25519 points, because x25519 *additionally*
* accepts inputs on the quadratic twist, which can't be moved to ed25519
*
* @example
* Converts ed public key to x public key.
*
* ```js
* const someonesPub_ed = ed25519.getPublicKey(ed25519.utils.randomSecretKey());
* const someonesPub = ed25519.utils.toMontgomery(someonesPub);
* const aPriv = x25519.utils.randomSecretKey();
* const shared = x25519.getSharedSecret(aPriv, someonesPub)
* ```
*/
toMontgomery: (publicKey: TArg<Uint8Array>) => TRet<Uint8Array>;
/**
* Converts ed secret key to x secret key.
* @example
* Converts ed secret key to x secret key.
*
* ```js
* const someonesPub = x25519.getPublicKey(x25519.utils.randomSecretKey());
* const aPriv_ed = ed25519.utils.randomSecretKey();
* const aPriv = ed25519.utils.toMontgomerySecret(aPriv_ed);
* const shared = x25519.getSharedSecret(aPriv, someonesPub)
* ```
*/
toMontgomerySecret: (secretKey: TArg<Uint8Array>) => TRet<Uint8Array>;
/** Return the expanded private key components used by RFC8032 signing. */
getExtendedPublicKey: (key: TArg<Uint8Array>) => {
head: TRet<Uint8Array>;
prefix: TRet<Uint8Array>;
scalar: bigint;
point: EdwardsPoint;
pointBytes: TRet<Uint8Array>;
};
};
/** Byte lengths for keys and signatures exposed by this scheme. */
lengths: CurveLengths;
}
/**
* @param params - Curve parameters. See {@link EdwardsOpts}.
* @param extraOpts - Optional helpers and overrides. See {@link EdwardsExtraOpts}.
* @returns Edwards point constructor. Generator validation here only checks
* that `(Gx, Gy)` satisfies the affine Edwards equation.
* RFC 8032 base-point constraints like `B != (0,1)` and `[L]B = 0`
* are left to the caller's chosen parameters, since eager subgroup
* validation here adds about 10-15ms to heavyweight imports like ed448.
* The returned constructor also eagerly marks `Point.BASE` for W=8
* precompute caching. Some code paths still assume
* `Fp.BYTES === Fn.BYTES`, so mismatched byte lengths are not fully audited here.
* @throws If the curve parameters or Edwards overrides are invalid. {@link Error}
* @example
* ```ts
* import { edwards } from '@noble/curves/abstract/edwards.js';
* import { jubjub } from '@noble/curves/misc.js';
* // Build a point constructor from explicit curve parameters, then use its base point.
* const Point = edwards(jubjub.Point.CURVE());
* Point.BASE.toHex();
* ```
*/
export declare function edwards(params: TArg<EdwardsOpts>, extraOpts?: TArg<EdwardsExtraOpts>): EdwardsPointCons;
/**
* Base class for prime-order points like Ristretto255 and Decaf448.
* These points eliminate cofactor issues by representing equivalence classes
* of Edwards curve points. Multiple Edwards representatives can describe the
* same abstract wrapper element, so wrapper validity is not the same thing as
* the hidden representative being torsion-free.
* @param ep - Backing Edwards point.
* @example
* Base class for prime-order points like Ristretto255 and Decaf448.
*
* ```ts
* import { ristretto255 } from '@noble/curves/ed25519.js';
* const point = ristretto255.Point.BASE.multiply(2n);
* ```
*/
export declare abstract class PrimeEdwardsPoint<T extends PrimeEdwardsPoint<T>> implements CurvePoint<bigint, T> {
static BASE: PrimeEdwardsPoint<any>;
static ZERO: PrimeEdwardsPoint<any>;
static Fp: IField<bigint>;
static Fn: IField<bigint>;
protected readonly ep: EdwardsPoint;
/**
* Wrap one internal Edwards representative directly.
* This is not a canonical encoding boundary: alternate Edwards
* representatives may still describe the same abstract wrapper element.
*/
constructor(ep: EdwardsPoint);
abstract toBytes(): Uint8Array;
abstract equals(other: T): boolean;
static fromBytes(_bytes: Uint8Array): any;
static fromHex(_hex: string): any;
get x(): bigint;
get y(): bigint;
clearCofactor(): T;
assertValidity(): void;
/**
* Return affine coordinates of the current internal Edwards representative.
* This is a convenience helper, not a canonical Ristretto/Decaf encoding.
* Equal abstract elements may expose different `x` / `y`; use
* `toBytes()` / `fromBytes()` for canonical roundtrips.
*/
toAffine(invertedZ?: bigint): AffinePoint<bigint>;
toHex(): string;
toString(): string;
isTorsionFree(): boolean;
isSmallOrder(): boolean;
add(other: T): T;
subtract(other: T): T;
multiply(scalar: bigint): T;
multiplyUnsafe(scalar: bigint): T;
double(): T;
negate(): T;
precompute(windowSize?: number, isLazy?: boolean): T;
abstract is0(): boolean;
protected abstract assertSame(other: T): void;
protected abstract init(ep: EdwardsPoint): T;
}
/**
* Initializes EdDSA signatures over given Edwards curve.
* @param Point - Edwards point constructor.
* @param cHash - Hash function.
* @param eddsaOpts - Optional signature helpers. See {@link EdDSAOpts}.
* @returns EdDSA helper namespace.
* @throws If the hash function, options, or derived point operations are invalid. {@link Error}
* @example
* Initializes EdDSA signatures over given Edwards curve.
*
* ```ts
* import { eddsa } from '@noble/curves/abstract/edwards.js';
* import { jubjub } from '@noble/curves/misc.js';
* import { sha512 } from '@noble/hashes/sha2.js';
* const sigs = eddsa(jubjub.Point, sha512);
* const { secretKey, publicKey } = sigs.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = sigs.sign(msg, secretKey);
* const isValid = sigs.verify(sig, msg, publicKey);
* ```
*/
export declare function eddsa(Point: EdwardsPointCons, cHash: TArg<FHash>, eddsaOpts?: TArg<EdDSAOpts>): EdDSA;
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/**
* Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y².
* For design rationale of types / exports, see weierstrass module documentation.
* Untwisted Edwards curves exist, but they aren't used in real-world protocols.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { abool, abytes, aInRange, asafenumber, bytesToHex, bytesToNumberLE, concatBytes, copyBytes, hexToBytes, isBytes, notImplemented, validateObject, randomBytes as wcRandomBytes, } from "../utils.js";
import { createCurveFields, createKeygen, normalizeZ, wNAF, } from "./curve.js";
import {} from "./modular.js";
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n = /* @__PURE__ */ BigInt(0), _1n = /* @__PURE__ */ BigInt(1), _2n = /* @__PURE__ */ BigInt(2), _8n = /* @__PURE__ */ BigInt(8);
// Affine Edwards-equation check only; this does not prove subgroup membership, canonical
// encoding, prime-order base-point requirements, or identity exclusion.
function isEdValidXY(Fp, CURVE, x, y) {
const x2 = Fp.sqr(x);
const y2 = Fp.sqr(y);
const left = Fp.add(Fp.mul(CURVE.a, x2), y2);
const right = Fp.add(Fp.ONE, Fp.mul(CURVE.d, Fp.mul(x2, y2)));
return Fp.eql(left, right);
}
/**
* @param params - Curve parameters. See {@link EdwardsOpts}.
* @param extraOpts - Optional helpers and overrides. See {@link EdwardsExtraOpts}.
* @returns Edwards point constructor. Generator validation here only checks
* that `(Gx, Gy)` satisfies the affine Edwards equation.
* RFC 8032 base-point constraints like `B != (0,1)` and `[L]B = 0`
* are left to the caller's chosen parameters, since eager subgroup
* validation here adds about 10-15ms to heavyweight imports like ed448.
* The returned constructor also eagerly marks `Point.BASE` for W=8
* precompute caching. Some code paths still assume
* `Fp.BYTES === Fn.BYTES`, so mismatched byte lengths are not fully audited here.
* @throws If the curve parameters or Edwards overrides are invalid. {@link Error}
* @example
* ```ts
* import { edwards } from '@noble/curves/abstract/edwards.js';
* import { jubjub } from '@noble/curves/misc.js';
* // Build a point constructor from explicit curve parameters, then use its base point.
* const Point = edwards(jubjub.Point.CURVE());
* Point.BASE.toHex();
* ```
*/
export function edwards(params, extraOpts = {}) {
const opts = extraOpts;
const validated = createCurveFields('edwards', params, opts, opts.FpFnLE);
const { Fp, Fn } = validated;
let CURVE = validated.CURVE;
const { h: cofactor } = CURVE;
validateObject(opts, {}, { uvRatio: 'function' });
// Important:
// There are some places where Fp.BYTES is used instead of nByteLength.
// So far, everything has been tested with curves of Fp.BYTES == nByteLength.
// TODO: test and find curves which behave otherwise.
const MASK = _2n << (BigInt(Fn.BYTES * 8) - _1n);
const modP = (n) => Fp.create(n); // Function overrides
// sqrt(u/v)
const uvRatio = opts.uvRatio === undefined
? (u, v) => {
try {
return { isValid: true, value: Fp.sqrt(Fp.div(u, v)) };
}
catch (e) {
return { isValid: false, value: _0n };
}
}
: opts.uvRatio;
// Validate whether the passed curve params are valid.
// equation ax² + y² = 1 + dx²y² should work for generator point.
if (!isEdValidXY(Fp, CURVE, CURVE.Gx, CURVE.Gy))
throw new Error('bad curve params: generator point');
/**
* Asserts coordinate is valid: 0 <= n < MASK.
* Coordinates >= Fp.ORDER are allowed for zip215.
*/
function acoord(title, n, banZero = false) {
const min = banZero ? _1n : _0n;
aInRange('coordinate ' + title, n, min, MASK);
return n;
}
function aedpoint(other) {
if (!(other instanceof Point))
throw new Error('EdwardsPoint expected');
}
// Extended Point works in extended coordinates: (X, Y, Z, T) ∋ (x=X/Z, y=Y/Z, T=xy).
// https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinates
class Point {
// base / generator point
static BASE = new Point(CURVE.Gx, CURVE.Gy, _1n, modP(CURVE.Gx * CURVE.Gy));
// zero / infinity / identity point
static ZERO = new Point(_0n, _1n, _1n, _0n); // 0, 1, 1, 0
// math field
static Fp = Fp;
// scalar field
static Fn = Fn;
X;
Y;
Z;
T;
constructor(X, Y, Z, T) {
this.X = acoord('x', X);
this.Y = acoord('y', Y);
this.Z = acoord('z', Z, true);
this.T = acoord('t', T);
Object.freeze(this);
}
static CURVE() {
return CURVE;
}
/**
* Create one extended Edwards point from affine coordinates.
* Does NOT validate that the point is on-curve or torsion-free.
* Use `.assertValidity()` on adversarial inputs.
*/
static fromAffine(p) {
if (p instanceof Point)
throw new Error('extended point not allowed');
const { x, y } = p || {};
acoord('x', x);
acoord('y', y);
return new Point(x, y, _1n, modP(x * y));
}
// Uses algo from RFC8032 5.1.3.
static fromBytes(bytes, zip215 = false) {
const len = Fp.BYTES;
const { a, d } = CURVE;
bytes = copyBytes(abytes(bytes, len, 'point'));
abool(zip215, 'zip215');
const normed = copyBytes(bytes); // copy again, we'll manipulate it
const lastByte = bytes[len - 1]; // select last byte
normed[len - 1] = lastByte & ~0x80; // clear last bit
const y = bytesToNumberLE(normed);
// zip215=true is good for consensus-critical apps. =false follows RFC8032 / NIST186-5.
// RFC8032 prohibits >= p, but ZIP215 doesn't
// zip215=true: 0 <= y < MASK (2^256 for ed25519)
// zip215=false: 0 <= y < P (2^255-19 for ed25519)
const max = zip215 ? MASK : Fp.ORDER;
aInRange('point.y', y, _0n, max);
// Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:
// ax²+y²=1+dx²y² => y²-1=dx²y²-ax² => y²-1=x²(dy²-a) => x²=(y²-1)/(dy²-a)
const y2 = modP(y * y); // denominator is always non-0 mod p.
const u = modP(y2 - _1n); // u = y² - 1
const v = modP(d * y2 - a); // v = d y² + 1.
let { isValid, value: x } = uvRatio(u, v); // √(u/v)
if (!isValid)
throw new Error('bad point: invalid y coordinate');
const isXOdd = (x & _1n) === _1n; // There are 2 square roots. Use x_0 bit to select proper
const isLastByteOdd = (lastByte & 0x80) !== 0; // x_0, last bit
if (!zip215 && x === _0n && isLastByteOdd)
// if x=0 and x_0 = 1, fail
throw new Error('bad point: x=0 and x_0=1');
if (isLastByteOdd !== isXOdd)
x = modP(-x); // if x_0 != x mod 2, set x = p-x
return Point.fromAffine({ x, y });
}
static fromHex(hex, zip215 = false) {
return Point.fromBytes(hexToBytes(hex), zip215);
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
precompute(windowSize = 8, isLazy = true) {
wnaf.createCache(this, windowSize);
if (!isLazy)
this.multiply(_2n); // random number
return this;
}
// Useful in fromAffine() - not for fromBytes(), which always created valid points.
assertValidity() {
const p = this;
const { a, d } = CURVE;
// Keep generic Edwards validation fail-closed on the neutral point.
// Even though ZERO is algebraically valid and can roundtrip through encodings, higher-level
// callers often reach it only through broken hash/scalar plumbing; rejecting it here avoids
// silently treating that degenerate state as an ordinary public point.
if (p.is0())
throw new Error('bad point: ZERO'); // TODO: optimize, with vars below?
// Equation in affine coordinates: ax² + y² = 1 + dx²y²
// Equation in projective coordinates (X/Z, Y/Z, Z): (aX² + Y²)Z² = Z⁴ + dX²Y²
const { X, Y, Z, T } = p;
const X2 = modP(X * X); // X²
const Y2 = modP(Y * Y); // Y²
const Z2 = modP(Z * Z); // Z²
const Z4 = modP(Z2 * Z2); // Z⁴
const aX2 = modP(X2 * a); // aX²
const left = modP(Z2 * modP(aX2 + Y2)); // (aX² + Y²)Z²
const right = modP(Z4 + modP(d * modP(X2 * Y2))); // Z⁴ + dX²Y²
if (left !== right)
throw new Error('bad point: equation left != right (1)');
// In Extended coordinates we also have T, which is x*y=T/Z: check X*Y == Z*T
const XY = modP(X * Y);
const ZT = modP(Z * T);
if (XY !== ZT)
throw new Error('bad point: equation left != right (2)');
}
// Compare one point to another.
equals(other) {
aedpoint(other);
const { X: X1, Y: Y1, Z: Z1 } = this;
const { X: X2, Y: Y2, Z: Z2 } = other;
const X1Z2 = modP(X1 * Z2);
const X2Z1 = modP(X2 * Z1);
const Y1Z2 = modP(Y1 * Z2);
const Y2Z1 = modP(Y2 * Z1);
return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;
}
is0() {
return this.equals(Point.ZERO);
}
negate() {
// Flips point sign to a negative one (-x, y in affine coords)
return new Point(modP(-this.X), this.Y, this.Z, modP(-this.T));
}
// Fast algo for doubling Extended Point.
// https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#doubling-dbl-2008-hwcd
// Cost: 4M + 4S + 1*a + 6add + 1*2.
double() {
const { a } = CURVE;
const { X: X1, Y: Y1, Z: Z1 } = this;
const A = modP(X1 * X1); // A = X12
const B = modP(Y1 * Y1); // B = Y12
const C = modP(_2n * modP(Z1 * Z1)); // C = 2*Z12
const D = modP(a * A); // D = a*A
const x1y1 = X1 + Y1;
const E = modP(modP(x1y1 * x1y1) - A - B); // E = (X1+Y1)2-A-B
const G = D + B; // G = D+B
const F = G - C; // F = G-C
const H = D - B; // H = D-B
const X3 = modP(E * F); // X3 = E*F
const Y3 = modP(G * H); // Y3 = G*H
const T3 = modP(E * H); // T3 = E*H
const Z3 = modP(F * G); // Z3 = F*G
return new Point(X3, Y3, Z3, T3);
}
// Fast algo for adding 2 Extended Points.
// https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#addition-add-2008-hwcd
// Cost: 9M + 1*a + 1*d + 7add.
add(other) {
aedpoint(other);
const { a, d } = CURVE;
const { X: X1, Y: Y1, Z: Z1, T: T1 } = this;
const { X: X2, Y: Y2, Z: Z2, T: T2 } = other;
const A = modP(X1 * X2); // A = X1*X2
const B = modP(Y1 * Y2); // B = Y1*Y2
const C = modP(T1 * d * T2); // C = T1*d*T2
const D = modP(Z1 * Z2); // D = Z1*Z2
const E = modP((X1 + Y1) * (X2 + Y2) - A - B); // E = (X1+Y1)*(X2+Y2)-A-B
const F = D - C; // F = D-C
const G = D + C; // G = D+C
const H = modP(B - a * A); // H = B-a*A
const X3 = modP(E * F); // X3 = E*F
const Y3 = modP(G * H); // Y3 = G*H
const T3 = modP(E * H); // T3 = E*H
const Z3 = modP(F * G); // Z3 = F*G
return new Point(X3, Y3, Z3, T3);
}
subtract(other) {
// Validate before calling `negate()` so wrong inputs fail with the point guard
// instead of leaking a foreign `negate()` error.
aedpoint(other);
return this.add(other.negate());
}
// Constant-time multiplication.
multiply(scalar) {
// 1 <= scalar < L
// Keep the subgroup-scalar contract strict instead of reducing 0 / n to ZERO.
// In keygen/signing-style callers, those values usually mean broken hash/scalar plumbing,
// and failing closed is safer than silently producing the identity point.
if (!Fn.isValidNot0(scalar))
throw new RangeError('invalid scalar: expected 1 <= sc < curve.n');
const { p, f } = wnaf.cached(this, scalar, (p) => normalizeZ(Point, p));
return normalizeZ(Point, [p, f])[0];
}
// Non-constant-time multiplication. Uses double-and-add algorithm.
// It's faster, but should only be used when you don't care about
// an exposed private key e.g. sig verification.
// Keeps the same subgroup-scalar contract: 0 is allowed for public-scalar callers, but
// n and larger values are rejected instead of being reduced mod n to the identity point.
multiplyUnsafe(scalar) {
// 0 <= scalar < L
if (!Fn.isValid(scalar))
throw new RangeError('invalid scalar: expected 0 <= sc < curve.n');
if (scalar === _0n)
return Point.ZERO;
if (this.is0() || scalar === _1n)
return this;
return wnaf.unsafe(this, scalar, (p) => normalizeZ(Point, p));
}
// Checks if point is of small order.
// If you add something to small order point, you will have "dirty"
// point with torsion component.
// Clears cofactor and checks if the result is 0.
isSmallOrder() {
return this.clearCofactor().is0();
}
// Multiplies point by curve order and checks if the result is 0.
// Returns `false` is the point is dirty.
isTorsionFree() {
return wnaf.unsafe(this, CURVE.n).is0();
}
// Converts Extended point to default (x, y) coordinates.
// Can accept precomputed Z^-1 - for example, from invertBatch.
toAffine(invertedZ) {
const p = this;
let iz = invertedZ;
const { X, Y, Z } = p;
const is0 = p.is0();
if (iz == null)
iz = is0 ? _8n : Fp.inv(Z); // 8 was chosen arbitrarily
const x = modP(X * iz);
const y = modP(Y * iz);
const zz = Fp.mul(Z, iz);
if (is0)
return { x: _0n, y: _1n };
if (zz !== _1n)
throw new Error('invZ was invalid');
return { x, y };
}
clearCofactor() {
if (cofactor === _1n)
return this;
return this.multiplyUnsafe(cofactor);
}
toBytes() {
const { x, y } = this.toAffine();
// Fp.toBytes() allows non-canonical encoding of y (>= p).
const bytes = Fp.toBytes(y);
// Each y has 2 valid points: (x, y), (x,-y).
// When compressing, it's enough to store y and use the last byte to encode sign of x
bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0;
return bytes;
}
toHex() {
return bytesToHex(this.toBytes());
}
toString() {
return `<Point ${this.is0() ? 'ZERO' : this.toHex()}>`;
}
}
const wnaf = new wNAF(Point, Fn.BITS);
// Keep constructor work cheap: subgroup/generator validation belongs to the caller's curve
// parameters, and doing the extra checks here adds about 10-15ms to heavy module imports.
// Callers that construct custom curves are responsible for supplying the correct base point.
// try {
// Point.BASE.assertValidity();
// if (!Point.BASE.isTorsionFree()) throw new Error('bad point: not in prime-order subgroup');
// } catch {
// throw new Error('bad curve params: generator point');
// }
// Tiny toy curves can have scalar fields narrower than 8 bits. Skip the
// eager W=8 cache there instead of rejecting an otherwise valid constructor.
if (Fn.BITS >= 8)
Point.BASE.precompute(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
Object.freeze(Point.prototype);
Object.freeze(Point);
return Point;
}
/**
* Base class for prime-order points like Ristretto255 and Decaf448.
* These points eliminate cofactor issues by representing equivalence classes
* of Edwards curve points. Multiple Edwards representatives can describe the
* same abstract wrapper element, so wrapper validity is not the same thing as
* the hidden representative being torsion-free.
* @param ep - Backing Edwards point.
* @example
* Base class for prime-order points like Ristretto255 and Decaf448.
*
* ```ts
* import { ristretto255 } from '@noble/curves/ed25519.js';
* const point = ristretto255.Point.BASE.multiply(2n);
* ```
*/
export class PrimeEdwardsPoint {
static BASE;
static ZERO;
static Fp;
static Fn;
ep;
/**
* Wrap one internal Edwards representative directly.
* This is not a canonical encoding boundary: alternate Edwards
* representatives may still describe the same abstract wrapper element.
*/
constructor(ep) {
this.ep = ep;
}
// Static methods that must be implemented by subclasses
static fromBytes(_bytes) {
notImplemented();
}
static fromHex(_hex) {
notImplemented();
}
get x() {
return this.toAffine().x;
}
get y() {
return this.toAffine().y;
}
// Common implementations
clearCofactor() {
// no-op for the abstract prime-order wrapper group; this is about the
// wrapper element, not the hidden Edwards representative.
return this;
}
assertValidity() {
// Keep wrapper validity at the abstract-group boundary. Canonical decode
// may choose Edwards representatives that differ by small torsion, so
// checking `this.ep.isTorsionFree()` here would reject valid wrapper points.
this.ep.assertValidity();
}
/**
* Return affine coordinates of the current internal Edwards representative.
* This is a convenience helper, not a canonical Ristretto/Decaf encoding.
* Equal abstract elements may expose different `x` / `y`; use
* `toBytes()` / `fromBytes()` for canonical roundtrips.
*/
toAffine(invertedZ) {
return this.ep.toAffine(invertedZ);
}
toHex() {
return bytesToHex(this.toBytes());
}
toString() {
return this.toHex();
}
isTorsionFree() {
// Abstract Ristretto/Decaf elements are already prime-order even when the
// hidden Edwards representative is not torsion-free.
return true;
}
isSmallOrder() {
return false;
}
add(other) {
this.assertSame(other);
return this.init(this.ep.add(other.ep));
}
subtract(other) {
this.assertSame(other);
return this.init(this.ep.subtract(other.ep));
}
multiply(scalar) {
return this.init(this.ep.multiply(scalar));
}
multiplyUnsafe(scalar) {
return this.init(this.ep.multiplyUnsafe(scalar));
}
double() {
return this.init(this.ep.double());
}
negate() {
return this.init(this.ep.negate());
}
precompute(windowSize, isLazy) {
this.ep.precompute(windowSize, isLazy);
// Keep the wrapper identity stable like the backing Edwards API instead of
// allocating a fresh wrapper around the same cached point.
return this;
}
}
/**
* Initializes EdDSA signatures over given Edwards curve.
* @param Point - Edwards point constructor.
* @param cHash - Hash function.
* @param eddsaOpts - Optional signature helpers. See {@link EdDSAOpts}.
* @returns EdDSA helper namespace.
* @throws If the hash function, options, or derived point operations are invalid. {@link Error}
* @example
* Initializes EdDSA signatures over given Edwards curve.
*
* ```ts
* import { eddsa } from '@noble/curves/abstract/edwards.js';
* import { jubjub } from '@noble/curves/misc.js';
* import { sha512 } from '@noble/hashes/sha2.js';
* const sigs = eddsa(jubjub.Point, sha512);
* const { secretKey, publicKey } = sigs.keygen();
* const msg = new TextEncoder().encode('hello noble');
* const sig = sigs.sign(msg, secretKey);
* const isValid = sigs.verify(sig, msg, publicKey);
* ```
*/
export function eddsa(Point, cHash, eddsaOpts = {}) {
if (typeof cHash !== 'function')
throw new Error('"hash" function param is required');
const hash = cHash;
const opts = eddsaOpts;
validateObject(opts, {}, {
adjustScalarBytes: 'function',
randomBytes: 'function',
domain: 'function',
prehash: 'function',
zip215: 'boolean',
mapToCurve: 'function',
});
const { prehash } = opts;
const { BASE, Fp, Fn } = Point;
const outputLen = hash.outputLen;
const expectedLen = 2 * Fp.BYTES;
// When hash metadata is available, reject incompatible EdDSA wrappers at construction time
// instead of deferring the mismatch until the first keygen/sign call.
if (outputLen !== undefined) {
asafenumber(outputLen, 'hash.outputLen');
if (outputLen !== expectedLen)
throw new Error(`hash.outputLen must be ${expectedLen}, got ${outputLen}`);
}
const randomBytes = opts.randomBytes === undefined ? wcRandomBytes : opts.randomBytes;
const adjustScalarBytes = opts.adjustScalarBytes === undefined
? (bytes) => bytes
: opts.adjustScalarBytes;
const domain = opts.domain === undefined
? (data, ctx, phflag) => {
abool(phflag, 'phflag');
if (ctx.length || phflag)
throw new Error('Contexts/pre-hash are not supported');
return data;
}
: opts.domain; // NOOP
// Parse an EdDSA digest as a little-endian integer and reduce it modulo the scalar field order.
function modN_LE(hash) {
return Fn.create(bytesToNumberLE(hash)); // Not Fn.fromBytes: it has length limit
}
// Get the hashed private scalar per RFC8032 5.1.5
function getPrivateScalar(key) {
const len = lengths.secretKey;
abytes(key, lengths.secretKey, 'secretKey');
// Hash private key with curve's hash function to produce uniformingly random input
// Check byte lengths: ensure(64, h(ensure(32, key)))
const hashed = abytes(hash(key), 2 * len, 'hashedSecretKey');
// Slice before clamping so in-place adjustors don't corrupt the prefix half.
const head = adjustScalarBytes(hashed.slice(0, len)); // clear first half bits, produce FE
const prefix = hashed.slice(len, 2 * len); // second half is called key prefix (5.1.6)
const scalar = modN_LE(head); // The actual private scalar
return { head, prefix, scalar };
}
/** Convenience method that creates public key from scalar. RFC8032 5.1.5
* Also exposes the derived scalar/prefix tuple and point form reused by sign().
*/
function getExtendedPublicKey(secretKey) {
const { head, prefix, scalar } = getPrivateScalar(secretKey);
const point = BASE.multiply(scalar); // Point on Edwards curve aka public key
const pointBytes = point.toBytes();
return { head, prefix, scalar, point, pointBytes };
}
/** Calculates EdDSA pub key. RFC8032 5.1.5. */
function getPublicKey(secretKey) {
return getExtendedPublicKey(secretKey).pointBytes;
}
// Hash domain-separated chunks into a little-endian scalar modulo the group order.
function hashDomainToScalar(context = Uint8Array.of(), ...msgs) {
const msg = concatBytes(...msgs);
return modN_LE(hash(domain(msg, abytes(context, undefined, 'context'), !!prehash)));
}
/** Signs message with secret key. RFC8032 5.1.6 */
function sign(msg, secretKey, options = {}) {
msg = abytes(msg, undefined, 'message');
if (prehash)
msg = prehash(msg); // for ed25519ph etc.
const { prefix, scalar, pointBytes } = getExtendedPublicKey(secretKey);
const r = hashDomainToScalar(options.context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
// RFC 8032 5.1.6 allows r mod L = 0, and SUPERCOP ref10 accepts the resulting identity-point
// signature.
// We intentionally keep the safe multiply() rejection here so a miswired all-zero hash provider
// fails loudly instead of silently producing a degenerate signature.
const R = BASE.multiply(r).toBytes(); // R = rG
const k = hashDomainToScalar(options.context, R, pointBytes, msg); // R || A || PH(M)
const s = Fn.create(r + k * scalar); // S = (r + k * s) mod L
if (!Fn.isValid(s))
throw new Error('sign failed: invalid s'); // 0 <= s < L
const rs = concatBytes(R, Fn.toBytes(s));
return abytes(rs, lengths.signature, 'result');
}
// Keep the shared helper strict by default: RFC 8032 / NIST-style wrappers should reject
// non-canonical encodings unless they explicitly opt into ZIP-215's more permissive decode rules.
const verifyOpts = {
zip215: opts.zip215,
};
/**
* Verifies EdDSA signature against message and public key. RFC 8032 §§5.1.7 and 5.2.7.
* A cofactored verification equation is checked.
*/
function verify(sig, msg, publicKey, options = verifyOpts) {
// Preserve the wrapper-selected default for `{}` / `{ zip215: undefined }`, not just omitted opts.
const { context } = options;
const zip215 = options.zip215 === undefined ? !!verifyOpts.zip215 : options.zip215;
const len = lengths.signature;
sig = abytes(sig, len, 'signature');
msg = abytes(msg, undefined, 'message');
publicKey = abytes(publicKey, lengths.publicKey, 'publicKey');
if (zip215 !== undefined)
abool(zip215, 'zip215');
if (prehash)
msg = prehash(msg); // for ed25519ph, etc
const mid = len / 2;
const r = sig.subarray(0, mid);
const s = bytesToNumberLE(sig.subarray(mid, len));
let A, R, SB;
try {
// ZIP-215 is more permissive than RFC 8032 / NIST186-5. Use it only for wrappers that
// explicitly want consensus-style unreduced encoding acceptance.
// zip215=true: 0 <= y < MASK (2^256 for ed25519)
// zip215=false: 0 <= y < P (2^255-19 for ed25519)
A = Point.fromBytes(publicKey, zip215);
R = Point.fromBytes(r, zip215);
SB = BASE.multiplyUnsafe(s); // 0 <= s < l is done inside
}
catch (error) {
return false;
}
// RFC 8032 §§5.1.7/5.2.7 and FIPS 186-5 §§7.7.2/7.8.2 only decode A' and check the cofactored
// verification equation; they do not add a separate low-order-public-key rejection here.
// Strict mode still rejects small-order A' intentionally for SBS-style non-repudiation and to
// avoid ambiguous verification outcomes where unusual low-order keys can make distinct
// key/signature/message combinations verify.
if (!zip215 && A.isSmallOrder())
return false;
// ZIP-215 accepts noncanonical / unreduced point encodings, so the challenge hash must use the
// exact signature/public-key bytes rather than canonicalized re-encodings of the decoded points.
const k = hashDomainToScalar(context, r, publicKey, msg);
const RkA = R.add(A.multiplyUnsafe(k));
// Check the cofactored verification equation via the curve cofactor h.
// [h][S]B = [h]R + [h][k]A'
return RkA.subtract(SB).clearCofactor().is0();
}
const _size = Fp.BYTES; // 32 for ed25519, 57 for ed448
const lengths = {
secretKey: _size,
publicKey: _size,
signature: 2 * _size,
seed: _size,
};
function randomSecretKey(seed) {
seed = seed === undefined ? randomBytes(lengths.seed) : seed;
return abytes(seed, lengths.seed, 'seed');
}
function isValidSecretKey(key) {
return isBytes(key) && key.length === lengths.secretKey;
}
function isValidPublicKey(key, zip215) {
try {
// Preserve the wrapper-selected default for omitted / `undefined` ZIP-215 flags here too.
return !!Point.fromBytes(key, zip215 === undefined ? verifyOpts.zip215 : zip215);
}
catch (error) {
return false;
}
}
const utils = {
getExtendedPublicKey,
randomSecretKey,
isValidSecretKey,
isValidPublicKey,
/**
* Converts ed public key to x public key. Uses formula:
* - ed25519:
* - `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)`
* - `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))`
* - ed448:
* - `(u, v) = ((y-1)/(y+1), sqrt(156324)*u/x)`
* - `(x, y) = (sqrt(156324)*u/v, (1+u)/(1-u))`
*/
toMontgomery(publicKey) {
const { y } = Point.fromBytes(publicKey);
const size = lengths.publicKey;
const is25519 = size === 32;
if (!is25519 && size !== 57)
throw new Error('only defined for 25519 and 448');
const u = is25519 ? Fp.div(_1n + y, _1n - y) : Fp.div(y - _1n, y + _1n);
return Fp.toBytes(u);
},
toMontgomerySecret(secretKey) {
const size = lengths.secretKey;
abytes(secretKey, size);
const hashed = hash(secretKey.subarray(0, size));
return adjustScalarBytes(hashed).subarray(0, size);
},
};
Object.freeze(lengths);
Object.freeze(utils);
return Object.freeze({
keygen: createKeygen(randomSecretKey, getPublicKey),
getPublicKey,
sign,
verify,
utils,
Point,
lengths,
});
}
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/**
* Experimental implementation of NTT / FFT (Fast Fourier Transform) over finite fields.
* API may change at any time. The code has not been audited. Feature requests are welcome.
* @module
*/
import type { TArg } from '../utils.ts';
import type { IField } from './modular.ts';
/** Array-like coefficient storage that can be mutated in place. */
export interface MutableArrayLike<T> {
/** Element access by numeric index. */
[index: number]: T;
/** Current amount of stored coefficients. */
length: number;
/**
* Return a sliced copy using the same storage shape.
* @param start - Inclusive start index.
* @param end - Exclusive end index.
* @returns Sliced copy.
*/
slice(start?: number, end?: number): this;
/**
* Iterate over stored coefficients in order.
* @returns Coefficient iterator.
*/
[Symbol.iterator](): Iterator<T>;
}
/**
* Concrete polynomial containers accepted by the high-level `poly(...)` helpers.
* Lower-level FFT helpers can work with structural `MutableArrayLike`, but `poly(...)`
* intentionally keeps runtime dispatch on plain arrays and typed-array views.
*/
export type PolyStorage<T> = T[] | (MutableArrayLike<T> & ArrayBufferView);
/**
* Checks if integer is in form of `1 << X`.
* @param x - Integer to inspect.
* @returns `true` when the value is a power of two.
* @throws If `x` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Validate that an FFT size is a power of two.
*
* ```ts
* isPowerOfTwo(8);
* ```
*/
export declare function isPowerOfTwo(x: number): boolean;
/**
* @param n - Input value.
* @returns Next power of two within the u32/array-length domain.
* @throws If `n` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Round an integer up to the FFT size it needs.
*
* ```ts
* nextPowerOfTwo(9);
* ```
*/
export declare function nextPowerOfTwo(n: number): number;
/**
* @param n - Value to reverse.
* @param bits - Number of bits to use.
* @returns Bit-reversed integer.
* @throws If `n` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Reverse the low `bits` bits of one index.
*
* ```ts
* reverseBits(3, 3);
* ```
*/
export declare function reverseBits(n: number, bits: number): number;
/**
* Similar to `bitLen(x)-1` but much faster for small integers, like indices.
* @param n - Input value.
* @returns Base-2 logarithm. For `n = 0`, the current implementation returns `-1`.
* @throws If `n` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Compute the radix-2 stage count for one transform size.
*
* ```ts
* log2(8);
* ```
*/
export declare function log2(n: number): number;
/**
* Moves lowest bit to highest position, which at first step splits
* array on even and odd indices, then it applied again to each part,
* which is core of fft
* @param values - Mutable coefficient array.
* @returns Mutated input array.
* @throws If the array length is not a positive power of two. {@link Error}
* @example
* Reorder coefficients into bit-reversed order in place.
*
* ```ts
* const values = Uint8Array.from([0, 1, 2, 3]);
* bitReversalInplace(values);
* ```
*/
export declare function bitReversalInplace<T extends MutableArrayLike<any>>(values: T): T;
/**
* @param values - Input values.
* @returns Reordered copy.
* @throws If the array length is not a positive power of two. {@link Error}
* @example
* Return a reordered copy instead of mutating the input in place.
*
* ```ts
* const reordered = bitReversalPermutation([0, 1, 2, 3]);
* ```
*/
export declare function bitReversalPermutation<T>(values: T[]): T[];
/** Cached roots-of-unity tables derived from one finite field. */
export type RootsOfUnity = {
/** Generator and 2-adicity metadata for the cached field. */
info: {
G: bigint;
oddFactor: bigint;
powerOfTwo: number;
};
/**
* Return the natural-order roots of unity for one radix-2 size.
* @param bits - Transform size as `log2(N)`.
* @returns Natural-order roots for that size.
*/
roots: (bits: number) => bigint[];
/**
* Return the bit-reversal permutation of the roots for one radix-2 size.
* @param bits - Transform size as `log2(N)`.
* @returns Bit-reversed roots.
*/
brp(bits: number): bigint[];
/**
* Return the inverse roots of unity for one radix-2 size.
* @param bits - Transform size as `log2(N)`.
* @returns Inverse roots.
*/
inverse(bits: number): bigint[];
/**
* Return one primitive root used by a radix-2 stage.
* @param bits - Transform size as `log2(N)`.
* @returns Primitive root for that stage.
*/
omega: (bits: number) => bigint;
/**
* Drop all cached root tables.
* @returns Nothing.
*/
clear: () => void;
};
/**
* We limit roots up to 2**31, which is a lot: 2-billion polynomimal should be rare.
* @param field - Field implementation.
* @param generator - Optional generator override.
* @returns Roots-of-unity cache.
* @example
* Cache roots once, then ask for the omega table of one FFT size.
*
* ```ts
* import { rootsOfUnity } from '@noble/curves/abstract/fft.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const roots = rootsOfUnity(Field(17n));
* const omega = roots.omega(4);
* ```
*/
export declare function rootsOfUnity(field: TArg<IField<bigint>>, generator?: bigint): RootsOfUnity;
/** Polynomial coefficient container used by the FFT helpers. */
export type Polynomial<T> = MutableArrayLike<T>;
/**
* Arithmetic operations used by the generic FFT implementation.
*
* Maps great to Field<bigint>, but not to Group (EC points):
* - inv from scalar field
* - we need multiplyUnsafe here, instead of multiply for speed
* - multiplyUnsafe is safe in the context: we do mul(rootsOfUnity), which are public and sparse
*/
export type FFTOpts<T, R> = {
/**
* Add two coefficients.
* @param a - Left coefficient.
* @param b - Right coefficient.
* @returns Sum coefficient.
*/
add: (a: T, b: T) => T;
/**
* Subtract two coefficients.
* @param a - Left coefficient.
* @param b - Right coefficient.
* @returns Difference coefficient.
*/
sub: (a: T, b: T) => T;
/**
* Multiply one coefficient by a scalar/root factor.
* @param a - Coefficient value.
* @param scalar - Scalar/root factor.
* @returns Scaled coefficient.
*/
mul: (a: T, scalar: R) => T;
/**
* Invert one scalar/root factor.
* @param a - Scalar/root factor.
* @returns Inverse factor.
*/
inv: (a: R) => R;
};
/** Configuration for one low-level FFT loop. */
export type FFTCoreOpts<R> = {
/** Transform size. Must be a power of two. */
N: number;
/** Stage roots for the selected transform size. */
roots: Polynomial<R>;
/** Whether to run the DIT variant instead of DIF. */
dit: boolean;
/** Whether to invert butterfly placement for decode-oriented layouts. */
invertButterflies?: boolean;
/** Number of initial stages to skip. */
skipStages?: number;
/** Whether to apply bit-reversal permutation at the boundary. */
brp?: boolean;
};
/**
* Callable low-level FFT loop over one polynomial storage shape.
* @param values - Polynomial coefficients to transform in place.
* @returns The mutated input polynomial.
*/
export type FFTCoreLoop<T> = <P extends Polynomial<T>>(values: P) => P;
/**
* Constructs different flavors of FFT. radix2 implementation of low level mutating API. Flavors:
*
* - DIT (Decimation-in-Time): Bottom-Up (leaves to root), Cool-Turkey
* - DIF (Decimation-in-Frequency): Top-Down (root to leaves), Gentleman-Sande
*
* DIT takes brp input, returns natural output.
* DIF takes natural input, returns brp output.
*
* The output is actually identical. Time / frequence distinction is not meaningful
* for Polynomial multiplication in fields.
* Which means if protocol supports/needs brp output/inputs, then we can skip this step.
*
* Cyclic NTT: Rq = Zq[x]/(x^n-1). butterfly_DIT+loop_DIT OR butterfly_DIF+loop_DIT, roots are omega
* Negacyclic NTT: Rq = Zq[x]/(x^n+1). butterfly_DIT+loop_DIF, at least for mlkem / mldsa
* @param F - Field operations.
* @param coreOpts - FFT configuration:
* - `N`: Transform size. Must be a power of two.
* - `roots`: Stage roots for the selected transform size.
* - `dit`: Whether to run the DIT variant instead of DIF.
* - `invertButterflies` (optional): Whether to invert butterfly placement.
* - `skipStages` (optional): Number of initial stages to skip.
* - `brp` (optional): Whether to apply bit-reversal permutation at the boundary.
* @returns Low-level FFT loop.
* @throws If the FFT options or cached roots are invalid for the requested size. {@link Error}
* @example
* Constructs different flavors of FFT.
*
* ```ts
* import { FFTCore, rootsOfUnity } from '@noble/curves/abstract/fft.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const roots = rootsOfUnity(Fp).roots(2);
* const loop = FFTCore(Fp, { N: 4, roots, dit: true });
* const values = loop([1n, 2n, 3n, 4n]);
* ```
*/
export declare const FFTCore: <T, R>(F: FFTOpts<T, R>, coreOpts: FFTCoreOpts<R>) => FFTCoreLoop<T>;
/** Forward and inverse FFT helpers for one coefficient domain. */
export type FFTMethods<T> = {
/**
* Apply the forward transform.
* @param values - Polynomial coefficients to transform.
* @param brpInput - Whether the input is already bit-reversed.
* @param brpOutput - Whether to keep the output bit-reversed.
* @returns Transformed copy.
*/
direct<P extends Polynomial<T>>(values: P, brpInput?: boolean, brpOutput?: boolean): P;
/**
* Apply the inverse transform.
* @param values - Polynomial coefficients to transform.
* @param brpInput - Whether the input is already bit-reversed.
* @param brpOutput - Whether to keep the output bit-reversed.
* @returns Inverse-transformed copy.
*/
inverse<P extends Polynomial<T>>(values: P, brpInput?: boolean, brpOutput?: boolean): P;
};
/**
* NTT aka FFT over finite field (NOT over complex numbers).
* Naming mirrors other libraries.
* @param roots - Roots-of-unity cache.
* @param opts - Field operations. See {@link FFTOpts}.
* @returns Forward and inverse FFT helpers.
* @example
* NTT aka FFT over finite field (NOT over complex numbers).
*
* ```ts
* import { FFT, rootsOfUnity } from '@noble/curves/abstract/fft.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const fft = FFT(rootsOfUnity(Fp), Fp);
* const values = fft.direct([1n, 2n, 3n, 4n]);
* ```
*/
export declare function FFT<T>(roots: RootsOfUnity, opts: FFTOpts<T, bigint>): FFTMethods<T>;
/**
* Factory that allocates one polynomial storage container.
* Callers must ensure `_create(len)` returns field-zero-filled storage when `elm` is omitted,
* because the quadratic `mul()` / `convolve()` paths and the Kronecker-δ shortcut in
* `lagrange.basis()` rely on that default instead of always passing `field.ZERO` explicitly.
* @param len - Requested amount of coefficients.
* @param elm - Optional fill value.
* @returns Newly allocated polynomial container.
*/
export type CreatePolyFn<P extends PolyStorage<T>, T> = (len: number, elm?: T) => P;
/** High-level polynomial helpers layered on top of FFT and field arithmetic. */
export type PolyFn<P extends PolyStorage<T>, T> = {
/** Roots-of-unity cache used by the helper namespace. */
roots: RootsOfUnity;
/** Factory used to allocate new polynomial containers. */
create: CreatePolyFn<P, T>;
/** Optional enforced polynomial length. */
length?: number;
/**
* Compute the polynomial degree.
* @param a - Polynomial coefficients.
* @returns Polynomial degree.
*/
degree: (a: P) => number;
/**
* Extend or truncate one polynomial to a requested length.
* @param a - Polynomial coefficients.
* @param len - Target length.
* @returns Resized polynomial.
*/
extend: (a: P, len: number) => P;
/**
* Add two polynomials coefficient-wise.
* @param a - Left polynomial.
* @param b - Right polynomial.
* @returns Sum polynomial.
*/
add: (a: P, b: P) => P;
/**
* Subtract two polynomials coefficient-wise.
* @param a - Left polynomial.
* @param b - Right polynomial.
* @returns Difference polynomial.
*/
sub: (a: P, b: P) => P;
/**
* Multiply by another polynomial or by one scalar.
* @param a - Left polynomial.
* @param b - Right polynomial or scalar.
* @returns Product polynomial.
*/
mul: (a: P, b: P | T) => P;
/**
* Multiply coefficients point-wise.
* @param a - Left polynomial.
* @param b - Right polynomial.
* @returns Point-wise product polynomial.
*/
dot: (a: P, b: P) => P;
/**
* Multiply two polynomials with convolution.
* @param a - Left polynomial.
* @param b - Right polynomial.
* @returns Convolution product.
*/
convolve: (a: P, b: P) => P;
/**
* Apply a point-wise coefficient shift by powers of one factor.
* @param p - Polynomial coefficients.
* @param factor - Shift factor.
* @returns Shifted polynomial.
*/
shift: (p: P, factor: bigint) => P;
/**
* Clone one polynomial container.
* @param a - Polynomial coefficients.
* @returns Cloned polynomial.
*/
clone: (a: P) => P;
/**
* Evaluate one polynomial on a basis vector.
* @param a - Polynomial coefficients.
* @param basis - Basis vector.
* @returns Evaluated field element.
*/
eval: (a: P, basis: P) => T;
/** Helpers for monomial-basis polynomials. */
monomial: {
/** Build the monomial basis vector for one evaluation point. */
basis: (x: T, n: number) => P;
/** Evaluate a polynomial in the monomial basis. */
eval: (a: P, x: T) => T;
};
/** Helpers for Lagrange-basis polynomials. */
lagrange: {
/** Build the Lagrange basis vector for one evaluation point. */
basis: (x: T, n: number, brp?: boolean) => P;
/** Evaluate a polynomial in the Lagrange basis. */
eval: (a: P, x: T, brp?: boolean) => T;
};
/**
* Build the vanishing polynomial for a root set.
* @param roots - Root set.
* @returns Vanishing polynomial.
*/
vanishing: (roots: P) => P;
};
/**
* Poly wants a cracker.
*
* Polynomials are functions like `y=f(x)`, which means when we multiply two polynomials, result is
* function `f3(x) = f1(x) * f2(x)`, we don't multiply values. Key takeaways:
*
* - **Polynomial** is an array of coefficients: `f(x) = sum(coeff[i] * basis[i](x))`
* - **Basis** is array of functions
* - **Monominal** is Polynomial where `basis[i](x) == x**i` (powers)
* - **Array size** is domain size
* - **Lattice** is matrix (Polynomial of Polynomials)
* @param field - Field implementation.
* @param roots - Roots-of-unity cache.
* @param create - Optional polynomial factory. Runtime input validation accepts only plain `Array`
* and typed-array polynomial containers; arbitrary structural wrappers are intentionally rejected.
* @param fft - Optional FFT implementation.
* @param length - Optional fixed polynomial length.
* @returns Polynomial helper namespace.
* @example
* Build polynomial helpers, then convolve two coefficient arrays.
*
* ```ts
* import { poly, rootsOfUnity } from '@noble/curves/abstract/fft.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const poly17 = poly(Fp, rootsOfUnity(Fp));
* const product = poly17.convolve([1n, 2n], [3n, 4n]);
* ```
*/
export declare function poly<T>(field: TArg<IField<T>>, roots: RootsOfUnity, create?: undefined, fft?: FFTMethods<T>, length?: number): PolyFn<T[], T>;
export declare function poly<T, P extends PolyStorage<T>>(field: TArg<IField<T>>, roots: RootsOfUnity, create: CreatePolyFn<P, T>, fft?: FFTMethods<T>, length?: number): PolyFn<P, T>;
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function checkU32(n) {
// 0xff_ff_ff_ff
if (!Number.isSafeInteger(n) || n < 0 || n > 0xffffffff)
throw new Error('wrong u32 integer:' + n);
return n;
}
/**
* Checks if integer is in form of `1 << X`.
* @param x - Integer to inspect.
* @returns `true` when the value is a power of two.
* @throws If `x` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Validate that an FFT size is a power of two.
*
* ```ts
* isPowerOfTwo(8);
* ```
*/
export function isPowerOfTwo(x) {
checkU32(x);
return (x & (x - 1)) === 0 && x !== 0;
}
/**
* @param n - Input value.
* @returns Next power of two within the u32/array-length domain.
* @throws If `n` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Round an integer up to the FFT size it needs.
*
* ```ts
* nextPowerOfTwo(9);
* ```
*/
export function nextPowerOfTwo(n) {
checkU32(n);
if (n <= 1)
return 1;
// FFT sizes here are used as JS array lengths, so `2^32` is not a meaningful result:
// keep the fast u32 bit-twiddling path and fail explicitly instead of wrapping to 1.
if (n > 0x8000_0000)
throw new Error('nextPowerOfTwo overflow: result does not fit u32');
return (1 << (log2(n - 1) + 1)) >>> 0;
}
/**
* @param n - Value to reverse.
* @param bits - Number of bits to use.
* @returns Bit-reversed integer.
* @throws If `n` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Reverse the low `bits` bits of one index.
*
* ```ts
* reverseBits(3, 3);
* ```
*/
export function reverseBits(n, bits) {
checkU32(n);
if (!Number.isSafeInteger(bits) || bits < 0 || bits > 32)
throw new Error(`expected integer 0 <= bits <= 32, got ${bits}`);
let reversed = 0;
for (let i = 0; i < bits; i++, n >>>= 1)
reversed = (reversed << 1) | (n & 1);
// JS bitwise ops are signed i32; cast back so 32-bit reversals stay in the unsigned u32 domain.
return reversed >>> 0;
}
/**
* Similar to `bitLen(x)-1` but much faster for small integers, like indices.
* @param n - Input value.
* @returns Base-2 logarithm. For `n = 0`, the current implementation returns `-1`.
* @throws If `n` is not a valid unsigned 32-bit integer. {@link Error}
* @example
* Compute the radix-2 stage count for one transform size.
*
* ```ts
* log2(8);
* ```
*/
export function log2(n) {
checkU32(n);
return 31 - Math.clz32(n);
}
/**
* Moves lowest bit to highest position, which at first step splits
* array on even and odd indices, then it applied again to each part,
* which is core of fft
* @param values - Mutable coefficient array.
* @returns Mutated input array.
* @throws If the array length is not a positive power of two. {@link Error}
* @example
* Reorder coefficients into bit-reversed order in place.
*
* ```ts
* const values = Uint8Array.from([0, 1, 2, 3]);
* bitReversalInplace(values);
* ```
*/
export function bitReversalInplace(values) {
const n = values.length;
// Size-1 FFT is the identity, so bit-reversal must stay a no-op there instead of rejecting it.
if (!isPowerOfTwo(n))
throw new Error('expected positive power-of-two length, got ' + n);
const bits = log2(n);
for (let i = 0; i < n; i++) {
const j = reverseBits(i, bits);
if (i < j) {
const tmp = values[i];
values[i] = values[j];
values[j] = tmp;
}
}
return values;
}
/**
* @param values - Input values.
* @returns Reordered copy.
* @throws If the array length is not a positive power of two. {@link Error}
* @example
* Return a reordered copy instead of mutating the input in place.
*
* ```ts
* const reordered = bitReversalPermutation([0, 1, 2, 3]);
* ```
*/
export function bitReversalPermutation(values) {
return bitReversalInplace(values.slice());
}
const _1n = /** @__PURE__ */ BigInt(1);
function findGenerator(field) {
let G = BigInt(2);
for (; field.eql(field.pow(G, field.ORDER >> _1n), field.ONE); G++)
;
return G;
}
/**
* We limit roots up to 2**31, which is a lot: 2-billion polynomimal should be rare.
* @param field - Field implementation.
* @param generator - Optional generator override.
* @returns Roots-of-unity cache.
* @example
* Cache roots once, then ask for the omega table of one FFT size.
*
* ```ts
* import { rootsOfUnity } from '@noble/curves/abstract/fft.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const roots = rootsOfUnity(Field(17n));
* const omega = roots.omega(4);
* ```
*/
export function rootsOfUnity(field, generator) {
// Factor field.ORDER-1 as oddFactor * 2^powerOfTwo
let oddFactor = field.ORDER - _1n;
let powerOfTwo = 0;
for (; (oddFactor & _1n) !== _1n; powerOfTwo++, oddFactor >>= _1n)
;
// Find non quadratic residue
let G = generator !== undefined ? BigInt(generator) : findGenerator(field);
// Powers of generator
const omegas = new Array(powerOfTwo + 1);
omegas[powerOfTwo] = field.pow(G, oddFactor);
for (let i = powerOfTwo; i > 0; i--)
omegas[i - 1] = field.sqr(omegas[i]);
// Compute all roots of unity for powers up to maxPower
const rootsCache = [];
const checkBits = (bits) => {
checkU32(bits);
if (bits > 31 || bits > powerOfTwo)
throw new Error('rootsOfUnity: wrong bits ' + bits + ' powerOfTwo=' + powerOfTwo);
return bits;
};
const precomputeRoots = (maxPower) => {
checkBits(maxPower);
for (let power = maxPower; power >= 0; power--) {
if (rootsCache[power])
continue; // Skip if we've already computed roots for this power
const rootsAtPower = [];
for (let j = 0, cur = field.ONE; j < 2 ** power; j++, cur = field.mul(cur, omegas[power]))
rootsAtPower.push(cur);
rootsCache[power] = rootsAtPower;
}
return rootsCache[maxPower];
};
const brpCache = new Map();
const inverseCache = new Map();
// roots()/brp()/inverse() expose shared cached arrays by reference for speed; callers must treat them as read-only.
// NOTE: we use bits instead of power, because power = 2**bits,
// but power is not neccesary isPowerOfTwo(power)!
return {
info: { G, powerOfTwo, oddFactor },
roots: (bits) => {
const b = checkBits(bits);
return precomputeRoots(b);
},
brp(bits) {
const b = checkBits(bits);
if (brpCache.has(b))
return brpCache.get(b);
else {
const res = bitReversalPermutation(this.roots(b));
brpCache.set(b, res);
return res;
}
},
inverse(bits) {
const b = checkBits(bits);
if (inverseCache.has(b))
return inverseCache.get(b);
else {
const res = field.invertBatch(this.roots(b));
inverseCache.set(b, res);
return res;
}
},
omega: (bits) => omegas[checkBits(bits)],
clear: () => {
rootsCache.splice(0, rootsCache.length);
brpCache.clear();
inverseCache.clear();
},
};
}
/**
* Constructs different flavors of FFT. radix2 implementation of low level mutating API. Flavors:
*
* - DIT (Decimation-in-Time): Bottom-Up (leaves to root), Cool-Turkey
* - DIF (Decimation-in-Frequency): Top-Down (root to leaves), Gentleman-Sande
*
* DIT takes brp input, returns natural output.
* DIF takes natural input, returns brp output.
*
* The output is actually identical. Time / frequence distinction is not meaningful
* for Polynomial multiplication in fields.
* Which means if protocol supports/needs brp output/inputs, then we can skip this step.
*
* Cyclic NTT: Rq = Zq[x]/(x^n-1). butterfly_DIT+loop_DIT OR butterfly_DIF+loop_DIT, roots are omega
* Negacyclic NTT: Rq = Zq[x]/(x^n+1). butterfly_DIT+loop_DIF, at least for mlkem / mldsa
* @param F - Field operations.
* @param coreOpts - FFT configuration:
* - `N`: Transform size. Must be a power of two.
* - `roots`: Stage roots for the selected transform size.
* - `dit`: Whether to run the DIT variant instead of DIF.
* - `invertButterflies` (optional): Whether to invert butterfly placement.
* - `skipStages` (optional): Number of initial stages to skip.
* - `brp` (optional): Whether to apply bit-reversal permutation at the boundary.
* @returns Low-level FFT loop.
* @throws If the FFT options or cached roots are invalid for the requested size. {@link Error}
* @example
* Constructs different flavors of FFT.
*
* ```ts
* import { FFTCore, rootsOfUnity } from '@noble/curves/abstract/fft.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const roots = rootsOfUnity(Fp).roots(2);
* const loop = FFTCore(Fp, { N: 4, roots, dit: true });
* const values = loop([1n, 2n, 3n, 4n]);
* ```
*/
export const FFTCore = (F, coreOpts) => {
const { N, roots, dit, invertButterflies = false, skipStages = 0, brp = true } = coreOpts;
const bits = log2(N);
if (!isPowerOfTwo(N))
throw new Error('FFT: Polynomial size should be power of two');
// Wrong-sized root tables can stay in-bounds for some loop shapes and silently compute nonsense.
if (roots.length !== N)
throw new Error(`FFT: wrong roots length: expected ${N}, got ${roots.length}`);
const isDit = dit !== invertButterflies;
isDit;
return (values) => {
if (values.length !== N)
throw new Error('FFT: wrong Polynomial length');
if (dit && brp)
bitReversalInplace(values);
for (let i = 0, g = 1; i < bits - skipStages; i++) {
// For each stage s (sub-FFT length m = 2^s)
const s = dit ? i + 1 + skipStages : bits - i;
const m = 1 << s;
const m2 = m >> 1;
const stride = N >> s;
// Loop over each subarray of length m
for (let k = 0; k < N; k += m) {
// Loop over each butterfly within the subarray
for (let j = 0, grp = g++; j < m2; j++) {
const rootPos = invertButterflies ? (dit ? N - grp : grp) : j * stride;
const i0 = k + j;
const i1 = k + j + m2;
const omega = roots[rootPos];
const b = values[i1];
const a = values[i0];
// Inlining gives us 10% perf in kyber vs functions
if (isDit) {
const t = F.mul(b, omega); // Standard DIT butterfly
values[i0] = F.add(a, t);
values[i1] = F.sub(a, t);
}
else if (invertButterflies) {
values[i0] = F.add(b, a); // DIT loop + inverted butterflies (Kyber decode)
values[i1] = F.mul(F.sub(b, a), omega);
}
else {
values[i0] = F.add(a, b); // Standard DIF butterfly
values[i1] = F.mul(F.sub(a, b), omega);
}
}
}
}
if (!dit && brp)
bitReversalInplace(values);
return values;
};
};
/**
* NTT aka FFT over finite field (NOT over complex numbers).
* Naming mirrors other libraries.
* @param roots - Roots-of-unity cache.
* @param opts - Field operations. See {@link FFTOpts}.
* @returns Forward and inverse FFT helpers.
* @example
* NTT aka FFT over finite field (NOT over complex numbers).
*
* ```ts
* import { FFT, rootsOfUnity } from '@noble/curves/abstract/fft.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const fft = FFT(rootsOfUnity(Fp), Fp);
* const values = fft.direct([1n, 2n, 3n, 4n]);
* ```
*/
export function FFT(roots, opts) {
const getLoop = (N, roots, brpInput = false, brpOutput = false) => {
if (brpInput && brpOutput) {
// we cannot optimize this case, but lets support it anyway
return (values) => FFTCore(opts, { N, roots, dit: false, brp: false })(bitReversalInplace(values));
}
if (brpInput)
return FFTCore(opts, { N, roots, dit: true, brp: false });
if (brpOutput)
return FFTCore(opts, { N, roots, dit: false, brp: false });
return FFTCore(opts, { N, roots, dit: true, brp: true }); // all natural
};
return {
direct(values, brpInput = false, brpOutput = false) {
const N = values.length;
if (!isPowerOfTwo(N))
throw new Error('FFT: Polynomial size should be power of two');
const bits = log2(N);
return getLoop(N, roots.roots(bits), brpInput, brpOutput)(values.slice());
},
inverse(values, brpInput = false, brpOutput = false) {
const N = values.length;
if (!isPowerOfTwo(N))
throw new Error('FFT: Polynomial size should be power of two');
const bits = log2(N);
const res = getLoop(N, roots.inverse(bits), brpInput, brpOutput)(values.slice());
const ivm = opts.inv(BigInt(values.length)); // scale
// we can get brp output if we use dif instead of dit!
for (let i = 0; i < res.length; i++)
res[i] = opts.mul(res[i], ivm);
// Allows to re-use non-inverted roots, but is VERY fragile
// return [res[0]].concat(res.slice(1).reverse());
// inverse calculated as pow(-1), which transforms into ω^{-kn} (-> reverses indices)
return res;
},
};
}
export function poly(field, roots, create, fft, length) {
const F = field;
const _create = create ||
((len, elm) => new Array(len).fill(elm ?? F.ZERO));
// `poly.mul(a, b)` distinguishes polynomial-vs-scalar at runtime, so keep accepted
// polynomial containers concrete instead of trying to support arbitrary wrappers.
const isPoly = (x) => {
if (Array.isArray(x))
return true;
if (!ArrayBuffer.isView(x))
return false;
const v = x;
return (typeof v.length === 'number' &&
typeof v.slice === 'function' &&
typeof v[Symbol.iterator] === 'function');
};
const checkLength = (...lst) => {
if (!lst.length)
return 0;
for (const i of lst)
if (!isPoly(i))
throw new Error('poly: not polynomial: ' + i);
const L = lst[0].length;
for (let i = 1; i < lst.length; i++)
if (lst[i].length !== L)
throw new Error(`poly: mismatched lengths ${L} vs ${lst[i].length}`);
if (length !== undefined && L !== length)
throw new Error(`poly: expected fixed length ${length}, got ${L}`);
return L;
};
function findOmegaIndex(x, n, brp = false) {
const bits = log2(n);
const omega = brp ? roots.brp(bits) : roots.roots(bits);
for (let i = 0; i < n; i++)
if (F.eql(x, omega[i]))
return i;
return -1;
}
// TODO: mutating versions for mlkem/mldsa
return {
roots,
create: _create,
length,
extend: (a, len) => {
checkLength(a);
const out = _create(len, F.ZERO);
// Plain arrays grow when writing past `out.length`, so cap the copy explicitly to keep
// `extend()` consistent with typed arrays and with its documented truncate behavior.
for (let i = 0; i < Math.min(a.length, len); i++)
out[i] = a[i];
return out;
},
degree: (a) => {
checkLength(a);
for (let i = a.length - 1; i >= 0; i--)
if (!F.is0(a[i]))
return i;
return -1;
},
add: (a, b) => {
const len = checkLength(a, b);
const out = _create(len);
for (let i = 0; i < len; i++)
out[i] = F.add(a[i], b[i]);
return out;
},
sub: (a, b) => {
const len = checkLength(a, b);
const out = _create(len);
for (let i = 0; i < len; i++)
out[i] = F.sub(a[i], b[i]);
return out;
},
dot: (a, b) => {
const len = checkLength(a, b);
const out = _create(len);
for (let i = 0; i < len; i++)
out[i] = F.mul(a[i], b[i]);
return out;
},
mul: (a, b) => {
if (isPoly(b)) {
const len = checkLength(a, b);
if (fft) {
const A = fft.direct(a, false, true);
const B = fft.direct(b, false, true);
for (let i = 0; i < A.length; i++)
A[i] = F.mul(A[i], B[i]);
return fft.inverse(A, true, false);
}
else {
// NOTE: this is quadratic and mostly for compat tests with FFT
const res = _create(len);
for (let i = 0; i < len; i++) {
for (let j = 0; j < len; j++) {
const k = (i + j) % len; // wrap mod length
res[k] = F.add(res[k], F.mul(a[i], b[j]));
}
}
return res;
}
}
else {
const out = _create(checkLength(a));
for (let i = 0; i < out.length; i++)
out[i] = F.mul(a[i], b);
return out;
}
},
convolve(a, b) {
const len = nextPowerOfTwo(a.length + b.length - 1);
return this.mul(this.extend(a, len), this.extend(b, len));
},
shift(p, factor) {
const out = _create(checkLength(p));
out[0] = p[0];
for (let i = 1, power = F.ONE; i < p.length; i++) {
power = F.mul(power, factor);
out[i] = F.mul(p[i], power);
}
return out;
},
clone: (a) => {
checkLength(a);
const out = _create(a.length);
for (let i = 0; i < a.length; i++)
out[i] = a[i];
return out;
},
eval: (a, basis) => {
checkLength(a, basis);
let acc = F.ZERO;
for (let i = 0; i < a.length; i++)
acc = F.add(acc, F.mul(a[i], basis[i]));
return acc;
},
monomial: {
basis: (x, n) => {
const out = _create(n);
let pow = F.ONE;
for (let i = 0; i < n; i++) {
out[i] = pow;
pow = F.mul(pow, x);
}
return out;
},
eval: (a, x) => {
checkLength(a);
// Same as eval(a, monomialBasis(x, a.length)), but it is faster this way
let acc = F.ZERO;
for (let i = a.length - 1; i >= 0; i--)
acc = F.add(F.mul(acc, x), a[i]);
return acc;
},
},
lagrange: {
basis: (x, n, brp = false, weights) => {
const bits = log2(n);
const cache = weights || (brp ? roots.brp(bits) : roots.roots(bits)); // [ω⁰, ω¹, ..., ωⁿ⁻¹]
const out = _create(n);
// Fast Kronecker-δ shortcut
const idx = findOmegaIndex(x, n, brp);
if (idx !== -1) {
out[idx] = F.ONE;
return out;
}
const tm = F.pow(x, BigInt(n));
const c = F.mul(F.sub(tm, F.ONE), F.inv(BigInt(n))); // c = (xⁿ - 1)/n
const denom = _create(n);
for (let i = 0; i < n; i++)
denom[i] = F.sub(x, cache[i]);
const inv = F.invertBatch(denom);
for (let i = 0; i < n; i++)
out[i] = F.mul(c, F.mul(cache[i], inv[i]));
return out;
},
eval(a, x, brp = false) {
checkLength(a);
const idx = findOmegaIndex(x, a.length, brp);
if (idx !== -1)
return a[idx]; // fast path
const L = this.basis(x, a.length, brp); // Lᵢ(x)
let acc = F.ZERO;
for (let i = 0; i < a.length; i++)
if (!F.is0(a[i]))
acc = F.add(acc, F.mul(a[i], L[i]));
return acc;
},
},
vanishing(roots) {
checkLength(roots);
const out = _create(roots.length + 1, F.ZERO);
out[0] = F.ONE;
for (const r of roots) {
const neg = F.neg(r);
for (let j = out.length - 1; j > 0; j--)
out[j] = F.add(F.mul(out[j], neg), out[j - 1]);
out[0] = F.mul(out[0], neg);
}
return out;
},
};
}
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import { randomBytes, type TArg, type TRet } from '../utils.ts';
import { type CurvePoint, type CurvePointCons } from './curve.ts';
import { type H2CDSTOpts } from './hash-to-curve.ts';
import { type IField } from './modular.ts';
export type RNG = typeof randomBytes;
export type Identifier = string;
export type Commitment = Uint8Array;
export type Coefficient = Uint8Array;
export type Signature = Uint8Array;
export type Signers = {
min: number;
max: number;
};
export type SecretKey = Uint8Array;
export type Bytes = Uint8Array;
type Point = Uint8Array;
export type DKG_Round1 = {
identifier: Identifier;
commitment: TRet<Commitment[]>;
proofOfKnowledge: TRet<Signature>;
};
export type DKG_Round2 = {
identifier: Identifier;
signingShare: TRet<Bytes>;
};
export type DKG_Secret = {
identifier: bigint;
coefficients?: bigint[];
commitment: TRet<Point[]>;
signers: Signers;
step?: 1 | 2 | 3;
};
export type FrostPublic = {
signers: Signers;
commitments: TRet<Bytes[]>;
verifyingShares: TRet<Record<Identifier, Bytes>>;
};
export type FrostSecret = {
identifier: Identifier;
signingShare: TRet<Bytes>;
};
export type Key = {
public: FrostPublic;
secret: FrostSecret;
};
export type DealerShares = {
public: FrostPublic;
secretShares: Record<Identifier, FrostSecret>;
};
export type Nonces = {
hiding: TRet<Bytes>;
binding: TRet<Bytes>;
};
export type NonceCommitments = {
identifier: Identifier;
hiding: TRet<Bytes>;
binding: TRet<Bytes>;
};
export type GenNonce = {
nonces: Nonces;
commitments: NonceCommitments;
};
export interface FROSTPoint<T extends CurvePoint<any, T>> extends CurvePoint<any, T> {
add(rhs: T): T;
multiply(rhs: bigint): T;
equals(rhs: T): boolean;
toBytes(compressed?: boolean): Bytes;
clearCofactor(): T;
}
export interface FROSTPointConstructor<T extends FROSTPoint<T>> extends CurvePointCons<T> {
fromBytes(a: Bytes): T;
Fn: IField<bigint>;
}
export type FrostOpts<P extends FROSTPoint<P>> = {
readonly name: string;
readonly Point: FROSTPointConstructor<P>;
readonly Fn?: IField<bigint>;
/** Optional suite hook that tightens canonical decoding with subgroup / identity checks. */
readonly validatePoint?: (p: P) => void;
/** Optional public-key parser. Implementations MUST preserve the same subgroup / identity policy
* as `validatePoint`, because this bypasses generic canonical decoding in `parsePoint()`. */
readonly parsePublicKey?: (bytes: TArg<Uint8Array>) => P;
readonly hash: (msg: TArg<Uint8Array>) => TRet<Uint8Array>;
/** Custom scalar hash hook. Implementations MUST treat `msg` and `options` as read-only. */
readonly hashToScalar?: (msg: TArg<Uint8Array>, options?: TArg<H2CDSTOpts>) => bigint;
readonly adjustScalar?: (n: bigint) => bigint;
readonly adjustPoint?: (n: P) => P;
readonly challenge?: (R: P, PK: P, msg: TArg<Uint8Array>) => bigint;
readonly adjustNonces?: (PK: P, nonces: TArg<Nonces>) => TRet<Nonces>;
readonly adjustSecret?: (secret: TArg<FrostSecret>, pub: TArg<FrostPublic>) => TRet<FrostSecret>;
readonly adjustPublic?: (pub: TArg<FrostPublic>) => TRet<FrostPublic>;
readonly adjustGroupCommitmentShare?: (GC: P, GCShare: P) => P;
readonly adjustTx?: {
readonly encode: (tx: TArg<Uint8Array>) => TRet<Uint8Array>;
readonly decode: (tx: TArg<Uint8Array>) => TRet<Uint8Array>;
};
readonly adjustDKG?: (k: TArg<Key>) => TRet<Key>;
readonly H1?: string;
readonly H2?: string;
readonly H3?: string;
readonly H4?: string;
readonly H5?: string;
readonly HDKG?: string;
readonly HID?: string;
};
/**
* FROST: Threshold Protocol for TwoRound Schnorr Signatures
* from [RFC 9591](https://datatracker.ietf.org/doc/rfc9591/).
*/
export type FROST = {
/**
* Methods to construct participant identifiers.
*/
Identifier: {
/**
* Constructs an identifier from a numeric index.
* @param n - A positive integer.
* @returns A canonical serialized Identifier.
*/
fromNumber(n: number): Identifier;
/**
* Derives an identifier deterministically from a string (e.g. an email).
* @param s - Arbitrary string.
* @returns A canonical serialized Identifier.
*/
derive(s: string): Identifier;
};
/**
* Distributed Key Generation (DKG) protocol interface.
* RFC 9591 leaves DKG out of scope; Appendix C only specifies dealer/VSS key generation.
* These helpers follow the split-round API used by frost-rs for interoperable testing.
*/
DKG: {
/**
* Generates the first round of DKG.
* @param id - Participant's identifier.
* @param signers - Set of all participants (min/max threshold).
* @param secret - Optional initial secret scalar.
* @param rng - Optional RNG for nonce generation.
* @returns Public broadcast and private DKG state. The returned `secret` package is mutable
* round state that will be consumed by `round2()` and `round3()`.
*/
round1: (id: Identifier, signers: Signers, secret?: TArg<SecretKey>, rng?: RNG) => {
public: DKG_Round1;
secret: DKG_Secret;
};
/**
* Executes DKG round 2 given public round1 data from others.
* @param secret - Private DKG state from round1. This mutates `secret.step` in place.
* @param others - Public round1 broadcasts from other participants.
* @returns A map of round2 messages to be sent to others.
*/
round2: (secret: TArg<DKG_Secret>, others: TArg<DKG_Round1[]>) => TRet<Record<string, DKG_Round2>>;
/**
* Finalizes key generation in round3 using received round1 + round2 messages.
* @param secret - Private DKG state. This consumes the remaining local polynomial coefficients
* and transitions the package to its final post-round3 state.
* @param round1 - Public round1 broadcasts from all participants.
* @param round2 - Round2 messages received from others.
* @returns Final secret/public key information for the participant.
* Callers MUST pass the same verified remote `round1` package set that was already
* accepted in `round2()`, rather than re-fetching or rebuilding it from the network.
*/
round3: (secret: TArg<DKG_Secret>, round1: TArg<DKG_Round1[]>, round2: TArg<DKG_Round2[]>) => TRet<Key>;
/**
* Best-effort erasure of internal secret state. Bigint/JIT copies may still survive outside the
* local object even after cleanup.
* @param secret - Private DKG state from round1.
*/
clean(secret: TArg<DKG_Secret>): void;
};
/**
* Trusted dealer mode: generates key shares from a central trusted authority.
* Mirrors RFC 9591 Appendix C and returns one shared VSS commitment package
* plus per-participant shares.
* @param signers - Threshold parameters (min/max).
* @param identifiers - Optional explicit participant list.
* @param secret - Optional secret scalar.
* @param rng - Optional RNG.
* @returns One shared public package plus the participant secret-share packages.
*/
trustedDealer(signers: Signers, identifiers?: Identifier[], secret?: TArg<SecretKey>, rng?: RNG): TRet<DealerShares>;
/**
* Validates the consistency of a secret share against the shared public commitments.
* This is the RFC 9591 Appendix C.2 `vss_verify` check against the shared dealer/DKG commitment.
* It does not relax RFC 9591 Section 3.1: public identity elements are still invalid even when
* the scalar/share algebra would otherwise be self-consistent.
* Throws if invalid.
* @param secret - A FrostSecret containing identifier and signing share.
* @param pub - Shared public package containing commitments.
*/
validateSecret(secret: TArg<FrostSecret>, pub: TArg<FrostPublic>): void;
/**
* Produces nonces and public commitments used in signing.
* RFC 9591 Section 5.1 `commit()`.
* @param secret - Participant's secret share.
* @param rng - Optional RNG.
* @returns Nonce values and their public commitments.
* Returned nonces are one-time-use and MUST NOT be reused across signing sessions.
* This API does not mutate or zeroize caller-owned nonce objects.
*/
commit(secret: TArg<FrostSecret>, rng?: RNG): TRet<GenNonce>;
/**
* Signs a message using the participant's secret and nonce.
* @param secret - Participant's secret share.
* @param pub - Shared public package containing commitments.
* @param nonces - Participant's nonce pair.
* @param commitmentList - Commitments from all signing participants.
* @param msg - Message to be signed.
* @returns Signature share as a byte array.
* RFC 9591 Sections 4.1/5.1 require round-one commitments to be one-time-use, and
* Section 5.2 signs with the nonce corresponding to that published commitment.
* The caller MUST pass fresh nonces from `commit()`. On successful signing, this helper
* consumes the caller-owned nonce object by zeroing both nonce byte arrays in place.
* Later calls reject an all-zero nonce package, so same-object reuse fails closed and an
* accidentally generated zero nonce package is not silently used for signing.
*/
signShare(secret: TArg<FrostSecret>, pub: TArg<FrostPublic>, nonces: TArg<Nonces>, commitmentList: TArg<NonceCommitments[]>, msg: TArg<Uint8Array>): TRet<Uint8Array>;
/**
* Verifies a signature share against public commitments.
* Matches the coordinator-side individual-share verification from RFC 9591 Section 5.4.
* @param pub - Group public key information.
* @param commitmentList - Commitments from all signing participants.
* @param msg - Message being signed.
* @param identifier - Identifier of the signer whose share is being verified.
* @param sigShare - Signature share to verify.
* @returns True if valid, false otherwise.
*/
verifyShare(pub: TArg<FrostPublic>, commitmentList: TArg<NonceCommitments[]>, msg: TArg<Uint8Array>, identifier: Identifier, sigShare: TArg<Uint8Array>): boolean;
/**
* Aggregates signature shares into a full signature.
* RFC 9591 Section 5.3 `aggregate()`.
* @param pub - Group public key.
* @param commitmentList - Nonce commitments from all signers.
* @param msg - Message to sign.
* @param sigShares - Map from identifier to their signature share.
* @returns Final aggregated signature.
*/
aggregate(pub: TArg<FrostPublic>, commitmentList: TArg<NonceCommitments[]>, msg: TArg<Uint8Array>, sigShares: TArg<Record<Identifier, Uint8Array>>): TRet<Uint8Array>;
/**
* Signs a message using a raw secret key (e.g. from combineSecret).
* @param msg - Message to sign.
* @param secretKey - Group secret key as bytes.
* @returns Signature bytes.
*/
sign(msg: TArg<Uint8Array>, secretKey: TArg<Uint8Array>): TRet<Uint8Array>;
/**
* Verifies a full signature against the group public key.
* @param sig - Signature bytes.
* @param msg - Message that was signed.
* @param publicKey - Group public key.
* @returns True if valid, false otherwise.
*/
verify(sig: TArg<Signature>, msg: TArg<Uint8Array>, publicKey: TArg<Uint8Array>): boolean;
/**
* Combines multiple secret shares into a single secret key (e.g. for recovery).
* @param shares - Set of FrostSecret shares.
* @param signers - Threshold parameters.
* @returns Group secret key as bytes.
*/
combineSecret(shares: TArg<FrostSecret[]>, signers: Signers): TRet<Uint8Array>;
/**
* Low-level helper utilities (field arithmetic and polynomial tools).
*/
utils: {
/**
* Finite field used for scalars.
*/
Fn: IField<bigint>;
/**
* Generates a random scalar (private key).
* @param rng - Optional RNG source.
* @returns Scalar as 32-byte Uint8Array.
*/
randomScalar: (rng?: RNG) => TRet<Uint8Array>;
/**
* Generates a secret-sharing polynomial and its public commitments.
* @param signers - Threshold parameters.
* @param secret - Optional initial secret scalar.
* @param coeffs - Optional manual coefficients.
* @param rng - Optional RNG.
* @returns Polynomial coefficients, commitments, and secret value.
*/
generateSecretPolynomial: (signers: Signers, secret?: TArg<Uint8Array>, coeffs?: bigint[], rng?: RNG) => {
coefficients: bigint[];
commitment: TRet<Point[]>;
secret: bigint;
};
};
};
export declare function createFROST<P extends FROSTPoint<P>>(opts: FrostOpts<P>): TRet<FROST>;
export {};
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/**
* FROST: Flexible Round-Optimized Schnorr Threshold Protocol for Two-Round Schnorr Signatures.
*
* See [RFC 9591](https://datatracker.ietf.org/doc/rfc9591/) and [frost.zfnd.org](https://frost.zfnd.org).
* @module
*/
import { utf8ToBytes } from '@noble/hashes/utils.js';
import { bytesToHex, bytesToNumberBE, bytesToNumberLE, concatBytes, hexToBytes, randomBytes, validateObject, } from "../utils.js";
import { pippenger, validatePointCons } from "./curve.js";
import { poly } from "./fft.js";
import {} from "./hash-to-curve.js";
import { getMinHashLength, mapHashToField } from "./modular.js";
// PubKey = commitments, verifyingShares
// PrivKey = id, signingShare, commitment
const validateSigners = (signers) => {
if (!Number.isSafeInteger(signers.min) || !Number.isSafeInteger(signers.max))
throw new Error('Wrong signers info: min=' + signers.min + ' max=' + signers.max);
// Compatibility with frost-rs intentionally narrows RFC 9591's positive-nonzero threshold rule
// to `min >= 2`, even though the RFC text itself allows `MIN_PARTICIPANTS = 1`.
// This API is for actual threshold signing across participants; 1-of-n degenerates to ordinary
// single-signer mode, which does not need FROST's network/coordination machinery at all.
if (signers.min < 2 || signers.max < 2 || signers.min > signers.max)
throw new Error('Wrong signers info: min=' + signers.min + ' max=' + signers.max);
};
const validateCommitmentsNum = (signers, len) => {
// RFC 9591 Sections 5.2/5.3 require MIN_PARTICIPANTS <= NUM_PARTICIPANTS <= MAX_PARTICIPANTS.
if (len < signers.min || len > signers.max)
throw new Error('Wrong number of commitments=' + len);
};
class AggErr extends Error {
// Empty means aggregation failed before per-share verification could attribute a signer.
cheaters;
constructor(msg, cheaters) {
super(msg);
this.cheaters = cheaters;
}
}
export function createFROST(opts) {
validateObject(opts, {
name: 'string',
hash: 'function',
}, {
hashToScalar: 'function',
validatePoint: 'function',
parsePublicKey: 'function',
adjustScalar: 'function',
adjustPoint: 'function',
challenge: 'function',
adjustNonces: 'function',
adjustSecret: 'function',
adjustPublic: 'function',
adjustGroupCommitmentShare: 'function',
adjustDKG: 'function',
});
// Cheap constructor-surface sanity check only: this verifies the generic static hooks/fields that
// FROST consumes, but it does not certify point semantics like BASE/ZERO correctness.
validatePointCons(opts.Point);
const { Point } = opts;
const Fn = opts.Fn === undefined ? Point.Fn : opts.Fn;
// Hashes
const hashBytes = opts.hash;
const hashToScalar = opts.hashToScalar === undefined
? (msg, opts = { DST: new Uint8Array() }) => {
const t = hashBytes(concatBytes(opts.DST, msg));
return Fn.create(Fn.isLE ? bytesToNumberLE(t) : bytesToNumberBE(t));
}
: opts.hashToScalar;
const H1Prefix = utf8ToBytes(opts.H1 !== undefined ? opts.H1 : opts.name + 'rho');
const H2Prefix = utf8ToBytes(opts.H2 !== undefined ? opts.H2 : opts.name + 'chal');
const H3Prefix = utf8ToBytes(opts.H3 !== undefined ? opts.H3 : opts.name + 'nonce');
const H4Prefix = utf8ToBytes(opts.H4 !== undefined ? opts.H4 : opts.name + 'msg');
const H5Prefix = utf8ToBytes(opts.H5 !== undefined ? opts.H5 : opts.name + 'com');
const HDKGPrefix = utf8ToBytes(opts.HDKG !== undefined ? opts.HDKG : opts.name + 'dkg');
const HIDPrefix = utf8ToBytes(opts.HID !== undefined ? opts.HID : opts.name + 'id');
const H1 = (msg) => hashToScalar(msg, { DST: H1Prefix });
// Empty H2 still passes `{ DST: new Uint8Array() }` into custom hashToScalar hooks.
// The built-in fallback hashes that identically to omitted DST, which is how
// the Ed25519 suite models RFC 9591's undecorated H2 challenge hash.
const H2 = (msg) => hashToScalar(msg, { DST: H2Prefix });
const H3 = (msg) => hashToScalar(msg, { DST: H3Prefix });
const H4 = (msg) => hashBytes(concatBytes(H4Prefix, msg));
const H5 = (msg) => hashBytes(concatBytes(H5Prefix, msg));
const HDKG = (msg) => hashToScalar(msg, { DST: HDKGPrefix });
const HID = (msg) => hashToScalar(msg, { DST: HIDPrefix });
// /Hashes
const randomScalar = (rng = randomBytes) => {
// Intentional divergence from RFC 9591 §4.1 / §5.1: the RFC nonce_generate helper outputs a
// Scalar in [0, p-1], but round-one commit publishes ScalarBaseMult(nonce) values and §3.1
// requires SerializeElement / DeserializeElement to reject the identity element. Keep noble's
// mapHashToField generation here so round-one public nonce commitments stay in 1..n-1.
const t = mapHashToField(rng(getMinHashLength(Fn.ORDER)), Fn.ORDER, Fn.isLE);
// We cannot use Fn.fromBytes here because the field can have a different
// byte width, like ed448.
return Fn.isLE ? bytesToNumberLE(t) : bytesToNumberBE(t);
};
const serializePoint = (p) => p.toBytes();
const parsePoint = (bytes) => {
// RFC 9591 Section 3.1 requires DeserializeElement validation. Suite-specific validatePoint
// hooks tighten this further for ciphersuites in Section 6. Bare createFROST(...) only gets
// canonical point decoding unless the caller installs those extra subgroup / identity checks.
const p = Point.fromBytes(bytes);
if (opts.validatePoint)
opts.validatePoint(p);
return p;
};
// RFC 9591 Sections 4.1/5.1 model each participant's round-one output as two public commitments.
const nonceCommitments = (identifier, nonces) => ({
identifier,
hiding: serializePoint(Point.BASE.multiply(Fn.fromBytes(nonces.hiding))),
binding: serializePoint(Point.BASE.multiply(Fn.fromBytes(nonces.binding))),
});
const adjustPoint = opts.adjustPoint === undefined ? (n) => n : opts.adjustPoint;
// We use hex to make it easier to use inside objects
const validateIdentifier = (n) => {
// Identifiers are canonical non-zero scalars. Custom / derived identifiers are allowed, so this
// is intentionally not bounded by the current signers.max slot count.
if (!Fn.isValid(n) || Fn.is0(n))
throw new Error('Invalid identifier ' + n);
return n;
};
const serializeIdentifier = (id) => bytesToHex(Fn.toBytes(validateIdentifier(id)));
const parseIdentifier = (id) => {
const n = validateIdentifier(Fn.fromBytes(hexToBytes(id)));
// Keep string-keyed maps stable by accepting only the canonical serialized form.
if (serializeIdentifier(n) !== id)
throw new Error('expected canonical identifier hex');
return n;
};
const Signature = {
// RFC 9591 Appendix A encodes signatures canonically as
// SerializeElement(R) || SerializeScalar(z).
encode: (R, z) => {
let res = concatBytes(serializePoint(R), Fn.toBytes(z));
if (opts.adjustTx)
res = opts.adjustTx.encode(res);
return res;
},
decode: (sig) => {
if (opts.adjustTx)
sig = opts.adjustTx.decode(sig);
// We don't know size of point, but we know size of scalar
const R = parsePoint(sig.subarray(0, -Fn.BYTES));
const z = Fn.fromBytes(sig.subarray(-Fn.BYTES));
return { R, z };
},
};
// Generates pair of (scalar, point)
const genPointScalarPair = (rng = randomBytes) => {
let n = randomScalar(rng);
if (opts.adjustScalar)
n = opts.adjustScalar(n);
let p = Point.BASE.multiply(n);
return { scalar: n, point: p };
};
// No roots here: root-based methods will throw.
// `poly` expects a structured roots-of-unity domain, but FROST uses an
// arbitrary domain and only needs the non-root operations below.
const nrErr = 'roots are unavailable in FROST polynomial mode';
const noRoots = {
info: { G: Fn.ZERO, oddFactor: Fn.ZERO, powerOfTwo: 0 },
roots() {
throw new Error(nrErr);
},
brp() {
throw new Error(nrErr);
},
inverse() {
throw new Error(nrErr);
},
omega() {
throw new Error(nrErr);
},
clear() { },
};
const Poly = poly(Fn, noRoots);
const msm = (points, scalars) => pippenger(Point, points, scalars);
// Internal stuff uses bigints & Points, external Uint8Arrays
const polynomialEvaluate = (x, coeffs) => {
if (!coeffs.length)
throw new Error('empty coefficients');
return Poly.monomial.eval(coeffs, x);
};
const deriveInterpolatingValue = (L, xi) => {
const err = 'invalid parameters';
// Generates lagrange coefficient
if (!L.some((x) => Fn.eql(x, xi)))
throw new Error(err);
// Throws error if any x-coordinate is represented more than once in L.
const Lset = new Set(L);
if (Lset.size !== L.length)
throw new Error(err);
// Or if xi is missing
if (!Lset.has(xi))
throw new Error(err);
let num = Fn.ONE;
let den = Fn.ONE;
for (const x of L) {
if (Fn.eql(x, xi))
continue;
num = Fn.mul(num, x); // num *= x
den = Fn.mul(den, Fn.sub(x, xi)); // RFC 9591 §4.2: denominator *= x_j - x_i
}
return Fn.div(num, den);
};
const evalutateVSS = (identifier, commitment) => {
// RFC 9591 Appendix C.2: S_i' = Σ_j ScalarMult(vss_commitment[j], i^j).
const monomial = Poly.monomial.basis(identifier, commitment.length);
return msm(commitment, monomial);
};
// High-level internal stuff
const generateSecretPolynomial = (signers, secret, coeffs, rng = randomBytes) => {
validateSigners(signers);
// Dealer/DKG polynomial sampling reuses the same hardened scalar derivation as round-one
// nonces: overriding `rng` only swaps the entropy source, not the non-zero `1..n-1` policy.
const secretScalar = secret === undefined ? randomScalar(rng) : Fn.fromBytes(secret);
if (!coeffs) {
coeffs = [];
for (let i = 0; i < signers.min - 1; i++)
coeffs.push(randomScalar(rng));
}
if (coeffs.length !== signers.min - 1)
throw new Error('wrong coefficients length');
const coefficients = [secretScalar, ...coeffs];
// RFC 9591 Appendix C.2 commits to every polynomial coefficient with ScalarBaseMult.
const commitment = coefficients.map((i) => Point.BASE.multiply(i));
return { coefficients, commitment, secret: secretScalar };
};
// Pretty much sign+verify, same as basic
const ProofOfKnowledge = {
challenge: (id, verKey, R) => HDKG(concatBytes(Fn.toBytes(id), serializePoint(verKey), serializePoint(R))),
compute(id, coefficents, commitments, rng = randomBytes) {
if (coefficents.length < 1)
throw new Error('coefficients should have at least one element');
const { point: R, scalar: k } = genPointScalarPair(rng);
const verKey = commitments[0]; // verify key is first one
const c = this.challenge(id, verKey, R);
const mu = Fn.add(k, Fn.mul(coefficents[0], c)); // mu = k + coeff[0] * c
return Signature.encode(R, mu);
},
validate(id, commitment, proof) {
if (commitment.length < 1)
throw new Error('commitment should have at least one element');
const { R, z } = Signature.decode(proof);
const phi = parsePoint(commitment[0]);
const c = this.challenge(id, phi, R);
// R === z*G - phi*c
if (!R.equals(Point.BASE.multiply(z).subtract(phi.multiply(c))))
throw new Error('invalid proof of knowledge');
},
};
const Basic = {
challenge: (R, PK, msg) => {
if (opts.challenge)
return opts.challenge(R, PK, msg);
return H2(concatBytes(serializePoint(R), serializePoint(PK), msg));
},
sign(msg, sk, rng = randomBytes) {
const { point: R, scalar: r } = genPointScalarPair(rng);
const PK = Point.BASE.multiply(sk); // sk*G
const c = this.challenge(R, PK, msg);
const z = Fn.add(r, Fn.mul(c, sk)); // r + c * sk
return [R, z];
},
verify(msg, R, z, PK) {
if (opts.adjustPoint)
PK = opts.adjustPoint(PK);
if (opts.adjustPoint)
R = opts.adjustPoint(R);
const c = this.challenge(R, PK, msg);
const zB = Point.BASE.multiply(z); // z*G
const cA = PK.multiply(c); // c*PK
let check = zB.subtract(cA).subtract(R); // zB - cA - R
// No clearCoffactor on ristretto
if (check.clearCofactor)
check = check.clearCofactor();
return Point.ZERO.equals(check);
},
};
// === vssVerify
const validateSecretShare = (identifier, commitment, signingShare) => {
// RFC 9591 Appendix C.2 `vss_verify(share_i, vss_commitment)` is purely algebraic.
// Public FROST packages still go through Section 3.1 element encoding,
// which rejects identity points, so a zero share or commitment does not
// become valid wire data just because VSS matches.
if (!Point.BASE.multiply(signingShare).equals(evalutateVSS(identifier, commitment)))
throw new Error('invalid secret share');
};
const Identifier = {
fromNumber(n) {
if (!Number.isSafeInteger(n))
throw new Error('expected safe interger');
return serializeIdentifier(BigInt(n));
},
// Not in spec, but in FROST implementation,
// seems useful and nice, no need to sync identifiers (would require more interactions)
derive(s) {
if (typeof s !== 'string')
throw new Error('wrong identifier string: ' + s);
// Derived identifiers may land anywhere in the scalar field; they are not restricted to
// sequential `1..max_signers` values.
return serializeIdentifier(HID(utf8ToBytes(s)));
},
};
// RFC 9591 §4.1: nonce_generate() hashes 32 fresh RNG bytes with SerializeScalar(secret).
const generateNonce = (secret, rng = randomBytes) => H3(concatBytes(rng(32), Fn.toBytes(secret)));
const getGroupCommitment = (GPK, commitmentList, msg) => {
const CL = commitmentList.map((i) => [
i.identifier,
parseIdentifier(i.identifier),
parsePoint(i.hiding),
parsePoint(i.binding),
]);
// RFC 9591 Sections 4.3/4.4/4.5 and 5.2/5.3 treat commitment_list as sorted by identifier.
CL.sort((a, b) => (a[1] < b[1] ? -1 : a[1] > b[1] ? 1 : 0));
// Encode commitment list
const Cbytes = [];
for (const [_, id, hC, bC] of CL)
Cbytes.push(Fn.toBytes(id), serializePoint(hC), serializePoint(bC));
const encodedCommitmentHash = H5(concatBytes(...Cbytes));
const rhoPrefix = concatBytes(serializePoint(GPK), H4(msg), encodedCommitmentHash);
// Compute binding factors
const bindingFactors = {};
for (const [i, id] of CL) {
bindingFactors[i] = H1(concatBytes(rhoPrefix, Fn.toBytes(id)));
}
const points = [];
const scalars = [];
for (const [i, _, hC, bC] of CL) {
if (Point.ZERO.equals(hC) || Point.ZERO.equals(bC))
throw new Error('infinity commitment');
points.push(hC, bC);
scalars.push(Fn.ONE, bindingFactors[i]);
}
const groupCommitment = msm(points, scalars); // GC += hC + bC*bindingFactor
const identifiers = CL.map((i) => i[1]);
return { identifiers, groupCommitment, bindingFactors };
};
const prepareShare = (PK, commitmentList, msg, identifier) => {
// RFC 9591 Sections 4.4/4.5/4.6 feed directly into the Section 5.2 signer computation.
const GPK = adjustPoint(parsePoint(PK));
const id = parseIdentifier(identifier);
const { identifiers, groupCommitment, bindingFactors } = getGroupCommitment(GPK, commitmentList, msg);
const bindingFactor = bindingFactors[identifier];
const lambda = deriveInterpolatingValue(identifiers, id);
const challenge = Basic.challenge(groupCommitment, GPK, msg);
return { lambda, challenge, bindingFactor, groupCommitment };
};
Object.freeze(Identifier);
const frost = {
Identifier,
// DKG is Distributed Key Generation, not Trusted Dealer Key Generation.
DKG: Object.freeze({
// NOTE: we allow to pass secret scalar from user side,
// this way it can be derived, instead of random generation
round1: (id, signers, secret, rng = randomBytes) => {
validateSigners(signers);
const idNum = parseIdentifier(id);
const { coefficients, commitment } = generateSecretPolynomial(signers, secret, undefined, rng);
const proofOfKnowledge = ProofOfKnowledge.compute(idNum, coefficients, commitment, rng);
const commitmentBytes = commitment.map(serializePoint);
const round1Public = {
identifier: serializeIdentifier(idNum),
commitment: commitmentBytes,
proofOfKnowledge,
};
// store secret information for signing
const round1Secret = {
identifier: idNum,
coefficients,
commitment: commitment.map(serializePoint),
// Copy threshold metadata instead of retaining the caller-owned object by reference.
signers: { min: signers.min, max: signers.max },
step: 1,
};
return { public: round1Public, secret: round1Secret };
},
round2: (secret, others) => {
if (others.length !== secret.signers.max - 1)
throw new Error('wrong number of round1 packages');
if (!secret.coefficients || secret.step === 3)
throw new Error('round3 package used in round2');
const res = {};
for (const p of others) {
if (p.commitment.length !== secret.signers.min)
throw new Error('wrong number of commitments');
const id = parseIdentifier(p.identifier);
if (id === secret.identifier)
throw new Error('duplicate id=' + serializeIdentifier(id));
ProofOfKnowledge.validate(id, p.commitment, p.proofOfKnowledge);
for (const c of p.commitment)
parsePoint(c);
if (res[p.identifier])
throw new Error('Duplicate id=' + id);
const signingShare = Fn.toBytes(polynomialEvaluate(id, secret.coefficients));
res[p.identifier] = {
identifier: serializeIdentifier(secret.identifier),
signingShare: signingShare,
};
}
secret.step = 2;
return res;
},
round3: (secret, round1, round2) => {
// DKG is outside RFC 9591's signing flow; callers are expected to reuse the same
// remote round1 packages already accepted in round2, like frost-rs documents.
if (round1.length !== secret.signers.max - 1)
throw new Error('wrong length of round1 packages');
if (!secret.coefficients || secret.step !== 2)
throw new Error('round2 package used in round3');
if (round2.length !== round1.length)
throw new Error('wrong length of round2 packages');
const merged = {};
for (const r1 of round1) {
if (!r1.identifier || !r1.commitment)
throw new Error('wrong round1 share');
merged[r1.identifier] = { ...r1 };
}
for (const r2 of round2) {
if (!r2.identifier || !r2.signingShare)
throw new Error('wrong round2 share');
if (!merged[r2.identifier])
throw new Error('round1 share for ' + r2.identifier + ' is missing');
merged[r2.identifier].signingShare = r2.signingShare;
}
if (Object.keys(merged).length !== round1.length)
throw new Error('mismatch identifiers between rounds');
let signingShare = Fn.ZERO;
if (secret.commitment.length !== secret.signers.min)
throw new Error('wrong commitments length');
const localCommitment = secret.commitment.map(parsePoint);
const localShare = polynomialEvaluate(secret.identifier, secret.coefficients);
validateSecretShare(secret.identifier, localCommitment, localShare);
const localCommitmentBytes = localCommitment.map(serializePoint);
const commitments = {
[serializeIdentifier(secret.identifier)]: localCommitmentBytes,
};
for (const k in merged) {
const v = merged[k];
if (!v.signingShare || !v.commitment)
throw new Error('mismatch identifiers');
const id = parseIdentifier(k); // from
const signingSharePart = Fn.fromBytes(v.signingShare);
const commitment = v.commitment.map(parsePoint);
validateSecretShare(secret.identifier, commitment, signingSharePart);
signingShare = Fn.add(signingShare, signingSharePart);
const idSer = serializeIdentifier(id);
if (commitments[idSer])
throw new Error('duplicated id=' + idSer);
commitments[idSer] = v.commitment;
}
signingShare = Fn.add(signingShare, localShare);
const mergedCommitment = new Array(secret.signers.min).fill(Point.ZERO);
for (const k in commitments) {
const v = commitments[k];
if (v.length !== secret.signers.min)
throw new Error('wrong commitments length');
for (let i = 0; i < v.length; i++)
mergedCommitment[i] = mergedCommitment[i].add(parsePoint(v[i]));
}
const mergedCommitmentBytes = mergedCommitment.map(serializePoint);
const verifyingShares = {};
for (const k in commitments)
verifyingShares[k] = serializePoint(evalutateVSS(parseIdentifier(k), mergedCommitment));
// This is enough to sign stuff
let res = {
public: {
signers: { min: secret.signers.min, max: secret.signers.max },
commitments: mergedCommitmentBytes,
verifyingShares: Object.fromEntries(Object.entries(verifyingShares).map(([k, v]) => [k, v.slice()])),
},
secret: {
identifier: serializeIdentifier(secret.identifier),
signingShare: Fn.toBytes(signingShare),
},
};
if (opts.adjustDKG)
res = opts.adjustDKG(res);
for (let i = 0; i < secret.coefficients.length; i++)
secret.coefficients[i] -= secret.coefficients[i];
delete secret.coefficients;
secret.step = 3;
return res;
},
clean(secret) {
// Instead of replacing secret bigint with another (zero?), we subtract it from itself
// in the hope that JIT will modify it inplace, instead of creating new value.
// This is unverified and may not work, but it is best we can do in regard of bigints.
secret.identifier -= secret.identifier;
if (secret.coefficients) {
for (let i = 0; i < secret.coefficients.length; i++)
secret.coefficients[i] -= secret.coefficients[i];
}
// for (const c of secret.commitment) c.fill(0);
secret.step = 3;
},
}),
// Trusted dealer setup
// Generates keys for all participants
trustedDealer(signers, identifiers, secret, rng = randomBytes) {
// if no identifiers provided, we generated default identifiers
validateSigners(signers);
if (identifiers === undefined) {
identifiers = [];
for (let i = 1; i <= signers.max; i++)
identifiers.push(Identifier.fromNumber(i));
}
else {
if (!Array.isArray(identifiers) || identifiers.length !== signers.max)
throw new Error('identifiers should be array of ' + signers.max);
}
const identifierNums = {};
for (const id of identifiers) {
const idNum = parseIdentifier(id);
if (id in identifierNums)
throw new Error('duplicated id=' + id);
identifierNums[id] = idNum;
}
const sp = generateSecretPolynomial(signers, secret, undefined, rng);
const commitmentBytes = sp.commitment.map(serializePoint);
const secretShares = {};
const verifyingShares = {};
for (const id of identifiers) {
const signingShare = polynomialEvaluate(identifierNums[id], sp.coefficients);
verifyingShares[id] = serializePoint(Point.BASE.multiply(signingShare));
secretShares[id] = {
identifier: id,
signingShare: Fn.toBytes(signingShare),
};
}
return {
public: {
signers: { min: signers.min, max: signers.max },
commitments: commitmentBytes,
verifyingShares,
},
secretShares,
};
},
// Validate secret (from trusted dealer or DKG)
validateSecret(secret, pub) {
const id = parseIdentifier(secret.identifier);
const commitment = pub.commitments.map(parsePoint);
const signingShare = Fn.fromBytes(secret.signingShare);
validateSecretShare(id, commitment, signingShare);
},
// Actual signing
// Round 1: each participant commit to nonces
// Nonces kept private, commitments sent to coordinator (or every other participant)
// NOTE: we don't need the message at this point, which lets a coordinator
// keep multiple nonce commitments per participant in advance and skip
// round1 for signing.
// But then each participant needs to remember generated shares
commit(secret, rng = randomBytes) {
const secretScalar = Fn.fromBytes(secret.signingShare);
const hiding = generateNonce(secretScalar, rng);
const binding = generateNonce(secretScalar, rng);
const nonces = { hiding: Fn.toBytes(hiding), binding: Fn.toBytes(binding) };
return { nonces, commitments: nonceCommitments(secret.identifier, nonces) };
},
// Round2: sign. Each participant creates a signature share from the secret
// and the selected nonce commitments.
signShare(secret, pub, nonces, commitmentList, msg) {
validateCommitmentsNum(pub.signers, commitmentList.length);
const hidingNonce0 = Fn.fromBytes(nonces.hiding);
const bindingNonce0 = Fn.fromBytes(nonces.binding);
if (Fn.is0(hidingNonce0) || Fn.is0(bindingNonce0))
throw new Error('signing nonces already used');
// Reject a coordinator-assigned commitment pair that does not match the signer's own nonce
// pair. This must happen before suite-specific nonce adjustment; secp256k1-tr may negate the
// actual signing nonces later, but the coordinator still assigns the original commitments.
const expectedCommitment = {
identifier: secret.identifier,
hiding: serializePoint(Point.BASE.multiply(hidingNonce0)),
binding: serializePoint(Point.BASE.multiply(bindingNonce0)),
};
const commitment = commitmentList.find((i) => i.identifier === secret.identifier);
if (!commitment)
throw new Error('missing signer commitment');
if (bytesToHex(commitment.hiding) !== bytesToHex(expectedCommitment.hiding) ||
bytesToHex(commitment.binding) !== bytesToHex(expectedCommitment.binding))
throw new Error('incorrect signer commitment');
if (opts.adjustSecret)
secret = opts.adjustSecret(secret, pub);
if (opts.adjustPublic)
pub = opts.adjustPublic(pub);
const SK = Fn.fromBytes(secret.signingShare);
const { lambda, challenge, bindingFactor, groupCommitment } = prepareShare(pub.commitments[0], commitmentList, msg, secret.identifier);
const N = opts.adjustNonces ? opts.adjustNonces(groupCommitment, nonces) : nonces;
const hidingNonce = opts.adjustNonces ? Fn.fromBytes(N.hiding) : hidingNonce0;
const bindingNonce = opts.adjustNonces ? Fn.fromBytes(N.binding) : bindingNonce0;
const t = Fn.mul(Fn.mul(lambda, SK), challenge); // challenge * lambda * SK
const t2 = Fn.mul(bindingNonce, bindingFactor); // bindingNonce * bindingFactor
const r = Fn.toBytes(Fn.add(Fn.add(hidingNonce, t2), t)); // t + t2 + hidingNonce
// RFC 9591 round-one commitments are one-time-use, and round two must use the nonce
// corresponding to the published commitment. This API returns mutable local nonce bytes,
// so consume them after a successful signShare() call: later all-zero reuse fails closed.
nonces.hiding.fill(0);
nonces.binding.fill(0);
return r;
},
// Each participant (or coordinator) can verify signatures from other participants
verifyShare(pub, commitmentList, msg, identifier, sigShare) {
if (opts.adjustPublic)
pub = opts.adjustPublic(pub);
const comm = commitmentList.find((i) => i.identifier === identifier);
if (!comm)
throw new Error('cannot find identifier commitment');
const PK = parsePoint(pub.verifyingShares[identifier]);
const hidingNonceCommitment = parsePoint(comm.hiding);
const bindingNonceCommitment = parsePoint(comm.binding);
const { lambda, challenge, bindingFactor, groupCommitment } = prepareShare(pub.commitments[0], commitmentList, msg, identifier);
// hC + bC * bF
let commShare = hidingNonceCommitment.add(bindingNonceCommitment.multiply(bindingFactor));
if (opts.adjustGroupCommitmentShare)
commShare = opts.adjustGroupCommitmentShare(groupCommitment, commShare);
const l = Point.BASE.multiply(Fn.fromBytes(sigShare)); // sigShare*G
// commShare + PK * (challenge * lambda)
const r = commShare.add(PK.multiply(Fn.mul(challenge, lambda)));
return l.equals(r);
},
// Aggregate multiple signature shares into groupSignature
aggregate(pub, commitmentList, msg, sigShares) {
if (opts.adjustPublic)
pub = opts.adjustPublic(pub);
try {
validateCommitmentsNum(pub.signers, commitmentList.length);
}
catch {
throw new AggErr('aggregation failed', []);
}
const ids = commitmentList.map((i) => i.identifier);
if (ids.length !== Object.keys(sigShares).length)
throw new AggErr('aggregation failed', []);
for (const id of ids) {
if (!(id in sigShares) || !(id in pub.verifyingShares))
throw new AggErr('aggregation failed', []);
}
const GPK = parsePoint(pub.commitments[0]);
const { groupCommitment } = getGroupCommitment(GPK, commitmentList, msg);
let z = Fn.ZERO;
// RFC 9591 Section 5.3 aggregates by summing the validated signature shares.
for (const id of ids)
z = Fn.add(z, Fn.fromBytes(sigShares[id])); // z += zi
if (!Basic.verify(msg, groupCommitment, z, GPK)) {
const cheaters = [];
for (const id of ids) {
if (!this.verifyShare(pub, commitmentList, msg, id, sigShares[id]))
cheaters.push(id);
}
throw new AggErr('aggregation failed', cheaters);
}
return Signature.encode(groupCommitment, z);
},
// Basic sign/verify using single key
sign(msg, secretKey) {
let sk = Fn.fromBytes(secretKey);
// Taproot single-key signing needs the same scalar normalization as threshold keys.
if (opts.adjustScalar)
sk = opts.adjustScalar(sk);
const [R, z] = Basic.sign(msg, sk);
return Signature.encode(R, z);
},
verify(sig, msg, publicKey) {
const PK = opts.parsePublicKey ? opts.parsePublicKey(publicKey) : parsePoint(publicKey);
const { R, z } = Signature.decode(sig);
return Basic.verify(msg, R, z, PK);
},
// Combine multiple secret shares to restore secret
combineSecret(shares, signers) {
validateSigners(signers);
if (!Array.isArray(shares) || shares.length < signers.min)
throw new Error('wrong secret shares array');
const points = [];
const seen = {};
// Interpolate over the full provided share set and reject duplicate identifiers.
for (const s of shares) {
const idNum = parseIdentifier(s.identifier);
const id = serializeIdentifier(idNum);
if (seen[id])
throw new Error('duplicated id=' + id);
seen[id] = true;
points.push([idNum, Fn.fromBytes(s.signingShare)]);
}
const xCoords = points.map(([x]) => x);
let res = Fn.ZERO;
for (const [x, y] of points)
res = Fn.add(res, Fn.mul(y, deriveInterpolatingValue(xCoords, x)));
return Fn.toBytes(res);
},
// Utils
utils: Object.freeze({
Fn, // NOTE: we re-export it here because it may be different from Point.Fn (ed448 is fun!)
// Test RNG overrides still go through noble's non-zero scalar derivation; this is not a raw
// "bytes become scalar" escape hatch.
randomScalar: (rng = randomBytes) => Fn.toBytes(genPointScalarPair(rng).scalar),
generateSecretPolynomial: (signers, secret, coeffs, rng) => {
const res = generateSecretPolynomial(signers, secret, coeffs, rng);
return { ...res, commitment: res.commitment.map(serializePoint) };
},
}),
};
return Object.freeze(frost);
}
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/**
* hash-to-curve from RFC 9380.
* Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.
* https://www.rfc-editor.org/rfc/rfc9380
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import type { CHash, TArg, TRet } from '../utils.ts';
import type { AffinePoint, PC_ANY, PC_F, PC_P } from './curve.ts';
import { type IField } from './modular.ts';
/** ASCII domain-separation tag or raw bytes. */
export type AsciiOrBytes = string | Uint8Array;
type H2CDefaults = {
DST: AsciiOrBytes;
expand: 'xmd' | 'xof';
hash: CHash;
p: bigint;
m: number;
k: number;
encodeDST?: AsciiOrBytes;
};
/**
* * `DST` is a domain separation tag, defined in section 2.2.5
* * `p` characteristic of F, where F is a finite field of characteristic p and order q = p^m
* * `m` is extension degree (1 for prime fields)
* * `k` is the target security target in bits (e.g. 128), from section 5.1
* * `expand` is `xmd` (SHA2, SHA3, BLAKE) or `xof` (SHAKE, BLAKE-XOF)
* * `hash` conforming to `utils.CHash` interface, with `outputLen` / `blockLen` props
*/
export type H2COpts = {
/** Domain separation tag. */
DST: AsciiOrBytes;
/** Expander family used by RFC 9380. */
expand: 'xmd' | 'xof';
/** Hash or XOF implementation used by the expander. */
hash: CHash;
/** Base-field characteristic. */
p: bigint;
/** Extension degree (`1` for prime fields). */
m: number;
/** Target security level in bits. */
k: number;
};
/** Hash-only subset of RFC 9380 options used by per-call overrides. */
export type H2CHashOpts = {
/** Expander family used by RFC 9380. */
expand: 'xmd' | 'xof';
/** Hash or XOF implementation used by the expander. */
hash: CHash;
};
/**
* Map one hash-to-field output tuple onto affine curve coordinates.
* Implementations receive the validated scalar tuple by reference for performance and MUST treat it
* as read-only. Callers that need scratch space should copy before mutating.
* @param scalar - Field-element tuple produced by `hash_to_field`.
* @returns Affine point before subgroup clearing.
*/
export type MapToCurve<T> = (scalar: bigint[]) => AffinePoint<T>;
/** Per-call override for the domain-separation tag. */
export type H2CDSTOpts = {
/** Domain-separation tag override. */
DST: AsciiOrBytes;
};
/** Base hash-to-curve helpers shared by `hashToCurve` and `encodeToCurve`. */
export type H2CHasherBase<PC extends PC_ANY> = {
/**
* Hash arbitrary bytes to one curve point.
* @param msg - Input message bytes.
* @param options - Optional domain-separation override. See {@link H2CDSTOpts}.
* @returns Curve point after hash-to-curve.
*/
hashToCurve(msg: TArg<Uint8Array>, options?: TArg<H2CDSTOpts>): PC_P<PC>;
/**
* Hash arbitrary bytes to one scalar.
* @param msg - Input message bytes.
* @param options - Optional domain-separation override. See {@link H2CDSTOpts}.
* @returns Scalar reduced into the target field.
*/
hashToScalar(msg: TArg<Uint8Array>, options?: TArg<H2CDSTOpts>): bigint;
/**
* Derive one curve point from non-uniform bytes without the random-oracle
* guarantees of `hashToCurve`.
* Accepts the same arguments as `hashToCurve`, but runs the encode-to-curve
* path instead of the random-oracle construction.
*/
deriveToCurve?(msg: TArg<Uint8Array>, options?: TArg<H2CDSTOpts>): PC_P<PC>;
/** Point constructor for the target curve. */
Point: PC;
};
/**
* RFC 9380 methods, with cofactor clearing. See {@link https://www.rfc-editor.org/rfc/rfc9380#section-3 | RFC 9380 section 3}.
*
* * hashToCurve: `map(hash(input))`, encodes RANDOM bytes to curve (WITH hashing)
* * encodeToCurve: `map(hash(input))`, encodes NON-UNIFORM bytes to curve (WITH hashing)
* * mapToCurve: `map(scalars)`, encodes NON-UNIFORM scalars to curve (NO hashing)
*/
export type H2CHasher<PC extends PC_ANY> = H2CHasherBase<PC> & {
/**
* Encode non-uniform bytes to one curve point.
* @param msg - Input message bytes.
* @param options - Optional domain-separation override. See {@link H2CDSTOpts}.
* @returns Curve point after encode-to-curve.
*/
encodeToCurve(msg: TArg<Uint8Array>, options?: TArg<H2CDSTOpts>): PC_P<PC>;
/** Deterministic map from `hash_to_field` tuples into affine coordinates. */
mapToCurve: MapToCurve<PC_F<PC>>;
/** Default RFC 9380 options captured by this hasher bundle. */
defaults: H2CDefaults;
};
/**
* Produces a uniformly random byte string using a cryptographic hash
* function H that outputs b bits.
* See {@link https://www.rfc-editor.org/rfc/rfc9380#section-5.3.1 | RFC 9380 section 5.3.1}.
* @param msg - Input message.
* @param DST - Domain separation tag. This helper normalizes DST, rejects empty DSTs, and
* oversize-hashes DST when needed.
* @param lenInBytes - Output length.
* @param H - Hash function.
* @returns Uniform byte string.
* @throws If the message, DST, hash, or output length is invalid. {@link Error}
* @example
* Expand one message into uniform bytes with the XMD construction.
*
* ```ts
* import { expand_message_xmd } from '@noble/curves/abstract/hash-to-curve.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const uniform = expand_message_xmd(new TextEncoder().encode('hello noble'), 'DST', 32, sha256);
* ```
*/
export declare function expand_message_xmd(msg: TArg<Uint8Array>, DST: TArg<AsciiOrBytes>, lenInBytes: number, H: TArg<CHash>): TRet<Uint8Array>;
/**
* Produces a uniformly random byte string using an extendable-output function (XOF) H.
* 1. The collision resistance of H MUST be at least k bits.
* 2. H MUST be an XOF that has been proved indifferentiable from
* a random oracle under a reasonable cryptographic assumption.
* See {@link https://www.rfc-editor.org/rfc/rfc9380#section-5.3.2 | RFC 9380 section 5.3.2}.
* @param msg - Input message.
* @param DST - Domain separation tag. This helper normalizes DST, rejects empty DSTs, and
* oversize-hashes DST when needed.
* @param lenInBytes - Output length.
* @param k - Target security level.
* @param H - XOF hash function.
* @returns Uniform byte string.
* @throws If the message, DST, XOF, or output length is invalid. {@link Error}
* @example
* Expand one message into uniform bytes with the XOF construction.
*
* ```ts
* import { expand_message_xof } from '@noble/curves/abstract/hash-to-curve.js';
* import { shake256 } from '@noble/hashes/sha3.js';
* const uniform = expand_message_xof(
* new TextEncoder().encode('hello noble'),
* 'DST',
* 32,
* 128,
* shake256
* );
* ```
*/
export declare function expand_message_xof(msg: TArg<Uint8Array>, DST: TArg<AsciiOrBytes>, lenInBytes: number, k: number, H: TArg<CHash>): TRet<Uint8Array>;
/**
* Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.
* See {@link https://www.rfc-editor.org/rfc/rfc9380#section-5.2 | RFC 9380 section 5.2}.
* @param msg - Input message bytes.
* @param count - Number of field elements to derive. Must be `>= 1`.
* @param options - RFC 9380 options. See {@link H2COpts}. `m` must be `>= 1`.
* @returns `[u_0, ..., u_(count - 1)]`, a list of field elements.
* @throws If the expander choice or RFC 9380 options are invalid. {@link Error}
* @example
* Hash one message into field elements before mapping it onto a curve.
*
* ```ts
* import { hash_to_field } from '@noble/curves/abstract/hash-to-curve.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const scalars = hash_to_field(new TextEncoder().encode('hello noble'), 2, {
* DST: 'DST',
* p: 17n,
* m: 1,
* k: 128,
* expand: 'xmd',
* hash: sha256,
* });
* ```
*/
export declare function hash_to_field(msg: TArg<Uint8Array>, count: number, options: TArg<H2COpts>): bigint[][];
type XY<T> = (x: T, y: T) => {
x: T;
y: T;
};
type XYRatio<T> = [T[], T[], T[], T[]];
/**
* @param field - Field implementation.
* @param map - Isogeny coefficients.
* @returns Isogeny mapping helper.
* @example
* Build one rational isogeny map, then apply it to affine x/y coordinates.
*
* ```ts
* import { isogenyMap } from '@noble/curves/abstract/hash-to-curve.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const iso = isogenyMap(Fp, [[0n, 1n], [1n], [1n], [1n]]);
* const point = iso(3n, 5n);
* ```
*/
export declare function isogenyMap<T, F extends IField<T>>(field: F, map: XYRatio<T>): XY<T>;
export declare const _DST_scalar: "HashToScalar-";
/**
* Creates hash-to-curve methods from EC Point and mapToCurve function. See {@link H2CHasher}.
* @param Point - Point constructor.
* @param mapToCurve - Map-to-curve function.
* @param defaults - Default hash-to-curve options. This object is frozen in place and reused as
* the shared defaults bundle for the returned helpers.
* @returns Hash-to-curve helper namespace.
* @throws If the map-to-curve callback or default hash-to-curve options are invalid. {@link Error}
* @example
* Bundle hash-to-curve, hash-to-scalar, and encode-to-curve helpers for one curve.
*
* ```ts
* import { createHasher } from '@noble/curves/abstract/hash-to-curve.js';
* import { p256 } from '@noble/curves/nist.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const hasher = createHasher(p256.Point, () => p256.Point.BASE.toAffine(), {
* DST: 'P256_XMD:SHA-256_SSWU_RO_',
* encodeDST: 'P256_XMD:SHA-256_SSWU_NU_',
* p: p256.Point.Fp.ORDER,
* m: 1,
* k: 128,
* expand: 'xmd',
* hash: sha256,
* });
* const point = hasher.encodeToCurve(new TextEncoder().encode('hello noble'));
* ```
*/
export declare function createHasher<PC extends PC_ANY>(Point: PC, mapToCurve: MapToCurve<PC_F<PC>>, defaults: TArg<H2COpts & {
encodeDST?: AsciiOrBytes;
}>): H2CHasher<PC>;
export {};
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import { abytes, asafenumber, asciiToBytes, bytesToNumberBE, copyBytes, concatBytes, isBytes, validateObject, } from "../utils.js";
import { FpInvertBatch, mod } from "./modular.js";
// Octet Stream to Integer. "spec" implementation of os2ip is 2.5x slower vs bytesToNumberBE.
const os2ip = bytesToNumberBE;
// Integer to Octet Stream (numberToBytesBE).
function i2osp(value, length) {
asafenumber(value);
asafenumber(length);
// This helper stays on the JS bitwise/u32 fast-path. Callers that need wider encodings should
// use bigint + numberToBytesBE instead of routing large widths through this small helper.
if (length < 0 || length > 4)
throw new Error('invalid I2OSP length: ' + length);
if (value < 0 || value > 2 ** (8 * length) - 1)
throw new Error('invalid I2OSP input: ' + value);
const res = Array.from({ length }).fill(0);
for (let i = length - 1; i >= 0; i--) {
res[i] = value & 0xff;
value >>>= 8;
}
return new Uint8Array(res);
}
// RFC 9380 only applies strxor() to equal-length strings; callers must preserve that invariant.
function strxor(a, b) {
const arr = new Uint8Array(a.length);
for (let i = 0; i < a.length; i++) {
arr[i] = a[i] ^ b[i];
}
return arr;
}
// User can always use utf8 if they want, by passing Uint8Array.
// If string is passed, we treat it as ASCII: other formats are likely a mistake.
function normDST(DST) {
if (!isBytes(DST) && typeof DST !== 'string')
throw new Error('DST must be Uint8Array or ascii string');
const dst = typeof DST === 'string' ? asciiToBytes(DST) : DST;
// RFC 9380 §3.1 requirement 2: tags "MUST have nonzero length".
if (dst.length === 0)
throw new Error('DST must be non-empty');
return dst;
}
/**
* Produces a uniformly random byte string using a cryptographic hash
* function H that outputs b bits.
* See {@link https://www.rfc-editor.org/rfc/rfc9380#section-5.3.1 | RFC 9380 section 5.3.1}.
* @param msg - Input message.
* @param DST - Domain separation tag. This helper normalizes DST, rejects empty DSTs, and
* oversize-hashes DST when needed.
* @param lenInBytes - Output length.
* @param H - Hash function.
* @returns Uniform byte string.
* @throws If the message, DST, hash, or output length is invalid. {@link Error}
* @example
* Expand one message into uniform bytes with the XMD construction.
*
* ```ts
* import { expand_message_xmd } from '@noble/curves/abstract/hash-to-curve.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const uniform = expand_message_xmd(new TextEncoder().encode('hello noble'), 'DST', 32, sha256);
* ```
*/
export function expand_message_xmd(msg, DST, lenInBytes, H) {
abytes(msg);
asafenumber(lenInBytes);
DST = normDST(DST);
// https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3
if (DST.length > 255)
DST = H(concatBytes(asciiToBytes('H2C-OVERSIZE-DST-'), DST));
const { outputLen: b_in_bytes, blockLen: r_in_bytes } = H;
const ell = Math.ceil(lenInBytes / b_in_bytes);
if (lenInBytes > 65535 || ell > 255)
throw new Error('expand_message_xmd: invalid lenInBytes');
const DST_prime = concatBytes(DST, i2osp(DST.length, 1));
const Z_pad = new Uint8Array(r_in_bytes); // RFC 9380: Z_pad = I2OSP(0, s_in_bytes)
const l_i_b_str = i2osp(lenInBytes, 2); // len_in_bytes_str
const b = new Array(ell);
const b_0 = H(concatBytes(Z_pad, msg, l_i_b_str, i2osp(0, 1), DST_prime));
b[0] = H(concatBytes(b_0, i2osp(1, 1), DST_prime));
// `b[0]` already stores RFC `b_1`, so only derive `b_2..b_ell` here. The old `<= ell`
// loop computed one extra tail block, which was usually sliced away but broke at max `ell=255`
// by reaching `I2OSP(256, 1)`.
for (let i = 1; i < ell; i++) {
const args = [strxor(b_0, b[i - 1]), i2osp(i + 1, 1), DST_prime];
b[i] = H(concatBytes(...args));
}
const pseudo_random_bytes = concatBytes(...b);
return pseudo_random_bytes.slice(0, lenInBytes);
}
/**
* Produces a uniformly random byte string using an extendable-output function (XOF) H.
* 1. The collision resistance of H MUST be at least k bits.
* 2. H MUST be an XOF that has been proved indifferentiable from
* a random oracle under a reasonable cryptographic assumption.
* See {@link https://www.rfc-editor.org/rfc/rfc9380#section-5.3.2 | RFC 9380 section 5.3.2}.
* @param msg - Input message.
* @param DST - Domain separation tag. This helper normalizes DST, rejects empty DSTs, and
* oversize-hashes DST when needed.
* @param lenInBytes - Output length.
* @param k - Target security level.
* @param H - XOF hash function.
* @returns Uniform byte string.
* @throws If the message, DST, XOF, or output length is invalid. {@link Error}
* @example
* Expand one message into uniform bytes with the XOF construction.
*
* ```ts
* import { expand_message_xof } from '@noble/curves/abstract/hash-to-curve.js';
* import { shake256 } from '@noble/hashes/sha3.js';
* const uniform = expand_message_xof(
* new TextEncoder().encode('hello noble'),
* 'DST',
* 32,
* 128,
* shake256
* );
* ```
*/
export function expand_message_xof(msg, DST, lenInBytes, k, H) {
abytes(msg);
asafenumber(lenInBytes);
DST = normDST(DST);
// https://www.rfc-editor.org/rfc/rfc9380#section-5.3.3
// RFC 9380 §5.3.3: DST = H("H2C-OVERSIZE-DST-" || a_very_long_DST, ceil(2 * k / 8)).
if (DST.length > 255) {
const dkLen = Math.ceil((2 * k) / 8);
DST = H.create({ dkLen }).update(asciiToBytes('H2C-OVERSIZE-DST-')).update(DST).digest();
}
if (lenInBytes > 65535 || DST.length > 255)
throw new Error('expand_message_xof: invalid lenInBytes');
return (H.create({ dkLen: lenInBytes })
.update(msg)
.update(i2osp(lenInBytes, 2))
// 2. DST_prime = DST || I2OSP(len(DST), 1)
.update(DST)
.update(i2osp(DST.length, 1))
.digest());
}
/**
* Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.
* See {@link https://www.rfc-editor.org/rfc/rfc9380#section-5.2 | RFC 9380 section 5.2}.
* @param msg - Input message bytes.
* @param count - Number of field elements to derive. Must be `>= 1`.
* @param options - RFC 9380 options. See {@link H2COpts}. `m` must be `>= 1`.
* @returns `[u_0, ..., u_(count - 1)]`, a list of field elements.
* @throws If the expander choice or RFC 9380 options are invalid. {@link Error}
* @example
* Hash one message into field elements before mapping it onto a curve.
*
* ```ts
* import { hash_to_field } from '@noble/curves/abstract/hash-to-curve.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const scalars = hash_to_field(new TextEncoder().encode('hello noble'), 2, {
* DST: 'DST',
* p: 17n,
* m: 1,
* k: 128,
* expand: 'xmd',
* hash: sha256,
* });
* ```
*/
export function hash_to_field(msg, count, options) {
validateObject(options, {
p: 'bigint',
m: 'number',
k: 'number',
hash: 'function',
});
const { p, k, m, hash, expand, DST } = options;
asafenumber(hash.outputLen, 'valid hash');
abytes(msg);
asafenumber(count);
// RFC 9380 §5.2 defines hash_to_field over a list of one or more field elements and requires
// extension degree `m >= 1`; rejecting here avoids degenerate `[]` / `[[]]` helper outputs.
if (count < 1)
throw new Error('hash_to_field: expected count >= 1');
if (m < 1)
throw new Error('hash_to_field: expected m >= 1');
const log2p = p.toString(2).length;
const L = Math.ceil((log2p + k) / 8); // section 5.1 of ietf draft link above
const len_in_bytes = count * m * L;
let prb; // pseudo_random_bytes
if (expand === 'xmd') {
prb = expand_message_xmd(msg, DST, len_in_bytes, hash);
}
else if (expand === 'xof') {
prb = expand_message_xof(msg, DST, len_in_bytes, k, hash);
}
else if (expand === '_internal_pass') {
// for internal tests only
prb = msg;
}
else {
throw new Error('expand must be "xmd" or "xof"');
}
const u = new Array(count);
for (let i = 0; i < count; i++) {
const e = new Array(m);
for (let j = 0; j < m; j++) {
const elm_offset = L * (j + i * m);
const tv = prb.subarray(elm_offset, elm_offset + L);
e[j] = mod(os2ip(tv), p);
}
u[i] = e;
}
return u;
}
/**
* @param field - Field implementation.
* @param map - Isogeny coefficients.
* @returns Isogeny mapping helper.
* @example
* Build one rational isogeny map, then apply it to affine x/y coordinates.
*
* ```ts
* import { isogenyMap } from '@noble/curves/abstract/hash-to-curve.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const iso = isogenyMap(Fp, [[0n, 1n], [1n], [1n], [1n]]);
* const point = iso(3n, 5n);
* ```
*/
export function isogenyMap(field, map) {
// Make same order as in spec
const coeff = map.map((i) => Array.from(i).reverse());
return (x, y) => {
const [xn, xd, yn, yd] = coeff.map((val) => val.reduce((acc, i) => field.add(field.mul(acc, x), i)));
// RFC 9380 §6.6.3 / Appendix E: denominator-zero exceptional cases must
// return the identity on E.
// Shipped Weierstrass consumers encode that affine identity as all-zero
// coordinates, so `passZero=true` intentionally collapses zero
// denominators to `{ x: 0, y: 0 }`.
const [xd_inv, yd_inv] = FpInvertBatch(field, [xd, yd], true);
x = field.mul(xn, xd_inv); // xNum / xDen
y = field.mul(y, field.mul(yn, yd_inv)); // y * (yNum / yDev)
return { x, y };
};
}
// Keep the shared DST removable when the selected bundle never hashes to scalar.
// Callers that need protocol-specific scalar domain separation must override this generic default.
// RFC 9497 §§4.1-4.5 use this ASCII prefix before appending the ciphersuite context string.
// Export a string instead of mutable bytes so callers cannot poison default hash-to-scalar behavior
// by mutating a shared Uint8Array in place.
export const _DST_scalar = 'HashToScalar-';
/**
* Creates hash-to-curve methods from EC Point and mapToCurve function. See {@link H2CHasher}.
* @param Point - Point constructor.
* @param mapToCurve - Map-to-curve function.
* @param defaults - Default hash-to-curve options. This object is frozen in place and reused as
* the shared defaults bundle for the returned helpers.
* @returns Hash-to-curve helper namespace.
* @throws If the map-to-curve callback or default hash-to-curve options are invalid. {@link Error}
* @example
* Bundle hash-to-curve, hash-to-scalar, and encode-to-curve helpers for one curve.
*
* ```ts
* import { createHasher } from '@noble/curves/abstract/hash-to-curve.js';
* import { p256 } from '@noble/curves/nist.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const hasher = createHasher(p256.Point, () => p256.Point.BASE.toAffine(), {
* DST: 'P256_XMD:SHA-256_SSWU_RO_',
* encodeDST: 'P256_XMD:SHA-256_SSWU_NU_',
* p: p256.Point.Fp.ORDER,
* m: 1,
* k: 128,
* expand: 'xmd',
* hash: sha256,
* });
* const point = hasher.encodeToCurve(new TextEncoder().encode('hello noble'));
* ```
*/
export function createHasher(Point, mapToCurve, defaults) {
if (typeof mapToCurve !== 'function')
throw new Error('mapToCurve() must be defined');
// `Point` is intentionally not shape-validated eagerly here: point constructors vary across
// curve families, so this helper only checks the hooks it can validate cheaply. Misconfigured
// suites fail later when hashing first touches Point.fromAffine / Point.ZERO / clearCofactor().
const snapshot = (src) => Object.freeze({
...src,
DST: isBytes(src.DST) ? copyBytes(src.DST) : src.DST,
...(src.encodeDST === undefined
? {}
: { encodeDST: isBytes(src.encodeDST) ? copyBytes(src.encodeDST) : src.encodeDST }),
});
// Keep one private defaults snapshot for actual hashing and expose fresh
// detached snapshots via the public getter.
// Otherwise a caller could mutate `hasher.defaults.DST` in place and poison
// the singleton hasher for every other consumer in the same process.
const safeDefaults = snapshot(defaults);
function map(num) {
return Point.fromAffine(mapToCurve(num));
}
function clear(initial) {
const P = initial.clearCofactor();
// Keep ZERO as the algebraic cofactor-clearing result here; strict public point-validity
// surfaces may still reject it later, but createHasher.clear() itself is not that boundary.
if (P.equals(Point.ZERO))
return Point.ZERO;
P.assertValidity();
return P;
}
return Object.freeze({
get defaults() {
return snapshot(safeDefaults);
},
Point,
hashToCurve(msg, options) {
const opts = Object.assign({}, safeDefaults, options);
const u = hash_to_field(msg, 2, opts);
const u0 = map(u[0]);
const u1 = map(u[1]);
return clear(u0.add(u1));
},
encodeToCurve(msg, options) {
const optsDst = safeDefaults.encodeDST ? { DST: safeDefaults.encodeDST } : {};
const opts = Object.assign({}, safeDefaults, optsDst, options);
const u = hash_to_field(msg, 1, opts);
const u0 = map(u[0]);
return clear(u0);
},
/** See {@link H2CHasher} */
mapToCurve(scalars) {
// Curves with m=1 accept only single scalar
if (safeDefaults.m === 1) {
if (typeof scalars !== 'bigint')
throw new Error('expected bigint (m=1)');
return clear(map([scalars]));
}
if (!Array.isArray(scalars))
throw new Error('expected array of bigints');
for (const i of scalars)
if (typeof i !== 'bigint')
throw new Error('expected array of bigints');
return clear(map(scalars));
},
// hash_to_scalar can produce 0: https://www.rfc-editor.org/errata/eid8393
// RFC 9380, draft-irtf-cfrg-bbs-signatures-08. Default scalar DST is the shared generic
// `HashToScalar-` prefix above unless the caller overrides it per invocation.
hashToScalar(msg, options) {
// @ts-ignore
const N = Point.Fn.ORDER;
const opts = Object.assign({}, safeDefaults, { p: N, m: 1, DST: _DST_scalar }, options);
return hash_to_field(msg, 1, opts)[0][0];
},
});
}
//# sourceMappingURL=hash-to-curve.js.map

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/**
* Utils for modular division and fields.
* Field over 11 is a finite (Galois) field is integer number operations `mod 11`.
* There is no division: it is replaced by modular multiplicative inverse.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type TArg, type TRet } from '../utils.ts';
/**
* @param a - Dividend value.
* @param b - Positive modulus.
* @returns Reduced value in `[0, b)` only when `b` is positive.
* @throws If the modulus is not positive. {@link Error}
* @example
* Normalize a bigint into one field residue.
*
* ```ts
* mod(-1n, 5n);
* ```
*/
export declare function mod(a: bigint, b: bigint): bigint;
/**
* Efficiently raise num to a power with modular reduction.
* Unsafe in some contexts: uses ladder, so can expose bigint bits.
* Low-level helper: callers that need canonical residues must pass a valid `num` for the chosen
* modulus instead of relying on the `power===0/1` fast paths to normalize it.
* @param num - Base value.
* @param power - Exponent value.
* @param modulo - Reduction modulus.
* @returns Modular exponentiation result.
* @throws If the modulus or exponent is invalid. {@link Error}
* @example
* Raise one bigint to a modular power.
*
* ```ts
* pow(2n, 6n, 11n) // 64n % 11n == 9n
* ```
*/
export declare function pow(num: bigint, power: bigint, modulo: bigint): bigint;
/**
* Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)`.
* Low-level helper: callers that need canonical residues must pass a valid `x` for the chosen
* modulus; the `power===0` fast path intentionally returns the input unchanged.
* @param x - Base value.
* @param power - Number of squarings.
* @param modulo - Reduction modulus.
* @returns Repeated-squaring result.
* @throws If the exponent is negative. {@link Error}
* @example
* Apply repeated squaring inside one field.
*
* ```ts
* pow2(3n, 2n, 11n);
* ```
*/
export declare function pow2(x: bigint, power: bigint, modulo: bigint): bigint;
/**
* Inverses number over modulo.
* Implemented using the {@link https://brilliant.org/wiki/extended-euclidean-algorithm/ | extended Euclidean algorithm}.
* @param number - Value to invert.
* @param modulo - Positive modulus.
* @returns Multiplicative inverse.
* @throws If the modulus is invalid or the inverse does not exist. {@link Error}
* @example
* Compute one modular inverse with the extended Euclidean algorithm.
*
* ```ts
* invert(3n, 11n);
* ```
*/
export declare function invert(number: bigint, modulo: bigint): bigint;
/**
* Tonelli-Shanks square root search algorithm.
* This implementation is variable-time: it searches data-dependently for the first non-residue `Z`
* and for the smallest `i` in the main loop, unlike RFC 9380 Appendix I.4's constant-time shape.
* 1. {@link https://eprint.iacr.org/2012/685.pdf | eprint 2012/685}, page 12
* 2. Square Roots from 1; 24, 51, 10 to Dan Shanks
* @param P - field order
* @returns function that takes field Fp (created from P) and number n
* @throws If the field is too small, non-prime, or the square root does not exist. {@link Error}
* @example
* Construct a square-root helper for primes that need Tonelli-Shanks.
*
* ```ts
* import { Field, tonelliShanks } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const sqrt = tonelliShanks(17n)(Fp, 4n);
* ```
*/
export declare function tonelliShanks(P: bigint): TRet<(<T>(Fp: IField<T>, n: T) => T)>;
/**
* Square root for a finite field. Will try optimized versions first:
*
* 1. P ≡ 3 (mod 4)
* 2. P ≡ 5 (mod 8)
* 3. P ≡ 9 (mod 16)
* 4. Tonelli-Shanks algorithm
*
* Different algorithms can give different roots, it is up to user to decide which one they want.
* For example there is FpSqrtOdd/FpSqrtEven to choose a root by oddness
* (used for hash-to-curve).
* @param P - Field order.
* @returns Square-root helper. The generic fallback inherits Tonelli-Shanks' variable-time
* behavior and this selector assumes prime-field-style integer moduli.
* @throws If the field is unsupported or the square root does not exist. {@link Error}
* @example
* Choose the square-root helper appropriate for one field modulus.
*
* ```ts
* import { Field, FpSqrt } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const sqrt = FpSqrt(17n)(Fp, 4n);
* ```
*/
export declare function FpSqrt(P: bigint): TRet<(<T>(Fp: IField<T>, n: T) => T)>;
/**
* @param num - Value to inspect.
* @param modulo - Field modulus.
* @returns `true` when the least-significant little-endian bit is set.
* @throws If the modulus is invalid for `mod(...)`. {@link Error}
* @example
* Inspect the low bit used by little-endian sign conventions.
*
* ```ts
* isNegativeLE(3n, 11n);
* ```
*/
export declare const isNegativeLE: (num: bigint, modulo: bigint) => boolean;
/** Generic field interface used by prime and extension fields alike.
* Generic helpers treat field operations as pure functions: implementations MUST treat provided
* values/byte buffers as read-only and return detached results instead of mutating arguments.
*/
export interface IField<T> {
/** Field order `q`, which may be prime or a prime power. */
ORDER: bigint;
/** Canonical encoded byte length. */
BYTES: number;
/** Canonical encoded bit length. */
BITS: number;
/** Whether encoded field elements use little-endian bytes. */
isLE: boolean;
/** Additive identity. */
ZERO: T;
/** Multiplicative identity. */
ONE: T;
/**
* Normalize one value into the field.
* @param num - Input value.
* @returns Normalized field value.
*/
create: (num: T) => T;
/**
* Check whether one value already belongs to the field.
* @param num - Input value.
* Implementations may throw `TypeError` on malformed input types instead of returning `false`.
* @returns Whether the value already belongs to the field.
*/
isValid: (num: T) => boolean;
/**
* Check whether one value is zero.
* @param num - Input value.
* @returns Whether the value is zero.
*/
is0: (num: T) => boolean;
/**
* Check whether one value is non-zero and belongs to the field.
* @param num - Input value.
* Implementations may throw `TypeError` on malformed input types instead of returning `false`.
* @returns Whether the value is non-zero and valid.
*/
isValidNot0: (num: T) => boolean;
/**
* Negate one value.
* @param num - Input value.
* @returns Negated value.
*/
neg(num: T): T;
/**
* Invert one value multiplicatively.
* @param num - Input value.
* @returns Multiplicative inverse.
*/
inv(num: T): T;
/**
* Compute one square root when it exists.
* @param num - Input value.
* @returns Square root.
*/
sqrt(num: T): T;
/**
* Square one value.
* @param num - Input value.
* @returns Squared value.
*/
sqr(num: T): T;
/**
* Compare two field values.
* @param lhs - Left value.
* @param rhs - Right value.
* @returns Whether both values are equal.
*/
eql(lhs: T, rhs: T): boolean;
/**
* Add two normalized field values.
* @param lhs - Left value.
* @param rhs - Right value.
* @returns Sum value.
*/
add(lhs: T, rhs: T): T;
/**
* Subtract two normalized field values.
* @param lhs - Left value.
* @param rhs - Right value.
* @returns Difference value.
*/
sub(lhs: T, rhs: T): T;
/**
* Multiply two field values.
* @param lhs - Left value.
* @param rhs - Right value or scalar.
* @returns Product value.
*/
mul(lhs: T, rhs: T | bigint): T;
/**
* Raise one field value to a power.
* @param lhs - Base value.
* @param power - Exponent.
* @returns Power value.
*/
pow(lhs: T, power: bigint): T;
/**
* Divide one field value by another.
* @param lhs - Dividend.
* @param rhs - Divisor or scalar.
* @returns Quotient value.
*/
div(lhs: T, rhs: T | bigint): T;
/**
* Add two values without re-normalizing the result.
* @param lhs - Left value.
* @param rhs - Right value.
* @returns Non-normalized sum.
*/
addN(lhs: T, rhs: T): T;
/**
* Subtract two values without re-normalizing the result.
* @param lhs - Left value.
* @param rhs - Right value.
* @returns Non-normalized difference.
*/
subN(lhs: T, rhs: T): T;
/**
* Multiply two values without re-normalizing the result.
* @param lhs - Left value.
* @param rhs - Right value or scalar.
* @returns Non-normalized product.
*/
mulN(lhs: T, rhs: T | bigint): T;
/**
* Square one value without re-normalizing the result.
* @param num - Input value.
* @returns Non-normalized square.
*/
sqrN(num: T): T;
/**
* Return the RFC 9380 `sgn0`-style oddness bit when supported.
* This uses oddness instead of evenness so extension fields like Fp2 can expose the same hook.
* Returns whether the value is odd under the field encoding.
*/
isOdd?(num: T): boolean;
/**
* Invert many field elements in one batch.
* @param lst - Values to invert.
* @returns Batch of inverses.
*/
invertBatch: (lst: T[]) => T[];
/**
* Encode one field value into fixed-width bytes.
* Callers that need canonical encodings MUST supply a valid field element.
* Low-level protocols may also use this to serialize raw / non-canonical residues.
* @param num - Input value.
* @returns Fixed-width byte encoding.
*/
toBytes(num: T): Uint8Array;
/**
* Decode one field value from fixed-width bytes.
* @param bytes - Fixed-width byte encoding.
* @param skipValidation - Whether to skip range validation.
* Implementations MUST treat `bytes` as read-only.
* @returns Decoded field value.
*/
fromBytes(bytes: Uint8Array, skipValidation?: boolean): T;
/**
* Constant-time conditional move.
* @param a - Value used when the condition is false.
* @param b - Value used when the condition is true.
* @param c - Selection bit.
* @returns Selected value.
*/
cmov(a: T, b: T, c: boolean): T;
}
/**
* @param field - Field implementation.
* @returns Validated field. This only checks the arithmetic subset needed by generic helpers; it
* does not guarantee full runtime-method coverage for serialization, batching, `cmov`, or
* field-specific extras beyond positive `BYTES` / `BITS`.
* @throws If the field shape or numeric metadata are invalid. {@link Error}
* @example
* Check that a field implementation exposes the operations curve code expects.
*
* ```ts
* import { Field, validateField } from '@noble/curves/abstract/modular.js';
* const Fp = validateField(Field(17n));
* ```
*/
export declare function validateField<T>(field: TArg<IField<T>>): TRet<IField<T>>;
/**
* Same as `pow` but for Fp: non-constant-time.
* Unsafe in some contexts: uses ladder, so can expose bigint bits.
* @param Fp - Field implementation.
* @param num - Base value.
* @param power - Exponent value.
* @returns Powered field element.
* @throws If the exponent is negative. {@link Error}
* @example
* Raise one field element to a public exponent.
*
* ```ts
* import { Field, FpPow } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const x = FpPow(Fp, 3n, 5n);
* ```
*/
export declare function FpPow<T>(Fp: TArg<IField<T>>, num: T, power: bigint): T;
/**
* Efficiently invert an array of Field elements.
* Exception-free. Zero-valued field elements stay `undefined` unless `passZero` is enabled.
* @param Fp - Field implementation.
* @param nums - Values to invert.
* @param passZero - map 0 to 0 (instead of undefined)
* @returns Inverted values.
* @example
* Invert several field elements with one shared inversion.
*
* ```ts
* import { Field, FpInvertBatch } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const inv = FpInvertBatch(Fp, [1n, 2n, 4n]);
* ```
*/
export declare function FpInvertBatch<T>(Fp: TArg<IField<T>>, nums: T[], passZero?: boolean): T[];
/**
* @param Fp - Field implementation.
* @param lhs - Dividend value.
* @param rhs - Divisor value.
* @returns Division result.
* @throws If the divisor is non-invertible. {@link Error}
* @example
* Divide one field element by another.
*
* ```ts
* import { Field, FpDiv } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const x = FpDiv(Fp, 6n, 3n);
* ```
*/
export declare function FpDiv<T>(Fp: TArg<IField<T>>, lhs: T, rhs: T | bigint): T;
/**
* Legendre symbol.
* Legendre constant is used to calculate Legendre symbol (a | p)
* which denotes the value of a^((p-1)/2) (mod p).
*
* * (a | p) ≡ 1 if a is a square (mod p), quadratic residue
* * (a | p) ≡ -1 if a is not a square (mod p), quadratic non residue
* * (a | p) ≡ 0 if a ≡ 0 (mod p)
* @param Fp - Field implementation.
* @param n - Value to inspect.
* @returns Legendre symbol.
* @throws If the field returns an invalid Legendre symbol value. {@link Error}
* @example
* Compute the Legendre symbol of one field element.
*
* ```ts
* import { Field, FpLegendre } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const symbol = FpLegendre(Fp, 4n);
* ```
*/
export declare function FpLegendre<T>(Fp: TArg<IField<T>>, n: T): -1 | 0 | 1;
/**
* @param Fp - Field implementation.
* @param n - Value to inspect.
* @returns `true` when `Fp.sqrt(n)` exists. This includes `0`, even though strict "quadratic
* residue" terminology often reserves that name for the non-zero square class.
* @throws If the field returns an invalid Legendre symbol value. {@link Error}
* @example
* Check whether one field element has a square root in the field.
*
* ```ts
* import { Field, FpIsSquare } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const isSquare = FpIsSquare(Fp, 4n);
* ```
*/
export declare function FpIsSquare<T>(Fp: TArg<IField<T>>, n: T): boolean;
/** Byte and bit lengths derived from one scalar order. */
export type NLength = {
/** Canonical byte length. */
nByteLength: number;
/** Canonical bit length. */
nBitLength: number;
};
/**
* @param n - Curve order. Callers are expected to pass a positive order.
* @param nBitLength - Optional cached bit length. Callers are expected to pass a positive cached
* value when overriding the derived bit length.
* @returns Byte and bit lengths.
* @throws If the order or cached bit length is invalid. {@link Error}
* @example
* Measure the encoding sizes needed for one modulus.
*
* ```ts
* nLength(255n);
* ```
*/
export declare function nLength(n: bigint, nBitLength?: number): NLength;
type FpField = IField<bigint> & Required<Pick<IField<bigint>, 'isOdd'>>;
type SqrtFn = (n: bigint) => bigint;
type FieldOpts = Partial<{
isLE: boolean;
BITS: number;
sqrt: SqrtFn;
allowedLengths?: readonly number[];
modFromBytes: boolean;
}>;
/**
* Creates a finite field. Major performance optimizations:
* * 1. Denormalized operations like mulN instead of mul.
* * 2. Identical object shape: never add or remove keys.
* * 3. Frozen stable object shape; the lazy sqrt cache lives in a module-level `WeakMap`.
* Fragile: always run a benchmark on a change.
* Security note: operations and low-level serializers like `toBytes` don't check `isValid` for
* all elements for performance and protocol-flexibility reasons; callers are responsible for
* supplying valid elements when they need canonical field behavior.
* This is low-level code, please make sure you know what you're doing.
*
* Note about field properties:
* * CHARACTERISTIC p = prime number, number of elements in main subgroup.
* * ORDER q = similar to cofactor in curves, may be composite `q = p^m`.
*
* @param ORDER - field order, probably prime, or could be composite
* @param opts - Field options such as bit length or endianness. See {@link FieldOpts}.
* @returns Frozen field instance with a stable object shape. This wrapper forwards `opts` straight
* into `_Field`, so it inherits `_Field`'s assumptions about cached sizes and `allowedLengths`.
* @example
* Construct one prime field with optional overrides.
*
* ```ts
* Field(11n);
* ```
*/
export declare function Field(ORDER: bigint, opts?: FieldOpts): TRet<Readonly<FpField>>;
/**
* @param Fp - Field implementation.
* @param elm - Value to square-root.
* @returns Odd square root when two roots exist. The special case `elm = 0` still returns `0`,
* which is the only square root but is not odd.
* @throws If the field lacks oddness checks or the square root does not exist. {@link Error}
* @example
* Select the odd square root when two roots exist.
*
* ```ts
* import { Field, FpSqrtOdd } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const root = FpSqrtOdd(Fp, 4n);
* ```
*/
export declare function FpSqrtOdd<T>(Fp: TArg<IField<T>>, elm: T): T;
/**
* @param Fp - Field implementation.
* @param elm - Value to square-root.
* @returns Even square root.
* @throws If the field lacks oddness checks or the square root does not exist. {@link Error}
* @example
* Select the even square root when two roots exist.
*
* ```ts
* import { Field, FpSqrtEven } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const root = FpSqrtEven(Fp, 4n);
* ```
*/
export declare function FpSqrtEven<T>(Fp: TArg<IField<T>>, elm: T): T;
/**
* Returns total number of bytes consumed by the field element.
* For example, 32 bytes for usual 256-bit weierstrass curve.
* @param fieldOrder - number of field elements, usually CURVE.n. Callers are expected to pass an
* order greater than 1.
* @returns byte length of field
* @throws If the field order is not a bigint. {@link Error}
* @example
* Read the fixed-width byte length of one field.
*
* ```ts
* getFieldBytesLength(255n);
* ```
*/
export declare function getFieldBytesLength(fieldOrder: bigint): number;
/**
* Returns minimal amount of bytes that can be safely reduced
* by field order.
* Should be 2^-128 for 128-bit curve such as P256.
* This is the reduction / modulo-bias lower bound; higher-level helpers may still impose a larger
* absolute floor for policy reasons.
* @param fieldOrder - number of field elements greater than 1, usually CURVE.n.
* @returns byte length of target hash
* @throws If the field order is invalid. {@link Error}
* @example
* Compute the minimum hash length needed for field reduction.
*
* ```ts
* getMinHashLength(255n);
* ```
*/
export declare function getMinHashLength(fieldOrder: bigint): number;
/**
* "Constant-time" private key generation utility.
* Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private scalar, with the modulo bias being negligible.
* Needs at least 48 bytes of input for 32-byte private key. The implementation also keeps a hard
* 16-byte minimum even when `getMinHashLength(...)` is smaller, so toy-small inputs do not look
* accidentally acceptable for real scalar derivation.
* See {@link https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/ | Kudelski's modulo-bias guide},
* {@link https://csrc.nist.gov/publications/detail/fips/186/5/final | FIPS 186-5 appendix A.2}, and
* {@link https://www.rfc-editor.org/rfc/rfc9380#section-5 | RFC 9380 section 5}. Unlike RFC 9380
* `hash_to_field`, this helper intentionally maps into the non-zero private-scalar range `1..n-1`.
* @param key - Uniform input bytes.
* @param fieldOrder - Size of subgroup.
* @param isLE - interpret hash bytes as LE num
* @returns valid private scalar
* @throws If the hash length or field order is invalid for scalar reduction. {@link Error}
* @example
* Map hash output into a private scalar range.
*
* ```ts
* mapHashToField(new Uint8Array(48).fill(1), 255n);
* ```
*/
export declare function mapHashToField(key: TArg<Uint8Array>, fieldOrder: bigint, isLE?: boolean): TRet<Uint8Array>;
export {};
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/**
* Utils for modular division and fields.
* Field over 11 is a finite (Galois) field is integer number operations `mod 11`.
* There is no division: it is replaced by modular multiplicative inverse.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { abool, abytes, anumber, asafenumber, bitLen, bytesToNumberBE, bytesToNumberLE, numberToBytesBE, numberToBytesLE, validateObject, } from "../utils.js";
// Numbers aren't used in x25519 / x448 builds
// prettier-ignore
const _0n = /* @__PURE__ */ BigInt(0), _1n = /* @__PURE__ */ BigInt(1), _2n = /* @__PURE__ */ BigInt(2);
// prettier-ignore
const _3n = /* @__PURE__ */ BigInt(3), _4n = /* @__PURE__ */ BigInt(4), _5n = /* @__PURE__ */ BigInt(5);
// prettier-ignore
const _7n = /* @__PURE__ */ BigInt(7), _8n = /* @__PURE__ */ BigInt(8), _9n = /* @__PURE__ */ BigInt(9);
const _16n = /* @__PURE__ */ BigInt(16);
/**
* @param a - Dividend value.
* @param b - Positive modulus.
* @returns Reduced value in `[0, b)` only when `b` is positive.
* @throws If the modulus is not positive. {@link Error}
* @example
* Normalize a bigint into one field residue.
*
* ```ts
* mod(-1n, 5n);
* ```
*/
export function mod(a, b) {
if (b <= _0n)
throw new Error('mod: expected positive modulus, got ' + b);
const result = a % b;
return result >= _0n ? result : b + result;
}
/**
* Efficiently raise num to a power with modular reduction.
* Unsafe in some contexts: uses ladder, so can expose bigint bits.
* Low-level helper: callers that need canonical residues must pass a valid `num` for the chosen
* modulus instead of relying on the `power===0/1` fast paths to normalize it.
* @param num - Base value.
* @param power - Exponent value.
* @param modulo - Reduction modulus.
* @returns Modular exponentiation result.
* @throws If the modulus or exponent is invalid. {@link Error}
* @example
* Raise one bigint to a modular power.
*
* ```ts
* pow(2n, 6n, 11n) // 64n % 11n == 9n
* ```
*/
export function pow(num, power, modulo) {
return FpPow(Field(modulo), num, power);
}
/**
* Does `x^(2^power)` mod p. `pow2(30, 4)` == `30^(2^4)`.
* Low-level helper: callers that need canonical residues must pass a valid `x` for the chosen
* modulus; the `power===0` fast path intentionally returns the input unchanged.
* @param x - Base value.
* @param power - Number of squarings.
* @param modulo - Reduction modulus.
* @returns Repeated-squaring result.
* @throws If the exponent is negative. {@link Error}
* @example
* Apply repeated squaring inside one field.
*
* ```ts
* pow2(3n, 2n, 11n);
* ```
*/
export function pow2(x, power, modulo) {
if (power < _0n)
throw new Error('pow2: expected non-negative exponent, got ' + power);
let res = x;
while (power-- > _0n) {
res *= res;
res %= modulo;
}
return res;
}
/**
* Inverses number over modulo.
* Implemented using the {@link https://brilliant.org/wiki/extended-euclidean-algorithm/ | extended Euclidean algorithm}.
* @param number - Value to invert.
* @param modulo - Positive modulus.
* @returns Multiplicative inverse.
* @throws If the modulus is invalid or the inverse does not exist. {@link Error}
* @example
* Compute one modular inverse with the extended Euclidean algorithm.
*
* ```ts
* invert(3n, 11n);
* ```
*/
export function invert(number, modulo) {
if (number === _0n)
throw new Error('invert: expected non-zero number');
if (modulo <= _0n)
throw new Error('invert: expected positive modulus, got ' + modulo);
// Fermat's little theorem "CT-like" version inv(n) = n^(m-2) mod m is 30x slower.
let a = mod(number, modulo);
let b = modulo;
// prettier-ignore
let x = _0n, y = _1n, u = _1n, v = _0n;
while (a !== _0n) {
const q = b / a;
const r = b - a * q;
const m = x - u * q;
const n = y - v * q;
// prettier-ignore
b = a, a = r, x = u, y = v, u = m, v = n;
}
const gcd = b;
if (gcd !== _1n)
throw new Error('invert: does not exist');
return mod(x, modulo);
}
function assertIsSquare(Fp, root, n) {
const F = Fp;
if (!F.eql(F.sqr(root), n))
throw new Error('Cannot find square root');
}
// Not all roots are possible! Example which will throw:
// const NUM =
// n = 72057594037927816n;
// Fp = Field(BigInt('0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'));
function sqrt3mod4(Fp, n) {
const F = Fp;
const p1div4 = (F.ORDER + _1n) / _4n;
const root = F.pow(n, p1div4);
assertIsSquare(F, root, n);
return root;
}
// Equivalent `q = 5 (mod 8)` square-root formula (Atkin-style), not the RFC Appendix I.2 CMOV
// pseudocode verbatim.
function sqrt5mod8(Fp, n) {
const F = Fp;
const p5div8 = (F.ORDER - _5n) / _8n;
const n2 = F.mul(n, _2n);
const v = F.pow(n2, p5div8);
const nv = F.mul(n, v);
const i = F.mul(F.mul(nv, _2n), v);
const root = F.mul(nv, F.sub(i, F.ONE));
assertIsSquare(F, root, n);
return root;
}
// Based on RFC9380, Kong algorithm
// prettier-ignore
function sqrt9mod16(P) {
const Fp_ = Field(P);
const tn = tonelliShanks(P);
const c1 = tn(Fp_, Fp_.neg(Fp_.ONE)); // 1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
const c2 = tn(Fp_, c1); // 2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F
const c3 = tn(Fp_, Fp_.neg(c1)); // 3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F
const c4 = (P + _7n) / _16n; // 4. c4 = (q + 7) / 16 # Integer arithmetic
return ((Fp, n) => {
const F = Fp;
let tv1 = F.pow(n, c4); // 1. tv1 = x^c4
let tv2 = F.mul(tv1, c1); // 2. tv2 = c1 * tv1
const tv3 = F.mul(tv1, c2); // 3. tv3 = c2 * tv1
const tv4 = F.mul(tv1, c3); // 4. tv4 = c3 * tv1
const e1 = F.eql(F.sqr(tv2), n); // 5. e1 = (tv2^2) == x
const e2 = F.eql(F.sqr(tv3), n); // 6. e2 = (tv3^2) == x
tv1 = F.cmov(tv1, tv2, e1); // 7. tv1 = CMOV(tv1, tv2, e1) # Select tv2 if (tv2^2) == x
tv2 = F.cmov(tv4, tv3, e2); // 8. tv2 = CMOV(tv4, tv3, e2) # Select tv3 if (tv3^2) == x
const e3 = F.eql(F.sqr(tv2), n); // 9. e3 = (tv2^2) == x
const root = F.cmov(tv1, tv2, e3); // 10. z = CMOV(tv1, tv2, e3) # Select sqrt from tv1 & tv2
assertIsSquare(F, root, n);
return root;
});
}
/**
* Tonelli-Shanks square root search algorithm.
* This implementation is variable-time: it searches data-dependently for the first non-residue `Z`
* and for the smallest `i` in the main loop, unlike RFC 9380 Appendix I.4's constant-time shape.
* 1. {@link https://eprint.iacr.org/2012/685.pdf | eprint 2012/685}, page 12
* 2. Square Roots from 1; 24, 51, 10 to Dan Shanks
* @param P - field order
* @returns function that takes field Fp (created from P) and number n
* @throws If the field is too small, non-prime, or the square root does not exist. {@link Error}
* @example
* Construct a square-root helper for primes that need Tonelli-Shanks.
*
* ```ts
* import { Field, tonelliShanks } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const sqrt = tonelliShanks(17n)(Fp, 4n);
* ```
*/
export function tonelliShanks(P) {
// Initialization (precomputation).
// Caching initialization could boost perf by 7%.
if (P < _3n)
throw new Error('sqrt is not defined for small field');
// Factor P - 1 = Q * 2^S, where Q is odd
let Q = P - _1n;
let S = 0;
while (Q % _2n === _0n) {
Q /= _2n;
S++;
}
// Find the first quadratic non-residue Z >= 2
let Z = _2n;
const _Fp = Field(P);
while (FpLegendre(_Fp, Z) === 1) {
// Basic primality test for P. After x iterations, chance of
// not finding quadratic non-residue is 2^x, so 2^1000.
if (Z++ > 1000)
throw new Error('Cannot find square root: probably non-prime P');
}
// Fast-path; usually done before Z, but we do "primality test".
if (S === 1)
return sqrt3mod4;
// Slow-path
// TODO: test on Fp2 and others
let cc = _Fp.pow(Z, Q); // c = z^Q
const Q1div2 = (Q + _1n) / _2n;
return function tonelliSlow(Fp, n) {
const F = Fp;
if (F.is0(n))
return n;
// Check if n is a quadratic residue using Legendre symbol
if (FpLegendre(F, n) !== 1)
throw new Error('Cannot find square root');
// Initialize variables for the main loop
let M = S;
let c = F.mul(F.ONE, cc); // c = z^Q, move cc from field _Fp into field Fp
let t = F.pow(n, Q); // t = n^Q, first guess at the fudge factor
let R = F.pow(n, Q1div2); // R = n^((Q+1)/2), first guess at the square root
// Main loop
// while t != 1
while (!F.eql(t, F.ONE)) {
if (F.is0(t))
return F.ZERO; // if t=0 return R=0
let i = 1;
// Find the smallest i >= 1 such that t^(2^i) ≡ 1 (mod P)
let t_tmp = F.sqr(t); // t^(2^1)
while (!F.eql(t_tmp, F.ONE)) {
i++;
t_tmp = F.sqr(t_tmp); // t^(2^2)...
if (i === M)
throw new Error('Cannot find square root');
}
// Calculate the exponent for b: 2^(M - i - 1)
const exponent = _1n << BigInt(M - i - 1); // bigint is important
const b = F.pow(c, exponent); // b = 2^(M - i - 1)
// Update variables
M = i;
c = F.sqr(b); // c = b^2
t = F.mul(t, c); // t = (t * b^2)
R = F.mul(R, b); // R = R*b
}
return R;
};
}
/**
* Square root for a finite field. Will try optimized versions first:
*
* 1. P ≡ 3 (mod 4)
* 2. P ≡ 5 (mod 8)
* 3. P ≡ 9 (mod 16)
* 4. Tonelli-Shanks algorithm
*
* Different algorithms can give different roots, it is up to user to decide which one they want.
* For example there is FpSqrtOdd/FpSqrtEven to choose a root by oddness
* (used for hash-to-curve).
* @param P - Field order.
* @returns Square-root helper. The generic fallback inherits Tonelli-Shanks' variable-time
* behavior and this selector assumes prime-field-style integer moduli.
* @throws If the field is unsupported or the square root does not exist. {@link Error}
* @example
* Choose the square-root helper appropriate for one field modulus.
*
* ```ts
* import { Field, FpSqrt } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const sqrt = FpSqrt(17n)(Fp, 4n);
* ```
*/
export function FpSqrt(P) {
// P ≡ 3 (mod 4) => √n = n^((P+1)/4)
if (P % _4n === _3n)
return sqrt3mod4;
// P ≡ 5 (mod 8) => Atkin algorithm, page 10 of https://eprint.iacr.org/2012/685.pdf
if (P % _8n === _5n)
return sqrt5mod8;
// P ≡ 9 (mod 16) => Kong algorithm, page 11 of https://eprint.iacr.org/2012/685.pdf (algorithm 4)
if (P % _16n === _9n)
return sqrt9mod16(P);
// Tonelli-Shanks algorithm
return tonelliShanks(P);
}
/**
* @param num - Value to inspect.
* @param modulo - Field modulus.
* @returns `true` when the least-significant little-endian bit is set.
* @throws If the modulus is invalid for `mod(...)`. {@link Error}
* @example
* Inspect the low bit used by little-endian sign conventions.
*
* ```ts
* isNegativeLE(3n, 11n);
* ```
*/
export const isNegativeLE = (num, modulo) => (mod(num, modulo) & _1n) === _1n;
// prettier-ignore
// Arithmetic-only subset checked by validateField(). This is intentionally not the full runtime
// IField contract: helpers like `isValidNot0`, `invertBatch`, `toBytes`, `fromBytes`, `cmov`, and
// field-specific extras like `isOdd` are left to the callers that actually need them.
const FIELD_FIELDS = [
'create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr',
'eql', 'add', 'sub', 'mul', 'pow', 'div',
'addN', 'subN', 'mulN', 'sqrN'
];
/**
* @param field - Field implementation.
* @returns Validated field. This only checks the arithmetic subset needed by generic helpers; it
* does not guarantee full runtime-method coverage for serialization, batching, `cmov`, or
* field-specific extras beyond positive `BYTES` / `BITS`.
* @throws If the field shape or numeric metadata are invalid. {@link Error}
* @example
* Check that a field implementation exposes the operations curve code expects.
*
* ```ts
* import { Field, validateField } from '@noble/curves/abstract/modular.js';
* const Fp = validateField(Field(17n));
* ```
*/
export function validateField(field) {
const initial = {
ORDER: 'bigint',
BYTES: 'number',
BITS: 'number',
};
const opts = FIELD_FIELDS.reduce((map, val) => {
map[val] = 'function';
return map;
}, initial);
validateObject(field, opts);
// Runtime field implementations must expose real integer byte/bit sizes; fractional / NaN /
// infinite metadata leaks through validateObject(type='number') but breaks encoders and caches.
asafenumber(field.BYTES, 'BYTES');
asafenumber(field.BITS, 'BITS');
// Runtime field implementations must expose positive byte/bit sizes; zero leaks through the
// numeric shape checks above but still breaks encoding helpers and cached-length assumptions.
if (field.BYTES < 1 || field.BITS < 1)
throw new Error('invalid field: expected BYTES/BITS > 0');
if (field.ORDER <= _1n)
throw new Error('invalid field: expected ORDER > 1, got ' + field.ORDER);
return field;
}
// Generic field functions
/**
* Same as `pow` but for Fp: non-constant-time.
* Unsafe in some contexts: uses ladder, so can expose bigint bits.
* @param Fp - Field implementation.
* @param num - Base value.
* @param power - Exponent value.
* @returns Powered field element.
* @throws If the exponent is negative. {@link Error}
* @example
* Raise one field element to a public exponent.
*
* ```ts
* import { Field, FpPow } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const x = FpPow(Fp, 3n, 5n);
* ```
*/
export function FpPow(Fp, num, power) {
const F = Fp;
if (power < _0n)
throw new Error('invalid exponent, negatives unsupported');
if (power === _0n)
return F.ONE;
if (power === _1n)
return num;
let p = F.ONE;
let d = num;
while (power > _0n) {
if (power & _1n)
p = F.mul(p, d);
d = F.sqr(d);
power >>= _1n;
}
return p;
}
/**
* Efficiently invert an array of Field elements.
* Exception-free. Zero-valued field elements stay `undefined` unless `passZero` is enabled.
* @param Fp - Field implementation.
* @param nums - Values to invert.
* @param passZero - map 0 to 0 (instead of undefined)
* @returns Inverted values.
* @example
* Invert several field elements with one shared inversion.
*
* ```ts
* import { Field, FpInvertBatch } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const inv = FpInvertBatch(Fp, [1n, 2n, 4n]);
* ```
*/
export function FpInvertBatch(Fp, nums, passZero = false) {
const F = Fp;
const inverted = new Array(nums.length).fill(passZero ? F.ZERO : undefined);
// Walk from first to last, multiply them by each other MOD p
const multipliedAcc = nums.reduce((acc, num, i) => {
if (F.is0(num))
return acc;
inverted[i] = acc;
return F.mul(acc, num);
}, F.ONE);
// Invert last element
const invertedAcc = F.inv(multipliedAcc);
// Walk from last to first, multiply them by inverted each other MOD p
nums.reduceRight((acc, num, i) => {
if (F.is0(num))
return acc;
inverted[i] = F.mul(acc, inverted[i]);
return F.mul(acc, num);
}, invertedAcc);
return inverted;
}
/**
* @param Fp - Field implementation.
* @param lhs - Dividend value.
* @param rhs - Divisor value.
* @returns Division result.
* @throws If the divisor is non-invertible. {@link Error}
* @example
* Divide one field element by another.
*
* ```ts
* import { Field, FpDiv } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const x = FpDiv(Fp, 6n, 3n);
* ```
*/
export function FpDiv(Fp, lhs, rhs) {
const F = Fp;
return F.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, F.ORDER) : F.inv(rhs));
}
/**
* Legendre symbol.
* Legendre constant is used to calculate Legendre symbol (a | p)
* which denotes the value of a^((p-1)/2) (mod p).
*
* * (a | p) ≡ 1 if a is a square (mod p), quadratic residue
* * (a | p) ≡ -1 if a is not a square (mod p), quadratic non residue
* * (a | p) ≡ 0 if a ≡ 0 (mod p)
* @param Fp - Field implementation.
* @param n - Value to inspect.
* @returns Legendre symbol.
* @throws If the field returns an invalid Legendre symbol value. {@link Error}
* @example
* Compute the Legendre symbol of one field element.
*
* ```ts
* import { Field, FpLegendre } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const symbol = FpLegendre(Fp, 4n);
* ```
*/
export function FpLegendre(Fp, n) {
const F = Fp;
// We can use 3rd argument as optional cache of this value
// but seems unneeded for now. The operation is very fast.
const p1mod2 = (F.ORDER - _1n) / _2n;
const powered = F.pow(n, p1mod2);
const yes = F.eql(powered, F.ONE);
const zero = F.eql(powered, F.ZERO);
const no = F.eql(powered, F.neg(F.ONE));
if (!yes && !zero && !no)
throw new Error('invalid Legendre symbol result');
return yes ? 1 : zero ? 0 : -1;
}
/**
* @param Fp - Field implementation.
* @param n - Value to inspect.
* @returns `true` when `Fp.sqrt(n)` exists. This includes `0`, even though strict "quadratic
* residue" terminology often reserves that name for the non-zero square class.
* @throws If the field returns an invalid Legendre symbol value. {@link Error}
* @example
* Check whether one field element has a square root in the field.
*
* ```ts
* import { Field, FpIsSquare } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const isSquare = FpIsSquare(Fp, 4n);
* ```
*/
export function FpIsSquare(Fp, n) {
const l = FpLegendre(Fp, n);
// Zero is a square too: 0 = 0^2, and Fp.sqrt(0) already returns 0.
return l !== -1;
}
/**
* @param n - Curve order. Callers are expected to pass a positive order.
* @param nBitLength - Optional cached bit length. Callers are expected to pass a positive cached
* value when overriding the derived bit length.
* @returns Byte and bit lengths.
* @throws If the order or cached bit length is invalid. {@link Error}
* @example
* Measure the encoding sizes needed for one modulus.
*
* ```ts
* nLength(255n);
* ```
*/
export function nLength(n, nBitLength) {
// Bit size, byte size of CURVE.n
if (nBitLength !== undefined)
anumber(nBitLength);
if (n <= _0n)
throw new Error('invalid n length: expected positive n, got ' + n);
if (nBitLength !== undefined && nBitLength < 1)
throw new Error('invalid n length: expected positive bit length, got ' + nBitLength);
const bits = bitLen(n);
// Cached bit lengths smaller than ORDER would truncate serialized scalars/elements and poison
// any math that relies on the derived field metadata.
if (nBitLength !== undefined && nBitLength < bits)
throw new Error(`invalid n length: expected bit length (${bits}) >= n.length (${nBitLength})`);
const _nBitLength = nBitLength !== undefined ? nBitLength : bits;
const nByteLength = Math.ceil(_nBitLength / 8);
return { nBitLength: _nBitLength, nByteLength };
}
// Keep the lazy sqrt cache off-instance so Field(...) can return a frozen object. Otherwise the
// cached helper write would keep the field surface externally mutable.
const FIELD_SQRT = new WeakMap();
class _Field {
ORDER;
BITS;
BYTES;
isLE;
ZERO = _0n;
ONE = _1n;
_lengths;
_mod;
constructor(ORDER, opts = {}) {
// ORDER <= 1 is degenerate: ONE would not be a valid field element and helpers like pow/inv
// would stop modeling field arithmetic.
if (ORDER <= _1n)
throw new Error('invalid field: expected ORDER > 1, got ' + ORDER);
let _nbitLength = undefined;
this.isLE = false;
if (opts != null && typeof opts === 'object') {
// Cached bit lengths are trusted here and should already be positive / consistent with ORDER.
if (typeof opts.BITS === 'number')
_nbitLength = opts.BITS;
if (typeof opts.sqrt === 'function')
// `_Field.prototype` is frozen below, so custom sqrt hooks must become own properties
// explicitly instead of relying on writable prototype shadowing via assignment.
Object.defineProperty(this, 'sqrt', { value: opts.sqrt, enumerable: true });
if (typeof opts.isLE === 'boolean')
this.isLE = opts.isLE;
if (opts.allowedLengths)
this._lengths = Object.freeze(opts.allowedLengths.slice());
if (typeof opts.modFromBytes === 'boolean')
this._mod = opts.modFromBytes;
}
const { nBitLength, nByteLength } = nLength(ORDER, _nbitLength);
if (nByteLength > 2048)
throw new Error('invalid field: expected ORDER of <= 2048 bytes');
this.ORDER = ORDER;
this.BITS = nBitLength;
this.BYTES = nByteLength;
Object.freeze(this);
}
create(num) {
return mod(num, this.ORDER);
}
isValid(num) {
if (typeof num !== 'bigint')
throw new TypeError('invalid field element: expected bigint, got ' + typeof num);
return _0n <= num && num < this.ORDER; // 0 is valid element, but it's not invertible
}
is0(num) {
return num === _0n;
}
// is valid and invertible
isValidNot0(num) {
return !this.is0(num) && this.isValid(num);
}
isOdd(num) {
return (num & _1n) === _1n;
}
neg(num) {
return mod(-num, this.ORDER);
}
eql(lhs, rhs) {
return lhs === rhs;
}
sqr(num) {
return mod(num * num, this.ORDER);
}
add(lhs, rhs) {
return mod(lhs + rhs, this.ORDER);
}
sub(lhs, rhs) {
return mod(lhs - rhs, this.ORDER);
}
mul(lhs, rhs) {
return mod(lhs * rhs, this.ORDER);
}
pow(num, power) {
return FpPow(this, num, power);
}
div(lhs, rhs) {
return mod(lhs * invert(rhs, this.ORDER), this.ORDER);
}
// Same as above, but doesn't normalize
sqrN(num) {
return num * num;
}
addN(lhs, rhs) {
return lhs + rhs;
}
subN(lhs, rhs) {
return lhs - rhs;
}
mulN(lhs, rhs) {
return lhs * rhs;
}
inv(num) {
return invert(num, this.ORDER);
}
sqrt(num) {
// Caching sqrt helpers speeds up sqrt9mod16 by 5x and Tonelli-Shanks by about 10% without keeping
// the field instance itself mutable.
let sqrt = FIELD_SQRT.get(this);
if (!sqrt)
FIELD_SQRT.set(this, (sqrt = FpSqrt(this.ORDER)));
return sqrt(this, num);
}
toBytes(num) {
// Serialize fixed-width limbs without re-validating the field range. Callers that need a
// canonical encoding must pass a valid element; some protocols intentionally serialize raw
// residues here and reduce or validate them elsewhere.
return this.isLE ? numberToBytesLE(num, this.BYTES) : numberToBytesBE(num, this.BYTES);
}
fromBytes(bytes, skipValidation = false) {
abytes(bytes);
const { _lengths: allowedLengths, BYTES, isLE, ORDER, _mod: modFromBytes } = this;
if (allowedLengths) {
// `allowedLengths` must list real positive byte lengths; otherwise empty input would get
// padded into zero and silently decode as a field element.
if (bytes.length < 1 || !allowedLengths.includes(bytes.length) || bytes.length > BYTES) {
throw new Error('Field.fromBytes: expected ' + allowedLengths + ' bytes, got ' + bytes.length);
}
const padded = new Uint8Array(BYTES);
// isLE add 0 to right, !isLE to the left.
padded.set(bytes, isLE ? 0 : padded.length - bytes.length);
bytes = padded;
}
if (bytes.length !== BYTES)
throw new Error('Field.fromBytes: expected ' + BYTES + ' bytes, got ' + bytes.length);
let scalar = isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);
if (modFromBytes)
scalar = mod(scalar, ORDER);
if (!skipValidation)
if (!this.isValid(scalar))
throw new Error('invalid field element: outside of range 0..ORDER');
// Range validation is optional here because some protocols intentionally decode raw residues
// and reduce or validate them elsewhere.
return scalar;
}
// TODO: we don't need it here, move out to separate fn
invertBatch(lst) {
return FpInvertBatch(this, lst);
}
// We can't move this out because Fp6, Fp12 implement it
// and it's unclear what to return in there.
cmov(a, b, condition) {
// Field elements have `isValid(...)`; the CMOV branch bit is a direct runtime input, so reject
// non-boolean selectors here instead of letting JS truthiness silently change arithmetic.
abool(condition, 'condition');
return condition ? b : a;
}
}
// Freeze the shared method surface too; otherwise callers can still poison every Field instance by
// monkey-patching `_Field.prototype` even if each instance is frozen.
Object.freeze(_Field.prototype);
/**
* Creates a finite field. Major performance optimizations:
* * 1. Denormalized operations like mulN instead of mul.
* * 2. Identical object shape: never add or remove keys.
* * 3. Frozen stable object shape; the lazy sqrt cache lives in a module-level `WeakMap`.
* Fragile: always run a benchmark on a change.
* Security note: operations and low-level serializers like `toBytes` don't check `isValid` for
* all elements for performance and protocol-flexibility reasons; callers are responsible for
* supplying valid elements when they need canonical field behavior.
* This is low-level code, please make sure you know what you're doing.
*
* Note about field properties:
* * CHARACTERISTIC p = prime number, number of elements in main subgroup.
* * ORDER q = similar to cofactor in curves, may be composite `q = p^m`.
*
* @param ORDER - field order, probably prime, or could be composite
* @param opts - Field options such as bit length or endianness. See {@link FieldOpts}.
* @returns Frozen field instance with a stable object shape. This wrapper forwards `opts` straight
* into `_Field`, so it inherits `_Field`'s assumptions about cached sizes and `allowedLengths`.
* @example
* Construct one prime field with optional overrides.
*
* ```ts
* Field(11n);
* ```
*/
export function Field(ORDER, opts = {}) {
return new _Field(ORDER, opts);
}
// Generic random scalar, we can do same for other fields if via Fp2.mul(Fp2.ONE, Fp2.random)?
// This allows unsafe methods like ignore bias or zero. These unsafe, but often used in different protocols (if deterministic RNG).
// which mean we cannot force this via opts.
// Not sure what to do with randomBytes, we can accept it inside opts if wanted.
// Probably need to export getMinHashLength somewhere?
// random(bytes?: Uint8Array, unsafeAllowZero = false, unsafeAllowBias = false) {
// const LEN = !unsafeAllowBias ? getMinHashLength(ORDER) : BYTES;
// if (bytes === undefined) bytes = randomBytes(LEN); // _opts.randomBytes?
// const num = isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);
// // `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
// const reduced = unsafeAllowZero ? mod(num, ORDER) : mod(num, ORDER - _1n) + _1n;
// return reduced;
// },
/**
* @param Fp - Field implementation.
* @param elm - Value to square-root.
* @returns Odd square root when two roots exist. The special case `elm = 0` still returns `0`,
* which is the only square root but is not odd.
* @throws If the field lacks oddness checks or the square root does not exist. {@link Error}
* @example
* Select the odd square root when two roots exist.
*
* ```ts
* import { Field, FpSqrtOdd } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const root = FpSqrtOdd(Fp, 4n);
* ```
*/
export function FpSqrtOdd(Fp, elm) {
const F = Fp;
if (!F.isOdd)
throw new Error("Field doesn't have isOdd");
const root = F.sqrt(elm);
return F.isOdd(root) ? root : F.neg(root);
}
/**
* @param Fp - Field implementation.
* @param elm - Value to square-root.
* @returns Even square root.
* @throws If the field lacks oddness checks or the square root does not exist. {@link Error}
* @example
* Select the even square root when two roots exist.
*
* ```ts
* import { Field, FpSqrtEven } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const root = FpSqrtEven(Fp, 4n);
* ```
*/
export function FpSqrtEven(Fp, elm) {
const F = Fp;
if (!F.isOdd)
throw new Error("Field doesn't have isOdd");
const root = F.sqrt(elm);
return F.isOdd(root) ? F.neg(root) : root;
}
/**
* Returns total number of bytes consumed by the field element.
* For example, 32 bytes for usual 256-bit weierstrass curve.
* @param fieldOrder - number of field elements, usually CURVE.n. Callers are expected to pass an
* order greater than 1.
* @returns byte length of field
* @throws If the field order is not a bigint. {@link Error}
* @example
* Read the fixed-width byte length of one field.
*
* ```ts
* getFieldBytesLength(255n);
* ```
*/
export function getFieldBytesLength(fieldOrder) {
if (typeof fieldOrder !== 'bigint')
throw new Error('field order must be bigint');
// Valid field elements are in 0..ORDER-1, so ORDER <= 1 would make the encoded range degenerate.
if (fieldOrder <= _1n)
throw new Error('field order must be greater than 1');
// Valid field elements are < ORDER, so the maximal encoded element is ORDER - 1.
const bitLength = bitLen(fieldOrder - _1n);
return Math.ceil(bitLength / 8);
}
/**
* Returns minimal amount of bytes that can be safely reduced
* by field order.
* Should be 2^-128 for 128-bit curve such as P256.
* This is the reduction / modulo-bias lower bound; higher-level helpers may still impose a larger
* absolute floor for policy reasons.
* @param fieldOrder - number of field elements greater than 1, usually CURVE.n.
* @returns byte length of target hash
* @throws If the field order is invalid. {@link Error}
* @example
* Compute the minimum hash length needed for field reduction.
*
* ```ts
* getMinHashLength(255n);
* ```
*/
export function getMinHashLength(fieldOrder) {
const length = getFieldBytesLength(fieldOrder);
return length + Math.ceil(length / 2);
}
/**
* "Constant-time" private key generation utility.
* Can take (n + n/2) or more bytes of uniform input e.g. from CSPRNG or KDF
* and convert them into private scalar, with the modulo bias being negligible.
* Needs at least 48 bytes of input for 32-byte private key. The implementation also keeps a hard
* 16-byte minimum even when `getMinHashLength(...)` is smaller, so toy-small inputs do not look
* accidentally acceptable for real scalar derivation.
* See {@link https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/ | Kudelski's modulo-bias guide},
* {@link https://csrc.nist.gov/publications/detail/fips/186/5/final | FIPS 186-5 appendix A.2}, and
* {@link https://www.rfc-editor.org/rfc/rfc9380#section-5 | RFC 9380 section 5}. Unlike RFC 9380
* `hash_to_field`, this helper intentionally maps into the non-zero private-scalar range `1..n-1`.
* @param key - Uniform input bytes.
* @param fieldOrder - Size of subgroup.
* @param isLE - interpret hash bytes as LE num
* @returns valid private scalar
* @throws If the hash length or field order is invalid for scalar reduction. {@link Error}
* @example
* Map hash output into a private scalar range.
*
* ```ts
* mapHashToField(new Uint8Array(48).fill(1), 255n);
* ```
*/
export function mapHashToField(key, fieldOrder, isLE = false) {
abytes(key);
const len = key.length;
const fieldLen = getFieldBytesLength(fieldOrder);
const minLen = Math.max(getMinHashLength(fieldOrder), 16);
// No toy-small inputs: the helper is for real scalar derivation, not tiny test curves. No huge
// inputs: easier to reason about JS timing / allocation behavior.
if (len < minLen || len > 1024)
throw new Error('expected ' + minLen + '-1024 bytes of input, got ' + len);
const num = isLE ? bytesToNumberLE(key) : bytesToNumberBE(key);
// `mod(x, 11)` can sometimes produce 0. `mod(x, 10) + 1` is the same, but no 0
const reduced = mod(num, fieldOrder - _1n) + _1n;
return isLE ? numberToBytesLE(reduced, fieldLen) : numberToBytesBE(reduced, fieldLen);
}
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/**
* Montgomery curve methods. It's not really whole montgomery curve,
* just bunch of very specific methods for X25519 / X448 from
* [RFC 7748](https://www.rfc-editor.org/rfc/rfc7748)
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type TArg, type TRet } from '../utils.ts';
import { type CurveLengths } from './curve.ts';
/** Curve-specific hooks required to build one X25519/X448 helper. */
export type MontgomeryOpts = {
/** Prime field modulus. */
P: bigint;
/** RFC 7748 variant name. */
type: 'x25519' | 'x448';
/**
* Clamp or otherwise normalize one scalar byte string before use.
* @param bytes - Raw secret scalar bytes.
* @returns Adjusted scalar bytes ready for Montgomery multiplication.
*/
adjustScalarBytes: (bytes: TArg<Uint8Array>) => TRet<Uint8Array>;
/**
* Invert one field element with exponentiation by `p - 2`.
* @param x - Field element to invert.
* @returns Multiplicative inverse of `x`.
*/
powPminus2: (x: bigint) => bigint;
/**
* Optional randomness source for `keygen()` and `utils.randomSecretKey()`.
* Receives the requested byte length and returns fresh random bytes.
*/
randomBytes?: (bytesLength?: number) => TRet<Uint8Array>;
};
/** Public X25519/X448 ECDH API built on a Montgomery ladder. */
export type MontgomeryECDH = {
/**
* Multiply one scalar by one Montgomery `u` coordinate.
* @param scalar - Secret scalar bytes.
* @param u - Public Montgomery `u` coordinate.
* @returns Shared point encoded as bytes.
*/
scalarMult: (scalar: TArg<Uint8Array>, u: TArg<Uint8Array>) => TRet<Uint8Array>;
/**
* Multiply one scalar by the curve base point.
* @param scalar - Secret scalar bytes.
* @returns Public key bytes.
*/
scalarMultBase: (scalar: TArg<Uint8Array>) => TRet<Uint8Array>;
/**
* Derive a shared secret from a local secret key and peer public key.
* @param secretKeyA - Local secret key bytes.
* @param publicKeyB - Peer public key bytes.
* Rejects low-order public inputs instead of returning the all-zero shared secret.
* @returns Shared secret bytes.
*/
getSharedSecret: (secretKeyA: TArg<Uint8Array>, publicKeyB: TArg<Uint8Array>) => TRet<Uint8Array>;
/**
* Derive one public key from a secret key.
* @param secretKey - Secret key bytes.
* @returns Public key bytes.
*/
getPublicKey: (secretKey: TArg<Uint8Array>) => TRet<Uint8Array>;
/** Utility helpers for secret-key generation. */
utils: {
/** Generate one random secret key with the curve's expected byte length. */
randomSecretKey: () => TRet<Uint8Array>;
};
/** Encoded Montgomery base point `u`. */
GuBytes: TRet<Uint8Array>;
/** Public lengths for keys and seeds. */
lengths: CurveLengths;
/**
* Generate one random secret/public keypair.
* @param seed - Optional seed bytes to use instead of random generation.
* @returns Fresh secret/public keypair.
*/
keygen: (seed?: TArg<Uint8Array>) => {
secretKey: TRet<Uint8Array>;
publicKey: TRet<Uint8Array>;
};
};
/**
* @param curveDef - Montgomery curve definition.
* @returns ECDH helper namespace.
* @throws If the curve definition or derived shared point is invalid. {@link Error}
* @example
* Perform one X25519 key exchange through the generic Montgomery helper.
*
* ```ts
* import { x25519 } from '@noble/curves/ed25519.js';
* const alice = x25519.keygen();
* const shared = x25519.getSharedSecret(alice.secretKey, alice.publicKey);
* ```
*/
export declare function montgomery(curveDef: TArg<MontgomeryOpts>): TRet<MontgomeryECDH>;
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/**
* Montgomery curve methods. It's not really whole montgomery curve,
* just bunch of very specific methods for X25519 / X448 from
* [RFC 7748](https://www.rfc-editor.org/rfc/rfc7748)
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { abytes, aInRange, bytesToNumberLE, copyBytes, numberToBytesLE, randomBytes, validateObject, } from "../utils.js";
import { createKeygen } from "./curve.js";
import { mod } from "./modular.js";
const _0n = BigInt(0);
const _1n = BigInt(1);
const _2n = BigInt(2);
function validateOpts(curve) {
// Validate constructor config eagerly, but do not call user-provided hooks here:
// `randomBytes` may be transcript-backed or otherwise contextual. Runtime type checks are
// enough to fail fast on malformed configs without consuming user state.
validateObject(curve, {
P: 'bigint',
type: 'string',
adjustScalarBytes: 'function',
powPminus2: 'function',
}, {
randomBytes: 'function',
});
return Object.freeze({ ...curve });
}
/**
* @param curveDef - Montgomery curve definition.
* @returns ECDH helper namespace.
* @throws If the curve definition or derived shared point is invalid. {@link Error}
* @example
* Perform one X25519 key exchange through the generic Montgomery helper.
*
* ```ts
* import { x25519 } from '@noble/curves/ed25519.js';
* const alice = x25519.keygen();
* const shared = x25519.getSharedSecret(alice.secretKey, alice.publicKey);
* ```
*/
export function montgomery(curveDef) {
const CURVE = validateOpts(curveDef);
const { P, type, adjustScalarBytes, powPminus2, randomBytes: rand } = CURVE;
const is25519 = type === 'x25519';
if (!is25519 && type !== 'x448')
throw new Error('invalid type');
const randomBytes_ = rand === undefined ? randomBytes : rand;
const montgomeryBits = is25519 ? 255 : 448;
const fieldLen = is25519 ? 32 : 56;
const Gu = is25519 ? BigInt(9) : BigInt(5);
// RFC 7748 #5:
// The constant a24 is (486662 - 2) / 4 = 121665 for curve25519/X25519 and
// (156326 - 2) / 4 = 39081 for curve448/X448
// const a = is25519 ? 486662n : 156326n;
const a24 = is25519 ? BigInt(121665) : BigInt(39081);
// RFC: x25519 "the resulting integer is of the form 2^254 plus
// eight times a value between 0 and 2^251 - 1 (inclusive)"
// x448: "2^447 plus four times a value between 0 and 2^445 - 1 (inclusive)"
const minScalar = is25519 ? _2n ** BigInt(254) : _2n ** BigInt(447);
const maxAdded = is25519
? BigInt(8) * _2n ** BigInt(251) - _1n
: BigInt(4) * _2n ** BigInt(445) - _1n;
const maxScalar = minScalar + maxAdded + _1n; // (inclusive)
const modP = (n) => mod(n, P);
const GuBytes = encodeU(Gu);
function encodeU(u) {
return numberToBytesLE(modP(u), fieldLen);
}
function decodeU(u) {
const _u = copyBytes(abytes(u, fieldLen, 'uCoordinate'));
// RFC: When receiving such an array, implementations of X25519
// (but not X448) MUST mask the most significant bit in the final byte.
if (is25519)
_u[31] &= 127; // 0b0111_1111
// RFC: Implementations MUST accept non-canonical values and process them as
// if they had been reduced modulo the field prime. The non-canonical
// values are 2^255 - 19 through 2^255 - 1 for X25519 and 2^448 - 2^224
// - 1 through 2^448 - 1 for X448.
return modP(bytesToNumberLE(_u));
}
function decodeScalar(scalar) {
return bytesToNumberLE(adjustScalarBytes(copyBytes(abytes(scalar, fieldLen, 'scalar'))));
}
function scalarMult(scalar, u) {
const pu = montgomeryLadder(decodeU(u), decodeScalar(scalar));
// Some public keys are useless, of low-order. Curve author doesn't think
// it needs to be validated, but we do it nonetheless.
// https://cr.yp.to/ecdh.html#validate
if (pu === _0n)
throw new Error('invalid private or public key received');
return encodeU(pu);
}
// Computes public key from private. By doing scalar multiplication of base point.
function scalarMultBase(scalar) {
return scalarMult(scalar, GuBytes);
}
const getPublicKey = scalarMultBase;
const getSharedSecret = scalarMult;
// cswap from RFC7748 "example code"
function cswap(swap, x_2, x_3) {
// dummy = mask(swap) AND (x_2 XOR x_3)
// Where mask(swap) is the all-1 or all-0 word of the same length as x_2
// and x_3, computed, e.g., as mask(swap) = 0 - swap.
const dummy = modP(swap * (x_2 - x_3));
x_2 = modP(x_2 - dummy); // x_2 = x_2 XOR dummy
x_3 = modP(x_3 + dummy); // x_3 = x_3 XOR dummy
return { x_2, x_3 };
}
/**
* Montgomery x-only multiplication ladder for the selected X25519/X448 curve.
* @param pointU - decoded Montgomery u coordinate for the selected curve
* @param scalar - decoded clamped scalar by which the point is multiplied
* @returns resulting Montgomery u coordinate for the selected curve
*/
function montgomeryLadder(u, scalar) {
aInRange('u', u, _0n, P);
aInRange('scalar', scalar, minScalar, maxScalar);
const k = scalar;
const x_1 = u;
let x_2 = _1n;
let z_2 = _0n;
let x_3 = u;
let z_3 = _1n;
let swap = _0n;
for (let t = BigInt(montgomeryBits - 1); t >= _0n; t--) {
const k_t = (k >> t) & _1n;
swap ^= k_t;
({ x_2, x_3 } = cswap(swap, x_2, x_3));
({ x_2: z_2, x_3: z_3 } = cswap(swap, z_2, z_3));
swap = k_t;
const A = x_2 + z_2;
const AA = modP(A * A);
const B = x_2 - z_2;
const BB = modP(B * B);
const E = AA - BB;
const C = x_3 + z_3;
const D = x_3 - z_3;
const DA = modP(D * A);
const CB = modP(C * B);
const dacb = DA + CB;
const da_cb = DA - CB;
x_3 = modP(dacb * dacb);
z_3 = modP(x_1 * modP(da_cb * da_cb));
x_2 = modP(AA * BB);
z_2 = modP(E * (AA + modP(a24 * E)));
}
({ x_2, x_3 } = cswap(swap, x_2, x_3));
({ x_2: z_2, x_3: z_3 } = cswap(swap, z_2, z_3));
const z2 = powPminus2(z_2); // `Fp.pow(x, P - _2n)` is much slower equivalent
return modP(x_2 * z2); // Return x_2 * (z_2^(p - 2))
}
const lengths = {
secretKey: fieldLen,
publicKey: fieldLen,
seed: fieldLen,
};
const randomSecretKey = (seed) => {
seed = seed === undefined ? randomBytes_(fieldLen) : seed;
abytes(seed, lengths.seed, 'seed');
// Reuse caller-supplied seed bytes verbatim; clamping is deferred until
// decodeScalar(...) when the secret key is actually used.
return seed;
};
const utils = { randomSecretKey };
Object.freeze(lengths);
Object.freeze(utils);
return Object.freeze({
keygen: createKeygen(randomSecretKey, getPublicKey),
getSharedSecret,
getPublicKey,
scalarMult,
scalarMultBase,
utils,
GuBytes: GuBytes.slice(),
lengths,
});
}
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/**
* RFC 9497: Oblivious Pseudorandom Functions (OPRFs) Using Prime-Order Groups.
* https://www.rfc-editor.org/rfc/rfc9497
*
OPRF allows to interactively create an `Output = PRF(Input, serverSecretKey)`:
- Server cannot calculate Output by itself: it doesn't know Input
- Client cannot calculate Output by itself: it doesn't know server secretKey
- An attacker interception the communication can't restore Input/Output/serverSecretKey and can't
link Input to some value.
## Issues
- Low-entropy inputs (e.g. password '123') enable brute-forced dictionary attacks by the server
(solveable by domain separation in POPRF)
- High-level protocol needs to be constructed on top, because OPRF is low-level
## Use cases
1. **Password-Authenticated Key Exchange (PAKE):** Enables secure password login (e.g., OPAQUE)
without revealing the password to the server.
2. **Private Set Intersection (PSI):** Allows two parties to compute the intersection of their
private sets without revealing non-intersecting elements.
3. **Anonymous Credential Systems:** Supports issuance of anonymous, unlinkable credentials
(e.g., Privacy Pass) using blind OPRF evaluation.
4. **Private Information Retrieval (PIR):** Helps users query databases without revealing which
item they accessed.
5. **Encrypted Search / Secure Indexing:** Enables keyword search over encrypted data while keeping
queries private.
6. **Spam Prevention and Rate-Limiting:** Issues anonymous tokens to prevent abuse
(e.g., CAPTCHA bypass) without compromising user privacy.
## Modes
- OPRF: simple mode, client doesn't need to know server public key
- VOPRF: verifiable mode. It lets the client verify that the server used the
secret key corresponding to a known public key
- POPRF: partially oblivious mode, VOPRF + domain separation
There is also non-interactive mode (Evaluate), which creates Output
non-interactively with knowledge of the secret key.
Flow:
- (once) Server generates secret and public keys, distributes public keys to clients
- deterministically: `deriveKeyPair` or just random: `generateKeyPair`
- Client blinds input: `blind(secretInput)`
- Server evaluates blinded input: `blindEvaluate` generated by client, sends result to client
- Client creates output using result of evaluation via 'finalize'
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { randomBytes, type TArg, type TRet } from '../utils.ts';
import { type CurvePoint, type CurvePointCons } from './curve.ts';
import { type H2CDSTOpts } from './hash-to-curve.ts';
/** Serialized group element passed between OPRF participants. */
export type PointBytes = Uint8Array;
/** Serialized scalar used for blinds and server secret keys. */
export type ScalarBytes = Uint8Array;
/** Arbitrary byte input or output used by the OPRF protocol. */
export type Bytes = Uint8Array;
/** Cryptographically secure byte generator used for blinds and proofs. */
export type RNG = typeof randomBytes;
/** Curve and hash hooks required to instantiate one OPRF ciphersuite. */
export type OPRFOpts<P extends CurvePoint<any, P>> = {
/** Human-readable suite identifier used for domain separation. */
name: string;
/**
* Prime-order group used by the OPRF construction.
* Kept generic because the suite returns serialized points.
*/
Point: CurvePointCons<P>;
/**
* Hash function used for transcripts, proofs, and outputs.
* @param msg - Message bytes to hash.
* @returns Digest bytes.
*/
hash(msg: TArg<Bytes>): TRet<Bytes>;
/**
* Hash arbitrary bytes into one scalar in the suite order.
* @param msg - Message bytes to map.
* @param options - Hash-to-field domain-separation options. See {@link H2CDSTOpts}.
* Implementations MUST treat `msg` and `options` as read-only.
* @returns Scalar in the suite order.
*/
hashToScalar(msg: TArg<Uint8Array>, options: TArg<H2CDSTOpts>): bigint;
/**
* Hash arbitrary bytes directly onto one curve point.
* @param msg - Message bytes to map.
* @param options - Hash-to-curve domain-separation options. See {@link H2CDSTOpts}.
* Implementations MUST treat `msg` and `options` as read-only.
* @returns Point on the suite curve.
*/
hashToGroup(msg: TArg<Uint8Array>, options: TArg<H2CDSTOpts>): P;
};
/** Server keypair for one OPRF suite. */
export type OPRFKeys = {
/** Secret scalar kept by the server. */
secretKey: TRet<ScalarBytes>;
/** Public point distributed to clients in verifiable modes. */
publicKey: TRet<PointBytes>;
};
/** Result of the client-side blind step. */
export type OPRFBlind = {
/** Secret blind scalar that the client keeps locally. */
blind: TRet<ScalarBytes>;
/** Blinded group element sent to the server. */
blinded: TRet<PointBytes>;
};
/** Server response for one verifiable OPRF evaluation. */
export type OPRFBlindEval = {
/** Evaluated group element returned by the server. */
evaluated: TRet<PointBytes>;
/** DLEQ proof binding the evaluation to the server public key. */
proof: TRet<Bytes>;
};
/** Server response for a batch of verifiable OPRF evaluations. */
export type OPRFBlindEvalBatch = {
/** Evaluated group elements returned for each blinded input. */
evaluated: TRet<PointBytes[]>;
/** Batch proof covering all evaluated elements. */
proof: TRet<Bytes>;
};
/** One finalized transcript item used by batch verification helpers. */
export type OPRFFinalizeItem = {
/** Original client input. */
input: Bytes;
/** Secret blind scalar used for the input. */
blind: ScalarBytes;
/** Evaluated point returned by the server. */
evaluated: PointBytes;
/** Blinded point originally sent to the server. */
blinded: PointBytes;
};
/** Result of the POPRF client-side blind step with the tweaked server public key. */
export type OPRFBlindTweaked = OPRFBlind & {
tweakedKey: TRet<PointBytes>;
};
/**
* Represents a full OPRF ciphersuite implementation according to RFC 9497.
* This object bundles the three protocol variants (OPRF, VOPRF, POPRF) for a specific
* prime-order group and hash function combination.
*
* @see https://www.rfc-editor.org/rfc/rfc9497.html
*/
export type OPRF = {
/**
* The unique identifier for the ciphersuite, e.g., "ristretto255-SHA512".
* This name is used for domain separation to prevent cross-protocol attacks.
*/
readonly name: string;
/**
* The base Oblivious Pseudorandom Function (OPRF) mode (mode 0x00).
* This is a two-party protocol between a client and a server to compute F(k, x)
* where 'k' is the server's key and 'x' is the client's input.
*
* The client learns the output F(k, x) but nothing about 'k'.
* The server learns nothing about 'x' or F(k, x).
* This mode is NOT verifiable; the client cannot prove the server used a specific key.
*/
readonly oprf: {
/**
* (Server-side) Generates a new random private/public key pair for the server.
* @returns A new key pair.
*/
generateKeyPair(): TRet<OPRFKeys>;
/**
* (Server-side) Deterministically derives a private/public key pair from a seed.
* @param seed - A 32-byte cryptographically secure random seed.
* @param keyInfo - An optional byte string for domain separation.
* @returns The derived key pair.
*/
deriveKeyPair(seed: TArg<Bytes>, keyInfo: TArg<Bytes>): TRet<OPRFKeys>;
/**
* (Client-side) The first step of the protocol. The client blinds its private input.
* @param input - The client's private input bytes.
* @param rng - An optional cryptographically secure random number generator.
* @returns An object containing the `blind` scalar (which the client MUST keep secret)
* and the `blinded` element (which the client sends to the server).
*/
blind(input: TArg<Bytes>, rng?: RNG): TRet<OPRFBlind>;
/**
* (Server-side) The second step. The server evaluates the client's blinded element
* using its secret key.
* @param secretKey - The server's private key.
* @param blinded - The blinded group element received from the client.
* @returns The evaluated group element, to be sent back to the client.
*/
blindEvaluate(secretKey: TArg<ScalarBytes>, blinded: TArg<PointBytes>): TRet<PointBytes>;
/**
* (Client-side) The final step. The client unblinds the server's response to
* compute the final OPRF output.
* @param input - The original private input from the `blind` step.
* @param blind - The secret scalar from the `blind` step.
* @param evaluated - The evaluated group element received from the server.
* @returns The final OPRF output, `Hash(len(input)||input||len(unblinded)||unblinded||"Finalize")`.
*/
finalize(input: TArg<Bytes>, blind: TArg<ScalarBytes>, evaluated: TArg<PointBytes>): TRet<Bytes>;
};
/**
* The Verifiable Oblivious Pseudorandom Function (VOPRF) mode (mode 0x01).
* This mode extends the base OPRF by providing a proof that the server used the
* secret key corresponding to its known public key.
*/
readonly voprf: {
/** (Server-side) Generates a key pair for the VOPRF mode. */
generateKeyPair(): TRet<OPRFKeys>;
/** (Server-side) Deterministically derives a key pair for the VOPRF mode. */
deriveKeyPair(seed: TArg<Bytes>, keyInfo: TArg<Bytes>): TRet<OPRFKeys>;
/** (Client-side) Blinds the client's private input for the VOPRF protocol. */
blind(input: TArg<Bytes>, rng?: RNG): TRet<OPRFBlind>;
/**
* (Server-side) Evaluates the client's blinded element and generates a DLEQ proof
* of correctness.
* @param secretKey - The server's private key.
* @param publicKey - The server's public key, used in proof generation.
* @param blinded - The blinded group element received from the client.
* @param rng - An optional cryptographically secure random number generator for the proof.
* @returns The evaluated element and a proof of correct computation.
*/
blindEvaluate(secretKey: TArg<ScalarBytes>, publicKey: TArg<PointBytes>, blinded: TArg<PointBytes>, rng?: RNG): TRet<OPRFBlindEval>;
/**
* (Server-side) An optimized batch version of `blindEvaluate`. It evaluates multiple
* blinded elements and produces a single, constant-size proof for the entire batch,
* amortizing the cost of proof generation.
* @param secretKey - The server's private key.
* @param publicKey - The server's public key.
* @param blinded - An array of blinded group elements from one or more clients.
* @param rng - An optional cryptographically secure random number generator for the proof.
* @returns An array of evaluated elements and a single proof for the batch.
*/
blindEvaluateBatch(secretKey: TArg<ScalarBytes>, publicKey: TArg<PointBytes>, blinded: TArg<PointBytes[]>, rng?: RNG): TRet<OPRFBlindEvalBatch>;
/**
* (Client-side) The final step. The client verifies the server's proof, and if valid,
* unblinds the result to compute the final VOPRF output.
* @param input - The original private input.
* @param blind - The secret scalar from the `blind` step.
* @param evaluated - The evaluated element from the server.
* @param blinded - The blinded element sent to the server (needed for proof verification).
* @param publicKey - The server's public key against which the proof is verified.
* @param proof - The DLEQ proof from the server.
* @returns The final VOPRF output.
* @throws If the proof verification fails. {@link Error}
*/
finalize(input: TArg<Bytes>, blind: TArg<ScalarBytes>, evaluated: TArg<PointBytes>, blinded: TArg<PointBytes>, publicKey: TArg<PointBytes>, proof: TArg<Bytes>): TRet<Bytes>;
/**
* (Client-side) The batch-aware version of `finalize`. It verifies a single batch proof
* against a list of corresponding inputs and outputs.
* @param items - An array of objects, each containing the parameters for a single finalization.
* @param publicKey - The server's public key.
* @param proof - The single DLEQ proof for the entire batch.
* @returns An array of final VOPRF outputs, one for each item in the input.
* @throws If the proof verification fails. {@link Error}
*/
finalizeBatch(items: TArg<OPRFFinalizeItem[]>, publicKey: TArg<PointBytes>, proof: TArg<Bytes>): TRet<Bytes[]>;
};
/**
* A factory for the Partially Oblivious Pseudorandom Function (POPRF) mode (mode 0x02).
* This mode extends VOPRF to include a public `info` parameter, known to both client and
* server, which is cryptographically bound to the final output.
* This is useful for domain separation at the application level.
* @param info - A public byte string to be mixed into the computation.
* @returns An object with the POPRF protocol functions.
*/
readonly poprf: (info: TArg<Bytes>) => {
/** (Server-side) Generates a key pair for the POPRF mode. */
generateKeyPair(): TRet<OPRFKeys>;
/** (Server-side) Deterministically derives a key pair for the POPRF mode. */
deriveKeyPair(seed: TArg<Bytes>, keyInfo: TArg<Bytes>): TRet<OPRFKeys>;
/**
* (Client-side) Blinds the client's private input and computes the "tweaked key".
* The tweaked key is a public value derived from the server's public key and the public `info`.
* @param input - The client's private input.
* @param publicKey - The server's public key.
* @param rng - An optional cryptographically secure random number generator.
* @returns The `blind`, `blinded` element, and the `tweakedKey`
* the client uses for verification.
*/
blind(input: TArg<Bytes>, publicKey: TArg<PointBytes>, rng?: RNG): TRet<OPRFBlindTweaked>;
/**
* (Server-side) Evaluates the blinded element using a key derived from
* its secret key and the public `info`.
* It generates a DLEQ proof against the tweaked key.
* @param secretKey - The server's private key.
* @param blinded - The blinded element from the client.
* @param rng - An optional RNG for the proof.
* @returns The evaluated element and a proof of correct computation.
*/
blindEvaluate(secretKey: TArg<ScalarBytes>, blinded: TArg<PointBytes>, rng?: RNG): TRet<OPRFBlindEval>;
/**
* (Server-side) A batch-aware version of `blindEvaluate` for the POPRF mode.
* @param secretKey - The server's private key.
* @param blinded - An array of blinded elements.
* @param rng - An optional RNG for the proof.
* @returns An array of evaluated elements and a single proof for the batch.
*/
blindEvaluateBatch(secretKey: TArg<ScalarBytes>, blinded: TArg<PointBytes[]>, rng: RNG): TRet<OPRFBlindEvalBatch>;
/**
* (Client-side) A batch-aware version of `finalize` for the POPRF mode.
* It verifies the proof against the tweaked key.
* @param items - An array containing the parameters for each finalization.
* @param proof - The single DLEQ proof for the batch.
* @param tweakedKey - The tweaked key corresponding to the proof.
* All items must share the same `info` and `publicKey`.
* @returns An array of final POPRF outputs.
* @throws If proof verification fails. {@link Error}
*/
finalizeBatch(items: TArg<OPRFFinalizeItem[]>, proof: TArg<Bytes>, tweakedKey: TArg<PointBytes>): TRet<Bytes[]>;
/**
* (Client-side) Finalizes the POPRF protocol. It verifies the server's proof against the
* `tweakedKey` computed in the `blind` step. The final output is bound to the public `info`.
* @param input - The original private input.
* @param blind - The secret scalar.
* @param evaluated - The evaluated element from the server.
* @param blinded - The blinded element sent to the server.
* @param proof - The DLEQ proof from the server.
* @param tweakedKey - The public tweaked key computed by the client during the `blind` step.
* @returns The final POPRF output.
* @throws If proof verification fails. {@link Error}
*/
finalize(input: TArg<Bytes>, blind: TArg<ScalarBytes>, evaluated: TArg<PointBytes>, blinded: TArg<PointBytes>, proof: TArg<Bytes>, tweakedKey: TArg<PointBytes>): TRet<Bytes>;
/**
* A non-interactive evaluation function for an entity that knows all inputs.
* Computes the final POPRF output directly. Useful for testing or specific applications
* where the server needs to compute the output for a known input.
* @param secretKey - The server's private key.
* @param input - The client's private input.
* @returns The final POPRF output.
*/
evaluate(secretKey: TArg<ScalarBytes>, input: TArg<Bytes>): TRet<Bytes>;
};
};
/**
* @param opts - OPRF ciphersuite options. See {@link OPRFOpts}.
* @returns OPRF helper namespace.
* @example
* Instantiate an OPRF suite from curve-specific hashing hooks.
*
* ```ts
* import { createOPRF } from '@noble/curves/abstract/oprf.js';
* import { p256, p256_hasher } from '@noble/curves/nist.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const oprf = createOPRF({
* name: 'P256-SHA256',
* Point: p256.Point,
* hash: sha256,
* hashToGroup: p256_hasher.hashToCurve,
* hashToScalar: p256_hasher.hashToScalar,
* });
* const keys = oprf.oprf.generateKeyPair();
* ```
*/
export declare function createOPRF<P extends CurvePoint<any, P>>(opts: OPRFOpts<P>): TRet<OPRF>;
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/**
* RFC 9497: Oblivious Pseudorandom Functions (OPRFs) Using Prime-Order Groups.
* https://www.rfc-editor.org/rfc/rfc9497
*
OPRF allows to interactively create an `Output = PRF(Input, serverSecretKey)`:
- Server cannot calculate Output by itself: it doesn't know Input
- Client cannot calculate Output by itself: it doesn't know server secretKey
- An attacker interception the communication can't restore Input/Output/serverSecretKey and can't
link Input to some value.
## Issues
- Low-entropy inputs (e.g. password '123') enable brute-forced dictionary attacks by the server
(solveable by domain separation in POPRF)
- High-level protocol needs to be constructed on top, because OPRF is low-level
## Use cases
1. **Password-Authenticated Key Exchange (PAKE):** Enables secure password login (e.g., OPAQUE)
without revealing the password to the server.
2. **Private Set Intersection (PSI):** Allows two parties to compute the intersection of their
private sets without revealing non-intersecting elements.
3. **Anonymous Credential Systems:** Supports issuance of anonymous, unlinkable credentials
(e.g., Privacy Pass) using blind OPRF evaluation.
4. **Private Information Retrieval (PIR):** Helps users query databases without revealing which
item they accessed.
5. **Encrypted Search / Secure Indexing:** Enables keyword search over encrypted data while keeping
queries private.
6. **Spam Prevention and Rate-Limiting:** Issues anonymous tokens to prevent abuse
(e.g., CAPTCHA bypass) without compromising user privacy.
## Modes
- OPRF: simple mode, client doesn't need to know server public key
- VOPRF: verifiable mode. It lets the client verify that the server used the
secret key corresponding to a known public key
- POPRF: partially oblivious mode, VOPRF + domain separation
There is also non-interactive mode (Evaluate), which creates Output
non-interactively with knowledge of the secret key.
Flow:
- (once) Server generates secret and public keys, distributes public keys to clients
- deterministically: `deriveKeyPair` or just random: `generateKeyPair`
- Client blinds input: `blind(secretInput)`
- Server evaluates blinded input: `blindEvaluate` generated by client, sends result to client
- Client creates output using result of evaluation via 'finalize'
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { abytes, asciiToBytes, bytesToNumberBE, bytesToNumberLE, concatBytes, numberToBytesBE, randomBytes, validateObject, } from "../utils.js";
import { pippenger, validatePointCons } from "./curve.js";
import { _DST_scalar } from "./hash-to-curve.js";
import { getMinHashLength, mapHashToField } from "./modular.js";
const _DST_scalarBytes = /* @__PURE__ */ asciiToBytes(_DST_scalar);
// welcome to generic hell
/**
* @param opts - OPRF ciphersuite options. See {@link OPRFOpts}.
* @returns OPRF helper namespace.
* @example
* Instantiate an OPRF suite from curve-specific hashing hooks.
*
* ```ts
* import { createOPRF } from '@noble/curves/abstract/oprf.js';
* import { p256, p256_hasher } from '@noble/curves/nist.js';
* import { sha256 } from '@noble/hashes/sha2.js';
* const oprf = createOPRF({
* name: 'P256-SHA256',
* Point: p256.Point,
* hash: sha256,
* hashToGroup: p256_hasher.hashToCurve,
* hashToScalar: p256_hasher.hashToScalar,
* });
* const keys = oprf.oprf.generateKeyPair();
* ```
*/
export function createOPRF(opts) {
validateObject(opts, {
name: 'string',
hash: 'function',
hashToScalar: 'function',
hashToGroup: 'function',
});
// Cheap constructor-surface sanity check only: this verifies the generic static hooks/fields that
// OPRF consumes, but it does not certify point semantics like BASE/ZERO correctness.
validatePointCons(opts.Point);
const { name, Point, hash } = opts;
const { Fn } = Point;
const hashToGroup = (msg, ctx) => opts.hashToGroup(msg, {
DST: concatBytes(asciiToBytes('HashToGroup-'), ctx),
});
const hashToScalarPrefixed = (msg, ctx) => opts.hashToScalar(msg, { DST: concatBytes(_DST_scalarBytes, ctx) });
const randomScalar = (rng = randomBytes) => {
// RFC 9497 §2.1 defines RandomScalar as nonzero; blind inversion and generated public keys
// both rely on keeping this helper in the `1..n-1` range.
const t = mapHashToField(rng(getMinHashLength(Fn.ORDER)), Fn.ORDER, Fn.isLE);
// We cannot use Fn.fromBytes here, because field
// can have different number of bytes (like ed448)
return Fn.isLE ? bytesToNumberLE(t) : bytesToNumberBE(t);
};
const msm = (points, scalars) => pippenger(Point, points, scalars);
const getCtx = (mode) => concatBytes(asciiToBytes('OPRFV1-'), new Uint8Array([mode]), asciiToBytes('-' + name));
const ctxOPRF = getCtx(0x00);
const ctxVOPRF = getCtx(0x01);
const ctxPOPRF = getCtx(0x02);
function encode(...args) {
const res = [];
for (const a of args) {
if (typeof a === 'number')
res.push(numberToBytesBE(a, 2));
else if (typeof a === 'string')
res.push(asciiToBytes(a));
else {
abytes(a);
res.push(numberToBytesBE(a.length, 2), a);
}
}
// No wipe here, since will modify actual bytes
return concatBytes(...res);
}
const inputBytes = (title, bytes) => {
abytes(bytes, undefined, title);
// RFC 9497 §1.2 limits PrivateInput/PublicInput to 2^16 - 1 bytes because these values are
// length-prefixed with two bytes before use throughout the protocol.
if (bytes.length > 0xffff)
throw new Error(`"${title}" expected Uint8Array of length <= 65535, got length=${bytes.length}`);
return bytes;
};
const hashInput = (...bytes) => hash(encode(...bytes, 'Finalize'));
function getTranscripts(B, C, D, ctx) {
const Bm = B.toBytes();
const seed = hash(encode(Bm, concatBytes(asciiToBytes('Seed-'), ctx)));
const res = [];
for (let i = 0; i < C.length; i++) {
const Ci = C[i].toBytes();
const Di = D[i].toBytes();
const di = hashToScalarPrefixed(encode(seed, i, Ci, Di, 'Composite'), ctx);
res.push(di);
}
return res;
}
function computeComposites(B, C, D, ctx) {
const T = getTranscripts(B, C, D, ctx);
const M = msm(C, T);
const Z = msm(D, T);
return { M, Z };
}
function computeCompositesFast(k, B, C, D, ctx) {
const T = getTranscripts(B, C, D, ctx);
const M = msm(C, T);
// RFC 9497 §2.2.1 ComputeCompositesFast derives weights from both C and D in getTranscripts(),
// then uses the server shortcut Z = k * M instead of a second MSM over D.
const Z = M.multiply(k);
return { M, Z };
}
function challengeTranscript(B, M, Z, t2, t3, ctx) {
const [Bm, a0, a1, a2, a3] = [B, M, Z, t2, t3].map((i) => i.toBytes());
return hashToScalarPrefixed(encode(Bm, a0, a1, a2, a3, 'Challenge'), ctx);
}
function generateProof(ctx, k, B, C, D, rng) {
const { M, Z } = computeCompositesFast(k, B, C, D, ctx);
const r = randomScalar(rng);
const t2 = Point.BASE.multiply(r);
const t3 = M.multiply(r);
const c = challengeTranscript(B, M, Z, t2, t3, ctx);
const s = Fn.sub(r, Fn.mul(c, k)); // r - c*k
return concatBytes(...[c, s].map((i) => Fn.toBytes(i)));
}
function verifyProof(ctx, B, C, D, proof) {
abytes(proof, 2 * Fn.BYTES);
const { M, Z } = computeComposites(B, C, D, ctx);
const [c, s] = [proof.subarray(0, Fn.BYTES), proof.subarray(Fn.BYTES)].map((f) => Fn.fromBytes(f));
const t2 = Point.BASE.multiply(s).add(B.multiply(c)); // s*G + c*B
const t3 = M.multiply(s).add(Z.multiply(c)); // s*M + c*Z
const expectedC = challengeTranscript(B, M, Z, t2, t3, ctx);
if (!Fn.eql(c, expectedC))
throw new Error('proof verification failed');
}
function generateKeyPair() {
const skS = randomScalar();
const pkS = Point.BASE.multiply(skS);
return { secretKey: Fn.toBytes(skS), publicKey: pkS.toBytes() };
}
function deriveKeyPair(ctx, seed, info) {
// RFC 9497 §3.2.1 defines `seed[32]`; reject other sizes here because this public API already
// documents a 32-byte seed instead of generic input keying material.
abytes(seed, 32, 'seed');
info = inputBytes('keyInfo', info);
const dst = concatBytes(asciiToBytes('DeriveKeyPair'), ctx);
const msg = concatBytes(seed, encode(info), Uint8Array.of(0));
for (let counter = 0; counter <= 255; counter++) {
msg[msg.length - 1] = counter;
const skS = opts.hashToScalar(msg, { DST: dst });
if (Fn.is0(skS))
continue; // should not happen
return {
secretKey: Fn.toBytes(skS),
publicKey: Point.BASE.multiply(skS).toBytes(),
};
}
throw new Error('Cannot derive key');
}
const wirePoint = (label, bytes) => {
const point = Point.fromBytes(bytes);
// RFC 9497 §3.3 says applications MUST reject group-identity Elements received over the wire
// after deserialization, even if the suite decoder itself accepts the identity encoding.
if (point.equals(Point.ZERO))
throw new Error(label + ' point at infinity');
return point;
};
function blind(ctx, input, rng = randomBytes) {
input = inputBytes('input', input);
const blind = randomScalar(rng);
const inputPoint = hashToGroup(input, ctx);
if (inputPoint.equals(Point.ZERO))
throw new Error('Input point at infinity');
const blinded = inputPoint.multiply(blind);
return { blind: Fn.toBytes(blind), blinded: blinded.toBytes() };
}
function evaluate(ctx, secretKey, input) {
input = inputBytes('input', input);
const skS = Fn.fromBytes(secretKey);
const inputPoint = hashToGroup(input, ctx);
if (inputPoint.equals(Point.ZERO))
throw new Error('Input point at infinity');
const unblinded = inputPoint.multiply(skS).toBytes();
return hashInput(input, unblinded);
}
const oprf = Object.freeze({
generateKeyPair,
deriveKeyPair: (seed, keyInfo) => deriveKeyPair(ctxOPRF, seed, keyInfo),
blind: (input, rng = randomBytes) => blind(ctxOPRF, input, rng),
blindEvaluate(secretKey, blindedPoint) {
const skS = Fn.fromBytes(secretKey);
const elm = wirePoint('blinded', blindedPoint);
return elm.multiply(skS).toBytes();
},
finalize(input, blindBytes, evaluatedBytes) {
input = inputBytes('input', input);
const blind = Fn.fromBytes(blindBytes);
const evalPoint = wirePoint('evaluated', evaluatedBytes);
const unblinded = evalPoint.multiply(Fn.inv(blind)).toBytes();
return hashInput(input, unblinded);
},
evaluate: (secretKey, input) => evaluate(ctxOPRF, secretKey, input),
});
const voprf = Object.freeze({
generateKeyPair,
deriveKeyPair: (seed, keyInfo) => deriveKeyPair(ctxVOPRF, seed, keyInfo),
blind: (input, rng = randomBytes) => blind(ctxVOPRF, input, rng),
blindEvaluateBatch(secretKey, publicKey, blinded, rng = randomBytes) {
if (!Array.isArray(blinded))
throw new Error('expected array');
const skS = Fn.fromBytes(secretKey);
const pkS = wirePoint('public key', publicKey);
const blindedPoints = blinded.map((i) => wirePoint('blinded', i));
const evaluated = blindedPoints.map((i) => i.multiply(skS));
const proof = generateProof(ctxVOPRF, skS, pkS, blindedPoints, evaluated, rng);
return { evaluated: evaluated.map((i) => i.toBytes()), proof };
},
blindEvaluate(secretKey, publicKey, blinded, rng = randomBytes) {
const res = this.blindEvaluateBatch(secretKey, publicKey, [blinded], rng);
return { evaluated: res.evaluated[0], proof: res.proof };
},
finalizeBatch(items, publicKey, proof) {
if (!Array.isArray(items))
throw new Error('expected array');
const pkS = wirePoint('public key', publicKey);
const blindedPoints = items.map((i) => wirePoint('blinded', i.blinded));
const evalPoints = items.map((i) => wirePoint('evaluated', i.evaluated));
verifyProof(ctxVOPRF, pkS, blindedPoints, evalPoints, proof);
return items.map((i) => oprf.finalize(i.input, i.blind, i.evaluated));
},
finalize(input, blind, evaluated, blinded, publicKey, proof) {
return this.finalizeBatch([{ input, blind, evaluated, blinded }], publicKey, proof)[0];
},
evaluate: (secretKey, input) => evaluate(ctxVOPRF, secretKey, input),
});
// NOTE: info is domain separation
const poprf = (info) => {
info = inputBytes('info', info);
const m = hashToScalarPrefixed(encode('Info', info), ctxPOPRF);
const T = Point.BASE.multiply(m);
return Object.freeze({
generateKeyPair,
deriveKeyPair: (seed, keyInfo) => deriveKeyPair(ctxPOPRF, seed, keyInfo),
blind(input, publicKey, rng = randomBytes) {
input = inputBytes('input', input);
const pkS = wirePoint('public key', publicKey);
const tweakedKey = T.add(pkS);
if (tweakedKey.equals(Point.ZERO))
throw new Error('tweakedKey point at infinity');
const blind = randomScalar(rng);
const inputPoint = hashToGroup(input, ctxPOPRF);
if (inputPoint.equals(Point.ZERO))
throw new Error('Input point at infinity');
const blindedPoint = inputPoint.multiply(blind);
return {
blind: Fn.toBytes(blind),
blinded: blindedPoint.toBytes(),
tweakedKey: tweakedKey.toBytes(),
};
},
blindEvaluateBatch(secretKey, blinded, rng = randomBytes) {
if (!Array.isArray(blinded))
throw new Error('expected array');
const skS = Fn.fromBytes(secretKey);
const t = Fn.add(skS, m);
// "Hence, this error can be a signal for the server to replace its
// private key". We throw inside; this should be impossible.
const invT = Fn.inv(t);
const blindedPoints = blinded.map((i) => wirePoint('blinded', i));
const evalPoints = blindedPoints.map((i) => i.multiply(invT));
const tweakedKey = Point.BASE.multiply(t);
const proof = generateProof(ctxPOPRF, t, tweakedKey, evalPoints, blindedPoints, rng);
return { evaluated: evalPoints.map((i) => i.toBytes()), proof };
},
blindEvaluate(secretKey, blinded, rng = randomBytes) {
const res = this.blindEvaluateBatch(secretKey, [blinded], rng);
return { evaluated: res.evaluated[0], proof: res.proof };
},
finalizeBatch(items, proof, tweakedKey) {
if (!Array.isArray(items))
throw new Error('expected array');
const inputs = items.map((i) => inputBytes('input', i.input));
const evalPoints = items.map((i) => wirePoint('evaluated', i.evaluated));
verifyProof(ctxPOPRF, wirePoint('tweakedKey', tweakedKey), evalPoints, items.map((i) => wirePoint('blinded', i.blinded)), proof);
return items.map((i, j) => {
const blind = Fn.fromBytes(i.blind);
const point = evalPoints[j].multiply(Fn.inv(blind)).toBytes();
return hashInput(inputs[j], info, point);
});
},
finalize(input, blind, evaluated, blinded, proof, tweakedKey) {
return this.finalizeBatch([{ input, blind, evaluated, blinded }], proof, tweakedKey)[0];
},
evaluate(secretKey, input) {
input = inputBytes('input', input);
const skS = Fn.fromBytes(secretKey);
const inputPoint = hashToGroup(input, ctxPOPRF);
if (inputPoint.equals(Point.ZERO))
throw new Error('Input point at infinity');
const t = Fn.add(skS, m);
const invT = Fn.inv(t);
const unblinded = inputPoint.multiply(invT).toBytes();
return hashInput(input, info, unblinded);
},
});
};
const res = { name, oprf, voprf, poprf, __tests: Object.freeze({ Fn }) };
return Object.freeze(res);
}
//# sourceMappingURL=oprf.js.map

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/**
* Implements [Poseidon](https://www.poseidon-hash.info) ZK-friendly hash.
*
* There are many poseidon variants with different constants.
* We don't provide them: you should construct them manually.
* Check out [micro-starknet](https://github.com/paulmillr/micro-starknet) package for a proper example.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type TArg, type TRet } from '../utils.ts';
import { type IField } from './modular.ts';
/** Core Poseidon permutation parameters shared by all variants. */
export type PoseidonBasicOpts = {
/** Prime field used by the permutation. */
Fp: IField<bigint>;
/** Poseidon width `t = rate + capacity`. */
t: number;
/** Number of full S-box rounds. */
roundsFull: number;
/** Number of partial S-box rounds. */
roundsPartial: number;
/** Whether to use the inverse S-box variant. */
isSboxInverse?: boolean;
};
/** Poseidon settings used by the Grain-LFSR constant generator. */
export type PoseidonGrainOpts = PoseidonBasicOpts & {
/** S-box power used while generating constants. */
sboxPower?: number;
};
type PoseidonConstants = {
mds: bigint[][];
roundConstants: bigint[][];
};
/**
* @param opts - Poseidon grain options. See {@link PoseidonGrainOpts}.
* @param skipMDS - Number of MDS samples to skip.
* @returns Generated constants.
* @throws If the generated MDS matrix contains a zero denominator. {@link Error}
* @example
* Generate Poseidon round constants and an MDS matrix from the Grain LFSR.
*
* ```ts
* import { grainGenConstants } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* ```
*/
export declare function grainGenConstants(opts: TArg<PoseidonGrainOpts>, skipMDS?: number): PoseidonConstants;
/** Fully specified Poseidon permutation options with explicit constants. */
export type PoseidonOpts = PoseidonBasicOpts & PoseidonConstants & {
/** S-box power used by the permutation. */
sboxPower?: number;
/** Whether to reverse the partial-round S-box index. */
reversePartialPowIdx?: boolean;
};
/**
* @param opts - Poseidon options. See {@link PoseidonOpts}.
* @returns Normalized poseidon options.
* @throws If the Poseidon options, constants, or MDS matrix are invalid. {@link Error}
* @example
* Validate generated constants before constructing a permutation.
*
* ```ts
* import { grainGenConstants, validateOpts } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const opts = validateOpts({ ...constants, Fp, t: 2, roundsFull: 8, roundsPartial: 8, sboxPower: 3 });
* ```
*/
export declare function validateOpts(opts: TArg<PoseidonOpts>): TRet<Readonly<{
rounds: number;
sboxFn: (n: bigint) => bigint;
roundConstants: bigint[][];
mds: bigint[][];
Fp: IField<bigint>;
t: number;
roundsFull: number;
roundsPartial: number;
sboxPower?: number;
reversePartialPowIdx?: boolean;
}>>;
/**
* @param rc - Flattened round constants.
* @param t - Poseidon width.
* @returns Constants grouped by round.
* @throws If the width or flattened constant array is invalid. {@link Error}
* @example
* Regroup a flat constant list into per-round chunks.
*
* ```ts
* const rounds = splitConstants([1n, 2n, 3n, 4n], 2);
* ```
*/
export declare function splitConstants(rc: bigint[], t: number): bigint[][];
/**
* Poseidon permutation callable.
* @param values - Poseidon state vector. Non-canonical bigints are normalized with `Fp.create(...)`.
* @returns Permuted state vector.
*/
export type PoseidonFn = {
(values: bigint[]): bigint[];
/** Round constants captured by the permutation instance. */
roundConstants: bigint[][];
};
/** Poseidon NTT-friendly hash. */
/**
* @param opts - Poseidon options. See {@link PoseidonOpts}.
* @returns Poseidon permutation.
* @throws If the Poseidon options or state vector are invalid. {@link Error}
* @example
* Build a Poseidon permutation from validated parameters and constants.
*
* ```ts
* import { grainGenConstants, poseidon } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const hash = poseidon({ ...constants, Fp, t: 2, roundsFull: 8, roundsPartial: 8, sboxPower: 3 });
* const state = hash([1n, 2n]);
* ```
*/
export declare function poseidon(opts: TArg<PoseidonOpts>): PoseidonFn;
/**
* @param Fp - Field implementation.
* @param rate - Sponge rate.
* @param capacity - Sponge capacity.
* @param hash - Poseidon permutation.
* @example
* Wrap one Poseidon permutation in a sponge interface.
*
* ```ts
* import { PoseidonSponge, grainGenConstants, poseidon } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const hash = poseidon({ ...constants, Fp, t: 2, roundsFull: 8, roundsPartial: 8, sboxPower: 3 });
* const sponge = new PoseidonSponge(Fp, 1, 1, hash);
* sponge.absorb([1n]);
* const out = sponge.squeeze(1);
* ```
*/
export declare class PoseidonSponge {
private Fp;
readonly rate: number;
readonly capacity: number;
readonly hash: PoseidonFn;
private state;
private pos;
private isAbsorbing;
constructor(Fp: IField<bigint>, rate: number, capacity: number, hash: PoseidonFn);
private process;
absorb(input: bigint[]): void;
squeeze(count: number): bigint[];
clean(): void;
clone(): PoseidonSponge;
}
/** Options for the non-standard but commonly used Poseidon sponge wrapper. */
export type PoseidonSpongeOpts = Omit<PoseidonOpts, 't'> & {
/** Sponge rate. */
rate: number;
/** Sponge capacity. */
capacity: number;
};
/**
* The method is not defined in spec, but nevertheless used often.
* Check carefully for compatibility: there are many edge cases, like absorbing an empty array.
* We cross-test against:
* - {@link https://github.com/ProvableHQ/snarkVM/tree/staging/algorithms | snarkVM algorithms}
* - {@link https://github.com/arkworks-rs/crypto-primitives/tree/main | arkworks crypto-primitives}
* @param opts - Sponge options. See {@link PoseidonSpongeOpts}.
* @returns Factory for sponge instances.
* @throws If the sponge dimensions or backing permutation options are invalid. {@link Error}
* @example
* Use the sponge helper to absorb several field elements and squeeze one digest.
*
* ```ts
* import { grainGenConstants, poseidonSponge } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const makeSponge = poseidonSponge({
* ...constants,
* Fp,
* rate: 1,
* capacity: 1,
* roundsFull: 8,
* roundsPartial: 8,
* sboxPower: 3,
* });
* const sponge = makeSponge();
* sponge.absorb([1n]);
* const out = sponge.squeeze(1);
* ```
*/
export declare function poseidonSponge(opts: TArg<PoseidonSpongeOpts>): TRet<() => PoseidonSponge>;
export {};
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/**
* Implements [Poseidon](https://www.poseidon-hash.info) ZK-friendly hash.
*
* There are many poseidon variants with different constants.
* We don't provide them: you should construct them manually.
* Check out [micro-starknet](https://github.com/paulmillr/micro-starknet) package for a proper example.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { asafenumber, bitGet, validateObject } from "../utils.js";
import { FpInvertBatch, FpPow, validateField } from "./modular.js";
// Grain LFSR (Linear-Feedback Shift Register): https://eprint.iacr.org/2009/109.pdf
function grainLFSR(state) {
// Advances the caller-provided 80-entry state array in place; only the length
// is checked here, so entries are assumed to already be bits.
let pos = 0;
if (state.length !== 80)
throw new Error('grainLFRS: wrong state length, should be 80 bits');
const getBit = () => {
const r = (offset) => state[(pos + offset) % 80];
const bit = r(62) ^ r(51) ^ r(38) ^ r(23) ^ r(13) ^ r(0);
state[pos] = bit;
pos = ++pos % 80;
return !!bit;
};
for (let i = 0; i < 160; i++)
getBit();
return () => {
// https://en.wikipedia.org/wiki/Shrinking_generator
while (true) {
const b1 = getBit();
const b2 = getBit();
if (!b1)
continue;
return b2;
}
};
}
function assertValidPosOpts(opts) {
const { Fp, roundsFull } = opts;
validateField(Fp);
validateObject(opts, {
t: 'number',
roundsFull: 'number',
roundsPartial: 'number',
}, {
isSboxInverse: 'boolean',
});
for (const k of ['t', 'roundsFull', 'roundsPartial']) {
asafenumber(opts[k], k);
if (opts[k] < 1)
throw new Error('invalid number ' + k);
}
// Poseidon splits full rounds as `R_F / 2`, then partial rounds, then `R_F / 2` again.
if (roundsFull & 1)
throw new Error('roundsFull is not even' + roundsFull);
}
function poseidonGrain(opts) {
assertValidPosOpts(opts);
const { Fp } = opts;
const state = Array(80).fill(1);
let pos = 0;
const writeBits = (value, bitCount) => {
for (let i = bitCount - 1; i >= 0; i--)
state[pos++] = Number(bitGet(value, i));
};
const _0n = BigInt(0);
const _1n = BigInt(1);
// The Grain seed layout is fixed-width: `Fp.BITS` and `t` use 12 bits,
// `roundsFull` and `roundsPartial` use 10, so larger values are truncated here.
// This is intentional for compatibility with snarkVM / arkworks PoseidonGrainLFSR:
// they write the same fixed-width seed fields without range checks, then still consume
// the LFSR using the caller-provided round count for ARK/MDS generation.
// Normalizing or rejecting here would diverge from those implementations.
writeBits(_1n, 2); // prime field
writeBits(opts.isSboxInverse ? _1n : _0n, 4); // b2..b5
writeBits(BigInt(Fp.BITS), 12); // b6..b17
writeBits(BigInt(opts.t), 12); // b18..b29
writeBits(BigInt(opts.roundsFull), 10); // b30..b39
writeBits(BigInt(opts.roundsPartial), 10); // b40..b49
const getBit = grainLFSR(state);
return (count, reject) => {
const res = [];
for (let i = 0; i < count; i++) {
while (true) {
let num = _0n;
for (let i = 0; i < Fp.BITS; i++) {
num <<= _1n;
if (getBit())
num |= _1n;
}
if (reject && num >= Fp.ORDER)
continue; // rejection sampling
res.push(Fp.create(num));
break;
}
}
return res;
};
}
// NOTE: this is not standard but used often for constant generation for poseidon
// (grain LFRS-like structure)
/**
* @param opts - Poseidon grain options. See {@link PoseidonGrainOpts}.
* @param skipMDS - Number of MDS samples to skip.
* @returns Generated constants.
* @throws If the generated MDS matrix contains a zero denominator. {@link Error}
* @example
* Generate Poseidon round constants and an MDS matrix from the Grain LFSR.
*
* ```ts
* import { grainGenConstants } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* ```
*/
export function grainGenConstants(opts, skipMDS = 0) {
const { Fp, t, roundsFull, roundsPartial } = opts;
// `skipMDS` counts how many candidate matrices to discard before taking one.
asafenumber(skipMDS, 'skipMDS');
if (skipMDS < 0)
throw new Error('invalid number skipMDS');
const rounds = roundsFull + roundsPartial;
// `sboxPower` is carried in the opts shape for Poseidon compatibility, but
// Grain constant generation here only depends on field/size/round counts/inverse flag.
const sample = poseidonGrain(opts);
const roundConstants = [];
for (let r = 0; r < rounds; r++)
roundConstants.push(sample(t, true));
if (skipMDS > 0)
for (let i = 0; i < skipMDS; i++)
sample(2 * t, false);
const xs = sample(t, false);
const ys = sample(t, false);
// Construct MDS Matrix M[i][j] = 1 / (xs[i] + ys[j])
const mds = [];
for (let i = 0; i < t; i++) {
const row = [];
for (let j = 0; j < t; j++) {
const xy = Fp.add(xs[i], ys[j]);
if (Fp.is0(xy))
throw new Error(`Error generating MDS matrix: xs[${i}] + ys[${j}] resulted in zero.`);
row.push(xy);
}
mds.push(FpInvertBatch(Fp, row));
}
return { roundConstants, mds };
}
/**
* @param opts - Poseidon options. See {@link PoseidonOpts}.
* @returns Normalized poseidon options.
* @throws If the Poseidon options, constants, or MDS matrix are invalid. {@link Error}
* @example
* Validate generated constants before constructing a permutation.
*
* ```ts
* import { grainGenConstants, validateOpts } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const opts = validateOpts({ ...constants, Fp, t: 2, roundsFull: 8, roundsPartial: 8, sboxPower: 3 });
* ```
*/
export function validateOpts(opts) {
// This only normalizes shapes and field membership for the provided constants;
// it does not prove the stronger MDS/security criteria discussed in the specs.
assertValidPosOpts(opts);
const { Fp, mds, reversePartialPowIdx: rev, roundConstants: rc } = opts;
const { roundsFull, roundsPartial, sboxPower, t } = opts;
// MDS is TxT matrix
if (!Array.isArray(mds) || mds.length !== t)
throw new Error('Poseidon: invalid MDS matrix');
const _mds = mds.map((mdsRow) => {
if (!Array.isArray(mdsRow) || mdsRow.length !== t)
throw new Error('invalid MDS matrix row: ' + mdsRow);
return mdsRow.map((i) => {
if (typeof i !== 'bigint')
throw new Error('invalid MDS matrix bigint: ' + i);
// Hardcoded Poseidon MDS matrices often use signed entries like `-1`;
// accept bigint representatives here and reduce them into the field.
return Fp.create(i);
});
});
if (rev !== undefined && typeof rev !== 'boolean')
throw new Error('invalid param reversePartialPowIdx=' + rev);
if (roundsFull & 1)
throw new Error('roundsFull is not even' + roundsFull);
const rounds = roundsFull + roundsPartial;
if (!Array.isArray(rc) || rc.length !== rounds)
throw new Error('Poseidon: invalid round constants');
const roundConstants = rc.map((rc) => {
if (!Array.isArray(rc) || rc.length !== t)
throw new Error('invalid round constants');
return rc.map((i) => {
if (typeof i !== 'bigint' || !Fp.isValid(i))
throw new Error('invalid round constant');
return Fp.create(i);
});
});
// Freeze nested constants so exported handles cannot retune a live permutation instance.
const freezeRows = (rows) => Object.freeze(rows.map((row) => Object.freeze(row)));
if (!sboxPower || ![3, 5, 7, 17].includes(sboxPower))
throw new Error('invalid sboxPower');
const _sboxPower = BigInt(sboxPower);
let sboxFn = (n) => FpPow(Fp, n, _sboxPower);
// Unwrapped sbox power for common cases (195->142μs)
if (sboxPower === 3)
sboxFn = (n) => Fp.mul(Fp.sqrN(n), n);
else if (sboxPower === 5)
sboxFn = (n) => Fp.mul(Fp.sqrN(Fp.sqrN(n)), n);
return Object.freeze({
...opts,
rounds,
sboxFn,
roundConstants: freezeRows(roundConstants),
mds: freezeRows(_mds),
});
}
/**
* @param rc - Flattened round constants.
* @param t - Poseidon width.
* @returns Constants grouped by round.
* @throws If the width or flattened constant array is invalid. {@link Error}
* @example
* Regroup a flat constant list into per-round chunks.
*
* ```ts
* const rounds = splitConstants([1n, 2n, 3n, 4n], 2);
* ```
*/
export function splitConstants(rc, t) {
asafenumber(t, 't');
if (t < 1)
throw new Error('poseidonSplitConstants: invalid t');
if (!Array.isArray(rc) || rc.length % t)
throw new Error('poseidonSplitConstants: invalid rc');
const res = [];
let tmp = [];
for (let i = 0; i < rc.length; i++) {
const c = rc[i];
if (typeof c !== 'bigint')
throw new Error('invalid bigint=' + c);
tmp.push(c);
if (tmp.length === t) {
res.push(tmp);
tmp = [];
}
}
return res;
}
/** Poseidon NTT-friendly hash. */
/**
* @param opts - Poseidon options. See {@link PoseidonOpts}.
* @returns Poseidon permutation.
* @throws If the Poseidon options or state vector are invalid. {@link Error}
* @example
* Build a Poseidon permutation from validated parameters and constants.
*
* ```ts
* import { grainGenConstants, poseidon } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const hash = poseidon({ ...constants, Fp, t: 2, roundsFull: 8, roundsPartial: 8, sboxPower: 3 });
* const state = hash([1n, 2n]);
* ```
*/
export function poseidon(opts) {
const _opts = validateOpts(opts);
const { Fp, mds, roundConstants, rounds: totalRounds, roundsPartial, sboxFn, t } = _opts;
const halfRoundsFull = _opts.roundsFull / 2;
const partialIdx = _opts.reversePartialPowIdx ? t - 1 : 0;
const poseidonRound = (values, isFull, idx) => {
values = values.map((i, j) => Fp.add(i, roundConstants[idx][j]));
if (isFull)
values = values.map((i) => sboxFn(i));
else
values[partialIdx] = sboxFn(values[partialIdx]);
// Matrix multiplication
values = mds.map((i) => i.reduce((acc, i, j) => Fp.add(acc, Fp.mulN(i, values[j])), Fp.ZERO));
return values;
};
const poseidonHash = function poseidonHash(values) {
if (!Array.isArray(values) || values.length !== t)
throw new Error('invalid values, expected array of bigints with length ' + t);
// `.map()` skips sparse holes, which would leak `undefined` into round math below.
values = values.slice();
for (let j = 0; j < values.length; j++) {
const i = values[j];
if (typeof i !== 'bigint')
throw new Error('invalid bigint=' + i);
values[j] = Fp.create(i);
}
let lastRound = 0;
// Apply r_f/2 full rounds.
for (let i = 0; i < halfRoundsFull; i++)
values = poseidonRound(values, true, lastRound++);
// Apply r_p partial rounds.
for (let i = 0; i < roundsPartial; i++)
values = poseidonRound(values, false, lastRound++);
// Apply r_f/2 full rounds.
for (let i = 0; i < halfRoundsFull; i++)
values = poseidonRound(values, true, lastRound++);
if (lastRound !== totalRounds)
throw new Error('invalid number of rounds');
return values;
};
// For verification in tests
Object.defineProperty(poseidonHash, 'roundConstants', {
value: roundConstants,
enumerable: true,
});
return poseidonHash;
}
/**
* @param Fp - Field implementation.
* @param rate - Sponge rate.
* @param capacity - Sponge capacity.
* @param hash - Poseidon permutation.
* @example
* Wrap one Poseidon permutation in a sponge interface.
*
* ```ts
* import { PoseidonSponge, grainGenConstants, poseidon } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const hash = poseidon({ ...constants, Fp, t: 2, roundsFull: 8, roundsPartial: 8, sboxPower: 3 });
* const sponge = new PoseidonSponge(Fp, 1, 1, hash);
* sponge.absorb([1n]);
* const out = sponge.squeeze(1);
* ```
*/
export class PoseidonSponge {
Fp;
rate;
capacity;
hash;
state; // [...capacity, ...rate]
pos = 0;
isAbsorbing = true;
constructor(Fp, rate, capacity, hash) {
const width = spongeShape(rate, capacity);
// The direct constructor accepts an arbitrary permutation hook, but callers still
// need to preserve the `PoseidonFn.roundConstants` width metadata. Reject width
// mismatches here instead of deferring them until the first `process()` call.
if (width !== hash.roundConstants[0]?.length)
throw new Error(`invalid sponge width: expected ${hash.roundConstants[0]?.length}, got ${width}`);
this.Fp = Fp;
this.hash = hash;
this.rate = rate;
this.capacity = capacity;
this.state = new Array(width);
this.clean();
}
process() {
// The permutation is expected to return an owned state array. If callers inject a custom
// hook that reuses external storage, `clean()` will zero that shared buffer too.
this.state = this.hash(this.state);
}
absorb(input) {
for (const i of input)
if (typeof i !== 'bigint' || !this.Fp.isValid(i))
throw new Error('invalid input: ' + i);
for (let i = 0; i < input.length;) {
if (!this.isAbsorbing || this.pos === this.rate) {
this.process();
this.pos = 0;
this.isAbsorbing = true;
}
const chunk = Math.min(this.rate - this.pos, input.length - i);
for (let j = 0; j < chunk; j++) {
const idx = this.capacity + this.pos++;
this.state[idx] = this.Fp.add(this.state[idx], input[i++]);
}
}
}
squeeze(count) {
// Rust oracles use unsigned counts. In JS we keep `squeeze(0) => []` for
// compatibility, but still reject negative/fractional counts explicitly.
asafenumber(count, 'count');
if (count < 0)
throw new Error('invalid number count');
const res = [];
while (res.length < count) {
if (this.isAbsorbing || this.pos === this.rate) {
this.process();
this.pos = 0;
this.isAbsorbing = false;
}
const chunk = Math.min(this.rate - this.pos, count - res.length);
for (let i = 0; i < chunk; i++)
res.push(this.state[this.capacity + this.pos++]);
}
return res;
}
clean() {
this.state.fill(this.Fp.ZERO);
this.isAbsorbing = true;
this.pos = 0;
}
clone() {
const c = new PoseidonSponge(this.Fp, this.rate, this.capacity, this.hash);
c.pos = this.pos;
c.isAbsorbing = this.isAbsorbing;
c.state = [...this.state];
return c;
}
}
const spongeShape = (rate, capacity) => {
asafenumber(rate, 'rate');
asafenumber(capacity, 'capacity');
// A sponge with zero rate cannot absorb or squeeze any field elements.
if (rate < 1)
throw new Error('invalid number rate');
// Negative capacity can accidentally keep `rate + capacity` coherent while still
// producing a nonsensical sponge shape.
if (capacity < 0)
throw new Error('invalid number capacity');
return rate + capacity;
};
/**
* The method is not defined in spec, but nevertheless used often.
* Check carefully for compatibility: there are many edge cases, like absorbing an empty array.
* We cross-test against:
* - {@link https://github.com/ProvableHQ/snarkVM/tree/staging/algorithms | snarkVM algorithms}
* - {@link https://github.com/arkworks-rs/crypto-primitives/tree/main | arkworks crypto-primitives}
* @param opts - Sponge options. See {@link PoseidonSpongeOpts}.
* @returns Factory for sponge instances.
* @throws If the sponge dimensions or backing permutation options are invalid. {@link Error}
* @example
* Use the sponge helper to absorb several field elements and squeeze one digest.
*
* ```ts
* import { grainGenConstants, poseidonSponge } from '@noble/curves/abstract/poseidon.js';
* import { Field } from '@noble/curves/abstract/modular.js';
* const Fp = Field(17n);
* const constants = grainGenConstants({ Fp, t: 2, roundsFull: 8, roundsPartial: 8 });
* const makeSponge = poseidonSponge({
* ...constants,
* Fp,
* rate: 1,
* capacity: 1,
* roundsFull: 8,
* roundsPartial: 8,
* sboxPower: 3,
* });
* const sponge = makeSponge();
* sponge.absorb([1n]);
* const out = sponge.squeeze(1);
* ```
*/
export function poseidonSponge(opts) {
const { rate, capacity } = opts;
const t = spongeShape(rate, capacity);
// Re-use one hash instance between sponge instances; isolation depends on
// poseidon(...) itself staying immutable and not carrying mutable call state.
const hash = poseidon({ ...opts, t });
const { Fp } = opts;
return (() => new PoseidonSponge(Fp, rate, capacity, hash));
}
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/**
* Towered extension fields.
* Rather than implementing a massive 12th-degree extension directly, it is more efficient
* to build it up from smaller extensions: a tower of extensions.
*
* For BLS12-381, the Fp12 field is implemented as a quadratic (degree two) extension,
* on top of a cubic (degree three) extension, on top of a quadratic extension of Fp.
*
* For more info: "Pairings for beginners" by Costello, section 7.3.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { type TArg, type TRet } from '../utils.ts';
import * as mod from './modular.ts';
import type { WeierstrassPoint, WeierstrassPointCons } from './weierstrass.ts';
/** Pair of bigints used for quadratic-extension tuples. */
export type BigintTuple = [bigint, bigint];
/** Prime-field element. */
export type Fp = bigint;
/** Quadratic-extension field element `c0 + c1 * u`. */
export type Fp2 = {
/** Real component. */
c0: bigint;
/** Imaginary component. */
c1: bigint;
};
/** Six bigints used for sextic-extension tuples. */
export type BigintSix = [bigint, bigint, bigint, bigint, bigint, bigint];
/** Sextic-extension field element `c0 + c1 * v + c2 * v^2`. */
export type Fp6 = {
/** Constant coefficient. */
c0: Fp2;
/** Linear coefficient. */
c1: Fp2;
/** Quadratic coefficient. */
c2: Fp2;
};
/**
* Degree-12 extension field element `c0 + c1 * w`.
* Fp₁₂ = Fp₆² over Fp₂³, with Fp₆(w) / (w² - γ) where γ = v.
*/
export type Fp12 = {
/** Constant coefficient. */
c0: Fp6;
/** Linear coefficient. */
c1: Fp6;
};
/** Twelve bigints used for degree-12 extension tuples. */
export type BigintTwelve = [
bigint,
bigint,
bigint,
bigint,
bigint,
bigint,
bigint,
bigint,
bigint,
bigint,
bigint,
bigint
];
/** BLS-friendly helpers on top of the quadratic extension field. */
export type Fp2Bls = mod.IField<Fp2> & {
/** Underlying prime field. */
Fp: mod.IField<Fp>;
/** Apply one Frobenius map. */
frobeniusMap(num: Fp2, power: number): Fp2;
/** Build one field element from a raw bigint tuple. */
fromBigTuple(num: BigintTuple): Fp2;
/** Multiply by the curve `b` constant. */
mulByB: (num: Fp2) => Fp2;
/** Multiply by the quadratic non-residue. */
mulByNonresidue: (num: Fp2) => Fp2;
/** Split one quadratic element into real and imaginary components. */
reim: (num: Fp2) => {
re: Fp;
im: Fp;
};
/** Specialized helper used by sextic squaring formulas. */
Fp4Square: (a: Fp2, b: Fp2) => {
first: Fp2;
second: Fp2;
};
/** Quadratic non-residue used by the extension. */
NONRESIDUE: Fp2;
};
/** BLS-friendly helpers on top of the sextic extension field. */
export type Fp6Bls = mod.IField<Fp6> & {
/** Underlying quadratic extension field. */
Fp2: Fp2Bls;
/** Apply one Frobenius map. */
frobeniusMap(num: Fp6, power: number): Fp6;
/** Build one field element from a raw six-bigint tuple. */
fromBigSix: (tuple: BigintSix) => Fp6;
/** Multiply by a sparse `(0, b1, 0)` sextic element. */
mul1(num: Fp6, b1: Fp2): Fp6;
/** Multiply by a sparse `(b0, b1, 0)` sextic element. */
mul01(num: Fp6, b0: Fp2, b1: Fp2): Fp6;
/** Multiply by one quadratic-extension element. */
mulByFp2(lhs: Fp6, rhs: Fp2): Fp6;
/** Multiply by the sextic non-residue. */
mulByNonresidue: (num: Fp6) => Fp6;
};
/** BLS-friendly helpers on top of the degree-12 extension field. */
export type Fp12Bls = mod.IField<Fp12> & {
/** Underlying sextic extension field. */
Fp6: Fp6Bls;
/** Apply one Frobenius map. */
frobeniusMap(num: Fp12, power: number): Fp12;
/** Build one field element from a raw twelve-bigint tuple. */
fromBigTwelve: (t: BigintTwelve) => Fp12;
/** Multiply by a sparse `(o0, o1, 0, 0, o4, 0)` element. */
mul014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;
/** Multiply by a sparse `(o0, 0, 0, o3, o4, 0)` element. */
mul034(num: Fp12, o0: Fp2, o3: Fp2, o4: Fp2): Fp12;
/** Multiply by one quadratic-extension element. */
mulByFp2(lhs: Fp12, rhs: Fp2): Fp12;
/** Conjugate one degree-12 element. */
conjugate(num: Fp12): Fp12;
/** Apply the final exponentiation from pairing arithmetic. */
finalExponentiate(num: Fp12): Fp12;
/** Apply one cyclotomic square. */
_cyclotomicSquare(num: Fp12): Fp12;
/** Apply one cyclotomic exponentiation. */
_cyclotomicExp(num: Fp12, n: bigint): Fp12;
};
declare function calcFrobeniusCoefficients<T>(Fp: TArg<mod.IField<T>>, nonResidue: T, modulus: bigint, degree: number, num?: number, divisor?: number): T[][];
export declare const __TEST: {
calcFrobeniusCoefficients: typeof calcFrobeniusCoefficients;
};
/**
* @param Fp - Base field implementation.
* @param Fp2 - Quadratic extension field.
* @param base - Twist-specific Frobenius base whose powers yield the `c1` / `c2` constants.
* BLS12-381 uses `1 / NONRESIDUE`; BN254 uses `NONRESIDUE`.
* @returns Frobenius endomorphism helpers.
* @throws If the derived Frobenius constants are inconsistent for the tower. {@link Error}
* @example
* Build Frobenius endomorphism helpers for a BLS extension tower.
*
* ```ts
* import { psiFrobenius } from '@noble/curves/abstract/tower.js';
* import { bls12_381 } from '@noble/curves/bls12-381.js';
* const Fp = bls12_381.fields.Fp;
* const Fp2 = bls12_381.fields.Fp2;
* const frob = psiFrobenius(Fp, Fp2, Fp2.div(Fp2.ONE, Fp2.NONRESIDUE));
* const point = frob.G2psi(bls12_381.G2.Point, bls12_381.G2.Point.BASE);
* ```
*/
export declare function psiFrobenius(Fp: TArg<mod.IField<Fp>>, Fp2: TArg<Fp2Bls>, base: TArg<Fp2>): {
psi: (x: Fp2, y: Fp2) => [Fp2, Fp2];
psi2: (x: Fp2, y: Fp2) => [Fp2, Fp2];
G2psi: (c: WeierstrassPointCons<Fp2>, P: WeierstrassPoint<Fp2>) => WeierstrassPoint<Fp2>;
G2psi2: (c: WeierstrassPointCons<Fp2>, P: WeierstrassPoint<Fp2>) => WeierstrassPoint<Fp2>;
PSI_X: Fp2;
PSI_Y: Fp2;
PSI2_X: Fp2;
PSI2_Y: Fp2;
};
/** Construction options for the BLS-style degree-12 tower. */
export type Tower12Opts = {
/** Prime-field order. */
ORDER: bigint;
/** Bit length of the BLS parameter `x`. */
X_LEN: number;
/** Prime-field non-residue used by the quadratic extension. */
NONRESIDUE?: Fp;
/** Quadratic-extension non-residue used by the sextic tower. */
FP2_NONRESIDUE: BigintTuple;
/**
* Optional custom quadratic square-root helper.
* Receives one quadratic-extension element and returns one square root.
*/
Fp2sqrt?: (num: Fp2) => Fp2;
/**
* Multiply one quadratic element by the curve `b` constant.
* @param num - Quadratic-extension element to scale.
* @returns Product by the curve `b` constant.
*/
Fp2mulByB: (num: Fp2) => Fp2;
/**
* Final exponentiation used by pairing arithmetic.
* @param num - Degree-12 field element to exponentiate.
* @returns Pairing result after final exponentiation.
*/
Fp12finalExponentiate: (num: Fp12) => Fp12;
};
/**
* @param opts - Tower construction options. See {@link Tower12Opts}.
* @returns BLS tower fields.
* @throws If the tower options or derived Frobenius helpers are invalid. {@link Error}
* @example
* Construct the Fp2/Fp6/Fp12 tower used by a pairing-friendly curve.
*
* ```ts
* const fields = tower12({
* ORDER: 17n,
* X_LEN: 4,
* FP2_NONRESIDUE: [1n, 1n],
* Fp2mulByB: (num) => num,
* Fp12finalExponentiate: (num) => num,
* });
* const fp12 = fields.Fp12.ONE;
* ```
*/
export declare function tower12(opts: TArg<Tower12Opts>): TRet<{
Fp: Readonly<mod.IField<bigint> & Required<Pick<mod.IField<bigint>, 'isOdd'>>>;
Fp2: Fp2Bls;
Fp6: Fp6Bls;
Fp12: Fp12Bls;
}>;
export {};
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node_modules/@noble/curves/abstract/tower.js generated vendored Normal file
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/**
* Towered extension fields.
* Rather than implementing a massive 12th-degree extension directly, it is more efficient
* to build it up from smaller extensions: a tower of extensions.
*
* For BLS12-381, the Fp12 field is implemented as a quadratic (degree two) extension,
* on top of a cubic (degree three) extension, on top of a quadratic extension of Fp.
*
* For more info: "Pairings for beginners" by Costello, section 7.3.
* @module
*/
/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
import { abytes, aInRange, asafenumber, bitGet, bitLen, concatBytes, notImplemented, validateObject, } from "../utils.js";
import * as mod from "./modular.js";
// Be friendly to bad ECMAScript parsers by not using bigint literals
// prettier-ignore
const _0n = /* @__PURE__ */ BigInt(0), _1n = /* @__PURE__ */ BigInt(1), _2n = /* @__PURE__ */ BigInt(2), _3n = /* @__PURE__ */ BigInt(3), _6n = /* @__PURE__ */ BigInt(6), _12n = /* @__PURE__ */ BigInt(12);
const isObj = (value) => !!value && typeof value === 'object';
function calcFrobeniusCoefficients(Fp, nonResidue, modulus, degree, num = 1, divisor) {
asafenumber(num, 'num');
const F = Fp;
// Generic callers can hit empty / fractional row counts through `__TEST`; fail closed instead of
// silently returning `[]` or deriving extra Frobenius rows from a truncated loop bound.
if (num <= 0)
throw new Error('calcFrobeniusCoefficients: expected positive row count, got ' + num);
const _divisor = BigInt(divisor === undefined ? degree : divisor);
const towerModulus = modulus ** BigInt(degree);
const res = [];
// Derive tower-basis multipliers for the `p^k` Frobenius action. The
// divisions below are expected to be exact for the chosen tower parameters.
for (let i = 0; i < num; i++) {
const a = BigInt(i + 1);
const powers = [];
for (let j = 0, qPower = _1n; j < degree; j++) {
const numer = a * qPower - a;
// Shipped towers divide cleanly here, but generic callers can pick bad
// params. Bigint division would floor and derive the wrong Frobenius table.
if (numer % _divisor)
throw new Error('calcFrobeniusCoefficients: inexact tower exponent');
const power = (numer / _divisor) % towerModulus;
powers.push(F.pow(nonResidue, power));
qPower *= modulus;
}
res.push(powers);
}
return res;
}
export const __TEST =
/* @__PURE__ */ Object.freeze({
calcFrobeniusCoefficients,
});
// This works same at least for bls12-381, bn254 and bls12-377
/**
* @param Fp - Base field implementation.
* @param Fp2 - Quadratic extension field.
* @param base - Twist-specific Frobenius base whose powers yield the `c1` / `c2` constants.
* BLS12-381 uses `1 / NONRESIDUE`; BN254 uses `NONRESIDUE`.
* @returns Frobenius endomorphism helpers.
* @throws If the derived Frobenius constants are inconsistent for the tower. {@link Error}
* @example
* Build Frobenius endomorphism helpers for a BLS extension tower.
*
* ```ts
* import { psiFrobenius } from '@noble/curves/abstract/tower.js';
* import { bls12_381 } from '@noble/curves/bls12-381.js';
* const Fp = bls12_381.fields.Fp;
* const Fp2 = bls12_381.fields.Fp2;
* const frob = psiFrobenius(Fp, Fp2, Fp2.div(Fp2.ONE, Fp2.NONRESIDUE));
* const point = frob.G2psi(bls12_381.G2.Point, bls12_381.G2.Point.BASE);
* ```
*/
export function psiFrobenius(Fp, Fp2, base) {
// GLV endomorphism Ψ(P)
const PSI_X = Fp2.pow(base, (Fp.ORDER - _1n) / _3n); // u^((p-1)/3)
const PSI_Y = Fp2.pow(base, (Fp.ORDER - _1n) / _2n); // u^((p-1)/2)
function psi(x, y) {
// This x10 faster than previous version in bls12-381
const x2 = Fp2.mul(Fp2.frobeniusMap(x, 1), PSI_X);
const y2 = Fp2.mul(Fp2.frobeniusMap(y, 1), PSI_Y);
return [x2, y2];
}
// Ψ²(P) endomorphism (psi2(x) = psi(psi(x)))
const PSI2_X = Fp2.pow(base, (Fp.ORDER ** _2n - _1n) / _3n); // u^((p^2 - 1)/3)
// Current towers rely on this landing on `-1`, which lets psi2 map `y` with
// one negation instead of carrying a separate Frobenius multiplier.
const PSI2_Y = Fp2.pow(base, (Fp.ORDER ** _2n - _1n) / _2n); // u^((p^2 - 1)/2)
if (!Fp2.eql(PSI2_Y, Fp2.neg(Fp2.ONE)))
throw new Error('psiFrobenius: PSI2_Y!==-1');
function psi2(x, y) {
return [Fp2.mul(x, PSI2_X), Fp2.neg(y)];
}
// Map points
const mapAffine = (fn) => (c, P) => {
const affine = P.toAffine();
const p = fn(affine.x, affine.y);
return c.fromAffine({ x: p[0], y: p[1] });
};
const G2psi = mapAffine(psi);
const G2psi2 = mapAffine(psi2);
return { psi, psi2, G2psi, G2psi2, PSI_X, PSI_Y, PSI2_X, PSI2_Y };
}
class _Field2 {
ORDER;
BITS;
BYTES;
isLE;
ZERO;
ONE;
Fp;
NONRESIDUE;
mulByB;
Fp_NONRESIDUE;
Fp_div2;
FROBENIUS_COEFFICIENTS;
constructor(Fp, opts = {}) {
const { NONRESIDUE = BigInt(-1), FP2_NONRESIDUE, Fp2mulByB } = opts;
const ORDER = Fp.ORDER;
const FP2_ORDER = ORDER * ORDER;
this.Fp = Fp;
this.ORDER = FP2_ORDER;
this.BITS = bitLen(FP2_ORDER);
this.BYTES = Math.ceil(bitLen(FP2_ORDER) / 8);
this.isLE = Fp.isLE;
this.ZERO = this.create({ c0: Fp.ZERO, c1: Fp.ZERO });
this.ONE = this.create({ c0: Fp.ONE, c1: Fp.ZERO });
// These knobs only swap constants for the shipped quadratic tower shape:
// arithmetic below assumes `u^2 = -1`, and bytes are handled as two adjacent
// `Fp` limbs (`fromBytes` / `toBytes` expect the shipped `2 * Fp.BYTES` layout).
this.Fp_NONRESIDUE = Fp.create(NONRESIDUE);
this.Fp_div2 = Fp.div(Fp.ONE, _2n); // 1/2
this.NONRESIDUE = this.create({ c0: FP2_NONRESIDUE[0], c1: FP2_NONRESIDUE[1] });
// const Fp2Nonresidue = this.create({ c0: FP2_NONRESIDUE![0], c1: FP2_NONRESIDUE![1] });
this.FROBENIUS_COEFFICIENTS = Object.freeze(calcFrobeniusCoefficients(Fp, this.Fp_NONRESIDUE, Fp.ORDER, 2)[0]);
this.mulByB = (num) => {
// This config hook is trusted to return a canonical Fp2 value already.
// Copy+freeze it to keep the tower immutability invariant without mutating caller objects.
const { c0, c1 } = Fp2mulByB(num);
return Object.freeze({ c0, c1 });
};
Object.freeze(this);
}
fromBigTuple(tuple) {
if (!Array.isArray(tuple) || tuple.length !== 2)
throw new Error('invalid Fp2.fromBigTuple');
const [c0, c1] = tuple;
if (typeof c0 !== 'bigint' || typeof c1 !== 'bigint')
throw new Error('invalid Fp2.fromBigTuple');
return this.create({ c0, c1 });
}
create(num) {
const { Fp } = this;
const c0 = Fp.create(num.c0);
const c1 = Fp.create(num.c1);
// Bigint field elements are immutable values, and higher-level code relies on
// that invariant. Copy+freeze tower values too without mutating caller-owned objects.
return Object.freeze({ c0, c1 });
}
isValid(num) {
if (!isObj(num))
throw new TypeError('invalid field element: expected object, got ' + typeof num);
const { c0, c1 } = num;
const { Fp } = this;
// Match base-field `isValid(...)`: malformed coordinate types are errors, not a `false`
// predicate result.
return Fp.isValid(c0) && Fp.isValid(c1);
}
is0(num) {
if (!isObj(num))
return false;
const { c0, c1 } = num;
const { Fp } = this;
return Fp.is0(c0) && Fp.is0(c1);
}
isValidNot0(num) {
return !this.is0(num) && this.isValid(num);
}
eql({ c0, c1 }, { c0: r0, c1: r1 }) {
const { Fp } = this;
return Fp.eql(c0, r0) && Fp.eql(c1, r1);
}
neg({ c0, c1 }) {
const { Fp } = this;
return Object.freeze({ c0: Fp.neg(c0), c1: Fp.neg(c1) });
}
pow(num, power) {
return mod.FpPow(this, num, power);
}
invertBatch(nums) {
return mod.FpInvertBatch(this, nums);
}
// Normalized
add(f1, f2) {
const { Fp } = this;
const { c0, c1 } = f1;
const { c0: r0, c1: r1 } = f2;
return Object.freeze({
c0: Fp.add(c0, r0),
c1: Fp.add(c1, r1),
});
}
sub({ c0, c1 }, { c0: r0, c1: r1 }) {
const { Fp } = this;
return Object.freeze({
c0: Fp.sub(c0, r0),
c1: Fp.sub(c1, r1),
});
}
mul({ c0, c1 }, rhs) {
const { Fp } = this;
if (typeof rhs === 'bigint')
return Object.freeze({ c0: Fp.mul(c0, rhs), c1: Fp.mul(c1, rhs) });
// (a+bi)(c+di) = (acbd) + (ad+bc)i
const { c0: r0, c1: r1 } = rhs;
let t1 = Fp.mul(c0, r0); // c0 * o0
let t2 = Fp.mul(c1, r1); // c1 * o1
// (T1 - T2) + ((c0 + c1) * (r0 + r1) - (T1 + T2))*i
const o0 = Fp.sub(t1, t2);
const o1 = Fp.sub(Fp.mul(Fp.add(c0, c1), Fp.add(r0, r1)), Fp.add(t1, t2));
return Object.freeze({ c0: o0, c1: o1 });
}
sqr({ c0, c1 }) {
const { Fp } = this;
const a = Fp.add(c0, c1);
const b = Fp.sub(c0, c1);
const c = Fp.add(c0, c0);
return Object.freeze({ c0: Fp.mul(a, b), c1: Fp.mul(c, c1) });
}
// NonNormalized stuff
addN(a, b) {
return this.add(a, b);
}
subN(a, b) {
return this.sub(a, b);
}
mulN(a, b) {
return this.mul(a, b);
}
sqrN(a) {
return this.sqr(a);
}
// Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
div(lhs, rhs) {
const { Fp } = this;
// @ts-ignore
return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
}
inv({ c0: a, c1: b }) {
// We wish to find the multiplicative inverse of a nonzero
// element a + bu in Fp2. We leverage an identity
//
// (a + bu)(a - bu) = a² + b²
//
// which holds because u² = -1. This can be rewritten as
//
// (a + bu)(a - bu)/(a² + b²) = 1
//
// because a² + b² = 0 has no nonzero solutions for (a, b).
// This gives that (a - bu)/(a² + b²) is the inverse
// of (a + bu). Importantly, this can be computing using
// only a single inversion in Fp.
const { Fp } = this;
const factor = Fp.inv(Fp.create(a * a + b * b));
return Object.freeze({ c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) });
}
sqrt(num) {
// This is generic for all quadratic extensions (Fp2)
const { Fp } = this;
const Fp2 = this;
const { c0, c1 } = num;
if (Fp.is0(c1)) {
// if c0 is quadratic residue
if (mod.FpLegendre(Fp, c0) === 1)
return Fp2.create({ c0: Fp.sqrt(c0), c1: Fp.ZERO });
else
return Fp2.create({ c0: Fp.ZERO, c1: Fp.sqrt(Fp.div(c0, this.Fp_NONRESIDUE)) });
}
const a = Fp.sqrt(Fp.sub(Fp.sqr(c0), Fp.mul(Fp.sqr(c1), this.Fp_NONRESIDUE)));
let d = Fp.mul(Fp.add(a, c0), this.Fp_div2);
const legendre = mod.FpLegendre(Fp, d);
// -1, Quadratic non residue
if (legendre === -1)
d = Fp.sub(d, a);
const a0 = Fp.sqrt(d);
const candidateSqrt = Fp2.create({ c0: a0, c1: Fp.div(Fp.mul(c1, this.Fp_div2), a0) });
if (!Fp2.eql(Fp2.sqr(candidateSqrt), num))
throw new Error('Cannot find square root');
// Normalize root: at this point candidateSqrt ** 2 = num, but also -candidateSqrt ** 2 = num
const x1 = candidateSqrt;
const x2 = Fp2.neg(x1);
const { re: re1, im: im1 } = Fp2.reim(x1);
const { re: re2, im: im2 } = Fp2.reim(x2);
if (im1 > im2 || (im1 === im2 && re1 > re2))
return x1;
return x2;
}
// Same as sgn0_m_eq_2 in RFC 9380
isOdd(x) {
const { re: x0, im: x1 } = this.reim(x);
const sign_0 = x0 % _2n;
const zero_0 = x0 === _0n;
const sign_1 = x1 % _2n;
return BigInt(sign_0 || (zero_0 && sign_1)) == _1n;
}
// Bytes util
fromBytes(b) {
const { Fp } = this;
abytes(b);
if (b.length !== this.BYTES)
throw new Error('fromBytes invalid length=' + b.length);
return this.create({
c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)),
c1: Fp.fromBytes(b.subarray(Fp.BYTES)),
});
}
toBytes({ c0, c1 }) {
return concatBytes(this.Fp.toBytes(c0), this.Fp.toBytes(c1));
}
cmov({ c0, c1 }, { c0: r0, c1: r1 }, c) {
const { Fp } = this;
return this.create({
c0: Fp.cmov(c0, r0, c),
c1: Fp.cmov(c1, r1, c),
});
}
reim({ c0, c1 }) {
return { re: c0, im: c1 };
}
Fp4Square(a, b) {
const Fp2 = this;
const a2 = Fp2.sqr(a);
const b2 = Fp2.sqr(b);
return {
first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
};
}
// multiply by u + 1
mulByNonresidue({ c0, c1 }) {
return this.mul({ c0, c1 }, this.NONRESIDUE);
}
frobeniusMap({ c0, c1 }, power) {
return Object.freeze({
c0,
c1: this.Fp.mul(c1, this.FROBENIUS_COEFFICIENTS[power % 2]),
});
}
}
class _Field6 {
ORDER;
BITS;
BYTES;
isLE;
ZERO;
ONE;
Fp2;
constructor(Fp2) {
this.Fp2 = Fp2;
// `IField.ORDER` is the field cardinality `q`; for sextic extensions that is `p^6`.
// Generic helpers like Frobenius-style `x^q = x` checks rely on the literal field size here.
this.ORDER = Fp2.Fp.ORDER ** _6n;
this.BITS = 3 * Fp2.BITS;
this.BYTES = 3 * Fp2.BYTES;
this.isLE = Fp2.isLE;
this.ZERO = this.create({ c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO });
this.ONE = this.create({ c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO });
Object.freeze(this);
}
// Most callers never touch Frobenius maps, so keep the sextic tables lazy:
// eagerly deriving them dominates `bls12-381.js` / `bn254.js` import time.
get FROBENIUS_COEFFICIENTS_1() {
const frob = _FROBENIUS_COEFFICIENTS_6.get(this);
if (frob)
return frob[0];
const { Fp2 } = this;
const { Fp } = Fp2;
const rows = calcFrobeniusCoefficients(Fp2, Fp2.NONRESIDUE, Fp.ORDER, 6, 2, 3);
const cache = [Object.freeze(rows[0]), Object.freeze(rows[1])];
_FROBENIUS_COEFFICIENTS_6.set(this, cache);
return cache[0];
}
get FROBENIUS_COEFFICIENTS_2() {
const frob = _FROBENIUS_COEFFICIENTS_6.get(this);
if (frob)
return frob[1];
void this.FROBENIUS_COEFFICIENTS_1;
return _FROBENIUS_COEFFICIENTS_6.get(this)[1];
}
add({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
const { Fp2 } = this;
return Object.freeze({
c0: Fp2.add(c0, r0),
c1: Fp2.add(c1, r1),
c2: Fp2.add(c2, r2),
});
}
sub({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
const { Fp2 } = this;
return Object.freeze({
c0: Fp2.sub(c0, r0),
c1: Fp2.sub(c1, r1),
c2: Fp2.sub(c2, r2),
});
}
mul({ c0, c1, c2 }, rhs) {
const { Fp2 } = this;
if (typeof rhs === 'bigint') {
return Object.freeze({
c0: Fp2.mul(c0, rhs),
c1: Fp2.mul(c1, rhs),
c2: Fp2.mul(c2, rhs),
});
}
const { c0: r0, c1: r1, c2: r2 } = rhs;
const t0 = Fp2.mul(c0, r0); // c0 * o0
const t1 = Fp2.mul(c1, r1); // c1 * o1
const t2 = Fp2.mul(c2, r2); // c2 * o2
return Object.freeze({
// t0 + (c1 + c2) * (r1 * r2) - (T1 + T2) * (u + 1)
c0: Fp2.add(t0, Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), Fp2.add(r1, r2)), Fp2.add(t1, t2)))),
// (c0 + c1) * (r0 + r1) - (T0 + T1) + T2 * (u + 1)
c1: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c1), Fp2.add(r0, r1)), Fp2.add(t0, t1)), Fp2.mulByNonresidue(t2)),
// T1 + (c0 + c2) * (r0 + r2) - T0 + T2
c2: Fp2.sub(Fp2.add(t1, Fp2.mul(Fp2.add(c0, c2), Fp2.add(r0, r2))), Fp2.add(t0, t2)),
});
}
sqr({ c0, c1, c2 }) {
const { Fp2 } = this;
let t0 = Fp2.sqr(c0); // c0²
let t1 = Fp2.mul(Fp2.mul(c0, c1), _2n); // 2 * c0 * c1
let t3 = Fp2.mul(Fp2.mul(c1, c2), _2n); // 2 * c1 * c2
let t4 = Fp2.sqr(c2); // c2²
return Object.freeze({
c0: Fp2.add(Fp2.mulByNonresidue(t3), t0), // T3 * (u + 1) + T0
c1: Fp2.add(Fp2.mulByNonresidue(t4), t1), // T4 * (u + 1) + T1
// T1 + (c0 - c1 + c2)² + T3 - T0 - T4
c2: Fp2.sub(Fp2.sub(Fp2.add(Fp2.add(t1, Fp2.sqr(Fp2.add(Fp2.sub(c0, c1), c2))), t3), t0), t4),
});
}
addN(a, b) {
return this.add(a, b);
}
subN(a, b) {
return this.sub(a, b);
}
mulN(a, b) {
return this.mul(a, b);
}
sqrN(a) {
return this.sqr(a);
}
create(num) {
const { Fp2 } = this;
const c0 = Fp2.create(num.c0);
const c1 = Fp2.create(num.c1);
const c2 = Fp2.create(num.c2);
return Object.freeze({ c0, c1, c2 });
}
isValid(num) {
if (!isObj(num))
throw new TypeError('invalid field element: expected object, got ' + typeof num);
const { c0, c1, c2 } = num;
const { Fp2 } = this;
return Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2);
}
is0(num) {
if (!isObj(num))
return false;
const { c0, c1, c2 } = num;
const { Fp2 } = this;
return Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2);
}
isValidNot0(num) {
return !this.is0(num) && this.isValid(num);
}
neg({ c0, c1, c2 }) {
const { Fp2 } = this;
return Object.freeze({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) });
}
eql({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) {
const { Fp2 } = this;
return Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2);
}
sqrt(_) {
// Sextic extensions can use generic odd-field Tonelli-Shanks, but the helper must work
// over `IField<T>` with a quadratic non-residue from Fp6 itself. The current
// `mod.tonelliShanks(P)` precomputation only searches integer residues in the base field.
return notImplemented();
}
// Do we need division by bigint at all? Should be done via order:
div(lhs, rhs) {
const { Fp2 } = this;
const { Fp } = Fp2;
return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
}
pow(num, power) {
return mod.FpPow(this, num, power);
}
invertBatch(nums) {
return mod.FpInvertBatch(this, nums);
}
inv({ c0, c1, c2 }) {
const { Fp2 } = this;
let t0 = Fp2.sub(Fp2.sqr(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
let t2 = Fp2.sub(Fp2.sqr(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
// 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0)
let t4 = Fp2.inv(Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0)));
return Object.freeze({ c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) });
}
// Bytes utils
fromBytes(b) {
const { Fp2 } = this;
abytes(b);
if (b.length !== this.BYTES)
throw new Error('fromBytes invalid length=' + b.length);
const B2 = Fp2.BYTES;
return this.create({
c0: Fp2.fromBytes(b.subarray(0, B2)),
c1: Fp2.fromBytes(b.subarray(B2, B2 * 2)),
c2: Fp2.fromBytes(b.subarray(2 * B2)),
});
}
toBytes({ c0, c1, c2 }) {
const { Fp2 } = this;
return concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2));
}
cmov({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }, c) {
const { Fp2 } = this;
return this.create({
c0: Fp2.cmov(c0, r0, c),
c1: Fp2.cmov(c1, r1, c),
c2: Fp2.cmov(c2, r2, c),
});
}
fromBigSix(tuple) {
const { Fp2 } = this;
if (!Array.isArray(tuple) || tuple.length !== 6)
throw new Error('invalid Fp6.fromBigSix');
for (let i = 0; i < 6; i++)
if (typeof tuple[i] !== 'bigint')
throw new Error('invalid Fp6.fromBigSix');
const t = tuple;
return this.create({
c0: Fp2.fromBigTuple(t.slice(0, 2)),
c1: Fp2.fromBigTuple(t.slice(2, 4)),
c2: Fp2.fromBigTuple(t.slice(4, 6)),
});
}
frobeniusMap({ c0, c1, c2 }, power) {
const { Fp2 } = this;
return Object.freeze({
c0: Fp2.frobeniusMap(c0, power),
c1: Fp2.mul(Fp2.frobeniusMap(c1, power), this.FROBENIUS_COEFFICIENTS_1[power % 6]),
c2: Fp2.mul(Fp2.frobeniusMap(c2, power), this.FROBENIUS_COEFFICIENTS_2[power % 6]),
});
}
mulByFp2({ c0, c1, c2 }, rhs) {
const { Fp2 } = this;
return Object.freeze({
c0: Fp2.mul(c0, rhs),
c1: Fp2.mul(c1, rhs),
c2: Fp2.mul(c2, rhs),
});
}
mulByNonresidue({ c0, c1, c2 }) {
const { Fp2 } = this;
return Object.freeze({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 });
}
// Sparse multiplication
mul1({ c0, c1, c2 }, b1) {
const { Fp2 } = this;
return Object.freeze({
c0: Fp2.mulByNonresidue(Fp2.mul(c2, b1)),
c1: Fp2.mul(c0, b1),
c2: Fp2.mul(c1, b1),
});
}
// Sparse multiplication
mul01({ c0, c1, c2 }, b0, b1) {
const { Fp2 } = this;
let t0 = Fp2.mul(c0, b0); // c0 * b0
let t1 = Fp2.mul(c1, b1); // c1 * b1
return Object.freeze({
// ((c1 + c2) * b1 - T1) * (u + 1) + T0
c0: Fp2.add(Fp2.mulByNonresidue(Fp2.sub(Fp2.mul(Fp2.add(c1, c2), b1), t1)), t0),
// (b0 + b1) * (c0 + c1) - T0 - T1
c1: Fp2.sub(Fp2.sub(Fp2.mul(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1),
// (c0 + c2) * b0 - T0 + T1
c2: Fp2.add(Fp2.sub(Fp2.mul(Fp2.add(c0, c2), b0), t0), t1),
});
}
}
// Keep lazy tower caches off-object: field instances stay frozen, and debugger output
// stays readable without JS private slots while second/subsequent lookups still hit cache.
const _FROBENIUS_COEFFICIENTS_6 = new WeakMap();
class _Field12 {
ORDER;
BITS;
BYTES;
isLE;
ZERO;
ONE;
Fp6;
X_LEN;
finalExponentiate;
constructor(Fp6, opts) {
const { X_LEN, Fp12finalExponentiate } = opts;
const { Fp2 } = Fp6;
const { Fp } = Fp2;
this.Fp6 = Fp6;
// `IField.ORDER` is the field cardinality `q`; for degree-12 extensions that is `p^12`.
// Keeping `p^2` here breaks generic field identities like `x^q = x` on Fp12.
this.ORDER = Fp.ORDER ** _12n;
this.BITS = 2 * Fp6.BITS;
this.BYTES = 2 * Fp6.BYTES;
this.isLE = Fp6.isLE;
// Returned tower values are frozen, so larger constants can safely reuse
// already-frozen child coefficients instead of cloning them.
this.ZERO = this.create({ c0: Fp6.ZERO, c1: Fp6.ZERO });
this.ONE = this.create({ c0: Fp6.ONE, c1: Fp6.ZERO });
this.X_LEN = X_LEN;
this.finalExponentiate = (num) => {
const copy2 = ({ c0, c1 }) => Object.freeze({ c0, c1 });
const copy6 = ({ c0, c1, c2 }) => Object.freeze({ c0: copy2(c0), c1: copy2(c1), c2: copy2(c2) });
// This config hook is trusted to return a canonical Fp12 value already.
// Copy+freeze it to keep the tower immutability invariant without mutating caller objects.
const res = Fp12finalExponentiate(num);
return Object.freeze({ c0: copy6(res.c0), c1: copy6(res.c1) });
};
Object.freeze(this);
}
// Keep the degree-12 Frobenius row lazy too; after the first lookup the cached
// array is reused exactly like the old eager table.
get FROBENIUS_COEFFICIENTS() {
const frob = _FROBENIUS_COEFFICIENTS_12.get(this);
if (frob)
return frob;
const { Fp2 } = this.Fp6;
const { Fp } = Fp2;
const cache = Object.freeze(calcFrobeniusCoefficients(Fp2, Fp2.NONRESIDUE, Fp.ORDER, 12, 1, 6)[0]);
_FROBENIUS_COEFFICIENTS_12.set(this, cache);
return cache;
}
create(num) {
const { Fp6 } = this;
const c0 = Fp6.create(num.c0);
const c1 = Fp6.create(num.c1);
return Object.freeze({ c0, c1 });
}
isValid(num) {
if (!isObj(num))
throw new TypeError('invalid field element: expected object, got ' + typeof num);
const { c0, c1 } = num;
const { Fp6 } = this;
return Fp6.isValid(c0) && Fp6.isValid(c1);
}
is0(num) {
if (!isObj(num))
return false;
const { c0, c1 } = num;
const { Fp6 } = this;
return Fp6.is0(c0) && Fp6.is0(c1);
}
isValidNot0(num) {
return !this.is0(num) && this.isValid(num);
}
neg({ c0, c1 }) {
const { Fp6 } = this;
return Object.freeze({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) });
}
eql({ c0, c1 }, { c0: r0, c1: r1 }) {
const { Fp6 } = this;
return Fp6.eql(c0, r0) && Fp6.eql(c1, r1);
}
sqrt(_) {
// Fp12 is quadratic over Fp6, so a dedicated quadratic-extension sqrt is possible here
// once Fp6.sqrt() exists. Without that lower-level sqrt, only a field-generic
// Tonelli-Shanks path over Fp12 itself would work.
return notImplemented();
}
inv({ c0, c1 }) {
const { Fp6 } = this;
let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
// ((C0 * T) * T) + (-C1 * T) * w
return Object.freeze({ c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) });
}
div(lhs, rhs) {
const { Fp6 } = this;
const { Fp2 } = Fp6;
const { Fp } = Fp2;
return this.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : this.inv(rhs));
}
pow(num, power) {
return mod.FpPow(this, num, power);
}
invertBatch(nums) {
return mod.FpInvertBatch(this, nums);
}
// Normalized
add({ c0, c1 }, { c0: r0, c1: r1 }) {
const { Fp6 } = this;
return Object.freeze({
c0: Fp6.add(c0, r0),
c1: Fp6.add(c1, r1),
});
}
sub({ c0, c1 }, { c0: r0, c1: r1 }) {
const { Fp6 } = this;
return Object.freeze({
c0: Fp6.sub(c0, r0),
c1: Fp6.sub(c1, r1),
});
}
mul({ c0, c1 }, rhs) {
const { Fp6 } = this;
if (typeof rhs === 'bigint')
return Object.freeze({ c0: Fp6.mul(c0, rhs), c1: Fp6.mul(c1, rhs) });
let { c0: r0, c1: r1 } = rhs;
let t1 = Fp6.mul(c0, r0); // c0 * r0
let t2 = Fp6.mul(c1, r1); // c1 * r1
return Object.freeze({
c0: Fp6.add(t1, Fp6.mulByNonresidue(t2)), // T1 + T2 * v
// (c0 + c1) * (r0 + r1) - (T1 + T2)
c1: Fp6.sub(Fp6.mul(Fp6.add(c0, c1), Fp6.add(r0, r1)), Fp6.add(t1, t2)),
});
}
sqr({ c0, c1 }) {
const { Fp6 } = this;
let ab = Fp6.mul(c0, c1); // c0 * c1
return Object.freeze({
// (c1 * v + c0) * (c0 + c1) - AB - AB * v
c0: Fp6.sub(Fp6.sub(Fp6.mul(Fp6.add(Fp6.mulByNonresidue(c1), c0), Fp6.add(c0, c1)), ab), Fp6.mulByNonresidue(ab)),
c1: Fp6.add(ab, ab),
}); // AB + AB
}
// NonNormalized stuff
addN(a, b) {
return this.add(a, b);
}
subN(a, b) {
return this.sub(a, b);
}
mulN(a, b) {
return this.mul(a, b);
}
sqrN(a) {
return this.sqr(a);
}
// Bytes utils
fromBytes(b) {
const { Fp6 } = this;
abytes(b);
if (b.length !== this.BYTES)
throw new Error('fromBytes invalid length=' + b.length);
return this.create({
c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)),
c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
});
}
toBytes({ c0, c1 }) {
const { Fp6 } = this;
return concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1));
}
cmov({ c0, c1 }, { c0: r0, c1: r1 }, c) {
const { Fp6 } = this;
return this.create({
c0: Fp6.cmov(c0, r0, c),
c1: Fp6.cmov(c1, r1, c),
});
}
// Utils
// toString() {
// return '' + 'Fp12(' + this.c0 + this.c1 + '* w');
// },
// fromTuple(c: [Fp6, Fp6]) {
// return new Fp12(...c);
// }
fromBigTwelve(tuple) {
const { Fp6 } = this;
if (!Array.isArray(tuple) || tuple.length !== 12)
throw new Error('invalid Fp12.fromBigTwelve');
for (let i = 0; i < 12; i++)
if (typeof tuple[i] !== 'bigint')
throw new Error('invalid Fp12.fromBigTwelve');
const t = tuple;
return this.create({
c0: Fp6.fromBigSix(t.slice(0, 6)),
c1: Fp6.fromBigSix(t.slice(6, 12)),
});
}
// Raises to q**i -th power
frobeniusMap(lhs, power) {
const { Fp6 } = this;
const { Fp2 } = Fp6;
const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power);
const coeff = this.FROBENIUS_COEFFICIENTS[power % 12];
return Object.freeze({
c0: Fp6.frobeniusMap(lhs.c0, power),
c1: Object.freeze({
c0: Fp2.mul(c0, coeff),
c1: Fp2.mul(c1, coeff),
c2: Fp2.mul(c2, coeff),
}),
});
}
mulByFp2({ c0, c1 }, rhs) {
const { Fp6 } = this;
return Object.freeze({
c0: Fp6.mulByFp2(c0, rhs),
c1: Fp6.mulByFp2(c1, rhs),
});
}
conjugate({ c0, c1 }) {
// Reuse `c0` by reference and only negate the `w` coefficient.
return Object.freeze({ c0, c1: this.Fp6.neg(c1) });
}
// Sparse multiplication
mul014({ c0, c1 }, o0, o1, o4) {
const { Fp6 } = this;
const { Fp2 } = Fp6;
let t0 = Fp6.mul01(c0, o0, o1);
let t1 = Fp6.mul1(c1, o4);
return Object.freeze({
c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0
// (c1 + c0) * [o0, o1+o4] - T0 - T1
c1: Fp6.sub(Fp6.sub(Fp6.mul01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), t1),
});
}
mul034({ c0, c1 }, o0, o3, o4) {
const { Fp6 } = this;
const { Fp2 } = Fp6;
const a = Object.freeze({
c0: Fp2.mul(c0.c0, o0),
c1: Fp2.mul(c0.c1, o0),
c2: Fp2.mul(c0.c2, o0),
});
const b = Fp6.mul01(c1, o3, o4);
const e = Fp6.mul01(Fp6.add(c0, c1), Fp2.add(o0, o3), o4);
return Object.freeze({
c0: Fp6.add(Fp6.mulByNonresidue(b), a),
c1: Fp6.sub(e, Fp6.add(a, b)),
});
}
// A cyclotomic group is a subgroup of Fp^n defined by
// GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
// The result of any pairing is in a cyclotomic subgroup
// https://eprint.iacr.org/2009/565.pdf
// https://eprint.iacr.org/2010/354.pdf
_cyclotomicSquare({ c0, c1 }) {
const { Fp6 } = this;
const { Fp2 } = Fp6;
const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0;
const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1;
const { first: t3, second: t4 } = Fp2.Fp4Square(c0c0, c1c1);
const { first: t5, second: t6 } = Fp2.Fp4Square(c1c0, c0c2);
const { first: t7, second: t8 } = Fp2.Fp4Square(c0c1, c1c2);
const t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1)
return Object.freeze({
c0: Object.freeze({
c0: Fp2.add(Fp2.mul(Fp2.sub(t3, c0c0), _2n), t3), // 2 * (T3 - c0c0) + T3
c1: Fp2.add(Fp2.mul(Fp2.sub(t5, c0c1), _2n), t5), // 2 * (T5 - c0c1) + T5
c2: Fp2.add(Fp2.mul(Fp2.sub(t7, c0c2), _2n), t7),
}), // 2 * (T7 - c0c2) + T7
c1: Object.freeze({
c0: Fp2.add(Fp2.mul(Fp2.add(t9, c1c0), _2n), t9), // 2 * (T9 + c1c0) + T9
c1: Fp2.add(Fp2.mul(Fp2.add(t4, c1c1), _2n), t4), // 2 * (T4 + c1c1) + T4
c2: Fp2.add(Fp2.mul(Fp2.add(t6, c1c2), _2n), t6),
}),
}); // 2 * (T6 + c1c2) + T6
}
// https://eprint.iacr.org/2009/565.pdf
_cyclotomicExp(num, n) {
// The loop only consumes `X_LEN` bits, so out-of-range exponents would otherwise get silently
// truncated (or sign-extended for negatives) instead of matching the caller's requested power.
aInRange('cyclotomic exponent', n, _0n, _1n << BigInt(this.X_LEN));
let z = this.ONE;
for (let i = this.X_LEN - 1; i >= 0; i--) {
z = this._cyclotomicSquare(z);
if (bitGet(n, i))
z = this.mul(z, num);
}
return z;
}
}
const _FROBENIUS_COEFFICIENTS_12 = new WeakMap();
/**
* @param opts - Tower construction options. See {@link Tower12Opts}.
* @returns BLS tower fields.
* @throws If the tower options or derived Frobenius helpers are invalid. {@link Error}
* @example
* Construct the Fp2/Fp6/Fp12 tower used by a pairing-friendly curve.
*
* ```ts
* const fields = tower12({
* ORDER: 17n,
* X_LEN: 4,
* FP2_NONRESIDUE: [1n, 1n],
* Fp2mulByB: (num) => num,
* Fp12finalExponentiate: (num) => num,
* });
* const fp12 = fields.Fp12.ONE;
* ```
*/
export function tower12(opts) {
validateObject(opts, {
ORDER: 'bigint',
X_LEN: 'number',
FP2_NONRESIDUE: 'object',
Fp2mulByB: 'function',
Fp12finalExponentiate: 'function',
}, { NONRESIDUE: 'bigint' });
asafenumber(opts.X_LEN, 'X_LEN');
if (opts.X_LEN < 1)
throw new Error('invalid X_LEN');
const nonresidue = opts.FP2_NONRESIDUE;
if (!Array.isArray(nonresidue) || nonresidue.length !== 2)
throw new Error('invalid FP2_NONRESIDUE');
if (typeof nonresidue[0] !== 'bigint' || typeof nonresidue[1] !== 'bigint')
throw new Error('invalid FP2_NONRESIDUE');
const Fp = mod.Field(opts.ORDER);
const Fp2 = new _Field2(Fp, opts);
const Fp6 = new _Field6(Fp2);
const Fp12 = new _Field12(Fp6, opts);
return { Fp, Fp2, Fp6, Fp12 };
}
//# sourceMappingURL=tower.js.map

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