Release 1.1.0.

PURE annotation helps bundlers during tree-shaking and eliminates dead code.

* secp256k1: 75.4kb => 62.3kb

* ed25519: 67.5kb => 51.1kb

* ed448: 55.1kb => 44.0kb

* p256: 67.8kb => 59.8kb

* p384: 75.4kb => 67.4kb

* p521: 75.8kb => 67.8kb

.github/workflows/nodejs.yml

@@ -3,15 +3,18 @@ name: Node CI
 on: [push, pull_request]
 jobs:
   test:
-    name: v18 @ ubuntu-latest
+    name: v${{ matrix.node }} @ ubuntu-latest
     runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        node: [18, 20]
     steps:
     - uses: actions/checkout@v3
     - name: Use Node.js ${{ matrix.node }}
       uses: actions/setup-node@v3
       with:
-        node-version: 18
+        node-version: ${{ matrix.node }}
     - run: npm install
     - run: npm run build --if-present
-    - run: npm run lint --if-present
     - run: npm test
+    - run: npm run lint --if-present

.github/workflows/publish-npm.yml

@@ -0,0 +1,23 @@
+name: Publish Package to npm
+on:
+ release:
+   types: [created]
+jobs:
+ build:
+   runs-on: ubuntu-latest
+   permissions:
+     contents: read
+     id-token: write
+   steps:
+     - uses: actions/checkout@8e5e7e5ab8b370d6c329ec480221332ada57f0ab # v3
+     - uses: actions/setup-node@64ed1c7eab4cce3362f8c340dee64e5eaeef8f7c # v3
+       with:
+         node-version: 20
+         registry-url: 'https://registry.npmjs.org'
+         cache: npm
+     - run: npm install -g npm
+     - run: npm ci
+     - run: npm run build
+     - run: npm publish --provenance --access public
+       env:
+         NODE_AUTH_TOKEN: ${{ secrets.NPM_PUBLISH_TOKEN }}

README.md

@@ -8,6 +8,7 @@ Audited & minimal JS implementation of elliptic curve cryptography.
 - 🔍 Unique tests ensure correctness: property-based, cross-library and Wycheproof vectors, fuzzing
 - ➰ Short Weierstrass, Edwards, Montgomery curves
 - ✍️ ECDSA, EdDSA, Schnorr, BLS signature schemes, ECDH key agreement
+- 🔖 SUF-CMA and SBS (non-repudiation) for ed25519, ed448 and others
 - #️⃣ Hash-to-curve
   for encoding or hashing an arbitrary string to an elliptic curve point
 - 🧜‍♂️ Poseidon ZK-friendly hash
@@ -31,41 +32,34 @@ packages. See [Resources](#resources) for articles and real-world software that
 
 ## Usage
 
-Browser, deno and node.js are supported:
-
 > npm install @noble/curves
 
-For [Deno](https://deno.land), use it with
+We support all major platforms and runtimes.
-[npm specifier](https://deno.land/manual@v1.28.0/node/npm_specifiers).
+For [Deno](https://deno.land), ensure to use [npm specifier](https://deno.land/manual@v1.28.0/node/npm_specifiers).
-In browser, you could also include the single file from
+For React Native, you may need a [polyfill for crypto.getRandomValues](https://github.com/LinusU/react-native-get-random-values).
-[GitHub's releases page](https://github.com/paulmillr/noble-curves/releases).
+If you don't like NPM, a standalone [noble-curves.js](https://github.com/paulmillr/noble-curves/releases) is also available.
 
-The library is tree-shaking-friendly and does NOT expose root entry point as
+The library is tree-shaking-friendly and does not expose root entry point as
-`import c from '@noble/curves'`. Instead, you need to import specific primitives.
+`@noble/curves`. Instead, you need to import specific primitives.
 This is done to ensure small size of your apps.
 
-Package consists of two parts:
+The package consists of two parts:
 
-1. [Implementations](#implementations), utilizing one dependency [noble-hashes](https://github.com/paulmillr/noble-hashes),
+* [Implementations](#implementations), utilizing one dependency [noble-hashes](https://github.com/paulmillr/noble-hashes),
    providing ready-to-use:
    - NIST curves secp256r1 / p256, secp384r1 / p384, secp521r1 / p521
    - SECG curve secp256k1
-   - ed25519 / curve25519 / x25519 / ristretto255,
+   - ed25519 / curve25519 / x25519 / ristretto255, edwards448 / curve448 / x448
-     edwards448 / curve448 / x448
-     implementing
-     [RFC7748](https://www.rfc-editor.org/rfc/rfc7748) /
-     [RFC8032](https://www.rfc-editor.org/rfc/rfc8032) /
-     [FIPS 186-5](https://csrc.nist.gov/publications/detail/fips/186/5/final) /
-     [ZIP215](https://zips.z.cash/zip-0215) standards
    - pairing-friendly curves bls12-381, bn254
    - [pasta](https://electriccoin.co/blog/the-pasta-curves-for-halo-2-and-beyond/) curves
-2. [Abstract](#abstract-api), zero-dependency EC algorithms
+2. [Abstract](#abstract-api), zero-dependency elliptic curve algorithms
 
 ### Implementations
 
-Each curve can be used in the following way:
+#### Generic example for all curves, secp256k1
 
 ```ts
+// Each curve has similar methods
 import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
 // import { secp256k1 } from 'npm:@noble/curves@1.2.0/secp256k1'; // Deno
 const priv = secp256k1.utils.randomPrivateKey();
@@ -79,7 +73,7 @@ const privHex = '46c930bc7bb4db7f55da20798697421b98c4175a52c630294d75a84b9c12623
 const pub2 = secp256k1.getPublicKey(privHex);
 ```
 
-All curves:
+#### All imports
 
 ```typescript
 import { secp256k1, schnorr } from '@noble/curves/secp256k1';
@@ -94,7 +88,7 @@ import { bn254 } from '@noble/curves/bn254';
 import { jubjub } from '@noble/curves/jubjub';
 ```
 
-Recovering public keys from weierstrass ECDSA signatures; using ECDH:
+#### ECDSA public key recovery & ECDH
 
 ```ts
 // extraEntropy https://moderncrypto.org/mail-archive/curves/2017/000925.html
@@ -104,8 +98,7 @@ const someonesPub = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
 const shared = secp256k1.getSharedSecret(priv, someonesPub); // ECDH
 ```
 
-Schnorr signatures over secp256k1 following
+#### Schnorr signatures over secp256k1 (BIP340)
-[BIP340](https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki):
 
 ```ts
 import { schnorr } from '@noble/curves/secp256k1';
@@ -116,12 +109,7 @@ const sig = schnorr.sign(msg, priv);
 const isValid = schnorr.verify(sig, msg, pub);
 ```
 
-ed25519 module has ed25519ctx / ed25519ph variants,
+#### ed25519, X25519, ristretto255
-x25519 ECDH and [ristretto255](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448).
-
-Default `verify` behavior follows [ZIP215](https://zips.z.cash/zip-0215) and
-[can be used in consensus-critical applications](https://hdevalence.ca/blog/2020-10-04-its-25519am).
-`zip215: false` option switches verification criteria to RFC8032 / FIPS 186-5.
 
 ```ts
 import { ed25519 } from '@noble/curves/ed25519';
@@ -131,7 +119,19 @@ const msg = new TextEncoder().encode('hello');
 const sig = ed25519.sign(msg, priv);
 ed25519.verify(sig, msg, pub); // Default mode: follows ZIP215
 ed25519.verify(sig, msg, pub, { zip215: false }); // RFC8032 / FIPS 186-5
+```
 
+Default `verify` behavior follows [ZIP215](https://zips.z.cash/zip-0215) and
+[can be used in consensus-critical applications](https://hdevalence.ca/blog/2020-10-04-its-25519am).
+It has SUF-CMA (strong unforgeability under chosen message attacks).
+`zip215: false` option switches verification criteria to strict
+[RFC8032](https://www.rfc-editor.org/rfc/rfc8032) / [FIPS 186-5](https://csrc.nist.gov/publications/detail/fips/186/5/final)
+and additionally provides non-repudiation with SBS [(Strongly Binding Signatures)](https://eprint.iacr.org/2020/1244).
+
+X25519 follows [RFC7748](https://www.rfc-editor.org/rfc/rfc7748).
+ristretto255 follows [irtf draft](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448).
+
+```ts
 // Variants from RFC8032: with context, prehashed
 import { ed25519ctx, ed25519ph } from '@noble/curves/ed25519';
 
@@ -141,11 +141,15 @@ const priv = 'a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4';
 const pub = 'e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c';
 x25519.getSharedSecret(priv, pub) === x25519.scalarMult(priv, pub); // aliases
 x25519.getPublicKey(priv) === x25519.scalarMultBase(priv);
+x25519.getPublicKey(x25519.utils.randomPrivateKey());
 
-// hash-to-curve
+// ed25519 => x25519 conversion
-import { hashToCurve, encodeToCurve } from '@noble/curves/ed25519';
+import { edwardsToMontgomeryPub, edwardsToMontgomeryPriv } from '@noble/curves/ed25519';
+edwardsToMontgomeryPub(ed25519.getPublicKey(ed25519.utils.randomPrivateKey()));
+edwardsToMontgomeryPriv(ed25519.utils.randomPrivateKey());
 
-import { RistrettoPoint } from '@noble/curves/ed25519';
+// hash-to-curve, ristretto255
+import { hashToCurve, encodeToCurve, RistrettoPoint } from '@noble/curves/ed25519';
 const rp = RistrettoPoint.fromHex(
   '6a493210f7499cd17fecb510ae0cea23a110e8d5b901f8acadd3095c73a3b919'
 );
@@ -153,19 +157,36 @@ RistrettoPoint.hashToCurve('Ristretto is traditionally a short shot of espresso
 // also has add(), equals(), multiply(), toRawBytes() methods
 ```
 
-ed448 is similar:
+#### ed448, X448
 
 ```ts
-import { ed448, ed448ph, ed448ctx, x448 } from '@noble/curves/ed448';
+import { ed448 } from '@noble/curves/ed448';
-import { hashToCurve, encodeToCurve } from '@noble/curves/ed448';
+const priv = ed448.utils.randomPrivateKey();
-ed448.getPublicKey(ed448.utils.randomPrivateKey());
+const pub = ed448.getPublicKey(priv);
+const msg = new TextEncoder().encode('whatsup');
+const sig = ed448.sign(msg, priv);
+ed448.verify(sig, msg, pub);
+
+import { ed448ph, ed448ctx, x448, hashToCurve, encodeToCurve } from '@noble/curves/ed448';
+x448.getSharedSecret(priv, pub) === x448.scalarMult(priv, pub); // aliases
+x448.getPublicKey(priv) === x448.scalarMultBase(priv);
 ```
 
-Every curve has `CURVE` object that contains its parameters, field, and others:
+Same RFC7748 / RFC8032 are followed.
+
+#### bls12-381
+
+See [abstract/bls](#abstractbls-barreto-lynn-scott-curves).
+
+#### Accessing a curve's variables
 
 ```ts
-import { secp256k1 } from '@noble/curves/secp256k1'; // ESM and Common.js
+import { secp256k1 } from '@noble/curves/secp256k1';
-console.log(secp256k1.CURVE.p, secp256k1.CURVE.n, secp256k1.CURVE.a, secp256k1.CURVE.b);
+// Every curve has `CURVE` object that contains its parameters, field, and others
+console.log(secp256k1.CURVE.p); // field modulus
+console.log(secp256k1.CURVE.n); // curve order
+console.log(secp256k1.CURVE.a, secp256k1.CURVE.b); // equation params
+console.log(secp256k1.CURVE.Gx, secp256k1.CURVE.Gy); // base point coordinates
 ```
 
 ## Abstract API
@@ -734,9 +755,9 @@ utils.equalBytes(Uint8Array.from([0xde]), Uint8Array.from([0xde]));
 
 ## Security
 
-1. The library has been audited during Jan-Feb 2023 by an independent security firm [Trail of Bits](https://www.trailofbits.com):
+1. The library has been audited in Feb 2023 by an independent security firm [Trail of Bits](https://www.trailofbits.com):
 [PDF](https://github.com/trailofbits/publications/blob/master/reviews/2023-01-ryanshea-noblecurveslibrary-securityreview.pdf).
-The audit has been funded by Ryan Shea. Audit scope was abstract modules `curve`, `hash-to-curve`, `modular`, `poseidon`, `utils`, `weierstrass`, and top-level modules `_shortw_utils` and `secp256k1`. See [changes since audit](https://github.com/paulmillr/noble-curves/compare/0.7.3..main).
+The audit has been funded by [Ryan Shea](https://www.shea.io). Audit scope was abstract modules `curve`, `hash-to-curve`, `modular`, `poseidon`, `utils`, `weierstrass`, and top-level modules `_shortw_utils` and `secp256k1`. See [changes since audit](https://github.com/paulmillr/noble-curves/compare/0.7.3..main).
 2. The library has been fuzzed by [Guido Vranken's cryptofuzz](https://github.com/guidovranken/cryptofuzz). You can run the fuzzer by yourself to check it.
 3. [Timing attack](https://en.wikipedia.org/wiki/Timing_attack) considerations: _JIT-compiler_ and _Garbage Collector_ make "constant time" extremely hard to achieve 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. Nonetheless we're targetting algorithmic constant time.
 
@@ -749,81 +770,89 @@ We consider infrastructure attacks like rogue NPM modules very important; that's
   The packages are big, which makes it hard to audit their source code thoroughly and fully.
 - They are only used if you clone the git repo and want to add some feature to it. End-users won't use them.
 
+As for key generation, we're deferring to built-in
+[crypto.getRandomValues](https://developer.mozilla.org/en-US/docs/Web/API/Crypto/getRandomValues)
+which is considered cryptographically secure (CSPRNG).
+
 ## Speed
 
-Benchmark results on Apple M2 with node v19:
+Benchmark results on Apple M2 with node v20:
 
 ```
 secp256k1
-init x 58 ops/sec @ 17ms/op
+init x 68 ops/sec @ 14ms/op
-getPublicKey x 5,640 ops/sec @ 177μs/op
+getPublicKey x 6,750 ops/sec @ 148μs/op
-sign x 4,471 ops/sec @ 223μs/op
+sign x 5,206 ops/sec @ 192μs/op
-verify x 780 ops/sec @ 1ms/op
+verify x 880 ops/sec @ 1ms/op
-getSharedSecret x 465 ops/sec @ 2ms/op
+getSharedSecret x 536 ops/sec @ 1ms/op
-recoverPublicKey x 740 ops/sec @ 1ms/op
+recoverPublicKey x 852 ops/sec @ 1ms/op
-schnorr.sign x 597 ops/sec @ 1ms/op
+schnorr.sign x 685 ops/sec @ 1ms/op
-schnorr.verify x 775 ops/sec @ 1ms/op
+schnorr.verify x 908 ops/sec @ 1ms/op
 
-P256
+p256
-init x 31 ops/sec @ 31ms/op
+init x 38 ops/sec @ 26ms/op
-getPublicKey x 5,607 ops/sec @ 178μs/op
+getPublicKey x 6,530 ops/sec @ 153μs/op
-sign x 4,583 ops/sec @ 218μs/op
+sign x 5,074 ops/sec @ 197μs/op
-verify x 540 ops/sec @ 1ms/op
+verify x 626 ops/sec @ 1ms/op
 
-P384
+p384
-init x 15 ops/sec @ 63ms/op
+init x 17 ops/sec @ 57ms/op
-getPublicKey x 2,622 ops/sec @ 381μs/op
+getPublicKey x 2,883 ops/sec @ 346μs/op
-sign x 2,106 ops/sec @ 474μs/op
+sign x 2,358 ops/sec @ 424μs/op
-verify x 222 ops/sec @ 4ms/op
+verify x 245 ops/sec @ 4ms/op
 
-P521
+p521
-init x 8 ops/sec @ 119ms/op
+init x 9 ops/sec @ 109ms/op
-getPublicKey x 1,371 ops/sec @ 729μs/op
+getPublicKey x 1,516 ops/sec @ 659μs/op
-sign x 1,164 ops/sec @ 858μs/op
+sign x 1,271 ops/sec @ 786μs/op
-verify x 118 ops/sec @ 8ms/op
+verify x 123 ops/sec @ 8ms/op
 
 ed25519
-init x 47 ops/sec @ 20ms/op
+init x 54 ops/sec @ 18ms/op
-getPublicKey x 9,414 ops/sec @ 106μs/op
+getPublicKey x 10,269 ops/sec @ 97μs/op
-sign x 4,516 ops/sec @ 221μs/op
+sign x 5,110 ops/sec @ 195μs/op
-verify x 912 ops/sec @ 1ms/op
+verify x 1,049 ops/sec @ 952μs/op
 
 ed448
-init x 17 ops/sec @ 56ms/op
+init x 19 ops/sec @ 51ms/op
-getPublicKey x 3,363 ops/sec @ 297μs/op
+getPublicKey x 3,775 ops/sec @ 264μs/op
-sign x 1,615 ops/sec @ 619μs/op
+sign x 1,771 ops/sec @ 564μs/op
-verify x 319 ops/sec @ 3ms/op
+verify x 351 ops/sec @ 2ms/op
 
 ecdh
-├─x25519 x 1,337 ops/sec @ 747μs/op
+├─x25519 x 1,466 ops/sec @ 682μs/op
-├─secp256k1 x 461 ops/sec @ 2ms/op
+├─secp256k1 x 539 ops/sec @ 1ms/op
-├─P256 x 441 ops/sec @ 2ms/op
+├─p256 x 511 ops/sec @ 1ms/op
-├─P384 x 179 ops/sec @ 5ms/op
+├─p384 x 199 ops/sec @ 5ms/op
-├─P521 x 93 ops/sec @ 10ms/op
+├─p521 x 103 ops/sec @ 9ms/op
-└─x448 x 496 ops/sec @ 2ms/op
+└─x448 x 548 ops/sec @ 1ms/op
 
 bls12-381
-init x 32 ops/sec @ 30ms/op
+init x 36 ops/sec @ 27ms/op
-getPublicKey 1-bit x 858 ops/sec @ 1ms/op
+getPublicKey 1-bit x 973 ops/sec @ 1ms/op
-getPublicKey x 858 ops/sec @ 1ms/op
+getPublicKey x 970 ops/sec @ 1ms/op
-sign x 49 ops/sec @ 20ms/op
+sign x 55 ops/sec @ 17ms/op
-verify x 34 ops/sec @ 28ms/op
+verify x 39 ops/sec @ 25ms/op
-pairing x 94 ops/sec @ 10ms/op
+pairing x 106 ops/sec @ 9ms/op
-aggregatePublicKeys/8 x 116 ops/sec @ 8ms/op
+aggregatePublicKeys/8 x 129 ops/sec @ 7ms/op
-aggregatePublicKeys/32 x 31 ops/sec @ 31ms/op
+aggregatePublicKeys/32 x 34 ops/sec @ 28ms/op
-aggregatePublicKeys/128 x 7 ops/sec @ 125ms/op
+aggregatePublicKeys/128 x 8 ops/sec @ 112ms/op
-aggregateSignatures/8 x 45 ops/sec @ 22ms/op
+aggregatePublicKeys/512 x 2 ops/sec @ 446ms/op
-aggregateSignatures/32 x 11 ops/sec @ 84ms/op
+aggregatePublicKeys/2048 x 0 ops/sec @ 1778ms/op
-aggregateSignatures/128 x 3 ops/sec @ 332ms/opp
+aggregateSignatures/8 x 50 ops/sec @ 19ms/op
+aggregateSignatures/32 x 13 ops/sec @ 74ms/op
+aggregateSignatures/128 x 3 ops/sec @ 296ms/op
+aggregateSignatures/512 x 0 ops/sec @ 1180ms/op
+aggregateSignatures/2048 x 0 ops/sec @ 4715ms/op
 
 hash-to-curve
-hash_to_field x 850,340 ops/sec @ 1μs/op
+hash_to_field x 91,600 ops/sec @ 10μs/op
-secp256k1 x 2,143 ops/sec @ 466μs/op
+secp256k1 x 2,373 ops/sec @ 421μs/op
-P256 x 3,861 ops/sec @ 258μs/op
+p256 x 4,310 ops/sec @ 231μs/op
-P384 x 1,526 ops/sec @ 655μs/op
+p384 x 1,664 ops/sec @ 600μs/op
-P521 x 748 ops/sec @ 1ms/op
+p521 x 807 ops/sec @ 1ms/op
-ed25519 x 2,772 ops/sec @ 360μs/op
+ed25519 x 3,088 ops/sec @ 323μs/op
-ed448 x 1,146 ops/sec @ 871μs/op
+ed448 x 1,247 ops/sec @ 801μs/op
 ```
 
 ## Contributing & testing
@@ -836,9 +865,11 @@ ed448 x 1,146 ops/sec @ 871μs/op
 ## Upgrading
 
 Previously, the library was split into single-feature packages
-noble-secp256k1 and noble-ed25519. curves can be thought as a continuation of their
+noble-secp256k1, noble-ed25519 and noble-bls12-381.
-original work. The libraries now changed their direction towards providing
+
-minimal 4kb implementations of cryptography and are not as feature-complete.
+Curves continue their original work. The single-feature packages changed their
+direction towards providing minimal 4kb implementations of cryptography,
+which means they have less features.
 
 Upgrading from @noble/secp256k1 2.0 or @noble/ed25519 2.0: no changes, libraries are compatible.
 
@@ -878,6 +909,7 @@ Upgrading from [@noble/ed25519](https://github.com/paulmillr/noble-ed25519) 1.7:
 - `utils` were split into `utils` (same api as in noble-curves) and
   `etc` (`sha512Sync` and others)
 - `getSharedSecret` was moved to `x25519` module
+- `toX25519` has been moved to `edwardsToMontgomeryPub` and `edwardsToMontgomeryPriv` methods
 
 Upgrading from [@noble/bls12-381](https://github.com/paulmillr/noble-bls12-381):
 
@@ -888,10 +920,13 @@ Upgrading from [@noble/bls12-381](https://github.com/paulmillr/noble-bls12-381):
 
 ## Resources
 
-Useful articles about the library or its primitives:
+Useful documentation and articles about the library or its primitives:
 
 - [Learning fast elliptic-curve cryptography](https://paulmillr.com/posts/noble-secp256k1-fast-ecc/)
+- [Taming the many EdDSAs](https://csrc.nist.gov/csrc/media/Presentations/2023/crclub-2023-03-08/images-media/20230308-crypto-club-slides--taming-the-many-EdDSAs.pdf)
+  that describes concepts of Strong UnForgeability under Chosen Message Attacks and Strongly Binding Signatures
 - Pairings and BLS
+    - [BLS signatures for busy people](https://gist.github.com/paulmillr/18b802ad219b1aee34d773d08ec26ca2)
     - [BLS12-381 for the rest of us](https://hackmd.io/@benjaminion/bls12-381)
     - [Key concepts of pairings](https://medium.com/@alonmuroch_65570/bls-signatures-part-2-key-concepts-of-pairings-27a8a9533d0c)
     - Pairing over bls12-381:
@@ -900,17 +935,31 @@ Useful articles about the library or its primitives:
       [part 3](https://research.nccgroup.com/2020/08/13/pairing-over-bls12-381-part-3-pairing/)
     - [Estimating the bit security of pairing-friendly curves](https://research.nccgroup.com/2022/02/03/estimating-the-bit-security-of-pairing-friendly-curves/)
 
-Real-world software that uses curves:
+Online demos:
+
+- [Elliptic Curve Calculator](https://paulmillr.com/noble): add / multiply points, sign messages
+- [BLS threshold signatures](https://genthresh.com)
+
+Projects using noble-curves:
 
-- [Elliptic Curve Calculator](https://paulmillr.com/noble) online demo: add / multiply points, sign messages
-- Signers for web3 projects:
-  [btc-signer](https://github.com/paulmillr/scure-btc-signer), [eth-signer](https://github.com/paulmillr/micro-eth-signer),
-  [sol-signer](https://github.com/paulmillr/micro-sol-signer) for Solana
 - [scure-bip32](https://github.com/paulmillr/scure-bip32) and separate [bip32](https://github.com/bitcoinjs/bip32) HDkey libraries
+- Ethereum libraries:
+    - [ethereum-cryptography](https://github.com/ethereum/js-ethereum-cryptography)
+    - [@ethereumjs](https://github.com/ethereumjs/ethereumjs-monorepo)
+    - [micro-eth-signer](https://github.com/paulmillr/micro-eth-signer)
+    - [ethers](https://github.com/ethers-io/ethers.js) (old noble-secp256k1 for now)
+    - [viem.sh](https://viem.sh)
+    - [metamask's eth-sig-util](https://github.com/MetaMask/eth-sig-util)
+    - [gridplus lattice sdk](https://github.com/GridPlus/lattice-eth2-utils)
+- Bitcoin libraries: [scure-btc-signer](https://github.com/paulmillr/scure-btc-signer)
+- Solana libraries: [micro-sol-signer](https://github.com/paulmillr/micro-sol-signer), [solana-web3.js](https://github.com/solana-labs/solana-web3.js)
+- [polkadot.js](https://github.com/polkadot-js/common), [micro-starknet](https://github.com/paulmillr/micro-starknet)
+- [protonmail](https://github.com/ProtonMail/WebClients) (old noble-ed25519 for now)
+- [did-jwt](https://github.com/decentralized-identity/did-jwt), [hpke-js](https://github.com/dajiaji/hpke-js), [nostr-tools](https://github.com/nbd-wtf/nostr-tools)
 - [ed25519-keygen](https://github.com/paulmillr/ed25519-keygen) SSH, PGP, TOR key generation
-- [micro-starknet](https://github.com/paulmillr/micro-starknet) stark-friendly elliptic curve algorithms.
+- [secp256k1 compatibility layer](https://github.com/ethereum/js-ethereum-cryptography/blob/2.0.0/src/secp256k1-compat.ts)
-- BLS threshold sigs demo [genthresh.com](https://genthresh.com)
+for users who want to switch from secp256k1-node or tiny-secp256k1. Allows to see which methods map to corresponding noble code.
-- BLS BBS signatures [github.com/Wind4Greg/BBS-Draft-Checks](https://github.com/Wind4Greg/BBS-Draft-Checks) following [draft-irtf-cfrg-bbs-signatures-latest](https://identity.foundation/bbs-signature/draft-irtf-cfrg-bbs-signatures.html)
+- [BLS BBS signatures](https://github.com/Wind4Greg/BBS-Draft-Checks) following [draft-irtf-cfrg-bbs-signatures-latest](https://identity.foundation/bbs-signature/draft-irtf-cfrg-bbs-signatures.html)
 - [KZG trusted setup ceremony](https://github.com/dsrvlabs/czg-keremony)
 
 ## License

benchmark/bls.js

@@ -39,6 +39,21 @@ run(async () => {
   await mark('sign', 50, () => bls.sign('09', priv));
   await mark('verify', 50, () => bls.verify(sig, '09', pub));
   await mark('pairing', 100, () => bls.pairing(p1, p2));
+
+  const scalars1 = Array(4096).fill(0).map(i => 2n ** 235n - BigInt(i));
+  const scalars2 = Array(4096).fill(0).map(i => 2n ** 241n + BigInt(i));
+  const points = scalars1.map(s => bls.G1.ProjectivePoint.BASE.multiply(s));
+  await mark('MSM 4096 scalars x points', 1, () => {
+    // naive approach, not using multi-scalar-multiplication
+    let sum = bls.G1.ProjectivePoint.ZERO;
+    for (let i = 0; i < 4096; i++) {
+      const scalar = scalars2[i];
+      const G1 = points[i];
+      const mutliplied = G1.multiplyUnsafe(scalar);
+      sum = sum.add(mutliplied);
+    }
+  });
+
   await mark('aggregatePublicKeys/8', 100, () => bls.aggregatePublicKeys(pubs.slice(0, 8)));
   await mark('aggregatePublicKeys/32', 50, () => bls.aggregatePublicKeys(pub32));
   await mark('aggregatePublicKeys/128', 20, () => bls.aggregatePublicKeys(pub128));

benchmark/curves.js

@@ -8,7 +8,7 @@ import { ed448 } from '../ed448.js';
 
 run(async () => {
   const RAM = false
-  for (let kv of Object.entries({ p256, p384, p521, ed25519, ed448 })) {
+  for (let kv of Object.entries({ ed25519, ed448, p256, p384, p521 })) {
     const [name, curve] = kv;
     console.log();
     console.log(`\x1b[36m${name}\x1b[0m`);

build/README.md

@@ -0,0 +1,7 @@
+# build
+
+The directory is used to build a single file `noble-curves.js` which contains everything.
+
+The output file uses iife wrapper and can be used in browsers as-is.
+
+Don't use it unless you can't use NPM/ESM, which support tree shaking.

build/input.js

@@ -0,0 +1,11 @@
+import { bytesToHex, concatBytes, hexToBytes } from '@noble/curves/abstract/utils';
+
+export { secp256k1 } from '@noble/curves/secp256k1';
+export { ed25519, x25519 } from '@noble/curves/ed25519';
+export { ed448, x448 } from '@noble/curves/ed448';
+export { p256 } from '@noble/curves/p256';
+export { p384 } from '@noble/curves/p384';
+export { p521 } from '@noble/curves/p521';
+export { bls12_381 } from '@noble/curves/bls12-381';
+
+export const utils = { bytesToHex, concatBytes, hexToBytes };

build/package.json

@@ -0,0 +1,18 @@
+{
+  "name": "build",
+  "private": true,
+  "version": "1.0.0",
+  "description": "Used to build a single file",
+  "main": "input.js",
+  "keywords": [],
+  "type": "module",
+  "author": "",
+  "license": "MIT",
+  "devDependencies": {
+    "@noble/curves": "..",
+    "esbuild": "0.17.19"
+  },
+  "scripts": {
+    "build": "npx esbuild --bundle input.js --outfile=noble-curves.js --global-name=nobleCurves"
+  }
+}

package-lock.json

@@ -1,21 +1,15 @@
 {
   "name": "@noble/curves",
-  "version": "1.0.0",
+  "version": "1.1.0",
   "lockfileVersion": 3,
   "requires": true,
   "packages": {
     "": {
       "name": "@noble/curves",
-      "version": "1.0.0",
+      "version": "1.1.0",
-      "funding": [
-        {
-          "type": "individual",
-          "url": "https://paulmillr.com/funding/"
-        }
-      ],
       "license": "MIT",
       "dependencies": {
-        "@noble/hashes": "1.3.0"
+        "@noble/hashes": "1.3.1"
       },
       "devDependencies": {
         "fast-check": "3.0.0",
@@ -23,18 +17,21 @@
         "micro-should": "0.4.0",
         "prettier": "2.8.4",
         "typescript": "5.0.2"
+      },
+      "funding": {
+        "url": "https://paulmillr.com/funding/"
       }
     },
     "node_modules/@noble/hashes": {
-      "version": "1.3.0",
+      "version": "1.3.1",
-      "resolved": "https://registry.npmjs.org/@noble/hashes/-/hashes-1.3.0.tgz",
+      "resolved": "https://registry.npmjs.org/@noble/hashes/-/hashes-1.3.1.tgz",
-      "integrity": "sha512-ilHEACi9DwqJB0pw7kv+Apvh50jiiSyR/cQ3y4W7lOR5mhvn/50FLUfsnfJz0BDZtl/RR16kXvptiv6q1msYZg==",
+      "integrity": "sha512-EbqwksQwz9xDRGfDST86whPBgM65E0OH/pCgqW0GBVzO22bNE+NuIbeTb714+IfSjU3aRk47EUvXIb5bTsenKA==",
-      "funding": [
+      "engines": {
-        {
+        "node": ">= 16"
-          "type": "individual",
+      },
+      "funding": {
         "url": "https://paulmillr.com/funding/"
       }
-      ]
     },
     "node_modules/fast-check": {
       "version": "3.0.0",

package.json

@@ -1,6 +1,6 @@
 {
   "name": "@noble/curves",
-  "version": "1.0.0",
+  "version": "1.1.0",
   "description": "Audited & minimal JS implementation of elliptic curve cryptography",
   "files": [
     "abstract",
@@ -28,7 +28,7 @@
   },
   "license": "MIT",
   "dependencies": {
-    "@noble/hashes": "1.3.0"
+    "@noble/hashes": "1.3.1"
   },
   "devDependencies": {
     "fast-check": "3.0.0",
@@ -164,6 +164,8 @@
     "secp256k1",
     "ed25519",
     "ed448",
+    "x25519",
+    "ed25519",
     "bls12-381",
     "bn254",
     "pasta",
@@ -174,10 +176,5 @@
     "eddsa",
     "schnorr"
   ],
-  "funding": [
+  "funding": "https://paulmillr.com/funding/"
-    {
-      "type": "individual",
-      "url": "https://paulmillr.com/funding/"
-    }
-  ]
 }

src/abstract/edwards.ts

@@ -75,8 +75,13 @@ export interface ExtPointConstructor extends GroupConstructor<ExtPointType> {
 export type CurveFn = {
   CURVE: ReturnType<typeof validateOpts>;
   getPublicKey: (privateKey: Hex) => Uint8Array;
-  sign: (message: Hex, privateKey: Hex) => Uint8Array;
+  sign: (message: Hex, privateKey: Hex, options?: { context?: Hex }) => Uint8Array;
-  verify: (sig: Hex, message: Hex, publicKey: Hex) => boolean;
+  verify: (
+    sig: Hex,
+    message: Hex,
+    publicKey: Hex,
+    options?: { context?: Hex; zip215: boolean }
+  ) => boolean;
   ExtendedPoint: ExtPointConstructor;
   utils: {
     randomPrivateKey: () => Uint8Array;
@@ -102,7 +107,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     nByteLength,
     h: cofactor,
   } = CURVE;
-  const MASK = _2n ** BigInt(nByteLength * 8);
+  const MASK = _2n << (BigInt(nByteLength * 8) - _1n);
   const modP = Fp.create; // Function overrides
 
   // sqrt(u/v)
@@ -379,7 +384,10 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       let { isValid, value: x } = uvRatio(u, v); // √(u/v)
       if (!isValid) throw new Error('Point.fromHex: 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; // if x=0 and x_0 = 1, fail
+      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('Point.fromHex: 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 });
     }
@@ -466,6 +474,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     } catch (error) {
       return false;
     }
+    if (!zip215 && A.isSmallOrder()) return false;
 
     const k = hashDomainToScalar(context, R.toRawBytes(), A.toRawBytes(), msg);
     const RkA = R.add(A.multiplyUnsafe(k));

src/abstract/modular.ts

@@ -22,10 +22,10 @@ export function mod(a: bigint, b: bigint): bigint {
   return result >= _0n ? result : b + result;
 }
 /**
- * Efficiently exponentiate num to power and do modular division.
+ * Efficiently raise num to power and do modular division.
  * Unsafe in some contexts: uses ladder, so can expose bigint bits.
  * @example
- * powMod(2n, 6n, 11n) // 64n % 11n == 9n
+ * pow(2n, 6n, 11n) // 64n % 11n == 9n
  */
 // TODO: use field version && remove
 export function pow(num: bigint, power: bigint, modulo: bigint): bigint {
@@ -55,7 +55,7 @@ export function invert(number: bigint, modulo: bigint): bigint {
   if (number === _0n || modulo <= _0n) {
     throw new Error(`invert: expected positive integers, got n=${number} mod=${modulo}`);
   }
-  // Eucledian GCD https://brilliant.org/wiki/extended-euclidean-algorithm/
+  // Euclidean GCD https://brilliant.org/wiki/extended-euclidean-algorithm/
   // 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;
@@ -198,10 +198,6 @@ export function FpSqrt(P: bigint) {
 // Little-endian check for first LE bit (last BE bit);
 export const isNegativeLE = (num: bigint, modulo: bigint) => (mod(num, modulo) & _1n) === _1n;
 
-// Currently completly inconsistent naming:
-// - readable: add, mul, sqr, sqrt, inv, div, pow, eq, sub
-// - unreadable mess: addition, multiply, square, squareRoot, inversion, divide, power, equals, subtract
-
 // Field is not always over prime, Fp2 for example has ORDER(q)=p^m
 export interface IField<T> {
   ORDER: bigint;
@@ -406,10 +402,12 @@ export function FpSqrtEven<T>(Fp: IField<T>, elm: T) {
 /**
  * FIPS 186 B.4.1-compliant "constant-time" private key generation utility.
  * Can take (n+8) or more bytes of uniform input e.g. from CSPRNG or KDF
- * and convert them into private scalar, with the modulo bias being neglible.
+ * and convert them into private scalar, with the modulo bias being negligible.
  * Needs at least 40 bytes of input for 32-byte private key.
  * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
  * @param hash hash output from SHA3 or a similar function
+ * @param groupOrder size of subgroup - (e.g. curveFn.CURVE.n)
+ * @param isLE interpret hash bytes as LE num
  * @returns valid private scalar
  */
 export function hashToPrivateScalar(

src/abstract/utils.ts

@@ -1,13 +1,14 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+// 100 lines of code in the file are duplicated from noble-hashes (utils).
+// This is OK: `abstract` directory does not use noble-hashes.
+// User may opt-in into using different hashing library. This way, noble-hashes
+// won't be included into their bundle.
 const _0n = BigInt(0);
 const _1n = BigInt(1);
 const _2n = BigInt(2);
 const u8a = (a: any): a is Uint8Array => a instanceof Uint8Array;
-
+export type Hex = Uint8Array | string; // hex strings are accepted for simplicity
-// We accept hex strings besides Uint8Array for simplicity
+export type PrivKey = Hex | bigint; // bigints are accepted to ease learning curve
-export type Hex = Uint8Array | string;
-// Very few implementations accept numbers, we do it to ease learning curve
-export type PrivKey = Hex | bigint;
 export type CHash = {
   (message: Uint8Array | string): Uint8Array;
   blockLen: number;
@@ -17,6 +18,9 @@ export type CHash = {
 export type FHash = (message: Uint8Array | string) => Uint8Array;
 
 const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
+/**
+ * @example bytesToHex(Uint8Array.from([0xca, 0xfe, 0x01, 0x23])) // 'cafe0123'
+ */
 export function bytesToHex(bytes: Uint8Array): string {
   if (!u8a(bytes)) throw new Error('Uint8Array expected');
   // pre-caching improves the speed 6x
@@ -38,22 +42,25 @@ export function hexToNumber(hex: string): bigint {
   return BigInt(hex === '' ? '0' : `0x${hex}`);
 }
 
-// Caching slows it down 2-3x
+/**
+ * @example hexToBytes('cafe0123') // Uint8Array.from([0xca, 0xfe, 0x01, 0x23])
+ */
 export function hexToBytes(hex: string): Uint8Array {
   if (typeof hex !== 'string') throw new Error('hex string expected, got ' + typeof hex);
-  if (hex.length % 2) throw new Error('hex string is invalid: unpadded ' + hex.length);
+  const len = hex.length;
-  const array = new Uint8Array(hex.length / 2);
+  if (len % 2) throw new Error('padded hex string expected, got unpadded hex of length ' + len);
+  const array = new Uint8Array(len / 2);
   for (let i = 0; i < array.length; i++) {
     const j = i * 2;
     const hexByte = hex.slice(j, j + 2);
     const byte = Number.parseInt(hexByte, 16);
-    if (Number.isNaN(byte) || byte < 0) throw new Error('invalid byte sequence');
+    if (Number.isNaN(byte) || byte < 0) throw new Error('Invalid byte sequence');
     array[i] = byte;
   }
   return array;
 }
 
-// Big Endian
+// BE: Big Endian, LE: Little Endian
 export function bytesToNumberBE(bytes: Uint8Array): bigint {
   return hexToNumber(bytesToHex(bytes));
 }
@@ -62,12 +69,26 @@ export function bytesToNumberLE(bytes: Uint8Array): bigint {
   return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));
 }
 
-export const numberToBytesBE = (n: bigint, len: number) =>
+export function numberToBytesBE(n: number | bigint, len: number): Uint8Array {
-  hexToBytes(n.toString(16).padStart(len * 2, '0'));
+  return hexToBytes(n.toString(16).padStart(len * 2, '0'));
-export const numberToBytesLE = (n: bigint, len: number) => numberToBytesBE(n, len).reverse();
+}
-// Returns variable number bytes (minimal bigint encoding?)
+export function numberToBytesLE(n: number | bigint, len: number): Uint8Array {
-export const numberToVarBytesBE = (n: bigint) => hexToBytes(numberToHexUnpadded(n));
+  return numberToBytesBE(n, len).reverse();
+}
+// Unpadded, rarely used
+export function numberToVarBytesBE(n: number | bigint): Uint8Array {
+  return hexToBytes(numberToHexUnpadded(n));
+}
 
+/**
+ * Takes hex string or Uint8Array, converts to Uint8Array.
+ * Validates output length.
+ * Will throw error for other types.
+ * @param title descriptive title for an error e.g. 'private key'
+ * @param hex hex string or Uint8Array
+ * @param expectedLength optional, will compare to result array's length
+ * @returns
+ */
 export function ensureBytes(title: string, hex: Hex, expectedLength?: number): Uint8Array {
   let res: Uint8Array;
   if (typeof hex === 'string') {
@@ -89,11 +110,13 @@ export function ensureBytes(title: string, hex: Hex, expectedLength?: number): U
   return res;
 }
 
-// Copies several Uint8Arrays into one.
+/**
-export function concatBytes(...arrs: Uint8Array[]): Uint8Array {
+ * Copies several Uint8Arrays into one.
-  const r = new Uint8Array(arrs.reduce((sum, a) => sum + a.length, 0));
+ */
+export function concatBytes(...arrays: Uint8Array[]): Uint8Array {
+  const r = new Uint8Array(arrays.reduce((sum, a) => sum + a.length, 0));
   let pad = 0; // walk through each item, ensure they have proper type
-  arrs.forEach((a) => {
+  arrays.forEach((a) => {
     if (!u8a(a)) throw new Error('Uint8Array expected');
     r.set(a, pad);
     pad += a.length;
@@ -111,29 +134,47 @@ export function equalBytes(b1: Uint8Array, b2: Uint8Array) {
 // Global symbols in both browsers and Node.js since v11
 // See https://github.com/microsoft/TypeScript/issues/31535
 declare const TextEncoder: any;
+
+/**
+ * @example utf8ToBytes('abc') // new Uint8Array([97, 98, 99])
+ */
 export function utf8ToBytes(str: string): Uint8Array {
-  if (typeof str !== 'string') {
+  if (typeof str !== 'string') throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
-    throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
+  return new Uint8Array(new TextEncoder().encode(str)); // https://bugzil.la/1681809
-  }
-  return new TextEncoder().encode(str);
 }
 
 // Bit operations
 
-// Amount of bits inside bigint (Same as n.toString(2).length)
+/**
+ * Calculates amount of bits in a bigint.
+ * Same as `n.toString(2).length`
+ */
 export function bitLen(n: bigint) {
   let len;
   for (len = 0; n > _0n; n >>= _1n, len += 1);
   return len;
 }
-// Gets single bit at position. NOTE: first bit position is 0 (same as arrays)
+
-// Same as !!+Array.from(n.toString(2)).reverse()[pos]
+/**
-export const bitGet = (n: bigint, pos: number) => (n >> BigInt(pos)) & _1n;
+ * Gets single bit at position.
-// Sets single bit at position
+ * NOTE: first bit position is 0 (same as arrays)
-export const bitSet = (n: bigint, pos: number, value: boolean) =>
+ * Same as `!!+Array.from(n.toString(2)).reverse()[pos]`
-  n | ((value ? _1n : _0n) << BigInt(pos));
+ */
-// Return mask for N bits (Same as BigInt(`0b${Array(i).fill('1').join('')}`))
+export function bitGet(n: bigint, pos: number) {
-// Not using ** operator with bigints for old engines.
+  return (n >> BigInt(pos)) & _1n;
+}
+
+/**
+ * Sets single bit at position.
+ */
+export const bitSet = (n: bigint, pos: number, value: boolean) => {
+  return n | ((value ? _1n : _0n) << BigInt(pos));
+};
+
+/**
+ * Calculate mask for N bits. Not using ** operator with bigints because of old engines.
+ * Same as BigInt(`0b${Array(i).fill('1').join('')}`)
+ */
 export const bitMask = (n: number) => (_2n << BigInt(n - 1)) - _1n;
 
 // DRBG

src/abstract/weierstrass.ts

@@ -618,7 +618,7 @@ export interface SignatureType {
   readonly s: bigint;
   readonly recovery?: number;
   assertValidity(): void;
-  addRecoveryBit(recovery: number): SignatureType;
+  addRecoveryBit(recovery: number): RecoveredSignatureType;
   hasHighS(): boolean;
   normalizeS(): SignatureType;
   recoverPublicKey(msgHash: Hex): ProjPointType<bigint>;
@@ -628,6 +628,9 @@ export interface SignatureType {
   toDERRawBytes(isCompressed?: boolean): Uint8Array;
   toDERHex(isCompressed?: boolean): string;
 }
+export type RecoveredSignatureType = SignatureType & {
+  readonly recovery: number;
+};
 // Static methods
 export type SignatureConstructor = {
   new (r: bigint, s: bigint): SignatureType;
@@ -669,7 +672,7 @@ export type CurveFn = {
   CURVE: ReturnType<typeof validateOpts>;
   getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
   getSharedSecret: (privateA: PrivKey, publicB: Hex, isCompressed?: boolean) => Uint8Array;
-  sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => SignatureType;
+  sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => RecoveredSignatureType;
   verify: (signature: Hex | SignatureLike, msgHash: Hex, publicKey: Hex, opts?: VerOpts) => boolean;
   ProjectivePoint: ProjConstructor<bigint>;
   Signature: SignatureConstructor;
@@ -782,8 +785,8 @@ export function weierstrass(curveDef: CurveType): CurveFn {
       if (!isWithinCurveOrder(this.s)) throw new Error('s must be 0 < s < CURVE.n');
     }
 
-    addRecoveryBit(recovery: number) {
+    addRecoveryBit(recovery: number): RecoveredSignature {
-      return new Signature(this.r, this.s, recovery);
+      return new Signature(this.r, this.s, recovery) as RecoveredSignature;
     }
 
     recoverPublicKey(msgHash: Hex): typeof Point.BASE {
@@ -828,6 +831,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
       return numToNByteStr(this.r) + numToNByteStr(this.s);
     }
   }
+  type RecoveredSignature = Signature & { recovery: number };
 
   const utils = {
     isValidPrivateKey(privateKey: PrivKey) {
@@ -965,7 +969,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
     const seed = ut.concatBytes(...seedArgs); // Step D of RFC6979 3.2
     const m = h1int; // NOTE: no need to call bits2int second time here, it is inside truncateHash!
     // Converts signature params into point w r/s, checks result for validity.
-    function k2sig(kBytes: Uint8Array): Signature | undefined {
+    function k2sig(kBytes: Uint8Array): RecoveredSignature | undefined {
       // RFC 6979 Section 3.2, step 3: k = bits2int(T)
       const k = bits2int(kBytes); // Cannot use fields methods, since it is group element
       if (!isWithinCurveOrder(k)) return; // Important: all mod() calls here must be done over N
@@ -984,7 +988,7 @@ export function weierstrass(curveDef: CurveType): CurveFn {
         normS = normalizeS(s); // if lowS was passed, ensure s is always
         recovery ^= 1; // // in the bottom half of N
       }
-      return new Signature(r, normS, recovery); // use normS, not s
+      return new Signature(r, normS, recovery) as RecoveredSignature; // use normS, not s
     }
     return { seed, k2sig };
   }
@@ -992,18 +996,22 @@ export function weierstrass(curveDef: CurveType): CurveFn {
   const defaultVerOpts: VerOpts = { lowS: CURVE.lowS, prehash: false };
 
   /**
-   * Signs message hash (not message: you need to hash it by yourself).
+   * Signs message hash with a private key.
    * ```
    * sign(m, d, k) where
    *   (x, y) = G × k
    *   r = x mod n
    *   s = (m + dr)/k mod n
    * ```
-   * @param opts `lowS, extraEntropy, prehash`
+   * @param msgHash NOT message. msg needs to be hashed to `msgHash`, or use `prehash`.
+   * @param privKey private key
+   * @param opts lowS for non-malleable sigs. extraEntropy for mixing randomness into k. prehash will hash first arg.
+   * @returns signature with recovery param
    */
-  function sign(msgHash: Hex, privKey: PrivKey, opts = defaultSigOpts): Signature {
+  function sign(msgHash: Hex, privKey: PrivKey, opts = defaultSigOpts): RecoveredSignature {
     const { seed, k2sig } = prepSig(msgHash, privKey, opts); // Steps A, D of RFC6979 3.2.
-    const drbg = ut.createHmacDrbg<Signature>(CURVE.hash.outputLen, CURVE.nByteLength, CURVE.hmac);
+    const C = CURVE;
+    const drbg = ut.createHmacDrbg<RecoveredSignature>(C.hash.outputLen, C.nByteLength, C.hmac);
     return drbg(seed, k2sig); // Steps B, C, D, E, F, G
   }
 
@@ -1084,20 +1092,29 @@ export function weierstrass(curveDef: CurveType): CurveFn {
   };
 }
 
-// Implementation of the Shallue and van de Woestijne method for any Weierstrass curve
+/**
-// TODO: check if there is a way to merge this with uvRatio in Edwards && move to modular?
+ * Implementation of the Shallue and van de Woestijne method for any weierstrass curve.
-// b = True and y = sqrt(u / v) if (u / v) is square in F, and
+ * TODO: check if there is a way to merge this with uvRatio in Edwards; move to modular.
-// b = False and y = sqrt(Z * (u / v)) otherwise.
+ * b = True and y = sqrt(u / v) if (u / v) is square in F, and
+ * b = False and y = sqrt(Z * (u / v)) otherwise.
+ * @param Fp
+ * @param Z
+ * @returns
+ */
 export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
   // Generic implementation
   const q = Fp.ORDER;
   let l = _0n;
   for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;
   const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
-  const c2 = (q - _1n) / _2n ** c1; // 2. c2 = (q - 1) / (2^c1)        # Integer arithmetic
+  // We need 2n ** c1 and 2n ** (c1-1). We can't use **; but we can use <<.
+  // 2n ** c1 == 2n << (c1-1)
+  const _2n_pow_c1_1 = _2n << (c1 - _1n - _1n);
+  const _2n_pow_c1 = _2n_pow_c1_1 * _2n;
+  const c2 = (q - _1n) / _2n_pow_c1; // 2. c2 = (q - 1) / (2^c1)  # Integer arithmetic
   const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic
-  const c4 = _2n ** c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic
+  const c4 = _2n_pow_c1 - _1n; // 4. c4 = 2^c1 - 1                # Integer arithmetic
-  const c5 = _2n ** (c1 - _1n); // 5. c5 = 2^(c1 - 1)              # Integer arithmetic
+  const c5 = _2n_pow_c1_1; // 5. c5 = 2^(c1 - 1)                  # Integer arithmetic
   const c6 = Fp.pow(Z, c2); // 6. c6 = Z^c2
   const c7 = Fp.pow(Z, (c2 + _1n) / _2n); // 7. c7 = Z^((c2 + 1) / 2)
   let sqrtRatio = (u: T, v: T): { isValid: boolean; value: T } => {
@@ -1119,7 +1136,8 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
     tv4 = Fp.cmov(tv5, tv4, isQR); // 16. tv4 = CMOV(tv5, tv4, isQR)
     // 17. for i in (c1, c1 - 1, ..., 2):
     for (let i = c1; i > _1n; i--) {
-      let tv5 = _2n ** (i - _2n); // 18.    tv5 = i - 2;    19.    tv5 = 2^tv5
+      let tv5 = i - _2n; // 18.    tv5 = i - 2
+      tv5 = _2n << (tv5 - _1n); // 19.    tv5 = 2^tv5
       let tvv5 = Fp.pow(tv4, tv5); // 20.    tv5 = tv4^tv5
       const e1 = Fp.eql(tvv5, Fp.ONE); // 21.    e1 = tv5 == 1
       tv2 = Fp.mul(tv3, tv1); // 22.    tv2 = tv3 * tv1
@@ -1151,7 +1169,9 @@ export function SWUFpSqrtRatio<T>(Fp: mod.IField<T>, Z: T) {
   // if (Fp.ORDER % _8n === _5n) // sqrt_ratio_5mod8
   return sqrtRatio;
 }
-// From draft-irtf-cfrg-hash-to-curve-16
+/**
+ * From draft-irtf-cfrg-hash-to-curve-16
+ */
 export function mapToCurveSimpleSWU<T>(
   Fp: mod.IField<T>,
   opts: {

src/bls12-381.ts

@@ -60,11 +60,10 @@ const _8n = BigInt(8), _16n = BigInt(16);
 
 // CURVE FIELDS
 // Finite field over p.
-const Fp = mod.Field(
+const Fp_raw = BigInt(
-  BigInt(
   '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'
-  )
 );
+const Fp = mod.Field(Fp_raw);
 type Fp = bigint;
 // Finite field over r.
 // This particular field is not used anywhere in bls12-381, but it is still useful.
@@ -110,10 +109,7 @@ type Fp2Utils = {
 // G² - 1
 // h2q
 // NOTE: ORDER was wrong!
-const FP2_ORDER =
+const FP2_ORDER = Fp_raw * Fp_raw;
-  BigInt(
-    '0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab'
-  ) ** _2n;
 
 const Fp2: mod.IField<Fp2> & Fp2Utils = {
   ORDER: FP2_ORDER,
@@ -1197,7 +1193,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
       ),
     ]),
     a: Fp2.ZERO,
-    b: Fp2.fromBigTuple([4n, _4n]),
+    b: Fp2.fromBigTuple([_4n, _4n]),
     hEff: BigInt(
       '0xbc69f08f2ee75b3584c6a0ea91b352888e2a8e9145ad7689986ff031508ffe1329c2f178731db956d82bf015d1212b02ec0ec69d7477c1ae954cbc06689f6a359894c0adebbf6b4e8020005aaa95551'
     ),

src/ed25519.ts

@@ -1,18 +1,18 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { sha512 } from '@noble/hashes/sha512';
 import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';
-import { twistedEdwards, ExtPointType } from './abstract/edwards.js';
+import { ExtPointType, twistedEdwards } from './abstract/edwards.js';
 import { montgomery } from './abstract/montgomery.js';
-import { mod, pow2, isNegativeLE, Field, FpSqrtEven } from './abstract/modular.js';
+import { Field, FpSqrtEven, isNegativeLE, mod, pow2 } from './abstract/modular.js';
 import {
-  equalBytes,
   bytesToHex,
   bytesToNumberLE,
-  numberToBytesLE,
-  Hex,
   ensureBytes,
+  equalBytes,
+  Hex,
+  numberToBytesLE,
 } from './abstract/utils.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher, htfBasicOpts, expand_message_xmd } from './abstract/hash-to-curve.js';
 import { AffinePoint } from './abstract/curve.js';
 
 /**
@@ -34,6 +34,7 @@ const ED25519_SQRT_M1 = BigInt(
 const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _5n = BigInt(5);
 // prettier-ignore
 const _10n = BigInt(10), _20n = BigInt(20), _40n = BigInt(40), _80n = BigInt(80);
+
 function ed25519_pow_2_252_3(x: bigint) {
   const P = ED25519_P;
   const x2 = (x * x) % P;
@@ -51,6 +52,7 @@ function ed25519_pow_2_252_3(x: bigint) {
   // ^ To pow to (p+3)/8, multiply it by x.
   return { pow_p_5_8, b2 };
 }
+
 function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
   // Section 5: For X25519, in order to decode 32 random bytes as an integer scalar,
   // set the three least significant bits of the first byte
@@ -61,6 +63,7 @@ function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
   bytes[31] |= 64; // 0b0100_0000
   return bytes;
 }
+
 // sqrt(u/v)
 function uvRatio(u: bigint, v: bigint): { isValid: boolean; value: bigint } {
   const P = ED25519_P;
@@ -101,10 +104,10 @@ const ed25519Defaults = {
   // d is equal to -121665/121666 over finite field.
   // Negative number is P - number, and division is invert(number, P)
   d: BigInt('37095705934669439343138083508754565189542113879843219016388785533085940283555'),
-  // Finite field 𝔽p over which we'll do calculations; 2n ** 255n - 19n
+  // Finite field 𝔽p over which we'll do calculations; 2n**255n - 19n
   Fp,
   // Subgroup order: how many points curve has
-  // 2n ** 252n + 27742317777372353535851937790883648493n;
+  // 2n**252n + 27742317777372353535851937790883648493n;
   n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'),
   // Cofactor
   h: BigInt(8),
@@ -121,6 +124,7 @@ const ed25519Defaults = {
 } as const;
 
 export const ed25519 = twistedEdwards(ed25519Defaults);
+
 function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
   if (ctx.length > 255) throw new Error('Context is too big');
   return concatBytes(
@@ -130,6 +134,7 @@ function ed25519_domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
     data
   );
 }
+
 export const ed25519ctx = twistedEdwards({ ...ed25519Defaults, domain: ed25519_domain });
 export const ed25519ph = twistedEdwards({
   ...ed25519Defaults,
@@ -137,7 +142,8 @@ export const ed25519ph = twistedEdwards({
   prehash: sha512,
 });
 
-export const x25519 = montgomery({
+export const x25519 = /* @__PURE__ */ (() =>
+  montgomery({
     P: ED25519_P,
     a: BigInt(486662),
     montgomeryBits: 255, // n is 253 bits
@@ -151,20 +157,34 @@ export const x25519 = montgomery({
     },
     adjustScalarBytes,
     randomBytes,
-});
+  }))();
 
 /**
  * Converts ed25519 public key to x25519 public key. Uses formula:
  * * `(u, v) = ((1+y)/(1-y), sqrt(-486664)*u/x)`
  * * `(x, y) = (sqrt(-486664)*u/v, (u-1)/(u+1))`
  * @example
- *   const aPub = ed25519.getPublicKey(utils.randomPrivateKey());
+ *   const someonesPub = ed25519.getPublicKey(ed25519.utils.randomPrivateKey());
- *   x25519.getSharedSecret(edwardsToMontgomery(aPub), edwardsToMontgomery(someonesPub))
+ *   const aPriv = x25519.utils.randomPrivateKey();
+ *   x25519.getSharedSecret(aPriv, edwardsToMontgomeryPub(someonesPub))
  */
-export function edwardsToMontgomery(edwardsPub: Hex): Uint8Array {
+export function edwardsToMontgomeryPub(edwardsPub: Hex): Uint8Array {
   const { y } = ed25519.ExtendedPoint.fromHex(edwardsPub);
   const _1n = BigInt(1);
-  return Fp.toBytes(Fp.create((y - _1n) * Fp.inv(y + _1n)));
+  return Fp.toBytes(Fp.create((_1n + y) * Fp.inv(_1n - y)));
+}
+export const edwardsToMontgomery = edwardsToMontgomeryPub; // deprecated
+
+/**
+ * Converts ed25519 secret key to x25519 secret key.
+ * @example
+ *   const someonesPub = x25519.getPublicKey(x25519.utils.randomPrivateKey());
+ *   const aPriv = ed25519.utils.randomPrivateKey();
+ *   x25519.getSharedSecret(edwardsToMontgomeryPriv(aPriv), someonesPub)
+ */
+export function edwardsToMontgomeryPriv(edwardsPriv: Uint8Array): Uint8Array {
+  const hashed = ed25519Defaults.hash(edwardsPriv.subarray(0, 32));
+  return ed25519Defaults.adjustScalarBytes(hashed).subarray(0, 32);
 }
 
 // Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)
@@ -223,7 +243,8 @@ function map_to_curve_elligator2_curve25519(u: bigint) {
 
 const ELL2_C1_EDWARDS = FpSqrtEven(Fp, Fp.neg(BigInt(486664))); // sgn0(c1) MUST equal 0
 function map_to_curve_elligator2_edwards25519(u: bigint) {
-  const { xMn, xMd, yMn, yMd } = map_to_curve_elligator2_curve25519(u); //  1.  (xMn, xMd, yMn, yMd) = map_to_curve_elligator2_curve25519(u)
+  const { xMn, xMd, yMn, yMd } = map_to_curve_elligator2_curve25519(u); //  1.  (xMn, xMd, yMn, yMd) =
+  // map_to_curve_elligator2_curve25519(u)
   let xn = Fp.mul(xMn, yMd); //  2.  xn = xMn * yMd
   xn = Fp.mul(xn, ELL2_C1_EDWARDS); //  3.  xn = xn * c1
   let xd = Fp.mul(xMd, yMn); //  4.  xd = xMd * yMn    # xn / xd = c1 * xM / yM
@@ -239,7 +260,9 @@ function map_to_curve_elligator2_edwards25519(u: bigint) {
   const inv = Fp.invertBatch([xd, yd]); // batch division
   return { x: Fp.mul(xn, inv[0]), y: Fp.mul(yn, inv[1]) }; //  13. return (xn, xd, yn, yd)
 }
-const { hashToCurve, encodeToCurve } = htf.createHasher(
+
+const htf = /* @__PURE__ */ (() =>
+  createHasher(
     ed25519.ExtendedPoint,
     (scalars: bigint[]) => map_to_curve_elligator2_edwards25519(scalars[0]),
     {
@@ -251,16 +274,16 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
       expand: 'xmd',
       hash: sha512,
     }
-);
+  ))();
-export { hashToCurve, encodeToCurve };
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();
 
 function assertRstPoint(other: unknown) {
-  if (!(other instanceof RistrettoPoint)) throw new Error('RistrettoPoint expected');
+  if (!(other instanceof RistPoint)) throw new Error('RistrettoPoint expected');
 }
+
 // √(-1) aka √(a) aka 2^((p-1)/4)
-const SQRT_M1 = BigInt(
+const SQRT_M1 = ED25519_SQRT_M1;
-  '19681161376707505956807079304988542015446066515923890162744021073123829784752'
-);
 // √(ad - 1)
 const SQRT_AD_MINUS_ONE = BigInt(
   '25063068953384623474111414158702152701244531502492656460079210482610430750235'
@@ -317,32 +340,31 @@ function calcElligatorRistrettoMap(r0: bigint): ExtendedPoint {
  * but it should work in its own namespace: do not combine those two.
  * https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-ristretto255-decaf448
  */
-export class RistrettoPoint {
+class RistPoint {
-  static BASE = new RistrettoPoint(ed25519.ExtendedPoint.BASE);
+  static BASE: RistPoint;
-  static ZERO = new RistrettoPoint(ed25519.ExtendedPoint.ZERO);
+  static ZERO: RistPoint;
-
   // Private property to discourage combining ExtendedPoint + RistrettoPoint
   // Always use Ristretto encoding/decoding instead.
   constructor(private readonly ep: ExtendedPoint) {}
 
   static fromAffine(ap: AffinePoint<bigint>) {
-    return new RistrettoPoint(ed25519.ExtendedPoint.fromAffine(ap));
+    return new RistPoint(ed25519.ExtendedPoint.fromAffine(ap));
   }
 
   /**
-   * Takes uniform output of 64-bit hash function like sha512 and converts it to `RistrettoPoint`.
+   * Takes uniform output of 64-byte hash function like sha512 and converts it to `RistrettoPoint`.
    * The hash-to-group operation applies Elligator twice and adds the results.
    * **Note:** this is one-way map, there is no conversion from point to hash.
    * https://ristretto.group/formulas/elligator.html
-   * @param hex 64-bit output of a hash function
+   * @param hex 64-byte output of a hash function
    */
-  static hashToCurve(hex: Hex): RistrettoPoint {
+  static hashToCurve(hex: Hex): RistPoint {
     hex = ensureBytes('ristrettoHash', hex, 64);
     const r1 = bytes255ToNumberLE(hex.slice(0, 32));
     const R1 = calcElligatorRistrettoMap(r1);
     const r2 = bytes255ToNumberLE(hex.slice(32, 64));
     const R2 = calcElligatorRistrettoMap(r2);
-    return new RistrettoPoint(R1.add(R2));
+    return new RistPoint(R1.add(R2));
   }
 
   /**
@@ -350,7 +372,7 @@ export class RistrettoPoint {
    * https://ristretto.group/formulas/decoding.html
    * @param hex Ristretto-encoded 32 bytes. Not every 32-byte string is valid ristretto encoding
    */
-  static fromHex(hex: Hex): RistrettoPoint {
+  static fromHex(hex: Hex): RistPoint {
     hex = ensureBytes('ristrettoHex', hex, 32);
     const { a, d } = ed25519.CURVE;
     const P = ed25519.CURVE.Fp.ORDER;
@@ -374,7 +396,7 @@ export class RistrettoPoint {
     const y = mod(u1 * Dy); // 11
     const t = mod(x * y); // 12
     if (!isValid || isNegativeLE(t, P) || y === _0n) throw new Error(emsg);
-    return new RistrettoPoint(new ed25519.ExtendedPoint(x, y, _1n, t));
+    return new RistPoint(new ed25519.ExtendedPoint(x, y, _1n, t));
   }
 
   /**
@@ -418,7 +440,7 @@ export class RistrettoPoint {
   }
 
   // Compare one point to another.
-  equals(other: RistrettoPoint): boolean {
+  equals(other: RistPoint): boolean {
     assertRstPoint(other);
     const { ex: X1, ey: Y1 } = this.ep;
     const { ex: X2, ey: Y2 } = other.ep;
@@ -429,31 +451,36 @@ export class RistrettoPoint {
     return one || two;
   }
 
-  add(other: RistrettoPoint): RistrettoPoint {
+  add(other: RistPoint): RistPoint {
     assertRstPoint(other);
-    return new RistrettoPoint(this.ep.add(other.ep));
+    return new RistPoint(this.ep.add(other.ep));
   }
 
-  subtract(other: RistrettoPoint): RistrettoPoint {
+  subtract(other: RistPoint): RistPoint {
     assertRstPoint(other);
-    return new RistrettoPoint(this.ep.subtract(other.ep));
+    return new RistPoint(this.ep.subtract(other.ep));
   }
 
-  multiply(scalar: bigint): RistrettoPoint {
+  multiply(scalar: bigint): RistPoint {
-    return new RistrettoPoint(this.ep.multiply(scalar));
+    return new RistPoint(this.ep.multiply(scalar));
   }
 
-  multiplyUnsafe(scalar: bigint): RistrettoPoint {
+  multiplyUnsafe(scalar: bigint): RistPoint {
-    return new RistrettoPoint(this.ep.multiplyUnsafe(scalar));
+    return new RistPoint(this.ep.multiplyUnsafe(scalar));
   }
 }
+export const RistrettoPoint = /* @__PURE__ */ (() => {
+  if (!RistPoint.BASE) RistPoint.BASE = new RistPoint(ed25519.ExtendedPoint.BASE);
+  if (!RistPoint.ZERO) RistPoint.ZERO = new RistPoint(ed25519.ExtendedPoint.ZERO);
+  return RistPoint;
+})();
 
 // https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/14/
 // Appendix B.  Hashing to ristretto255
-export const hash_to_ristretto255 = (msg: Uint8Array, options: htf.htfBasicOpts) => {
+export const hash_to_ristretto255 = (msg: Uint8Array, options: htfBasicOpts) => {
   const d = options.DST;
   const DST = typeof d === 'string' ? utf8ToBytes(d) : d;
-  const uniform_bytes = htf.expand_message_xmd(msg, DST, 64, sha512);
+  const uniform_bytes = expand_message_xmd(msg, DST, 64, sha512);
-  const P = RistrettoPoint.hashToCurve(uniform_bytes);
+  const P = RistPoint.hashToCurve(uniform_bytes);
   return P;
 };

src/ed448.ts

@@ -4,7 +4,7 @@ import { concatBytes, randomBytes, utf8ToBytes, wrapConstructor } from '@noble/h
 import { twistedEdwards } from './abstract/edwards.js';
 import { mod, pow2, Field } from './abstract/modular.js';
 import { montgomery } from './abstract/montgomery.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher } from './abstract/hash-to-curve.js';
 
 /**
  * Edwards448 (not Ed448-Goldilocks) curve with following addons:
@@ -63,7 +63,7 @@ const ED448_DEF = {
   d: BigInt(
     '726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018326358'
   ),
-  // Finite field 𝔽p over which we'll do calculations; 2n ** 448n - 2n ** 224n - 1n
+  // Finite field 𝔽p over which we'll do calculations; 2n**448n - 2n**224n - 1n
   Fp,
   // Subgroup order: how many points curve has;
   // 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
@@ -122,7 +122,8 @@ export const ed448 = twistedEdwards(ED448_DEF);
 // NOTE: there is no ed448ctx, since ed448 supports ctx by default
 export const ed448ph = twistedEdwards({ ...ED448_DEF, prehash: shake256_64 });
 
-export const x448 = montgomery({
+export const x448 = /* @__PURE__ */ (() =>
+  montgomery({
     a: BigInt(156326),
     montgomeryBits: 448,
     nByteLength: 57,
@@ -136,7 +137,7 @@ export const x448 = montgomery({
     },
     adjustScalarBytes,
     randomBytes,
-});
+  }))();
 
 /**
  * Converts edwards448 public key to x448 public key. Uses formula:
@@ -146,11 +147,12 @@ export const x448 = montgomery({
  *   const aPub = ed448.getPublicKey(utils.randomPrivateKey());
  *   x448.getSharedSecret(edwardsToMontgomery(aPub), edwardsToMontgomery(someonesPub))
  */
-export function edwardsToMontgomery(edwardsPub: string | Uint8Array): Uint8Array {
+export function edwardsToMontgomeryPub(edwardsPub: string | Uint8Array): Uint8Array {
   const { y } = ed448.ExtendedPoint.fromHex(edwardsPub);
   const _1n = BigInt(1);
   return Fp.toBytes(Fp.create((y - _1n) * Fp.inv(y + _1n)));
 }
+export const edwardsToMontgomery = edwardsToMontgomeryPub; // deprecated
 
 // Hash To Curve Elligator2 Map
 const ELL2_C1 = (Fp.ORDER - BigInt(3)) / BigInt(4); // 1. c1 = (q - 3) / 4         # Integer arithmetic
@@ -227,7 +229,8 @@ function map_to_curve_elligator2_edwards448(u: bigint) {
   return { x: Fp.mul(xEn, inv[0]), y: Fp.mul(yEn, inv[1]) }; // 38. return (xEn, xEd, yEn, yEd)
 }
 
-const { hashToCurve, encodeToCurve } = htf.createHasher(
+const htf = /* @__PURE__ */ (() =>
+  createHasher(
     ed448.ExtendedPoint,
     (scalars: bigint[]) => map_to_curve_elligator2_edwards448(scalars[0]),
     {
@@ -239,5 +242,6 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
       expand: 'xof',
       hash: shake256,
     }
-);
+  ))();
-export { hashToCurve, encodeToCurve };
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();

src/p256.ts

@@ -3,7 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha256 } from '@noble/hashes/sha256';
 import { Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher } from './abstract/hash-to-curve.js';
 
 // NIST secp256r1 aka p256
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256
@@ -12,12 +12,6 @@ const Fp = Field(BigInt('0xffffffff00000001000000000000000000000000fffffffffffff
 const CURVE_A = Fp.create(BigInt('-3'));
 const CURVE_B = BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b');
 
-const mapSWU = mapToCurveSimpleSWU(Fp, {
-  A: CURVE_A,
-  B: CURVE_B,
-  Z: Fp.create(BigInt('-10')),
-});
-
 // prettier-ignore
 export const p256 = createCurve({
   a: CURVE_A, // Equation params: a, b
@@ -33,10 +27,15 @@ export const p256 = createCurve({
 } as const, sha256);
 export const secp256r1 = p256;
 
-const { hashToCurve, encodeToCurve } = htf.createHasher(
+const mapSWU = /* @__PURE__ */ (() =>
-  secp256r1.ProjectivePoint,
+  mapToCurveSimpleSWU(Fp, {
-  (scalars: bigint[]) => mapSWU(scalars[0]),
+    A: CURVE_A,
-  {
+    B: CURVE_B,
+    Z: Fp.create(BigInt('-10')),
+  }))();
+
+const htf = /* @__PURE__ */ (() =>
+  createHasher(secp256r1.ProjectivePoint, (scalars: bigint[]) => mapSWU(scalars[0]), {
     DST: 'P256_XMD:SHA-256_SSWU_RO_',
     encodeDST: 'P256_XMD:SHA-256_SSWU_NU_',
     p: Fp.ORDER,
@@ -44,6 +43,6 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
     k: 128,
     expand: 'xmd',
     hash: sha256,
-  }
+  }))();
-);
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
-export { hashToCurve, encodeToCurve };
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();

src/p384.ts

@@ -3,7 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha384 } from '@noble/hashes/sha512';
 import { Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher } from './abstract/hash-to-curve.js';
 
 // NIST secp384r1 aka p384
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384
@@ -31,16 +31,15 @@ export const p384 = createCurve({
 } as const, sha384);
 export const secp384r1 = p384;
 
-const mapSWU = mapToCurveSimpleSWU(Fp, {
+const mapSWU = /* @__PURE__ */ (() =>
+  mapToCurveSimpleSWU(Fp, {
     A: CURVE_A,
     B: CURVE_B,
     Z: Fp.create(BigInt('-12')),
-});
+  }))();
 
-const { hashToCurve, encodeToCurve } = htf.createHasher(
+const htf = /* @__PURE__ */ (() =>
-  secp384r1.ProjectivePoint,
+  createHasher(secp384r1.ProjectivePoint, (scalars: bigint[]) => mapSWU(scalars[0]), {
-  (scalars: bigint[]) => mapSWU(scalars[0]),
-  {
     DST: 'P384_XMD:SHA-384_SSWU_RO_',
     encodeDST: 'P384_XMD:SHA-384_SSWU_NU_',
     p: Fp.ORDER,
@@ -48,6 +47,6 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
     k: 192,
     expand: 'xmd',
     hash: sha384,
-  }
+  }))();
-);
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
-export { hashToCurve, encodeToCurve };
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();

src/p521.ts

@@ -3,7 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha512 } from '@noble/hashes/sha512';
 import { Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher } from './abstract/hash-to-curve.js';
 
 // NIST secp521r1 aka p521
 // Note that it's 521, which differs from 512 of its hash function.
@@ -47,16 +47,15 @@ export const p521 = createCurve({
 } as const, sha512);
 export const secp521r1 = p521;
 
-const mapSWU = mapToCurveSimpleSWU(Fp, {
+const mapSWU = /* @__PURE__ */ (() =>
+  mapToCurveSimpleSWU(Fp, {
     A: CURVE.a,
     B: CURVE.b,
     Z: Fp.create(BigInt('-4')),
-});
+  }))();
 
-const { hashToCurve, encodeToCurve } = htf.createHasher(
+const htf = /* @__PURE__ */ (() =>
-  secp521r1.ProjectivePoint,
+  createHasher(secp521r1.ProjectivePoint, (scalars: bigint[]) => mapSWU(scalars[0]), {
-  (scalars: bigint[]) => mapSWU(scalars[0]),
-  {
     DST: 'P521_XMD:SHA-512_SSWU_RO_',
     encodeDST: 'P521_XMD:SHA-512_SSWU_NU_',
     p: Fp.ORDER,
@@ -64,6 +63,6 @@ const { hashToCurve, encodeToCurve } = htf.createHasher(
     k: 256,
     expand: 'xmd',
     hash: sha512,
-  }
+  }))();
-);
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
-export { hashToCurve, encodeToCurve };
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();

src/secp256k1.ts

@@ -5,7 +5,7 @@ import { Field, mod, pow2 } from './abstract/modular.js';
 import { ProjPointType as PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js';
 import type { Hex, PrivKey } from './abstract/utils.js';
 import { bytesToNumberBE, concatBytes, ensureBytes, numberToBytesBE } from './abstract/utils.js';
-import * as htf from './abstract/hash-to-curve.js';
+import { createHasher, isogenyMap } from './abstract/hash-to-curve.js';
 import { createCurve } from './_shortw_utils.js';
 
 const secp256k1P = BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f');
@@ -199,7 +199,7 @@ function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
   }
 }
 
-export const schnorr = {
+export const schnorr = /* @__PURE__ */ (() => ({
   getPublicKey: schnorrGetPublicKey,
   sign: schnorrSign,
   verify: schnorrVerify,
@@ -212,9 +212,10 @@ export const schnorr = {
     taggedHash,
     mod,
   },
-};
+}))();
 
-const isoMap = htf.isogenyMap(
+const isoMap = /* @__PURE__ */ (() =>
+  isogenyMap(
     Fp,
     [
       // xNum
@@ -245,13 +246,15 @@ const isoMap = htf.isogenyMap(
         '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
       ],
     ].map((i) => i.map((j) => BigInt(j))) as [bigint[], bigint[], bigint[], bigint[]]
-);
+  ))();
-const mapSWU = mapToCurveSimpleSWU(Fp, {
+const mapSWU = /* @__PURE__ */ (() =>
+  mapToCurveSimpleSWU(Fp, {
     A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
     B: BigInt('1771'),
     Z: Fp.create(BigInt('-11')),
-});
+  }))();
-export const { hashToCurve, encodeToCurve } = htf.createHasher(
+const htf = /* @__PURE__ */ (() =>
+  createHasher(
     secp256k1.ProjectivePoint,
     (scalars: bigint[]) => {
       const { x, y } = mapSWU(Fp.create(scalars[0]));
@@ -266,4 +269,6 @@ export const { hashToCurve, encodeToCurve } = htf.createHasher(
       expand: 'xmd',
       hash: sha256,
     }
-);
+  ))();
+export const hashToCurve = /* @__PURE__ */ (() => htf.hashToCurve)();
+export const encodeToCurve = /* @__PURE__ */ (() => htf.encodeToCurve)();

test/ed25519-addons.test.js

@@ -1,10 +1,18 @@
 import { sha512 } from '@noble/hashes/sha512';
-import { hexToBytes, bytesToHex as hex } from '@noble/hashes/utils';
+import { bytesToHex as hex, hexToBytes } from '@noble/hashes/utils';
 import { deepStrictEqual, throws } from 'assert';
 import { describe, should } from 'micro-should';
 import { bytesToNumberLE, numberToBytesLE } from '../esm/abstract/utils.js';
 import { default as x25519vectors } from './wycheproof/x25519_test.json' assert { type: 'json' };
-import { ed25519ctx, ed25519ph, RistrettoPoint, x25519 } from '../esm/ed25519.js';
+import {
+  ed25519,
+  ed25519ctx,
+  ed25519ph,
+  edwardsToMontgomeryPub,
+  edwardsToMontgomeryPriv,
+  RistrettoPoint,
+  x25519,
+} from '../esm/ed25519.js';
 
 const VECTORS_RFC8032_CTX = [
   {
@@ -141,6 +149,56 @@ describe('RFC7748 X25519 ECDH', () => {
     deepStrictEqual(hex(x25519.scalarMult(bobPrivate, alicePublic)), shared);
   });
 
+  should('X25519/getSharedSecret() should be commutative', () => {
+    for (let i = 0; i < 512; i++) {
+      const asec = x25519.utils.randomPrivateKey();
+      const apub = x25519.getPublicKey(asec);
+      const bsec = x25519.utils.randomPrivateKey();
+      const bpub = x25519.getPublicKey(bsec);
+      try {
+        deepStrictEqual(x25519.getSharedSecret(asec, bpub), x25519.getSharedSecret(bsec, apub));
+      } catch (error) {
+        console.error('not commutative', { asec, apub, bsec, bpub });
+        throw error;
+      }
+    }
+  });
+
+  should('edwardsToMontgomery should produce correct output', () => {
+    const edSecret = hexToBytes('77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a');
+    const edPublic = ed25519.getPublicKey(edSecret);
+    const xPrivate = edwardsToMontgomeryPriv(edSecret);
+    deepStrictEqual(
+      hex(xPrivate),
+      'a8cd44eb8e93319c0570bc11005c0e0189d34ff02f6c17773411ad191293c94f'
+    );
+    const xPublic = edwardsToMontgomeryPub(edPublic);
+    deepStrictEqual(
+      hex(xPublic),
+      'ed7749b4d989f6957f3bfde6c56767e988e21c9f8784d91d610011cd553f9b06'
+    );
+  });
+
+  should('edwardsToMontgomery should produce correct keyPair', () => {
+    const edSecret = ed25519.utils.randomPrivateKey();
+    const edPublic = ed25519.getPublicKey(edSecret);
+    const xSecret = edwardsToMontgomeryPriv(edSecret);
+    const expectedXPublic = x25519.getPublicKey(xSecret);
+    const xPublic = edwardsToMontgomeryPub(edPublic);
+    deepStrictEqual(xPublic, expectedXPublic);
+  });
+
+  should('ECDH through edwardsToMontgomery should be commutative', () => {
+    const edSecret1 = ed25519.utils.randomPrivateKey();
+    const edPublic1 = ed25519.getPublicKey(edSecret1);
+    const edSecret2 = ed25519.utils.randomPrivateKey();
+    const edPublic2 = ed25519.getPublicKey(edSecret2);
+    deepStrictEqual(
+      x25519.getSharedSecret(edwardsToMontgomeryPriv(edSecret1), edwardsToMontgomeryPub(edPublic2)),
+      x25519.getSharedSecret(edwardsToMontgomeryPriv(edSecret2), edwardsToMontgomeryPub(edPublic1))
+    );
+  });
+
   should('base point', () => {
     const { y } = ed25519ph.ExtendedPoint.BASE;
     const { Fp } = ed25519ph.CURVE;
@@ -298,7 +356,7 @@ describe('ristretto255', () => {
 
 // ESM is broken.
 import url from 'url';
-import { assert } from 'console';
+
 if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
   should.run();
 }

test/ed25519.test.js

@@ -1,17 +1,19 @@
 import { deepStrictEqual, strictEqual, throws } from 'assert';
 import { readFileSync } from 'fs';
-import { bytesToHex, concatBytes, hexToBytes, randomBytes } from '@noble/hashes/utils';
+import { bytesToHex, concatBytes, hexToBytes, utf8ToBytes, randomBytes } from '@noble/hashes/utils';
 import * as fc from 'fast-check';
 import { describe, should } from 'micro-should';
-import { ed25519, ED25519_TORSION_SUBGROUP, numberToBytesLE } from './ed25519.helpers.js';
+import { ed25519 as ed, ED25519_TORSION_SUBGROUP, numberToBytesLE } from './ed25519.helpers.js';
 // Old vectors allow to test sign() because they include private key
 import { default as ed25519vectors_OLD } from './ed25519/ed25519_test_OLD.json' assert { type: 'json' };
 import { default as ed25519vectors } from './wycheproof/ed25519_test.json' assert { type: 'json' };
-
 import { default as zip215 } from './ed25519/zip215.json' assert { type: 'json' };
+import { default as edgeCases } from './ed25519/edge-cases.json' assert { type: 'json' };
+
+// Any changes to the file will need to be aware of the fact
+// the file is shared between noble-curves and noble-ed25519.
 
 describe('ed25519', () => {
-  const ed = ed25519;
   const hex = bytesToHex;
   const Point = ed.ExtendedPoint;
 
@@ -20,13 +22,6 @@ describe('ed25519', () => {
     return hexToBytes(hex.padStart(64, '0'));
   }
 
-  function utf8ToBytes(str) {
-    if (typeof str !== 'string') {
-      throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
-    }
-    return new TextEncoder().encode(str);
-  }
-
   ed.utils.precompute(8);
 
   should('not accept >32byte private keys', () => {
@@ -415,27 +410,36 @@ describe('ed25519', () => {
     }
   });
 
+  should('have strict SUF-CMA and SBS properties', () => {
+    // https://eprint.iacr.org/2020/1244
+    const list = [0, 1, 6, 7, 8, 9, 10, 11].map((i) => edgeCases[i]);
+    for (let v of list) {
+      const result = ed.verify(v.signature, v.message, v.pub_key, { zip215: false });
+      strictEqual(result, false, `zip215: false must not validate: ${v.signature}`);
+    }
+  });
+
   should('not verify when sig.s >= CURVE.n', () => {
-    const privateKey = ed25519.utils.randomPrivateKey();
+    const privateKey = ed.utils.randomPrivateKey();
     const message = Uint8Array.from([0xab, 0xbc, 0xcd, 0xde]);
-    const publicKey = ed25519.getPublicKey(privateKey);
+    const publicKey = ed.getPublicKey(privateKey);
-    const signature = ed25519.sign(message, privateKey);
+    const signature = ed.sign(message, privateKey);
 
     const R = signature.slice(0, 32);
     let s = signature.slice(32, 64);
 
     s = bytesToHex(s.slice().reverse());
     s = BigInt('0x' + s);
-    s = s + ed25519.CURVE.n;
+    s = s + ed.CURVE.n;
     s = numberToBytesLE(s, 32);
 
     const sig_invalid = concatBytes(R, s);
-    deepStrictEqual(ed25519.verify(sig_invalid, message, publicKey), false);
+    deepStrictEqual(ed.verify(sig_invalid, message, publicKey), false);
   });
 
   should('not accept point without z, t', () => {
     const t = 81718630521762619991978402609047527194981150691135404693881672112315521837062n;
-    const point = ed25519.ExtendedPoint.fromAffine({ x: t, y: t });
+    const point = Point.fromAffine({ x: t, y: t });
     throws(() => point.assertValidity());
     // Otherwise (without assertValidity):
     // const point2 = point.double();

test/ed25519/edge-cases.json

@@ -0,0 +1 @@
+[{"message":"8c93255d71dcab10e8f379c26200f3c7bd5f09d9bc3068d3ef4edeb4853022b6","pub_key":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa","signature":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac037a0000000000000000000000000000000000000000000000000000000000000000"},{"message":"9bd9f44f4dcc75bd531b56b2cd280b0bb38fc1cd6d1230e14861d861de092e79","pub_key":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa","signature":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43a5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04"},{"message":"aebf3f2601a0c8c5d39cc7d8911642f740b78168218da8471772b35f9d35b9ab","pub_key":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43","signature":"c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa8c4bd45aecaca5b24fb97bc10ac27ac8751a7dfe1baff8b953ec9f5833ca260e"},{"message":"9bd9f44f4dcc75bd531b56b2cd280b0bb38fc1cd6d1230e14861d861de092e79","pub_key":"cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d","signature":"9046a64750444938de19f227bb80485e92b83fdb4b6506c160484c016cc1852f87909e14428a7a1d62e9f22f3d3ad7802db02eb2e688b6c52fcd6648a98bd009"},{"message":"e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c","pub_key":"cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d","signature":"160a1cb0dc9c0258cd0a7d23e94d8fa878bcb1925f2c64246b2dee1796bed5125ec6bc982a269b723e0668e540911a9a6a58921d6925e434ab10aa7940551a09"},{"message":"e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec4011eaccd55b53f56c","pub_key":"cdb267ce40c5cd45306fa5d2f29731459387dbf9eb933b7bd5aed9a765b88d4d","signature":"21122a84e0b5fca4052f5b1235c80a537878b38f3142356b2c2384ebad4668b7e40bc836dac0f71076f9abe3a53f9c03c1ceeeddb658d0030494ace586687405"},{"message":"85e241a07d148b41e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec40","pub_key":"442aad9f089ad9e14647b1ef9099a1ff4798d78589e66f28eca69c11f582a623","signature":"e96f66be976d82e60150baecff9906684aebb1ef181f67a7189ac78ea23b6c0e547f7690a0e2ddcd04d87dbc3490dc19b3b3052f7ff0538cb68afb369ba3a514"},{"message":"85e241a07d148b41e47d62c63f830dc7a6851a0b1f33ae4bb2f507fb6cffec40","pub_key":"442aad9f089ad9e14647b1ef9099a1ff4798d78589e66f28eca69c11f582a623","signature":"8ce5b96c8f26d0ab6c47958c9e68b937104cd36e13c33566acd2fe8d38aa19427e71f98a473474f2f13f06f97c20d58cc3f54b8bd0d272f42b695dd7e89a8c22"},{"message":"9bedc267423725d473888631ebf45988bad3db83851ee85c85e241a07d148b41","pub_key":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43","signature":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff03be9678ac102edcd92b0210bb34d7428d12ffc5df5f37e359941266a4e35f0f"},{"message":"9bedc267423725d473888631ebf45988bad3db83851ee85c85e241a07d148b41","pub_key":"f7badec5b8abeaf699583992219b7b223f1df3fbbea919844e3f7c554a43dd43","signature":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffca8c5b64cd208982aa38d4936621a4775aa233aa0505711d8fdcfdaa943d4908"},{"message":"e96b7021eb39c1a163b6da4e3093dcd3f21387da4cc4572be588fafae23c155b","pub_key":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff","signature":"a9d55260f765261eb9b84e106f665e00b867287a761990d7135963ee0a7d59dca5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04"},{"message":"39a591f5321bbe07fd5a23dc2f39d025d74526615746727ceefd6e82ae65c06f","pub_key":"ecffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff","signature":"a9d55260f765261eb9b84e106f665e00b867287a761990d7135963ee0a7d59dca5bb704786be79fc476f91d3f3f89b03984d8068dcf1bb7dfc6637b45450ac04"}]

test/index.test.js

@@ -5,6 +5,7 @@ import './basic.test.js';
 import './nist.test.js';
 import './ed448.test.js';
 import './ed25519.test.js';
+import './ed25519-addons.test.js';
 import './secp256k1.test.js';
 import './secp256k1-schnorr.test.js';
 import './jubjub.test.js';

test/nist.test.js

@@ -10,6 +10,7 @@ import { hexToBytes, bytesToHex } from '../esm/abstract/utils.js';
 import { default as ecdsa } from './wycheproof/ecdsa_test.json' assert { type: 'json' };
 import { default as ecdh } from './wycheproof/ecdh_test.json' assert { type: 'json' };
 import { default as rfc6979 } from './vectors/rfc6979.json' assert { type: 'json' };
+import { default as endoVectors } from './vectors/secp256k1/endomorphism.json' assert { type: 'json' };
 
 import { default as ecdh_secp224r1_test } from './wycheproof/ecdh_secp224r1_test.json' assert { type: 'json' };
 import { default as ecdh_secp256r1_test } from './wycheproof/ecdh_secp256r1_test.json' assert { type: 'json' };
@@ -438,7 +439,7 @@ describe('RFC6979', () => {
   }
 });
 
-should('DER Leading zero', () => {
+should('properly add leading zero to DER', () => {
   // Valid DER
   deepStrictEqual(
     DER.toSig(
@@ -465,6 +466,16 @@ should('DER Leading zero', () => {
   );
 });
 
+should('have proper GLV endomorphism logic in secp256k1', () => {
+  const Point = secp256k1.ProjectivePoint;
+  for (let item of endoVectors) {
+    const point = Point.fromAffine({ x: BigInt(item.ax), y: BigInt(item.ay) });
+    const c = point.multiplyUnsafe(BigInt(item.scalar)).toAffine();
+    deepStrictEqual(c.x, BigInt(item.cx));
+    deepStrictEqual(c.y, BigInt(item.cy));
+  }
+});
+
 // ESM is broken.
 import url from 'url';
 if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {

test/secp256k1.test.js

@@ -14,6 +14,9 @@ import { default as privates } from './vectors/secp256k1/privates.json' assert {
 import { default as points } from './vectors/secp256k1/points.json' assert { type: 'json' };
 import { default as wp } from './wycheproof/ecdsa_secp256k1_sha256_test.json' assert { type: 'json' };
 
+// Any changes to the file will need to be aware of the fact
+// the file is shared between noble-curves and noble-secp256k1.
+
 const Point = secp.ProjectivePoint;
 const privatesTxt = readFileSync('./test/vectors/secp256k1/privates-2.txt', 'utf-8');
 

test/vectors/secp256k1/endomorphism.json

@@ -0,0 +1,26 @@
+[
+  {
+    "desc": "k1neg=true, k2neg=false",
+    "ax": "55066263022277343669578718895168534326250603453777594175500187360389116729240",
+    "ay": "32670510020758816978083085130507043184471273380659243275938904335757337482424",
+    "scalar": "2704427838213584814824020837927043695889",
+    "cx": "70912011419250646761259860556624974262679413898110209707622032756145750038852",
+    "cy": "46481114889376149700487001434152190585794282401306514438088690968308506923285"
+  },
+  {
+    "desc": "k1neg=false, k2neg=true",
+    "ax": "55066263022277343669578718895168534326250603453777594175500187360389116729240",
+    "ay": "32670510020758816978083085130507043184471273380659243275938904335757337482424",
+    "scalar": "367917413016453100223835821029139468248",
+    "cx": "10322688129782350538653828383726187034025074756440739323015371090593152139135",
+    "cy": "68793242610611269092604721689053086352541804982835045879816374698216278704126"
+  },
+  {
+    "desc": "k1neg=true, k2neg=true",
+    "ax": "55066263022277343669578718895168534326250603453777594175500187360389116729240",
+    "ay": "32670510020758816978083085130507043184471273380659243275938904335757337482424",
+    "scalar": "3808180077262944115495528301014462100633",
+    "cx": "14215418389480067884450074673878587420586762919133643262861030012154939932102",
+    "cy": "29847359538023735520768762420255189621104408153695873716448888266404867737302"
+  }
+]