Release 0.6.1.

README.md

@@ -6,11 +6,12 @@ Minimal, auditable JS implementation of elliptic curve cryptography.
 - ECDSA, EdDSA, Schnorr, BLS signature schemes, ECDH key agreement
 - [hash to curve](https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/)
   for encoding or hashing an arbitrary string to a point on an elliptic curve
-- Auditable, [fast](#speed)
+- [Poseidon](https://www.poseidon-hash.info) ZK-friendly hash
+- 🏎 [Ultra-fast](#speed), hand-optimized for caveats of JS engines
 - 🔍 Unique tests ensure correctness. Wycheproof vectors included
 - 🔻 Tree-shaking-friendly: there is no entry point, which ensures small size of your app
 
-There are two parts of the package:
+Package consists of two parts:
 
 1. `abstract/` directory specifies zero-dependency EC algorithms
 2. root directory utilizes one dependency `@noble/hashes` and provides ready-to-use:
@@ -24,7 +25,7 @@ Curves incorporate work from previous noble packages
 [ed25519](https://github.com/paulmillr/noble-ed25519),
 [bls12-381](https://github.com/paulmillr/noble-bls12-381)),
 which had security audits and were developed from 2019 to 2022.
-The goal is to replace them with lean UMD builds based on single-codebase noble-curves.
+Check out [Upgrading](#upgrading) section if you've used them before.
 
 ### This library belongs to _noble_ crypto
 
@@ -88,6 +89,7 @@ To define a custom curve, check out API below.
 - [abstract/montgomery: Montgomery curve](#abstractmontgomery-montgomery-curve)
 - [abstract/weierstrass: Short Weierstrass curve](#abstractweierstrass-short-weierstrass-curve)
 - [abstract/hash-to-curve: Hashing strings to curve points](#abstracthash-to-curve-hashing-strings-to-curve-points)
+- [abstract/poseidon: Poseidon hash](#abstractposeidon-poseidon-hash)
 - [abstract/modular](#abstractmodular)
 - [abstract/utils](#abstractutils)
 
@@ -302,13 +304,12 @@ const shared = secp256k1.getSharedSecret(key, someonesPubkey);
 export type CurveFn = {
   CURVE: ReturnType<typeof validateOpts>;
   getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
-  getSharedSecret: (privateA: PrivKey, publicB: PubKey, isCompressed?: boolean) => Uint8Array;
+  getSharedSecret: (privateA: PrivKey, publicB: Hex, isCompressed?: boolean) => Uint8Array;
   sign: (msgHash: Hex, privKey: PrivKey, opts?: SignOpts) => SignatureType;
-  signUnhashed: (msg: Uint8Array, privKey: PrivKey, opts?: SignOpts) => SignatureType;
   verify: (
     signature: Hex | SignatureType,
     msgHash: Hex,
-    publicKey: PubKey,
+    publicKey: Hex,
     opts?: { lowS?: boolean }
   ) => boolean;
   Point: PointConstructor;
@@ -370,6 +371,30 @@ hashes arbitrary-length byte strings to a list of one or more elements of a fini
     };
     ```
 
+### abstract/poseidon: Poseidon hash
+
+Implements [Poseidon](https://www.poseidon-hash.info) ZK-friendly hash.
+
+There are many poseidon instances with different constants. We don't provide them,
+but we provide ability to specify them manually. For actual usage, check out
+stark curve source code.
+
+```ts
+import { poseidon } from '@noble/curves/abstract/poseidon';
+
+type PoseidonOpts = {
+  Fp: Field<bigint>;
+  t: number;
+  roundsFull: number;
+  roundsPartial: number;
+  sboxPower?: number;
+  reversePartialPowIdx?: boolean; // Hack for stark
+  mds: bigint[][];
+  roundConstants: bigint[][];
+};
+const instance = poseidon(opts: PoseidonOpts);
+```
+
 ### abstract/modular
 
 Modular arithmetics utilities.
@@ -420,45 +445,94 @@ We consider infrastructure attacks like rogue NPM modules very important; that's
 Benchmark results on Apple M2 with node v18.10:
 
 ```
-getPublicKey
+secp256k1
-  secp256k1 x 5,241 ops/sec @ 190μs/op
+init x 57 ops/sec @ 17ms/op
-  P256 x 7,993 ops/sec @ 125μs/op
+getPublicKey x 4,946 ops/sec @ 202μs/op
-  P384 x 3,819 ops/sec @ 261μs/op
+sign x 3,914 ops/sec @ 255μs/op
-  P521 x 2,074 ops/sec @ 481μs/op
+verify x 682 ops/sec @ 1ms/op
-  ed25519 x 8,390 ops/sec @ 119μs/op
+getSharedSecret x 427 ops/sec @ 2ms/op
-  ed448 x 3,224 ops/sec @ 310μs/op
+recoverPublicKey x 683 ops/sec @ 1ms/op
-sign
+schnorr.sign x 539 ops/sec @ 1ms/op
-  secp256k1 x 3,934 ops/sec @ 254μs/op
+schnorr.verify x 716 ops/sec @ 1ms/op
-  P256 x 5,327 ops/sec @ 187μs/op
+
-  P384 x 2,728 ops/sec @ 366μs/op
+P256
-  P521 x 1,594 ops/sec @ 626μs/op
+init x 30 ops/sec @ 32ms/op
-  ed25519 x 4,233 ops/sec @ 236μs/op
+getPublicKey x 5,008 ops/sec @ 199μs/op
-  ed448 x 1,561 ops/sec @ 640μs/op
+sign x 3,970 ops/sec @ 251μs/op
-verify
+verify x 515 ops/sec @ 1ms/op
-  secp256k1 x 731 ops/sec @ 1ms/op
+
-  P256 x 806 ops/sec @ 1ms/op
+P384
-  P384 x 353 ops/sec @ 2ms/op
+init x 14 ops/sec @ 66ms/op
-  P521 x 171 ops/sec @ 5ms/op
+getPublicKey x 2,434 ops/sec @ 410μs/op
-  ed25519 x 860 ops/sec @ 1ms/op
+sign x 1,942 ops/sec @ 514μs/op
-  ed448 x 313 ops/sec @ 3ms/op
+verify x 206 ops/sec @ 4ms/op
-getSharedSecret
+
-  secp256k1 x 445 ops/sec @ 2ms/op
+P521
-recoverPublicKey
+init x 7 ops/sec @ 126ms/op
-  secp256k1 x 732 ops/sec @ 1ms/op
+getPublicKey x 1,282 ops/sec @ 779μs/op
-==== bls12-381 ====
+sign x 1,077 ops/sec @ 928μs/op
-getPublicKey x 817 ops/sec @ 1ms/op
+verify x 110 ops/sec @ 9ms/op
-sign x 50 ops/sec @ 19ms/op
+
-verify x 34 ops/sec @ 28ms/op
+ed25519
-pairing x 89 ops/sec @ 11ms/op
+init x 37 ops/sec @ 26ms/op
-==== stark ====
+getPublicKey x 8,147 ops/sec @ 122μs/op
+sign x 3,979 ops/sec @ 251μs/op
+verify x 848 ops/sec @ 1ms/op
+
+ed448
+init x 17 ops/sec @ 58ms/op
+getPublicKey x 3,083 ops/sec @ 324μs/op
+sign x 1,473 ops/sec @ 678μs/op
+verify x 323 ops/sec @ 3ms/op
+
+bls12-381
+init x 30 ops/sec @ 33ms/op
+getPublicKey x 788 ops/sec @ 1ms/op
+sign x 45 ops/sec @ 21ms/op
+verify x 32 ops/sec @ 30ms/op
+pairing x 88 ops/sec @ 11ms/op
+
+stark
+init x 31 ops/sec @ 31ms/op
 pedersen
-  old x 85 ops/sec @ 11ms/op
+├─old x 84 ops/sec @ 11ms/op
-  noble x 1,216 ops/sec @ 822μs/op
+└─noble x 802 ops/sec @ 1ms/op
+poseidon x 7,466 ops/sec @ 133μs/op
 verify
-  old x 302 ops/sec @ 3ms/op
+├─old x 300 ops/sec @ 3ms/op
-  noble x 698 ops/sec @ 1ms/op
+└─noble x 474 ops/sec @ 2ms/op
 ```
 
+## Upgrading
+
+If you're coming from single-curve noble packages, the following changes need to be kept in mind:
+
+- 2d affine (x, y) points have been removed to reduce complexity and improve speed
+- Removed `number` support as a type for private keys. `bigint` is still supported
+- `mod`, `invert` are no longer present in `utils`. Use `@noble/curves/abstract/modular.js` now.
+
+Upgrading from @noble/secp256k1 1.7:
+
+- Compressed (33-byte) public keys are now returned by default, instead of uncompressed
+- Methods are now synchronous. Setting `secp.utils.hmacSha256` is no longer required
+- `sign()`
+    - `der`, `recovered` options were removed
+    - `canonical` was renamed to `lowS`
+    - Return type is now `{ r: bigint, s: bigint, recovery: number }` instance of `Signature`
+- `verify()`
+    - `strict` was renamed to `lowS`
+- `recoverPublicKey()`: moved to sig instance `Signature#recoverPublicKey(msgHash)`
+- `Point` was removed: use `ProjectivePoint` in xyz coordinates
+- `utils`: Many methods were removed, others were moved to `schnorr` namespace
+
+Upgrading from @noble/ed25519 1.7:
+
+- Methods are now synchronous. Setting `secp.utils.hmacSha256` is no longer required
+- ed25519ph, ed25519ctx
+- `Point` was removed: use `ExtendedPoint` in xyzt coordinates
+- `Signature` was removed
+- `getSharedSecret` was removed: use separate x25519 sub-module
+
 ## Contributing & testing
 
 1. Clone the repository

benchmark/_shared.js

@@ -0,0 +1,7 @@
+export function generateData(curve) {
+  const priv = curve.utils.randomPrivateKey();
+  const pub = curve.getPublicKey(priv);
+  const msg = curve.utils.randomPrivateKey();
+  const sig = curve.sign(msg, priv);
+  return { priv, pub, msg, sig };
+}

benchmark/bls.js

@@ -0,0 +1,52 @@
+import { readFileSync } from 'fs';
+import { mark, run } from 'micro-bmark';
+import { bls12_381 as bls } from '../lib/bls12-381.js';
+
+const G2_VECTORS = readFileSync('../test/bls12-381/bls12-381-g2-test-vectors.txt', 'utf-8')
+  .trim()
+  .split('\n')
+  .map((l) => l.split(':'));
+
+run(async () => {
+  console.log(`\x1b[36mbls12-381\x1b[0m`);
+  let p1, p2, sig;
+  await mark('init', 1, () => {
+    p1 =
+      bls.G1.ProjectivePoint.BASE.multiply(
+        0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
+      );
+    p2 =
+      bls.G2.ProjectivePoint.BASE.multiply(
+        0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
+      );
+    bls.pairing(p1, p2);
+  });
+  const priv = '28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4c';
+  sig = bls.sign('09', priv);
+  const pubs = G2_VECTORS.map((v) => bls.getPublicKey(v[0]));
+  const sigs = G2_VECTORS.map((v) => v[2]);
+  const pub = bls.getPublicKey(priv);
+  const pub512 = pubs.slice(0, 512); // .map(bls.PointG1.fromHex)
+  const pub32 = pub512.slice(0, 32);
+  const pub128 = pub512.slice(0, 128);
+  const pub2048 = pub512.concat(pub512, pub512, pub512);
+  const sig512 = sigs.slice(0, 512); // .map(bls.PointG2.fromSignature);
+  const sig32 = sig512.slice(0, 32);
+  const sig128 = sig512.slice(0, 128);
+  const sig2048 = sig512.concat(sig512, sig512, sig512);
+  await mark('getPublicKey 1-bit', 1000, () => bls.getPublicKey('2'.padStart(64, '0')));
+  await mark('getPublicKey', 1000, () => bls.getPublicKey(priv));
+  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));
+  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));
+  await mark('aggregatePublicKeys/512', 10, () => bls.aggregatePublicKeys(pub512));
+  await mark('aggregatePublicKeys/2048', 5, () => bls.aggregatePublicKeys(pub2048));
+  await mark('aggregateSignatures/8', 100, () => bls.aggregateSignatures(sigs.slice(0, 8)));
+  await mark('aggregateSignatures/32', 50, () => bls.aggregateSignatures(sig32));
+  await mark('aggregateSignatures/128', 20, () => bls.aggregateSignatures(sig128));
+  await mark('aggregateSignatures/512', 10, () => bls.aggregateSignatures(sig512));
+  await mark('aggregateSignatures/2048', 5, () => bls.aggregateSignatures(sig2048));
+});

benchmark/curves.js

@@ -0,0 +1,23 @@
+import { run, mark, utils } from 'micro-bmark';
+import { generateData } from './_shared.js';
+import { P256 } from '../lib/p256.js';
+import { P384 } from '../lib/p384.js';
+import { P521 } from '../lib/p521.js';
+import { ed25519 } from '../lib/ed25519.js';
+import { ed448 } from '../lib/ed448.js';
+
+run(async () => {
+  const RAM = false
+  for (let kv of Object.entries({ P256, P384, P521, ed25519, ed448 })) {
+    const [name, curve] = kv;
+    console.log();
+    console.log(`\x1b[36m${name}\x1b[0m`);
+    if (RAM) utils.logMem();
+    await mark('init', 1, () => curve.utils.precompute(8));
+    const d = generateData(curve);
+    await mark('getPublicKey', 5000, () => curve.getPublicKey(d.priv));
+    await mark('sign', 5000, () => curve.sign(d.msg, d.priv));
+    await mark('verify', 500, () => curve.verify(d.sig, d.msg, d.pub));
+    if (RAM) utils.logMem();
+  }
+});

benchmark/index.js

@@ -1,416 +0,0 @@
-import * as bench from 'micro-bmark';
-const { run, mark } = bench; // or bench.mark
-import { readFileSync } from 'fs';
-
-// Curves
-import { secp256k1 } from '../lib/secp256k1.js';
-import { P256 } from '../lib/p256.js';
-import { P384 } from '../lib/p384.js';
-import { P521 } from '../lib/p521.js';
-import { ed25519 } from '../lib/ed25519.js';
-import { ed448 } from '../lib/ed448.js';
-import { bls12_381 as bls } from '../lib/bls12-381.js';
-
-// Others
-import { hmac } from '@noble/hashes/hmac';
-import { sha256 } from '@noble/hashes/sha256';
-import { sha512 } from '@noble/hashes/sha512';
-
-import * as old_secp from '@noble/secp256k1';
-import * as old_bls from '@noble/bls12-381';
-import { concatBytes, hexToBytes } from '@noble/hashes/utils';
-
-import * as starkwareCrypto from '@starkware-industries/starkware-crypto-utils';
-import * as stark from '../lib/stark.js';
-
-old_secp.utils.sha256Sync = (...msgs) =>
-  sha256
-    .create()
-    .update(concatBytes(...msgs))
-    .digest();
-old_secp.utils.hmacSha256Sync = (key, ...msgs) =>
-  hmac
-    .create(sha256, key)
-    .update(concatBytes(...msgs))
-    .digest();
-import * as noble_ed25519 from '@noble/ed25519';
-noble_ed25519.utils.sha512Sync = (...m) => sha512(concatBytes(...m));
-
-// BLS
-const G2_VECTORS = readFileSync('../test/bls12-381/bls12-381-g2-test-vectors.txt', 'utf-8')
-  .trim()
-  .split('\n')
-  .map((l) => l.split(':'));
-let p1, p2, oldp1, oldp2;
-// /BLS
-
-for (let item of [secp256k1, ed25519, ed448, P256, P384, P521, old_secp, noble_ed25519]) {
-  item.utils.precompute(8);
-}
-
-const ONLY_NOBLE = process.argv[2] === 'noble';
-
-function generateData(namespace) {
-  const priv = namespace.utils.randomPrivateKey();
-  const pub = namespace.getPublicKey(priv);
-  const msg = namespace.utils.randomPrivateKey();
-  const sig = namespace.sign(msg, priv);
-  return { priv, pub, msg, sig };
-}
-
-export const CURVES = {
-  secp256k1: {
-    data: () => {
-      return generateData(secp256k1);
-    },
-    getPublicKey1: {
-      samples: 10000,
-      secp256k1_old: () => old_secp.getPublicKey(3n),
-      secp256k1: () => secp256k1.getPublicKey(3n),
-    },
-    getPublicKey255: {
-      samples: 10000,
-      secp256k1_old: () => old_secp.getPublicKey(2n ** 255n - 1n),
-      secp256k1: () => secp256k1.getPublicKey(2n ** 255n - 1n),
-    },
-    sign: {
-      samples: 5000,
-      secp256k1_old: ({ msg, priv }) => old_secp.signSync(msg, priv),
-      secp256k1: ({ msg, priv }) => secp256k1.sign(msg, priv),
-    },
-    verify: {
-      samples: 1000,
-      secp256k1_old: ({ sig, msg, pub }) => {
-        return old_secp.verify(new old_secp.Signature(sig.r, sig.s), msg, pub);
-      },
-      secp256k1: ({ sig, msg, pub }) => secp256k1.verify(sig, msg, pub),
-    },
-    getSharedSecret: {
-      samples: 1000,
-      secp256k1_old: ({ pub, priv }) => old_secp.getSharedSecret(priv, pub),
-      secp256k1: ({ pub, priv }) => secp256k1.getSharedSecret(priv, pub),
-    },
-    recoverPublicKey: {
-      samples: 1000,
-      secp256k1_old: ({ sig, msg }) =>
-        old_secp.recoverPublicKey(msg, new old_secp.Signature(sig.r, sig.s), sig.recovery),
-      secp256k1: ({ sig, msg }) => sig.recoverPublicKey(msg),
-    },
-    hashToCurve: {
-      samples: 500,
-      noble: () => secp256k1.Point.hashToCurve('abcd'),
-    },
-  },
-  ed25519: {
-    data: () => {
-      function to32Bytes(numOrStr) {
-        const hex = typeof numOrStr === 'string' ? numOrStr : numOrStr.toString(16);
-        return hexToBytes(hex.padStart(64, '0'));
-      }
-      const priv = to32Bytes(0x9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60n);
-      const pub = noble_ed25519.sync.getPublicKey(priv);
-      const msg = to32Bytes('deadbeefdeadbeefdeadbeefdeadbeefdeadbeef');
-      const sig = noble_ed25519.sync.sign(msg, priv);
-      return { pub, priv, msg, sig };
-    },
-    getPublicKey: {
-      samples: 10000,
-      old: () => noble_ed25519.sync.getPublicKey(noble_ed25519.utils.randomPrivateKey()),
-      noble: () => ed25519.getPublicKey(ed25519.utils.randomPrivateKey()),
-    },
-    sign: {
-      samples: 5000,
-      old: ({ msg, priv }) => noble_ed25519.sync.sign(msg, priv),
-      noble: ({ msg, priv }) => ed25519.sign(msg, priv),
-    },
-    verify: {
-      samples: 1000,
-      old: ({ sig, msg, pub }) => noble_ed25519.sync.verify(sig, msg, pub),
-      noble: ({ sig, msg, pub }) => ed25519.verify(sig, msg, pub),
-    },
-    hashToCurve: {
-      samples: 500,
-      noble: () => ed25519.Point.hashToCurve('abcd'),
-    },
-  },
-  ed448: {
-    data: () => {
-      const priv = ed448.utils.randomPrivateKey();
-      const pub = ed448.getPublicKey(priv);
-      const msg = ed448.utils.randomPrivateKey();
-      const sig = ed448.sign(msg, priv);
-      return { priv, pub, msg, sig };
-    },
-    getPublicKey: {
-      samples: 5000,
-      noble: () => ed448.getPublicKey(ed448.utils.randomPrivateKey()),
-    },
-    sign: {
-      samples: 2500,
-      noble: ({ msg, priv }) => ed448.sign(msg, priv),
-    },
-    verify: {
-      samples: 500,
-      noble: ({ sig, msg, pub }) => ed448.verify(sig, msg, pub),
-    },
-    hashToCurve: {
-      samples: 500,
-      noble: () => ed448.Point.hashToCurve('abcd'),
-    },
-  },
-  nist: {
-    data: () => {
-      return { p256: generateData(P256), p384: generateData(P384), p521: generateData(P521) };
-    },
-    getPublicKey: {
-      samples: 2500,
-      P256: () => P256.getPublicKey(P256.utils.randomPrivateKey()),
-      P384: () => P384.getPublicKey(P384.utils.randomPrivateKey()),
-      P521: () => P521.getPublicKey(P521.utils.randomPrivateKey()),
-    },
-    sign: {
-      samples: 1000,
-      P256: ({ p256: { msg, priv } }) => P256.sign(msg, priv),
-      P384: ({ p384: { msg, priv } }) => P384.sign(msg, priv),
-      P521: ({ p521: { msg, priv } }) => P521.sign(msg, priv),
-    },
-    verify: {
-      samples: 250,
-      P256: ({ p256: { sig, msg, pub } }) => P256.verify(sig, msg, pub),
-      P384: ({ p384: { sig, msg, pub } }) => P384.verify(sig, msg, pub),
-      P521: ({ p521: { sig, msg, pub } }) => P521.verify(sig, msg, pub),
-    },
-    hashToCurve: {
-      samples: 500,
-      P256: () => P256.Point.hashToCurve('abcd'),
-      P384: () => P384.Point.hashToCurve('abcd'),
-      P521: () => P521.Point.hashToCurve('abcd'),
-    },
-  },
-  stark: {
-    data: () => {
-      const priv = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
-      const msg = 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47';
-      const pub = stark.getPublicKey(priv);
-      const sig = stark.sign(msg, priv);
-
-      const privateKey = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
-      const msgHash = 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47';
-      const keyPair = starkwareCrypto.default.ec.keyFromPrivate(privateKey, 'hex');
-      const publicKeyStark = starkwareCrypto.default.ec.keyFromPublic(
-        keyPair.getPublic(true, 'hex'),
-        'hex'
-      );
-
-      return { priv, sig, msg, pub, publicKeyStark, msgHash, keyPair };
-    },
-    pedersen: {
-      samples: 500,
-      old: () => {
-        return starkwareCrypto.default.pedersen([
-          '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
-          '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a',
-        ]);
-      },
-      noble: () => {
-        return stark.pedersen(
-          '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
-          '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a'
-        );
-      },
-    },
-    verify: {
-      samples: 500,
-      old: ({ publicKeyStark, msgHash, keyPair }) => {
-        return starkwareCrypto.default.verify(
-          publicKeyStark,
-          msgHash,
-          starkwareCrypto.default.sign(keyPair, msgHash)
-        );
-      },
-      noble: ({ priv, msg, pub }) => {
-        return stark.verify(stark.sign(msg, priv), msg, pub);
-      },
-    },
-  },
-  'bls12-381': {
-    data: async () => {
-      const priv = '28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4c';
-      const pubs = G2_VECTORS.map((v) => bls.getPublicKey(v[0]));
-      const sigs = G2_VECTORS.map((v) => v[2]);
-      const pub = bls.getPublicKey(priv);
-      const pub512 = pubs.slice(0, 512); // .map(bls.PointG1.fromHex)
-      const pub32 = pub512.slice(0, 32);
-      const pub128 = pub512.slice(0, 128);
-      const pub2048 = pub512.concat(pub512, pub512, pub512);
-      const sig512 = sigs.slice(0, 512); // .map(bls.PointG2.fromSignature);
-      const sig32 = sig512.slice(0, 32);
-      const sig128 = sig512.slice(0, 128);
-      const sig2048 = sig512.concat(sig512, sig512, sig512);
-      return {
-        priv,
-        pubs,
-        sigs,
-        pub,
-        pub512,
-        pub32,
-        pub128,
-        pub2048,
-        sig32,
-        sig128,
-        sig512,
-        sig2048,
-      };
-    },
-    init: {
-      samples: 1,
-      old: () => {
-        oldp1 =
-          old_bls.PointG1.BASE.multiply(
-            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
-          );
-        oldp2 =
-          old_bls.PointG2.BASE.multiply(
-            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
-          );
-        old_bls.pairing(oldp1, oldp2);
-      },
-      noble: () => {
-        p1 =
-          bls.G1.Point.BASE.multiply(
-            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
-          );
-        p2 =
-          bls.G2.Point.BASE.multiply(
-            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
-          );
-        bls.pairing(p1, p2);
-      },
-    },
-    'getPublicKey (1-bit)': {
-      samples: 1000,
-      old: () => old_bls.getPublicKey('2'.padStart(64, '0')),
-      noble: () => bls.getPublicKey('2'.padStart(64, '0')),
-    },
-    getPublicKey: {
-      samples: 1000,
-      old: ({ priv }) => old_bls.getPublicKey(priv),
-      noble: ({ priv }) => bls.getPublicKey(priv),
-    },
-    sign: {
-      samples: 50,
-      old: ({ priv }) => old_bls.sign('09', priv),
-      noble: ({ priv }) => bls.sign('09', priv),
-    },
-    verify: {
-      samples: 50,
-      old: ({ pub }) =>
-        old_bls.verify(
-          '8647aa9680cd0cdf065b94e818ff2bb948cc97838bcee987b9bc1b76d0a0a6e0d85db4e9d75aaedfc79d4ea2733a21ae0579014de7636dd2943d45b87c82b1c66a289006b0b9767921bb8edd3f6c5c5dec0d54cd65f61513113c50cc977849e5',
-          '09',
-          pub
-        ),
-      noble: ({ pub }) =>
-        bls.verify(
-          '8647aa9680cd0cdf065b94e818ff2bb948cc97838bcee987b9bc1b76d0a0a6e0d85db4e9d75aaedfc79d4ea2733a21ae0579014de7636dd2943d45b87c82b1c66a289006b0b9767921bb8edd3f6c5c5dec0d54cd65f61513113c50cc977849e5',
-          '09',
-          pub
-        ),
-    },
-    pairing: {
-      samples: 100,
-      old: () => old_bls.pairing(oldp1, oldp2),
-      noble: () => bls.pairing(p1, p2),
-    },
-    'hashToCurve/G1': {
-      samples: 500,
-      old: () => old_bls.PointG1.hashToCurve('abcd'),
-      noble: () => bls.G1.Point.hashToCurve('abcd'),
-    },
-    'hashToCurve/G2': {
-      samples: 200,
-      old: () => old_bls.PointG2.hashToCurve('abcd'),
-      noble: () => bls.G2.Point.hashToCurve('abcd'),
-    },
-    // SLOW PART
-    // Requires points which we cannot init before (data fn same for all)
-    // await mark('sign/nc', 30, () => bls.sign(msgp, priv));
-    // await mark('verify/nc', 30, () => bls.verify(sigp, msgp, pubp));
-    'aggregatePublicKeys/8': {
-      samples: 100,
-      old: ({ pubs }) => old_bls.aggregatePublicKeys(pubs.slice(0, 8)),
-      noble: ({ pubs }) => bls.aggregatePublicKeys(pubs.slice(0, 8)),
-    },
-    'aggregatePublicKeys/32': {
-      samples: 50,
-      old: ({ pub32 }) => old_bls.aggregatePublicKeys(pub32.map(old_bls.PointG1.fromHex)),
-      noble: ({ pub32 }) => bls.aggregatePublicKeys(pub32.map(bls.G1.Point.fromHex)),
-    },
-    'aggregatePublicKeys/128': {
-      samples: 20,
-      old: ({ pub128 }) => old_bls.aggregatePublicKeys(pub128.map(old_bls.PointG1.fromHex)),
-      noble: ({ pub128 }) => bls.aggregatePublicKeys(pub128.map(bls.G1.Point.fromHex)),
-    },
-    'aggregatePublicKeys/512': {
-      samples: 10,
-      old: ({ pub512 }) => old_bls.aggregatePublicKeys(pub512.map(old_bls.PointG1.fromHex)),
-      noble: ({ pub512 }) => bls.aggregatePublicKeys(pub512.map(bls.G1.Point.fromHex)),
-    },
-    'aggregatePublicKeys/2048': {
-      samples: 5,
-      old: ({ pub2048 }) => old_bls.aggregatePublicKeys(pub2048.map(old_bls.PointG1.fromHex)),
-      noble: ({ pub2048 }) => bls.aggregatePublicKeys(pub2048.map(bls.G1.Point.fromHex)),
-    },
-    'aggregateSignatures/8': {
-      samples: 50,
-      old: ({ sigs }) => old_bls.aggregateSignatures(sigs.slice(0, 8)),
-      noble: ({ sigs }) => bls.aggregateSignatures(sigs.slice(0, 8)),
-    },
-    'aggregateSignatures/32': {
-      samples: 10,
-      old: ({ sig32 }) => old_bls.aggregateSignatures(sig32.map(old_bls.PointG2.fromSignature)),
-      noble: ({ sig32 }) => bls.aggregateSignatures(sig32.map(bls.Signature.decode)),
-    },
-    'aggregateSignatures/128': {
-      samples: 5,
-      old: ({ sig128 }) => old_bls.aggregateSignatures(sig128.map(old_bls.PointG2.fromSignature)),
-      noble: ({ sig128 }) => bls.aggregateSignatures(sig128.map(bls.Signature.decode)),
-    },
-    'aggregateSignatures/512': {
-      samples: 3,
-      old: ({ sig512 }) => old_bls.aggregateSignatures(sig512.map(old_bls.PointG2.fromSignature)),
-      noble: ({ sig512 }) => bls.aggregateSignatures(sig512.map(bls.Signature.decode)),
-    },
-    'aggregateSignatures/2048': {
-      samples: 2,
-      old: ({ sig2048 }) => old_bls.aggregateSignatures(sig2048.map(old_bls.PointG2.fromSignature)),
-      noble: ({ sig2048 }) => bls.aggregateSignatures(sig2048.map(bls.Signature.decode)),
-    },
-  },
-};
-
-const main = () =>
-  run(async () => {
-    for (const [name, curve] of Object.entries(CURVES)) {
-      console.log(`==== ${name} ====`);
-      const data = await curve.data();
-      for (const [fnName, libs] of Object.entries(curve)) {
-        if (fnName === 'data') continue;
-        const samples = libs.samples;
-        console.log(`  - ${fnName} (samples: ${samples})`);
-        for (const [lib, fn] of Object.entries(libs)) {
-          if (lib === 'samples') continue;
-          if (ONLY_NOBLE && lib !== 'noble') continue;
-          await mark(`    ${lib}`, samples, () => fn(data));
-        }
-      }
-    }
-    // Log current RAM
-    bench.logMem();
-  });
-
-// ESM is broken.
-import url from 'url';
-if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
-  main();
-}

benchmark/package.json

@@ -1,26 +1,22 @@
 {
-    "name": "benchmark",
+  "name": "benchmark",
-    "private": true,
+  "private": true,
-    "version": "0.1.0",
+  "version": "0.1.0",
-    "description": "benchmarks",
+  "description": "benchmarks",
-    "main": "index.js",
+  "main": "index.js",
-    "type": "module",
+  "type": "module",
-    "scripts": {
+  "scripts": {
-        "bench": "node index.js"
+    "bench": "node index.js"
-    },
+  },
-    "keywords": [],
+  "keywords": [],
-    "author": "",
+  "author": "",
-    "license": "MIT",
+  "license": "MIT",
-    "devDependencies": {
+  "devDependencies": {
-        "micro-bmark": "0.2.1"
+    "micro-bmark": "0.3.0"
-    },
+  },
-    "dependencies": {
+  "dependencies": {
-        "@noble/bls12-381": "^1.4.0",
+    "@noble/hashes": "^1.1.5",
-        "@noble/ed25519": "^1.7.1",
+    "@starkware-industries/starkware-crypto-utils": "^0.0.2",
-        "@noble/hashes": "^1.1.5",
+    "elliptic": "^6.5.4"
-        "@noble/secp256k1": "^1.7.0",
+  }
-        "@starkware-industries/starkware-crypto-utils": "^0.0.2",
-        "calculate-correlation": "^1.2.3",
-        "elliptic": "^6.5.4"
-    }
 }

benchmark/secp256k1.js

@@ -0,0 +1,22 @@
+import { run, mark, utils } from 'micro-bmark';
+import { secp256k1, schnorr } from '../lib/secp256k1.js';
+import { generateData } from './_shared.js';
+
+run(async () => {
+  const RAM = false;
+  if (RAM) utils.logMem();
+  console.log(`\x1b[36msecp256k1\x1b[0m`);
+  await mark('init', 1, () => secp256k1.utils.precompute(8));
+  const d = generateData(secp256k1);
+  await mark('getPublicKey', 10000, () => secp256k1.getPublicKey(d.priv));
+  await mark('sign', 10000, () => secp256k1.sign(d.msg, d.priv));
+  await mark('verify', 1000, () => secp256k1.verify(d.sig, d.msg, d.pub));
+  const pub2 = secp256k1.getPublicKey(secp256k1.utils.randomPrivateKey());
+  await mark('getSharedSecret', 1000, () => secp256k1.getSharedSecret(d.priv, pub2));
+  await mark('recoverPublicKey', 1000, () => d.sig.recoverPublicKey(d.msg));
+  const s = schnorr.sign(d.msg, d.priv);
+  const spub = schnorr.getPublicKey(d.priv);
+  await mark('schnorr.sign', 1000, () => schnorr.sign(d.msg, d.priv));
+  await mark('schnorr.verify', 1000, () => schnorr.verify(s, d.msg, spub));
+  if (RAM) utils.logMem();
+});

benchmark/stark.js

@@ -0,0 +1,56 @@
+import { run, mark, compare, utils } from 'micro-bmark';
+import * as starkwareCrypto from '@starkware-industries/starkware-crypto-utils';
+import * as stark from '../lib/stark.js';
+
+run(async () => {
+  const RAM = false;
+  if (RAM) utils.logMem();
+  console.log(`\x1b[36mstark\x1b[0m`);
+  await mark('init', 1, () => stark.utils.precompute(8));
+  const d = (() => {
+    const priv = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
+    const msg = 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47';
+    const pub = stark.getPublicKey(priv);
+    const sig = stark.sign(msg, priv);
+
+    const privateKey = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
+    const msgHash = 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47';
+    const keyPair = starkwareCrypto.default.ec.keyFromPrivate(privateKey, 'hex');
+    const publicKeyStark = starkwareCrypto.default.ec.keyFromPublic(
+      keyPair.getPublic(true, 'hex'),
+      'hex'
+    );
+    return { priv, sig, msg, pub, publicKeyStark, msgHash, keyPair };
+  })();
+  await compare('pedersen', 500, {
+    old: () => {
+      return starkwareCrypto.default.pedersen([
+        '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
+        '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a',
+      ]);
+    },
+    noble: () => {
+      return stark.pedersen(
+        '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
+        '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a'
+      );
+    },
+  });
+  await mark('poseidon', 10000, () => stark.poseidonHash(
+    0x3d937c035c878245caf64531a5756109c53068da139362728feb561405371cbn,
+    0x208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31an
+  ));
+  await compare('verify', 500, {
+    old: () => {
+      return starkwareCrypto.default.verify(
+        d.publicKeyStark,
+        d.msgHash,
+        starkwareCrypto.default.sign(d.keyPair, d.msgHash)
+      );
+    },
+    noble: () => {
+      return stark.verify(stark.sign(d.msg, d.priv), d.msg, d.pub);
+    },
+  });
+  if (RAM) utils.logMem();
+});

package.json

@@ -1,12 +1,12 @@
 {
   "name": "@noble/curves",
-  "version": "0.5.2",
+  "version": "0.6.1",
   "description": "Minimal, auditable JS implementation of elliptic curve cryptography",
   "files": [
     "lib"
   ],
   "scripts": {
-    "bench": "node benchmark/index.js",
+    "bench": "cd benchmark; node secp256k1.js; node curves.js; node stark.js; node bls.js",
     "build": "tsc && tsc -p tsconfig.esm.json",
     "build:release": "rollup -c rollup.config.js",
     "lint": "prettier --check 'src/**/*.{js,ts}' 'test/*.js'",
@@ -30,9 +30,9 @@
     "@scure/bip39": "~1.1.0",
     "@types/node": "18.11.3",
     "fast-check": "3.0.0",
-    "micro-bmark": "0.2.0",
+    "micro-bmark": "0.3.0",
-    "micro-should": "0.3.0",
+    "micro-should": "0.4.0",
-    "prettier": "2.6.2",
+    "prettier": "2.8.3",
     "rollup": "2.75.5",
     "typescript": "4.7.3"
   },
@@ -73,16 +73,21 @@
       "import": "./lib/esm/abstract/hash-to-curve.js",
       "default": "./lib/abstract/hash-to-curve.js"
     },
-    "./abstract/group": {
+    "./abstract/curve": {
-      "types": "./lib/abstract/group.d.ts",
+      "types": "./lib/abstract/curve.d.ts",
-      "import": "./lib/esm/abstract/group.js",
+      "import": "./lib/esm/abstract/curve.js",
-      "default": "./lib/abstract/group.js"
+      "default": "./lib/abstract/curve.js"
     },
     "./abstract/utils": {
       "types": "./lib/abstract/utils.d.ts",
       "import": "./lib/esm/abstract/utils.js",
       "default": "./lib/abstract/utils.js"
     },
+    "./abstract/poseidon": {
+      "types": "./lib/abstract/poseidon.d.ts",
+      "import": "./lib/esm/abstract/poseidon.js",
+      "default": "./lib/abstract/poseidon.js"
+    },
     "./_shortw_utils": {
       "types": "./lib/_shortw_utils.d.ts",
       "import": "./lib/esm/_shortw_utils.js",
@@ -189,4 +194,4 @@
       "url": "https://paulmillr.com/funding/"
     }
   ]
-}
+}

src/abstract/bls.ts

@@ -11,93 +11,100 @@
  * We are using Fp for private keys (shorter) and Fp₂ for signatures (longer).
  * Some projects may prefer to swap this relation, it is not supported for now.
  */
-import * as mod from './modular.js';
+import { AffinePoint } from './curve.js';
-import * as ut from './utils.js';
+import { Field, hashToPrivateScalar } from './modular.js';
-// Types require separate import
+import { Hex, PrivKey, CHash, bitLen, bitGet, hexToBytes, bytesToHex } from './utils.js';
-import { Hex, PrivKey } from './utils.js';
+import * as htf from './hash-to-curve.js';
 import {
-  htfOpts,
+  CurvePointsType,
-  stringToBytes,
+  ProjPointType as ProjPointType,
-  hash_to_field as hashToField,
+  CurvePointsRes,
-  expand_message_xmd as expandMessageXMD,
+  weierstrassPoints,
-} from './hash-to-curve.js';
+} from './weierstrass.js';
-import { CurvePointsType, PointType, CurvePointsRes, weierstrassPoints } from './weierstrass.js';
 
 type Fp = bigint; // Can be different field?
 
 export type SignatureCoder<Fp2> = {
-  decode(hex: Hex): PointType<Fp2>;
+  decode(hex: Hex): ProjPointType<Fp2>;
-  encode(point: PointType<Fp2>): Uint8Array;
+  encode(point: ProjPointType<Fp2>): Uint8Array;
 };
 
 export type CurveType<Fp, Fp2, Fp6, Fp12> = {
   r: bigint;
-  G1: Omit<CurvePointsType<Fp>, 'n'>;
+  G1: Omit<CurvePointsType<Fp>, 'n'> & {
+    mapToCurve: htf.MapToCurve<Fp>;
+    htfDefaults: htf.Opts;
+  };
   G2: Omit<CurvePointsType<Fp2>, 'n'> & {
     Signature: SignatureCoder<Fp2>;
+    mapToCurve: htf.MapToCurve<Fp2>;
+    htfDefaults: htf.Opts;
   };
   x: bigint;
-  Fp: mod.Field<Fp>;
+  Fp: Field<Fp>;
-  Fr: mod.Field<bigint>;
+  Fr: Field<bigint>;
-  Fp2: mod.Field<Fp2> & {
+  Fp2: Field<Fp2> & {
     reim: (num: Fp2) => { re: bigint; im: bigint };
     multiplyByB: (num: Fp2) => Fp2;
     frobeniusMap(num: Fp2, power: number): Fp2;
   };
-  Fp6: mod.Field<Fp6>;
+  Fp6: Field<Fp6>;
-  Fp12: mod.Field<Fp12> & {
+  Fp12: Field<Fp12> & {
     frobeniusMap(num: Fp12, power: number): Fp12;
     multiplyBy014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12;
     conjugate(num: Fp12): Fp12;
     finalExponentiate(num: Fp12): Fp12;
   };
-  htfDefaults: htfOpts;
+  htfDefaults: htf.Opts;
-  hash: ut.CHash; // Because we need outputLen for DRBG
+  hash: CHash; // Because we need outputLen for DRBG
   randomBytes: (bytesLength?: number) => Uint8Array;
 };
 
 export type CurveFn<Fp, Fp2, Fp6, Fp12> = {
   CURVE: CurveType<Fp, Fp2, Fp6, Fp12>;
-  Fr: mod.Field<bigint>;
+  Fr: Field<bigint>;
-  Fp: mod.Field<Fp>;
+  Fp: Field<Fp>;
-  Fp2: mod.Field<Fp2>;
+  Fp2: Field<Fp2>;
-  Fp6: mod.Field<Fp6>;
+  Fp6: Field<Fp6>;
-  Fp12: mod.Field<Fp12>;
+  Fp12: Field<Fp12>;
   G1: CurvePointsRes<Fp>;
   G2: CurvePointsRes<Fp2>;
   Signature: SignatureCoder<Fp2>;
   millerLoop: (ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]) => Fp12;
-  calcPairingPrecomputes: (x: Fp2, y: Fp2) => [Fp2, Fp2, Fp2][];
+  calcPairingPrecomputes: (p: AffinePoint<Fp2>) => [Fp2, Fp2, Fp2][];
-  pairing: (P: PointType<Fp>, Q: PointType<Fp2>, withFinalExponent?: boolean) => Fp12;
+  // prettier-ignore
+  hashToCurve: {
+    G1: ReturnType<(typeof htf.hashToCurve<Fp>)>,
+    G2: ReturnType<(typeof htf.hashToCurve<Fp2>)>,
+  },
+  pairing: (P: ProjPointType<Fp>, Q: ProjPointType<Fp2>, withFinalExponent?: boolean) => Fp12;
   getPublicKey: (privateKey: PrivKey) => Uint8Array;
   sign: {
     (message: Hex, privateKey: PrivKey): Uint8Array;
-    (message: PointType<Fp2>, privateKey: PrivKey): PointType<Fp2>;
+    (message: ProjPointType<Fp2>, privateKey: PrivKey): ProjPointType<Fp2>;
   };
   verify: (
-    signature: Hex | PointType<Fp2>,
+    signature: Hex | ProjPointType<Fp2>,
-    message: Hex | PointType<Fp2>,
+    message: Hex | ProjPointType<Fp2>,
-    publicKey: Hex | PointType<Fp>
+    publicKey: Hex | ProjPointType<Fp>
   ) => boolean;
   aggregatePublicKeys: {
     (publicKeys: Hex[]): Uint8Array;
-    (publicKeys: PointType<Fp>[]): PointType<Fp>;
+    (publicKeys: ProjPointType<Fp>[]): ProjPointType<Fp>;
   };
   aggregateSignatures: {
     (signatures: Hex[]): Uint8Array;
-    (signatures: PointType<Fp2>[]): PointType<Fp2>;
+    (signatures: ProjPointType<Fp2>[]): ProjPointType<Fp2>;
   };
   verifyBatch: (
-    signature: Hex | PointType<Fp2>,
+    signature: Hex | ProjPointType<Fp2>,
-    messages: (Hex | PointType<Fp2>)[],
+    messages: (Hex | ProjPointType<Fp2>)[],
-    publicKeys: (Hex | PointType<Fp>)[]
+    publicKeys: (Hex | ProjPointType<Fp>)[]
   ) => boolean;
   utils: {
-    stringToBytes: typeof stringToBytes;
+    stringToBytes: typeof htf.stringToBytes;
-    hashToField: typeof hashToField;
+    hashToField: typeof htf.hash_to_field;
-    expandMessageXMD: typeof expandMessageXMD;
+    expandMessageXMD: typeof htf.expand_message_xmd;
-    getDSTLabel: () => string;
-    setDSTLabel(newLabel: string): void;
   };
 };
 
@@ -106,12 +113,13 @@ export function bls<Fp2, Fp6, Fp12>(
 ): CurveFn<Fp, Fp2, Fp6, Fp12> {
   // Fields looks pretty specific for curve, so for now we need to pass them with options
   const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE;
-  const BLS_X_LEN = ut.bitLen(CURVE.x);
+  const BLS_X_LEN = bitLen(CURVE.x);
   const groupLen = 32; // TODO: calculate; hardcoded for now
 
   // Pre-compute coefficients for sparse multiplication
   // Point addition and point double calculations is reused for coefficients
-  function calcPairingPrecomputes(x: Fp2, y: Fp2) {
+  function calcPairingPrecomputes(p: AffinePoint<Fp2>) {
+    const { x, y } = p;
     // prettier-ignore
     const Qx = x, Qy = y, Qz = Fp2.ONE;
     // prettier-ignore
@@ -119,32 +127,32 @@ export function bls<Fp2, Fp6, Fp12>(
     let ell_coeff: [Fp2, Fp2, Fp2][] = [];
     for (let i = BLS_X_LEN - 2; i >= 0; i--) {
       // Double
-      let t0 = Fp2.square(Ry); // Ry²
+      let t0 = Fp2.sqr(Ry); // Ry²
-      let t1 = Fp2.square(Rz); // Rz²
+      let t1 = Fp2.sqr(Rz); // Rz²
       let t2 = Fp2.multiplyByB(Fp2.mul(t1, 3n)); // 3 * T1 * B
       let t3 = Fp2.mul(t2, 3n); // 3 * T2
-      let t4 = Fp2.sub(Fp2.sub(Fp2.square(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0
+      let t4 = Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0
       ell_coeff.push([
         Fp2.sub(t2, t0), // T2 - T0
-        Fp2.mul(Fp2.square(Rx), 3n), // 3 * Rx²
+        Fp2.mul(Fp2.sqr(Rx), 3n), // 3 * Rx²
-        Fp2.negate(t4), // -T4
+        Fp2.neg(t4), // -T4
       ]);
       Rx = Fp2.div(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), 2n); // ((T0 - T3) * Rx * Ry) / 2
-      Ry = Fp2.sub(Fp2.square(Fp2.div(Fp2.add(t0, t3), 2n)), Fp2.mul(Fp2.square(t2), 3n)); // ((T0 + T3) / 2)² - 3 * T2²
+      Ry = Fp2.sub(Fp2.sqr(Fp2.div(Fp2.add(t0, t3), 2n)), Fp2.mul(Fp2.sqr(t2), 3n)); // ((T0 + T3) / 2)² - 3 * T2²
       Rz = Fp2.mul(t0, t4); // T0 * T4
-      if (ut.bitGet(CURVE.x, i)) {
+      if (bitGet(CURVE.x, i)) {
         // Addition
         let t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz
         let t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz
         ell_coeff.push([
           Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)), // T0 * Qx - T1 * Qy
-          Fp2.negate(t0), // -T0
+          Fp2.neg(t0), // -T0
           t1, // T1
         ]);
-        let t2 = Fp2.square(t1); // T1²
+        let t2 = Fp2.sqr(t1); // T1²
         let t3 = Fp2.mul(t2, t1); // T2 * T1
         let t4 = Fp2.mul(t2, Rx); // T2 * Rx
-        let t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, 2n)), Fp2.mul(Fp2.square(t0), Rz)); // T3 - 2 * T4 + T0² * Rz
+        let t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, 2n)), Fp2.mul(Fp2.sqr(t0), Rz)); // T3 - 2 * T4 + T0² * 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
@@ -161,39 +169,31 @@ export function bls<Fp2, Fp6, Fp12>(
     for (let j = 0, i = BLS_X_LEN - 2; i >= 0; i--, j++) {
       const E = ell[j];
       f12 = Fp12.multiplyBy014(f12, E[0], Fp2.mul(E[1], Px), Fp2.mul(E[2], Py));
-      if (ut.bitGet(x, i)) {
+      if (bitGet(x, i)) {
         j += 1;
         const F = ell[j];
         f12 = Fp12.multiplyBy014(f12, F[0], Fp2.mul(F[1], Px), Fp2.mul(F[2], Py));
       }
-      if (i !== 0) f12 = Fp12.square(f12);
+      if (i !== 0) f12 = Fp12.sqr(f12);
     }
     return Fp12.conjugate(f12);
   }
 
   const utils = {
-    hexToBytes: ut.hexToBytes,
+    hexToBytes: hexToBytes,
-    bytesToHex: ut.bytesToHex,
+    bytesToHex: bytesToHex,
-    stringToBytes: stringToBytes,
+    stringToBytes: htf.stringToBytes,
     // TODO: do we need to export it here?
     hashToField: (
       msg: Uint8Array,
       count: number,
       options: Partial<typeof CURVE.htfDefaults> = {}
-    ) => hashToField(msg, count, { ...CURVE.htfDefaults, ...options }),
+    ) => htf.hash_to_field(msg, count, { ...CURVE.htfDefaults, ...options }),
     expandMessageXMD: (msg: Uint8Array, DST: Uint8Array, lenInBytes: number, H = CURVE.hash) =>
-      expandMessageXMD(msg, DST, lenInBytes, H),
+      htf.expand_message_xmd(msg, DST, lenInBytes, H),
-    hashToPrivateKey: (hash: Hex): Uint8Array => Fr.toBytes(ut.hashToPrivateScalar(hash, CURVE.r)),
+    hashToPrivateKey: (hash: Hex): Uint8Array => Fr.toBytes(hashToPrivateScalar(hash, CURVE.r)),
     randomBytes: (bytesLength: number = groupLen): Uint8Array => CURVE.randomBytes(bytesLength),
     randomPrivateKey: (): Uint8Array => utils.hashToPrivateKey(utils.randomBytes(groupLen + 8)),
-    getDSTLabel: () => CURVE.htfDefaults.DST,
-    setDSTLabel(newLabel: string) {
-      // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3.1
-      if (typeof newLabel !== 'string' || newLabel.length > 2048 || newLabel.length === 0) {
-        throw new TypeError('Invalid DST');
-      }
-      CURVE.htfDefaults.DST = newLabel;
-    },
   };
 
   // Point on G1 curve: (x, y)
@@ -201,6 +201,10 @@ export function bls<Fp2, Fp6, Fp12>(
     n: Fr.ORDER,
     ...CURVE.G1,
   });
+  const G1HashToCurve = htf.hashToCurve(G1.ProjectivePoint, CURVE.G1.mapToCurve, {
+    ...CURVE.htfDefaults,
+    ...CURVE.G1.htfDefaults,
+  });
 
   // Sparse multiplication against precomputed coefficients
   // TODO: replace with weakmap?
@@ -208,83 +212,93 @@ export function bls<Fp2, Fp6, Fp12>(
   function pairingPrecomputes(point: G2): [Fp2, Fp2, Fp2][] {
     const p = point as G2 & withPairingPrecomputes;
     if (p._PPRECOMPUTES) return p._PPRECOMPUTES;
-    p._PPRECOMPUTES = calcPairingPrecomputes(p.x, p.y);
+    p._PPRECOMPUTES = calcPairingPrecomputes(point.toAffine());
     return p._PPRECOMPUTES;
   }
 
-  function clearPairingPrecomputes(point: G2) {
+  // TODO: export
-    const p = point as G2 & withPairingPrecomputes;
+  // function clearPairingPrecomputes(point: G2) {
-    p._PPRECOMPUTES = undefined;
+  //   const p = point as G2 & withPairingPrecomputes;
-  }
+  //   p._PPRECOMPUTES = undefined;
-  clearPairingPrecomputes;
+  // }
-
-  function millerLoopG1(Q: G1, P: G2): Fp12 {
-    return millerLoop(pairingPrecomputes(P), [Q.x, Q.y]);
-  }
 
   // Point on G2 curve (complex numbers): (x₁, x₂+i), (y₁, y₂+i)
   const G2 = weierstrassPoints({
     n: Fr.ORDER,
     ...CURVE.G2,
   });
+  const C = G2.ProjectivePoint as htf.H2CPointConstructor<Fp2>; // TODO: fix
+  const G2HashToCurve = htf.hashToCurve(C, CURVE.G2.mapToCurve, {
+    ...CURVE.htfDefaults,
+    ...CURVE.G2.htfDefaults,
+  });
+
   const { Signature } = CURVE.G2;
 
   // Calculates bilinear pairing
-  function pairing(P: G1, Q: G2, withFinalExponent: boolean = true): Fp12 {
+  function pairing(Q: G1, P: G2, withFinalExponent: boolean = true): Fp12 {
-    if (P.equals(G1.Point.ZERO) || Q.equals(G2.Point.ZERO))
+    if (Q.equals(G1.ProjectivePoint.ZERO) || P.equals(G2.ProjectivePoint.ZERO))
-      throw new Error('No pairings at point of Infinity');
+      throw new Error('pairing is not available for ZERO point');
-    P.assertValidity();
     Q.assertValidity();
+    P.assertValidity();
     // Performance: 9ms for millerLoop and ~14ms for exp.
-    const looped = millerLoopG1(P, Q);
+    const Qa = Q.toAffine();
+    const looped = millerLoop(pairingPrecomputes(P), [Qa.x, Qa.y]);
     return withFinalExponent ? Fp12.finalExponentiate(looped) : looped;
   }
-  type G1 = typeof G1.Point.BASE;
+  type G1 = typeof G1.ProjectivePoint.BASE;
-  type G2 = typeof G2.Point.BASE;
+  type G2 = typeof G2.ProjectivePoint.BASE;
 
   type G1Hex = Hex | G1;
   type G2Hex = Hex | G2;
   function normP1(point: G1Hex): G1 {
-    return point instanceof G1.Point ? (point as G1) : G1.Point.fromHex(point);
+    return point instanceof G1.ProjectivePoint ? (point as G1) : G1.ProjectivePoint.fromHex(point);
   }
   function normP2(point: G2Hex): G2 {
-    return point instanceof G2.Point ? point : Signature.decode(point);
+    return point instanceof G2.ProjectivePoint ? point : Signature.decode(point);
   }
-  function normP2Hash(point: G2Hex): G2 {
+  function normP2Hash(point: G2Hex, htfOpts?: htf.htfBasicOpts): G2 {
-    return point instanceof G2.Point ? point : G2.Point.hashToCurve(point);
+    return point instanceof G2.ProjectivePoint
+      ? point
+      : (G2HashToCurve.hashToCurve(point, htfOpts) as G2);
   }
 
   // Multiplies generator by private key.
   // P = pk x G
   function getPublicKey(privateKey: PrivKey): Uint8Array {
-    return G1.Point.fromPrivateKey(privateKey).toRawBytes(true);
+    return G1.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true);
   }
 
   // Executes `hashToCurve` on the message and then multiplies the result by private key.
   // S = pk x H(m)
-  function sign(message: Hex, privateKey: PrivKey): Uint8Array;
+  function sign(message: Hex, privateKey: PrivKey, htfOpts?: htf.htfBasicOpts): Uint8Array;
-  function sign(message: G2, privateKey: PrivKey): G2;
+  function sign(message: G2, privateKey: PrivKey, htfOpts?: htf.htfBasicOpts): G2;
-  function sign(message: G2Hex, privateKey: PrivKey): Uint8Array | G2 {
+  function sign(message: G2Hex, privateKey: PrivKey, htfOpts?: htf.htfBasicOpts): Uint8Array | G2 {
-    const msgPoint = normP2Hash(message);
+    const msgPoint = normP2Hash(message, htfOpts);
     msgPoint.assertValidity();
     const sigPoint = msgPoint.multiply(G1.normalizePrivateKey(privateKey));
-    if (message instanceof G2.Point) return sigPoint;
+    if (message instanceof G2.ProjectivePoint) return sigPoint;
     return Signature.encode(sigPoint);
   }
 
   // Checks if pairing of public key & hash is equal to pairing of generator & signature.
   // e(P, H(m)) == e(G, S)
-  function verify(signature: G2Hex, message: G2Hex, publicKey: G1Hex): boolean {
+  function verify(
+    signature: G2Hex,
+    message: G2Hex,
+    publicKey: G1Hex,
+    htfOpts?: htf.htfBasicOpts
+  ): boolean {
     const P = normP1(publicKey);
-    const Hm = normP2Hash(message);
+    const Hm = normP2Hash(message, htfOpts);
-    const G = G1.Point.BASE;
+    const G = G1.ProjectivePoint.BASE;
     const S = normP2(signature);
     // Instead of doing 2 exponentiations, we use property of billinear maps
     // and do one exp after multiplying 2 points.
     const ePHm = pairing(P.negate(), Hm, false);
     const eGS = pairing(G, S, false);
     const exp = Fp12.finalExponentiate(Fp12.mul(eGS, ePHm));
-    return Fp12.equals(exp, Fp12.ONE);
+    return Fp12.eql(exp, Fp12.ONE);
   }
 
   // Adds a bunch of public key points together.
@@ -293,11 +307,9 @@ export function bls<Fp2, Fp6, Fp12>(
   function aggregatePublicKeys(publicKeys: G1[]): G1;
   function aggregatePublicKeys(publicKeys: G1Hex[]): Uint8Array | G1 {
     if (!publicKeys.length) throw new Error('Expected non-empty array');
-    const agg = publicKeys
+    const agg = publicKeys.map(normP1).reduce((sum, p) => sum.add(p), G1.ProjectivePoint.ZERO);
-      .map(normP1)
+    const aggAffine = agg; //.toAffine();
-      .reduce((sum, p) => sum.add(G1.ProjectivePoint.fromAffine(p)), G1.ProjectivePoint.ZERO);
+    if (publicKeys[0] instanceof G1.ProjectivePoint) {
-    const aggAffine = agg.toAffine();
-    if (publicKeys[0] instanceof G1.Point) {
       aggAffine.assertValidity();
       return aggAffine;
     }
@@ -310,11 +322,9 @@ export function bls<Fp2, Fp6, Fp12>(
   function aggregateSignatures(signatures: G2[]): G2;
   function aggregateSignatures(signatures: G2Hex[]): Uint8Array | G2 {
     if (!signatures.length) throw new Error('Expected non-empty array');
-    const agg = signatures
+    const agg = signatures.map(normP2).reduce((sum, s) => sum.add(s), G2.ProjectivePoint.ZERO);
-      .map(normP2)
+    const aggAffine = agg; //.toAffine();
-      .reduce((sum, s) => sum.add(G2.ProjectivePoint.fromAffine(s)), G2.ProjectivePoint.ZERO);
+    if (signatures[0] instanceof G2.ProjectivePoint) {
-    const aggAffine = agg.toAffine();
-    if (signatures[0] instanceof G2.Point) {
       aggAffine.assertValidity();
       return aggAffine;
     }
@@ -323,12 +333,20 @@ export function bls<Fp2, Fp6, Fp12>(
 
   // https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407
   // e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))
-  function verifyBatch(signature: G2Hex, messages: G2Hex[], publicKeys: G1Hex[]): boolean {
+  function verifyBatch(
+    signature: G2Hex,
+    messages: G2Hex[],
+    publicKeys: G1Hex[],
+    htfOpts?: htf.htfBasicOpts
+  ): boolean {
+    // @ts-ignore
+    // console.log('verifyBatch', bytesToHex(signature as any), messages, publicKeys.map(bytesToHex));
+
     if (!messages.length) throw new Error('Expected non-empty messages array');
     if (publicKeys.length !== messages.length)
       throw new Error('Pubkey count should equal msg count');
     const sig = normP2(signature);
-    const nMessages = messages.map(normP2Hash);
+    const nMessages = messages.map((i) => normP2Hash(i, htfOpts));
     const nPublicKeys = publicKeys.map(normP1);
     try {
       const paired = [];
@@ -336,23 +354,23 @@ export function bls<Fp2, Fp6, Fp12>(
         const groupPublicKey = nMessages.reduce(
           (groupPublicKey, subMessage, i) =>
             subMessage === message ? groupPublicKey.add(nPublicKeys[i]) : groupPublicKey,
-          G1.Point.ZERO
+          G1.ProjectivePoint.ZERO
         );
         // const msg = message instanceof PointG2 ? message : await PointG2.hashToCurve(message);
         // Possible to batch pairing for same msg with different groupPublicKey here
         paired.push(pairing(groupPublicKey, message, false));
       }
-      paired.push(pairing(G1.Point.BASE.negate(), sig, false));
+      paired.push(pairing(G1.ProjectivePoint.BASE.negate(), sig, false));
       const product = paired.reduce((a, b) => Fp12.mul(a, b), Fp12.ONE);
       const exp = Fp12.finalExponentiate(product);
-      return Fp12.equals(exp, Fp12.ONE);
+      return Fp12.eql(exp, Fp12.ONE);
     } catch {
       return false;
     }
   }
 
-  // Pre-compute points. Refer to README.
+  G1.ProjectivePoint.BASE._setWindowSize(4);
-  G1.Point.BASE._setWindowSize(4);
+
   return {
     CURVE,
     Fr,
@@ -365,6 +383,7 @@ export function bls<Fp2, Fp6, Fp12>(
     Signature,
     millerLoop,
     calcPairingPrecomputes,
+    hashToCurve: { G1: G1HashToCurve, G2: G2HashToCurve },
     pairing,
     getPublicKey,
     sign,

src/abstract/curve.ts

@@ -1,22 +1,32 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 // Abelian group utilities
+import { Field, validateField, nLength } from './modular.js';
+import { validateObject } from './utils.js';
 const _0n = BigInt(0);
 const _1n = BigInt(1);
 
+export type AffinePoint<T> = {
+  x: T;
+  y: T;
+} & { z?: never; t?: never };
+
 export interface Group<T extends Group<T>> {
   double(): T;
   negate(): T;
   add(other: T): T;
   subtract(other: T): T;
   equals(other: T): boolean;
-  multiply(scalar: number | bigint): T;
+  multiply(scalar: bigint): T;
 }
 
 export type GroupConstructor<T> = {
   BASE: T;
   ZERO: T;
 };
-// Not big, but pretty complex and it is easy to break stuff. To avoid too much copy paste
+export type Mapper<T> = (i: T[]) => T[];
+
+// Elliptic curve multiplication of Point by scalar. Complicated and fragile. Uses wNAF method.
+// Windowed method is 10% faster, but takes 2x longer to generate & consumes 2x memory.
 export function wNAF<T extends Group<T>>(c: GroupConstructor<T>, bits: number) {
   const constTimeNegate = (condition: boolean, item: T): T => {
     const neg = item.negate();
@@ -125,5 +135,52 @@ export function wNAF<T extends Group<T>>(c: GroupConstructor<T>, bits: number) {
       // which makes it less const-time: around 1 bigint multiply.
       return { p, f };
     },
+
+    wNAFCached(P: T, precomputesMap: Map<T, T[]>, n: bigint, transform: Mapper<T>): { p: T; f: T } {
+      // @ts-ignore
+      const W: number = P._WINDOW_SIZE || 1;
+      // Calculate precomputes on a first run, reuse them after
+      let comp = precomputesMap.get(P);
+      if (!comp) {
+        comp = this.precomputeWindow(P, W) as T[];
+        if (W !== 1) {
+          precomputesMap.set(P, transform(comp));
+        }
+      }
+      return this.wNAF(W, comp, n);
+    },
   };
 }
+
+// Generic BasicCurve interface: works even for polynomial fields (BLS): P, n, h would be ok.
+// Though generator can be different (Fp2 / Fp6 for BLS).
+export type BasicCurve<T> = {
+  Fp: Field<T>; // Field over which we'll do calculations (Fp)
+  n: bigint; // Curve order, total count of valid points in the field
+  nBitLength?: number; // bit length of curve order
+  nByteLength?: number; // byte length of curve order
+  h: bigint; // cofactor. we can assign default=1, but users will just ignore it w/o validation
+  hEff?: bigint; // Number to multiply to clear cofactor
+  Gx: T; // base point X coordinate
+  Gy: T; // base point Y coordinate
+  allowInfinityPoint?: boolean; // bls12-381 requires it. ZERO point is valid, but invalid pubkey
+};
+
+export function validateBasic<FP, T>(curve: BasicCurve<FP> & T) {
+  validateField(curve.Fp);
+  validateObject(
+    curve,
+    {
+      n: 'bigint',
+      h: 'bigint',
+      Gx: 'field',
+      Gy: 'field',
+    },
+    {
+      nBitLength: 'isSafeInteger',
+      nByteLength: 'isSafeInteger',
+    }
+  );
+  // Set defaults
+  return Object.freeze({ ...nLength(curve.n, curve.nBitLength), ...curve } as const);
+}

src/abstract/edwards.ts

@@ -1,19 +1,9 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 // Twisted Edwards curve. The formula is: ax² + y² = 1 + dx²y²
-
+import { mod } from './modular.js';
-// Differences from @noble/ed25519 1.7:
-// 1. Variable field element lengths between EDDSA/ECDH:
-//   EDDSA (RFC8032) is 456 bits / 57 bytes, ECDH (RFC7748) is 448 bits / 56 bytes
-// 2. Different addition formula (doubling is same)
-// 3. uvRatio differs between curves (half-expected, not only pow fn changes)
-// 4. Point decompression code is different (unexpected), now using generalized formula
-// 5. Domain function was no-op for ed25519, but adds some data even with empty context for ed448
-
-import * as mod from './modular.js';
 import * as ut from './utils.js';
-import { ensureBytes, Hex, PrivKey } from './utils.js';
+import { ensureBytes, FHash, Hex } from './utils.js';
-import { Group, GroupConstructor, wNAF } from './group.js';
+import { Group, GroupConstructor, wNAF, BasicCurve, validateBasic, AffinePoint } from './curve.js';
-import { hash_to_field as hashToField, htfOpts, validateHTFOpts } from './hash-to-curve.js';
 
 // Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
 const _0n = BigInt(0);
@@ -22,142 +12,92 @@ const _2n = BigInt(2);
 const _8n = BigInt(8);
 
 // Edwards curves must declare params a & d.
-export type CurveType = ut.BasicCurve<bigint> & {
+export type CurveType = BasicCurve<bigint> & {
-  // Params: a, d
+  a: bigint; // curve param a
-  a: bigint;
+  d: bigint; // curve param d
-  d: bigint;
+  hash: FHash; // Hashing
-  // Hashes
+  randomBytes: (bytesLength?: number) => Uint8Array; // CSPRNG
-  // The interface, because we need outputLen for DRBG
+  adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array; // clears bits to get valid field elemtn
-  hash: ut.CHash;
+  domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array; // Used for hashing
-  // CSPRNG
+  uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint }; // Ratio √(u/v)
-  randomBytes: (bytesLength?: number) => Uint8Array;
+  preHash?: FHash; // RFC 8032 pre-hashing of messages to sign() / verify()
-  // Probably clears bits in a byte array to produce a valid field element
+  mapToCurve?: (scalar: bigint[]) => AffinePoint<bigint>; // for hash-to-curve standard
-  adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array;
-  // Used during hashing
-  domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array;
-  // Ratio √(u/v)
-  uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint };
-  // RFC 8032 pre-hashing of messages to sign() / verify()
-  preHash?: ut.CHash;
-  // Hash to field options
-  htfDefaults?: htfOpts;
-  mapToCurve?: (scalar: bigint[]) => { x: bigint; y: bigint };
 };
 
 function validateOpts(curve: CurveType) {
-  const opts = ut.validateOpts(curve);
+  const opts = validateBasic(curve);
-  if (typeof opts.hash !== 'function' || !ut.isPositiveInt(opts.hash.outputLen))
+  ut.validateObject(
-    throw new Error('Invalid hash function');
+    curve,
-  for (const i of ['a', 'd'] as const) {
+    {
-    const val = opts[i];
+      hash: 'function',
-    if (typeof val !== 'bigint') throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
+      a: 'bigint',
-  }
+      d: 'bigint',
-  for (const fn of ['randomBytes'] as const) {
+      randomBytes: 'function',
-    if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
+    },
-  }
+    {
-  for (const fn of ['adjustScalarBytes', 'domain', 'uvRatio', 'mapToCurve'] as const) {
+      adjustScalarBytes: 'function',
-    if (opts[fn] === undefined) continue; // Optional
+      domain: 'function',
-    if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
+      uvRatio: 'function',
-  }
+      mapToCurve: 'function',
-  if (opts.htfDefaults !== undefined) validateHTFOpts(opts.htfDefaults);
+    }
+  );
   // Set defaults
   return Object.freeze({ ...opts } as const);
 }
 
-// Instance
-export interface SignatureType {
-  readonly r: PointType;
-  readonly s: bigint;
-  assertValidity(): SignatureType;
-  toRawBytes(): Uint8Array;
-  toHex(): string;
-}
-// Static methods
-export type SignatureConstructor = {
-  new (r: PointType, s: bigint): SignatureType;
-  fromHex(hex: Hex): SignatureType;
-};
-
 // Instance of Extended Point with coordinates in X, Y, Z, T
-export interface ExtendedPointType extends Group<ExtendedPointType> {
+export interface ExtPointType extends Group<ExtPointType> {
-  readonly x: bigint;
+  readonly ex: bigint;
-  readonly y: bigint;
+  readonly ey: bigint;
-  readonly z: bigint;
+  readonly ez: bigint;
-  readonly t: bigint;
+  readonly et: bigint;
-  multiply(scalar: number | bigint, affinePoint?: PointType): ExtendedPointType;
+  assertValidity(): void;
-  multiplyUnsafe(scalar: number | bigint): ExtendedPointType;
+  multiply(scalar: bigint): ExtPointType;
+  multiplyUnsafe(scalar: bigint): ExtPointType;
   isSmallOrder(): boolean;
   isTorsionFree(): boolean;
-  toAffine(invZ?: bigint): PointType;
+  clearCofactor(): ExtPointType;
-  clearCofactor(): ExtendedPointType;
+  toAffine(iz?: bigint): AffinePoint<bigint>;
 }
 // Static methods of Extended Point with coordinates in X, Y, Z, T
-export interface ExtendedPointConstructor extends GroupConstructor<ExtendedPointType> {
+export interface ExtPointConstructor extends GroupConstructor<ExtPointType> {
-  new (x: bigint, y: bigint, z: bigint, t: bigint): ExtendedPointType;
+  new (x: bigint, y: bigint, z: bigint, t: bigint): ExtPointType;
-  fromAffine(p: PointType): ExtendedPointType;
+  fromAffine(p: AffinePoint<bigint>): ExtPointType;
-  toAffineBatch(points: ExtendedPointType[]): PointType[];
+  fromHex(hex: Hex): ExtPointType;
-  normalizeZ(points: ExtendedPointType[]): ExtendedPointType[];
+  fromPrivateKey(privateKey: Hex): ExtPointType;
 }
 
-// Instance of Affine Point with coordinates in X, Y
-export interface PointType extends Group<PointType> {
-  readonly x: bigint;
-  readonly y: bigint;
-  _setWindowSize(windowSize: number): void;
-  toRawBytes(isCompressed?: boolean): Uint8Array;
-  toHex(isCompressed?: boolean): string;
-  isTorsionFree(): boolean;
-  clearCofactor(): PointType;
-}
-// Static methods of Affine Point with coordinates in X, Y
-export interface PointConstructor extends GroupConstructor<PointType> {
-  new (x: bigint, y: bigint): PointType;
-  fromHex(hex: Hex): PointType;
-  fromPrivateKey(privateKey: PrivKey): PointType;
-  hashToCurve(msg: Hex, options?: Partial<htfOpts>): PointType;
-  encodeToCurve(msg: Hex, options?: Partial<htfOpts>): PointType;
-}
-
-export type PubKey = Hex | PointType;
-export type SigType = Hex | SignatureType;
-
 export type CurveFn = {
   CURVE: ReturnType<typeof validateOpts>;
-  getPublicKey: (privateKey: PrivKey, isCompressed?: boolean) => Uint8Array;
+  getPublicKey: (privateKey: Hex) => Uint8Array;
   sign: (message: Hex, privateKey: Hex) => Uint8Array;
-  verify: (sig: SigType, message: Hex, publicKey: PubKey) => boolean;
+  verify: (sig: Hex, message: Hex, publicKey: Hex) => boolean;
-  Point: PointConstructor;
+  ExtendedPoint: ExtPointConstructor;
-  ExtendedPoint: ExtendedPointConstructor;
-  Signature: SignatureConstructor;
   utils: {
     randomPrivateKey: () => Uint8Array;
-    getExtendedPublicKey: (key: PrivKey) => {
+    getExtendedPublicKey: (key: Hex) => {
       head: Uint8Array;
       prefix: Uint8Array;
       scalar: bigint;
-      point: PointType;
+      point: ExtPointType;
       pointBytes: Uint8Array;
     };
   };
 };
 
-// NOTE: it is not generic twisted curve for now, but ed25519/ed448 generic implementation
+// It is not generic twisted curve for now, but ed25519/ed448 generic implementation
 export function twistedEdwards(curveDef: CurveType): CurveFn {
   const CURVE = validateOpts(curveDef) as ReturnType<typeof validateOpts>;
-  const Fp = CURVE.Fp;
+  const { Fp, n: CURVE_ORDER, preHash, hash: cHash, randomBytes, nByteLength, h: cofactor } = CURVE;
-  const CURVE_ORDER = CURVE.n;
+  const MASK = _2n ** BigInt(nByteLength * 8);
-  const maxGroupElement = _2n ** BigInt(CURVE.nByteLength * 8);
+  const modP = Fp.create; // Function overrides
-
-  // Function overrides
-  const { randomBytes } = CURVE;
-  const modP = Fp.create;
 
   // sqrt(u/v)
   const uvRatio =
     CURVE.uvRatio ||
     ((u: bigint, v: bigint) => {
       try {
-        return { isValid: true, value: Fp.sqrt(u * Fp.invert(v)) };
+        return { isValid: true, value: Fp.sqrt(u * Fp.inv(v)) };
       } catch (e) {
         return { isValid: false, value: _0n };
       }
@@ -169,41 +109,76 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       if (ctx.length || phflag) throw new Error('Contexts/pre-hash are not supported');
       return data;
     }); // NOOP
+  const inBig = (n: bigint) => typeof n === 'bigint' && 0n < n; // n in [1..]
+  const inRange = (n: bigint, max: bigint) => inBig(n) && inBig(max) && n < max; // n in [1..max-1]
+  const in0MaskRange = (n: bigint) => n === _0n || inRange(n, MASK); // n in [0..MASK-1]
+  function assertInRange(n: bigint, max: bigint) {
+    // n in [1..max-1]
+    if (inRange(n, max)) return n;
+    throw new Error(`Expected valid scalar < ${max}, got ${typeof n} ${n}`);
+  }
+  function assertGE0(n: bigint) {
+    // n in [0..CURVE_ORDER-1]
+    return n === _0n ? n : assertInRange(n, CURVE_ORDER); // GE = prime subgroup, not full group
+  }
+  const pointPrecomputes = new Map<Point, Point[]>();
+  function isPoint(other: unknown) {
+    if (!(other instanceof Point)) throw new Error('ExtendedPoint 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 implements ExtPointType {
+    static readonly BASE = new Point(CURVE.Gx, CURVE.Gy, _1n, modP(CURVE.Gx * CURVE.Gy));
+    static readonly ZERO = new Point(_0n, _1n, _1n, _0n); // 0, 1, 1, 0
 
-  /**
+    constructor(
-   * Extended Point works in extended coordinates: (x, y, z, t) ∋ (x=x/z, y=y/z, t=xy).
+      readonly ex: bigint,
-   * Default Point works in affine coordinates: (x, y)
+      readonly ey: bigint,
-   * https://en.wikipedia.org/wiki/Twisted_Edwards_curve#Extended_coordinates
+      readonly ez: bigint,
-   */
+      readonly et: bigint
-  class ExtendedPoint implements ExtendedPointType {
+    ) {
-    constructor(readonly x: bigint, readonly y: bigint, readonly z: bigint, readonly t: bigint) {}
+      if (!in0MaskRange(ex)) throw new Error('x required');
-
+      if (!in0MaskRange(ey)) throw new Error('y required');
-    static BASE = new ExtendedPoint(CURVE.Gx, CURVE.Gy, _1n, modP(CURVE.Gx * CURVE.Gy));
+      if (!in0MaskRange(ez)) throw new Error('z required');
-    static ZERO = new ExtendedPoint(_0n, _1n, _1n, _0n);
+      if (!in0MaskRange(et)) throw new Error('t required');
-    static fromAffine(p: Point): ExtendedPoint {
-      if (!(p instanceof Point)) {
-        throw new TypeError('ExtendedPoint#fromAffine: expected Point');
-      }
-      if (p.equals(Point.ZERO)) return ExtendedPoint.ZERO;
-      return new ExtendedPoint(p.x, p.y, _1n, modP(p.x * p.y));
-    }
-    // Takes a bunch of Jacobian Points but executes only one
-    // invert on all of them. invert is very slow operation,
-    // so this improves performance massively.
-    static toAffineBatch(points: ExtendedPoint[]): Point[] {
-      const toInv = Fp.invertBatch(points.map((p) => p.z));
-      return points.map((p, i) => p.toAffine(toInv[i]));
     }
 
-    static normalizeZ(points: ExtendedPoint[]): ExtendedPoint[] {
+    get x(): bigint {
-      return this.toAffineBatch(points).map(this.fromAffine);
+      return this.toAffine().x;
     }
+    get y(): bigint {
+      return this.toAffine().y;
+    }
+
+    static fromAffine(p: AffinePoint<bigint>): Point {
+      if (p instanceof Point) throw new Error('extended point not allowed');
+      const { x, y } = p || {};
+      if (!in0MaskRange(x) || !in0MaskRange(y)) throw new Error('invalid affine point');
+      return new Point(x, y, _1n, modP(x * y));
+    }
+    static normalizeZ(points: Point[]): Point[] {
+      const toInv = Fp.invertBatch(points.map((p) => p.ez));
+      return points.map((p, i) => p.toAffine(toInv[i])).map(Point.fromAffine);
+    }
+
+    // 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.
+    _WINDOW_SIZE?: number;
+
+    // "Private method", don't use it directly
+    _setWindowSize(windowSize: number) {
+      this._WINDOW_SIZE = windowSize;
+      pointPrecomputes.delete(this);
+    }
+
+    assertValidity(): void {}
 
     // Compare one point to another.
-    equals(other: ExtendedPoint): boolean {
+    equals(other: Point): boolean {
-      assertExtPoint(other);
+      isPoint(other);
-      const { x: X1, y: Y1, z: Z1 } = this;
+      const { ex: X1, ey: Y1, ez: Z1 } = this;
-      const { x: X2, y: Y2, z: Z2 } = other;
+      const { ex: X2, ey: Y2, ez: Z2 } = other;
       const X1Z2 = modP(X1 * Z2);
       const X2Z1 = modP(X2 * Z1);
       const Y1Z2 = modP(Y1 * Z2);
@@ -211,17 +186,21 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       return X1Z2 === X2Z1 && Y1Z2 === Y2Z1;
     }
 
-    // Inverses point to one corresponding to (x, -y) in Affine coordinates.
+    protected is0(): boolean {
-    negate(): ExtendedPoint {
+      return this.equals(Point.ZERO);
-      return new ExtendedPoint(modP(-this.x), this.y, this.z, modP(-this.t));
+    }
+
+    negate(): Point {
+      // Flips point sign to a negative one (-x, y in affine coords)
+      return new Point(modP(-this.ex), this.ey, this.ez, modP(-this.et));
     }
 
     // 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(): ExtendedPoint {
+    double(): Point {
       const { a } = CURVE;
-      const { x: X1, y: Y1, z: Z1 } = this;
+      const { ex: X1, ey: Y1, ez: 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
@@ -235,17 +214,17 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       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 ExtendedPoint(X3, Y3, Z3, T3);
+      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: ExtendedPoint) {
+    add(other: Point) {
-      assertExtPoint(other);
+      isPoint(other);
       const { a, d } = CURVE;
-      const { x: X1, y: Y1, z: Z1, t: T1 } = this;
+      const { ex: X1, ey: Y1, ez: Z1, et: T1 } = this;
-      const { x: X2, y: Y2, z: Z2, t: T2 } = other;
+      const { ex: X2, ey: Y2, ez: Z2, et: T2 } = other;
       // Faster algo for adding 2 Extended Points when curve's a=-1.
       // http://hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html#addition-add-2008-hwcd-4
       // Cost: 8M + 8add + 2*2.
@@ -264,7 +243,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
         const Y3 = modP(G * H);
         const T3 = modP(E * H);
         const Z3 = modP(F * G);
-        return new ExtendedPoint(X3, Y3, Z3, T3);
+        return new Point(X3, Y3, Z3, T3);
       }
       const A = modP(X1 * X2); // A = X1*X2
       const B = modP(Y1 * Y2); // B = Y1*Y2
@@ -279,44 +258,31 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       const T3 = modP(E * H); // T3 = E*H
       const Z3 = modP(F * G); // Z3 = F*G
 
-      return new ExtendedPoint(X3, Y3, Z3, T3);
+      return new Point(X3, Y3, Z3, T3);
     }
 
-    subtract(other: ExtendedPoint): ExtendedPoint {
+    subtract(other: Point): Point {
       return this.add(other.negate());
     }
 
-    private wNAF(n: bigint, affinePoint?: Point): ExtendedPoint {
+    private wNAF(n: bigint): { p: Point; f: Point } {
-      if (!affinePoint && this.equals(ExtendedPoint.BASE)) affinePoint = Point.BASE;
+      return wnaf.wNAFCached(this, pointPrecomputes, n, Point.normalizeZ);
-      const W = (affinePoint && affinePoint._WINDOW_SIZE) || 1;
-      let precomputes = affinePoint && pointPrecomputes.get(affinePoint);
-      if (!precomputes) {
-        precomputes = wnaf.precomputeWindow(this, W) as ExtendedPoint[];
-        if (affinePoint && W !== 1) {
-          precomputes = ExtendedPoint.normalizeZ(precomputes);
-          pointPrecomputes.set(affinePoint, precomputes);
-        }
-      }
-      const { p, f } = wnaf.wNAF(W, precomputes, n);
-      return ExtendedPoint.normalizeZ([p, f])[0];
     }
 
-    // Constant time multiplication.
+    // Constant-time multiplication.
-    // Uses wNAF method. Windowed method may be 10% faster,
+    multiply(scalar: bigint): Point {
-    // but takes 2x longer to generate and consumes 2x memory.
+      const { p, f } = this.wNAF(assertInRange(scalar, CURVE_ORDER));
-    multiply(scalar: number | bigint, affinePoint?: Point): ExtendedPoint {
+      return Point.normalizeZ([p, f])[0];
-      return this.wNAF(normalizeScalar(scalar, CURVE_ORDER), affinePoint);
     }
 
     // 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.
-    multiplyUnsafe(scalar: number | bigint): ExtendedPoint {
+    multiplyUnsafe(scalar: bigint): Point {
-      let n = normalizeScalar(scalar, CURVE_ORDER, false);
+      let n = assertGE0(scalar);
-      const P0 = ExtendedPoint.ZERO;
+      if (n === _0n) return I;
-      if (n === _0n) return P0;
+      if (this.equals(I) || n === _1n) return this;
-      if (this.equals(P0) || n === _1n) return this;
+      if (this.equals(G)) return this.wNAF(n).p;
-      if (this.equals(ExtendedPoint.BASE)) return this.wNAF(n);
       return wnaf.unsafeLadder(this, n);
     }
 
@@ -325,350 +291,156 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     // point with torsion component.
     // Multiplies point by cofactor and checks if the result is 0.
     isSmallOrder(): boolean {
-      return this.multiplyUnsafe(CURVE.h).equals(ExtendedPoint.ZERO);
+      return this.multiplyUnsafe(cofactor).is0();
     }
 
-    // Multiplies point by curve order (very big scalar CURVE.n) and checks if the result is 0.
+    // Multiplies point by curve order and checks if the result is 0.
     // Returns `false` is the point is dirty.
     isTorsionFree(): boolean {
-      return wnaf.unsafeLadder(this, CURVE_ORDER).equals(ExtendedPoint.ZERO);
+      return wnaf.unsafeLadder(this, CURVE_ORDER).is0();
     }
 
     // Converts Extended point to default (x, y) coordinates.
     // Can accept precomputed Z^-1 - for example, from invertBatch.
-    toAffine(invZ?: bigint): Point {
+    toAffine(iz?: bigint): AffinePoint<bigint> {
-      const { x, y, z } = this;
+      const { ex: x, ey: y, ez: z } = this;
-      const is0 = this.equals(ExtendedPoint.ZERO);
+      const is0 = this.is0();
-      if (invZ == null) invZ = is0 ? _8n : (Fp.invert(z) as bigint); // 8 was chosen arbitrarily
+      if (iz == null) iz = is0 ? _8n : (Fp.inv(z) as bigint); // 8 was chosen arbitrarily
-      const ax = modP(x * invZ);
+      const ax = modP(x * iz);
-      const ay = modP(y * invZ);
+      const ay = modP(y * iz);
-      const zz = modP(z * invZ);
+      const zz = modP(z * iz);
-      if (is0) return Point.ZERO;
+      if (is0) return { x: _0n, y: _1n };
       if (zz !== _1n) throw new Error('invZ was invalid');
-      return new Point(ax, ay);
+      return { x: ax, y: ay };
     }
-    clearCofactor(): ExtendedPoint {
+
+    clearCofactor(): Point {
       const { h: cofactor } = CURVE;
       if (cofactor === _1n) return this;
       return this.multiplyUnsafe(cofactor);
     }
-  }
-  const wnaf = wNAF(ExtendedPoint, CURVE.nByteLength * 8);
-
-  function assertExtPoint(other: unknown) {
-    if (!(other instanceof ExtendedPoint)) throw new TypeError('ExtendedPoint expected');
-  }
-  // Stores precomputed values for points.
-  const pointPrecomputes = new WeakMap<Point, ExtendedPoint[]>();
-
-  /**
-   * Default Point works in affine coordinates: (x, y)
-   */
-  class Point implements PointType {
-    // Base point aka generator
-    // public_key = Point.BASE * private_key
-    static BASE: Point = new Point(CURVE.Gx, CURVE.Gy);
-    // Identity point aka point at infinity
-    // point = point + zero_point
-    static ZERO: Point = new Point(_0n, _1n);
-    // 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.
-    _WINDOW_SIZE?: number;
-
-    constructor(readonly x: bigint, readonly y: bigint) {}
-
-    // "Private method", don't use it directly.
-    _setWindowSize(windowSize: number) {
-      this._WINDOW_SIZE = windowSize;
-      pointPrecomputes.delete(this);
-    }
 
     // Converts hash string or Uint8Array to Point.
     // Uses algo from RFC8032 5.1.3.
-    static fromHex(hex: Hex, strict = true) {
+    static fromHex(hex: Hex, strict = true): Point {
       const { d, a } = CURVE;
       const len = Fp.BYTES;
-      hex = ensureBytes(hex, len);
+      hex = ensureBytes(hex, len); // copy hex to a new array
-      // 1.  First, interpret the string as an integer in little-endian
+      const normed = hex.slice(); // copy again, we'll manipulate it
-      // representation. Bit 255 of this number is the least significant
+      const lastByte = hex[len - 1]; // select last byte
-      // bit of the x-coordinate and denote this value x_0.  The
+      normed[len - 1] = lastByte & ~0x80; // clear last bit
-      // y-coordinate is recovered simply by clearing this bit.  If the
-      // resulting value is >= p, decoding fails.
-      const normed = hex.slice();
-      const lastByte = hex[len - 1];
-      normed[len - 1] = lastByte & ~0x80;
       const y = ut.bytesToNumberLE(normed);
-
+      if (y === _0n) {
-      if (strict && y >= Fp.ORDER) throw new Error('Expected 0 < hex < P');
+        // y=0 is allowed
-      if (!strict && y >= maxGroupElement) throw new Error('Expected 0 < hex < CURVE.n');
-
-      // 2.  To recover the x-coordinate, the curve equation implies
-      // Ed25519: x² = (y² - 1) / (d y² + 1) (mod p).
-      // Ed448: x² = (y² - 1) / (d y² - 1) (mod p).
-      // For generic case:
-      // a*x²+y²=1+d*x²*y²
-      // -> y²-1 = d*x²*y²-a*x²
-      // -> y²-1 = x² (d*y²-a)
-      // -> x² = (y²-1) / (d*y²-a)
-
-      // The denominator is always non-zero mod p.  Let u = y² - 1 and v = d y² + 1.
-      const y2 = modP(y * y);
-      const u = modP(y2 - _1n);
-      const v = modP(d * y2 - a);
-      let { isValid, value: x } = uvRatio(u, v);
-      if (!isValid) throw new Error('Point.fromHex: invalid y coordinate');
-      // 4.  Finally, use the x_0 bit to select the right square root.  If
-      // x = 0, and x_0 = 1, decoding fails.  Otherwise, if x_0 != x mod
-      // 2, set x <-- p - x.  Return the decoded point (x,y).
-      const isXOdd = (x & _1n) === _1n;
-      const isLastByteOdd = (lastByte & 0x80) !== 0;
-      if (isLastByteOdd !== isXOdd) x = modP(-x);
-      return new Point(x, y);
-    }
-
-    static fromPrivateKey(privateKey: PrivKey) {
-      return getExtendedPublicKey(privateKey).point;
-    }
-
-    // There can always be only two x values (x, -x) for any y
-    // When compressing point, it's enough to only store its y coordinate
-    // and use the last byte to encode sign of x.
-    toRawBytes(): Uint8Array {
-      const bytes = ut.numberToBytesLE(this.y, Fp.BYTES);
-      bytes[Fp.BYTES - 1] |= this.x & _1n ? 0x80 : 0;
-      return bytes;
-    }
-
-    // Same as toRawBytes, but returns string.
-    toHex(): string {
-      return ut.bytesToHex(this.toRawBytes());
-    }
-
-    // Determines if point is in prime-order subgroup.
-    // Returns `false` is the point is dirty.
-    isTorsionFree(): boolean {
-      return ExtendedPoint.fromAffine(this).isTorsionFree();
-    }
-
-    equals(other: Point): boolean {
-      if (!(other instanceof Point)) throw new TypeError('Point#equals: expected Point');
-      return this.x === other.x && this.y === other.y;
-    }
-
-    negate(): Point {
-      return new Point(modP(-this.x), this.y);
-    }
-
-    double(): Point {
-      return ExtendedPoint.fromAffine(this).double().toAffine();
-    }
-
-    add(other: Point) {
-      return ExtendedPoint.fromAffine(this).add(ExtendedPoint.fromAffine(other)).toAffine();
-    }
-
-    subtract(other: Point) {
-      return this.add(other.negate());
-    }
-
-    /**
-     * Constant time multiplication.
-     * @param scalar Big-Endian number
-     * @returns new point
-     */
-    multiply(scalar: number | bigint): Point {
-      return ExtendedPoint.fromAffine(this).multiply(scalar, this).toAffine();
-    }
-
-    clearCofactor() {
-      return ExtendedPoint.fromAffine(this).clearCofactor().toAffine();
-    }
-    // Encodes byte string to elliptic curve
-    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3
-    static hashToCurve(msg: Hex, options?: Partial<htfOpts>) {
-      const { mapToCurve, htfDefaults } = CURVE;
-      if (!mapToCurve) throw new Error('No mapToCurve defined for curve');
-      const u = hashToField(ensureBytes(msg), 2, { ...htfDefaults, ...options } as htfOpts);
-      const { x: x0, y: y0 } = mapToCurve(u[0]);
-      const { x: x1, y: y1 } = mapToCurve(u[1]);
-      const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor();
-      return p;
-    }
-    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
-    static encodeToCurve(msg: Hex, options?: Partial<htfOpts>) {
-      const { mapToCurve, htfDefaults } = CURVE;
-      if (!mapToCurve) throw new Error('No mapToCurve defined for curve');
-      const u = hashToField(ensureBytes(msg), 1, { ...htfDefaults, ...options } as htfOpts);
-      const { x, y } = mapToCurve(u[0]);
-      return new Point(x, y).clearCofactor();
-    }
-  }
-
-  /**
-   * EDDSA signature.
-   */
-  class Signature implements SignatureType {
-    constructor(readonly r: Point, readonly s: bigint) {
-      this.assertValidity();
-    }
-
-    static fromHex(hex: Hex) {
-      const len = Fp.BYTES;
-      const bytes = ensureBytes(hex, 2 * len);
-      const r = Point.fromHex(bytes.slice(0, len), false);
-      const s = ut.bytesToNumberLE(bytes.slice(len, 2 * len));
-      return new Signature(r, s);
-    }
-
-    assertValidity() {
-      const { r, s } = this;
-      if (!(r instanceof Point)) throw new Error('Expected Point instance');
-      // 0 <= s < l
-      normalizeScalar(s, CURVE_ORDER, false);
-      return this;
-    }
-
-    toRawBytes() {
-      return ut.concatBytes(this.r.toRawBytes(), ut.numberToBytesLE(this.s, Fp.BYTES));
-    }
-
-    toHex() {
-      return ut.bytesToHex(this.toRawBytes());
-    }
-  }
-
-  // Little-endian SHA512 with modulo n
-  function modnLE(hash: Uint8Array): bigint {
-    return mod.mod(ut.bytesToNumberLE(hash), CURVE_ORDER);
-  }
-
-  /**
-   * Checks for num to be in range:
-   * For strict == true:  `0 <  num < max`.
-   * For strict == false: `0 <= num < max`.
-   * Converts non-float safe numbers to bigints.
-   */
-  function normalizeScalar(num: number | bigint, max: bigint, strict = true): bigint {
-    if (!max) throw new TypeError('Specify max value');
-    if (ut.isPositiveInt(num)) num = BigInt(num);
-    if (typeof num === 'bigint' && num < max) {
-      if (strict) {
-        if (_0n < num) return num;
       } else {
-        if (_0n <= num) return num;
+        // RFC8032 prohibits >= p, but ZIP215 doesn't
+        if (strict) assertInRange(y, Fp.ORDER); // strict=true [1..P-1] (2^255-19-1 for ed25519)
+        else assertInRange(y, MASK); // strict=false [1..MASK-1] (2^256-1 for ed25519)
       }
+
+      // 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('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
+      if (isLastByteOdd !== isXOdd) x = modP(-x); // if x_0 != x mod 2, set x = p-x
+      return Point.fromAffine({ x, y });
     }
-    throw new TypeError(`Expected valid scalar: 0 < scalar < ${max}`);
+    static fromPrivateKey(privKey: Hex) {
+      return getExtendedPublicKey(privKey).point;
+    }
+    toRawBytes(): Uint8Array {
+      const { x, y } = this.toAffine();
+      const bytes = ut.numberToBytesLE(y, Fp.BYTES); // each y has 2 x values (x, -y)
+      bytes[bytes.length - 1] |= x & _1n ? 0x80 : 0; // when compressing, it's enough to store y
+      return bytes; // and use the last byte to encode sign of x
+    }
+    toHex(): string {
+      return ut.bytesToHex(this.toRawBytes()); // Same as toRawBytes, but returns string.
+    }
+  }
+  const { BASE: G, ZERO: I } = Point;
+  const wnaf = wNAF(Point, nByteLength * 8);
+
+  function modN(a: bigint) {
+    return mod(a, CURVE_ORDER);
+  }
+  // Little-endian SHA512 with modulo n
+  function modN_LE(hash: Uint8Array): bigint {
+    return modN(ut.bytesToNumberLE(hash));
+  }
+  function isHex(item: Hex, err: string) {
+    if (typeof item !== 'string' && !(item instanceof Uint8Array))
+      throw new Error(`${err} must be hex string or Uint8Array`);
   }
 
   /** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
-  function getExtendedPublicKey(key: PrivKey) {
+  function getExtendedPublicKey(key: Hex) {
-    const groupLen = CURVE.nByteLength;
+    isHex(key, 'private key');
-    // Normalize bigint / number / string to Uint8Array
+    const len = nByteLength;
-    const keyb =
-      typeof key === 'bigint' || typeof key === 'number'
-        ? ut.numberToBytesLE(normalizeScalar(key, maxGroupElement), groupLen)
-        : key;
     // Hash private key with curve's hash function to produce uniformingly random input
-    // We check byte lengths e.g.: ensureBytes(64, hash(ensureBytes(32, key)))
+    // Check byte lengths: ensure(64, h(ensure(32, key)))
-    const hashed = ensureBytes(CURVE.hash(ensureBytes(keyb, groupLen)), 2 * groupLen);
+    const hashed = ensureBytes(cHash(ensureBytes(key, len)), 2 * len);
-
+    const head = adjustScalarBytes(hashed.slice(0, len)); // clear first half bits, produce FE
-    // First half's bits are cleared to produce a random field element.
+    const prefix = hashed.slice(len, 2 * len); // second half is called key prefix (5.1.6)
-    const head = adjustScalarBytes(hashed.slice(0, groupLen));
+    const scalar = modN_LE(head); // The actual private scalar
-    // Second half is called key prefix (5.1.6)
+    const point = G.multiply(scalar); // Point on Edwards curve aka public key
-    const prefix = hashed.slice(groupLen, 2 * groupLen);
+    const pointBytes = point.toRawBytes(); // Uint8Array representation
-    // The actual private scalar
-    const scalar = modnLE(head);
-    // Point on Edwards curve aka public key
-    const point = Point.BASE.multiply(scalar);
-    // Uint8Array representation
-    const pointBytes = point.toRawBytes();
     return { head, prefix, scalar, point, pointBytes };
   }
 
-  /**
+  // Calculates EdDSA pub key. RFC8032 5.1.5. Privkey is hashed. Use first half with 3 bits cleared
-   * Calculates ed25519 public key. RFC8032 5.1.5
+  function getPublicKey(privKey: Hex): Uint8Array {
-   * 1. private key is hashed with sha512, then first 32 bytes are taken from the hash
+    return getExtendedPublicKey(privKey).pointBytes;
-   * 2. 3 least significant bits of the first byte are cleared
-   */
-  function getPublicKey(privateKey: PrivKey): Uint8Array {
-    return getExtendedPublicKey(privateKey).pointBytes;
   }
 
-  const EMPTY = new Uint8Array();
+  // int('LE', SHA512(dom2(F, C) || msgs)) mod N
-  function hashDomainToScalar(message: Uint8Array, context: Hex = EMPTY) {
+  function hashDomainToScalar(context: Hex = new Uint8Array(), ...msgs: Uint8Array[]) {
-    context = ensureBytes(context);
+    const msg = ut.concatBytes(...msgs);
-    return modnLE(CURVE.hash(domain(message, context, !!CURVE.preHash)));
+    return modN_LE(cHash(domain(msg, ensureBytes(context), !!preHash)));
   }
 
   /** Signs message with privateKey. RFC8032 5.1.6 */
-  function sign(message: Hex, privateKey: Hex, context?: Hex): Uint8Array {
+  function sign(msg: Hex, privKey: Hex, context?: Hex): Uint8Array {
-    message = ensureBytes(message);
+    isHex(msg, 'message');
-    if (CURVE.preHash) message = CURVE.preHash(message);
+    msg = ensureBytes(msg);
-    const { prefix, scalar, pointBytes } = getExtendedPublicKey(privateKey);
+    if (preHash) msg = preHash(msg); // for ed25519ph etc.
-    const r = hashDomainToScalar(ut.concatBytes(prefix, message), context);
+    const { prefix, scalar, pointBytes } = getExtendedPublicKey(privKey);
-    const R = Point.BASE.multiply(r); // R = rG
+    const r = hashDomainToScalar(context, prefix, msg); // r = dom2(F, C) || prefix || PH(M)
-    const k = hashDomainToScalar(ut.concatBytes(R.toRawBytes(), pointBytes, message), context); // k = hash(R+P+msg)
+    const R = G.multiply(r).toRawBytes(); // R = rG
-    const s = mod.mod(r + k * scalar, CURVE_ORDER); // s = r + kp
+    const k = hashDomainToScalar(context, R, pointBytes, msg); // R || A || PH(M)
-    return new Signature(R, s).toRawBytes();
+    const s = modN(r + k * scalar); // S = (r + k * s) mod L
+    assertGE0(s); // 0 <= s < l
+    const res = ut.concatBytes(R, ut.numberToBytesLE(s, Fp.BYTES));
+    return ensureBytes(res, nByteLength * 2); // 64-byte signature
   }
 
-  /**
+  function verify(sig: Hex, msg: Hex, publicKey: Hex, context?: Hex): boolean {
-   * Verifies EdDSA signature against message and public key.
+    isHex(sig, 'sig');
-   * An extended group equation is checked.
+    isHex(msg, 'message');
-   * RFC8032 5.1.7
+    const len = Fp.BYTES; // Verifies EdDSA signature against message and public key. RFC8032 5.1.7.
-   * Compliant with ZIP215:
+    sig = ensureBytes(sig, 2 * len); // An extended group equation is checked.
-   * 0 <= sig.R/publicKey < 2**256 (can be >= curve.P)
+    msg = ensureBytes(msg); // ZIP215 compliant, which means not fully RFC8032 compliant.
-   * 0 <= sig.s < l
+    if (preHash) msg = preHash(msg); // for ed25519ph, etc
-   * Not compliant with RFC8032: it's not possible to comply to both ZIP & RFC at the same time.
+    const A = Point.fromHex(publicKey, false); // Check for s bounds, hex validity
-   */
+    const R = Point.fromHex(sig.slice(0, len), false); // 0 <= R < 2^256: ZIP215 R can be >= P
-  function verify(sig: SigType, message: Hex, publicKey: PubKey, context?: Hex): boolean {
+    const s = ut.bytesToNumberLE(sig.slice(len, 2 * len)); // 0 <= s < l
-    message = ensureBytes(message);
+    const SB = G.multiplyUnsafe(s);
-    if (CURVE.preHash) message = CURVE.preHash(message);
+    const k = hashDomainToScalar(context, R.toRawBytes(), A.toRawBytes(), msg);
-    // When hex is passed, we check public key fully.
+    const RkA = R.add(A.multiplyUnsafe(k));
-    // When Point instance is passed, we assume it has already been checked, for performance.
-    // If user passes Point/Sig instance, we assume it has been already verified.
-    // We don't check its equations for performance. We do check for valid bounds for s though
-    // We always check for: a) s bounds. b) hex validity
-    if (publicKey instanceof Point) {
-      // ignore
-    } else if (publicKey instanceof Uint8Array || typeof publicKey === 'string') {
-      publicKey = Point.fromHex(publicKey, false);
-    } else {
-      throw new Error(`Invalid publicKey: ${publicKey}`);
-    }
-
-    if (sig instanceof Signature) sig.assertValidity();
-    else if (sig instanceof Uint8Array || typeof sig === 'string') sig = Signature.fromHex(sig);
-    else throw new Error(`Wrong signature: ${sig}`);
-
-    const { r, s } = sig;
-    const SB = ExtendedPoint.BASE.multiplyUnsafe(s);
-    const k = hashDomainToScalar(
-      ut.concatBytes(r.toRawBytes(), publicKey.toRawBytes(), message),
-      context
-    );
-    const kA = ExtendedPoint.fromAffine(publicKey).multiplyUnsafe(k);
-    const RkA = ExtendedPoint.fromAffine(r).add(kA);
     // [8][S]B = [8]R + [8][k]A'
-    return RkA.subtract(SB).clearCofactor().equals(ExtendedPoint.ZERO);
+    return RkA.subtract(SB).clearCofactor().equals(Point.ZERO);
   }
 
-  // Enable precomputes. Slows down first publicKey computation by 20ms.
+  G._setWindowSize(8); // Enable precomputes. Slows down first publicKey computation by 20ms.
-  Point.BASE._setWindowSize(8);
 
   const utils = {
     getExtendedPublicKey,
-    /**
+    // ed25519 private keys are uniform 32b. No need to check for modulo bias, like in secp256k1.
-     * Not needed for ed25519 private keys. Needed if you use scalars directly (rare).
-     */
-    hashToPrivateScalar: (hash: Hex): bigint => ut.hashToPrivateScalar(hash, CURVE_ORDER, true),
-
-    /**
-     * ed25519 private keys are uniform 32-bit strings. We do not need to check for
-     * modulo bias like we do in secp256k1 randomPrivateKey()
-     */
     randomPrivateKey: (): Uint8Array => randomBytes(Fp.BYTES),
 
     /**
@@ -677,11 +449,10 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
      * but allows to speed-up subsequent getPublicKey() calls up to 20x.
      * @param windowSize 2, 4, 8, 16
      */
-    precompute(windowSize = 8, point = Point.BASE): Point {
+    precompute(windowSize = 8, point = Point.BASE): typeof Point.BASE {
-      const cached = point.equals(Point.BASE) ? point : new Point(point.x, point.y);
+      point._setWindowSize(windowSize);
-      cached._setWindowSize(windowSize);
+      point.multiply(BigInt(3));
-      cached.multiply(_2n);
+      return point;
-      return cached;
     },
   };
 
@@ -690,9 +461,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     getPublicKey,
     sign,
     verify,
-    ExtendedPoint,
+    ExtendedPoint: Point,
-    Point,
-    Signature,
     utils,
   };
 }

src/abstract/hash-to-curve.ts

@@ -1,11 +1,13 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { CHash, concatBytes } from './utils.js';
+import type { Group, GroupConstructor, AffinePoint } from './curve.js';
-import * as mod from './modular.js';
+import { mod, Field } from './modular.js';
+import { CHash, Hex, concatBytes, ensureBytes } from './utils.js';
 
-export type htfOpts = {
+export type Opts = {
   // DST: a domain separation tag
   // defined in section 2.2.5
   DST: string;
+  encodeDST: string;
   // p: the characteristic of F
   //    where F is a finite field of characteristic p and order q = p^m
   p: bigint;
@@ -25,7 +27,7 @@ export type htfOpts = {
   hash: CHash;
 };
 
-export function validateHTFOpts(opts: htfOpts) {
+export function validateOpts(opts: Opts) {
   if (typeof opts.DST !== 'string') throw new Error('Invalid htf/DST');
   if (typeof opts.p !== 'bigint') throw new Error('Invalid htf/p');
   if (typeof opts.m !== 'number') throw new Error('Invalid htf/m');
@@ -36,12 +38,16 @@ export function validateHTFOpts(opts: htfOpts) {
     throw new Error('Invalid htf/hash function');
 }
 
-// UTF8 to ui8a
+// Global symbols in both browsers and Node.js since v11
-// TODO: looks broken, ASCII only, why not TextEncoder/TextDecoder? it is in hashes anyway
+// See https://github.com/microsoft/TypeScript/issues/31535
-export function stringToBytes(str: string) {
+declare const TextEncoder: any;
-  const bytes = new Uint8Array(str.length);
+declare const TextDecoder: any;
-  for (let i = 0; i < str.length; i++) bytes[i] = str.charCodeAt(i);
+
-  return bytes;
+export function stringToBytes(str: string): Uint8Array {
+  if (typeof str !== 'string') {
+    throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
+  }
+  return new TextEncoder().encode(str);
 }
 
 // Octet Stream to Integer (bytesToNumberBE)
@@ -137,7 +143,7 @@ export function expand_message_xof(
  * @param options `{DST: string, p: bigint, m: number, k: number, expand: 'xmd' | 'xof', hash: H}`
  * @returns [u_0, ..., u_(count - 1)], a list of field elements.
  */
-export function hash_to_field(msg: Uint8Array, count: number, options: htfOpts): bigint[][] {
+export function hash_to_field(msg: Uint8Array, count: number, options: Opts): bigint[][] {
   // if options is provided but incomplete, fill any missing fields with the
   // value in hftDefaults (ie hash to G2).
   const log2p = options.p.toString(2).length;
@@ -156,14 +162,14 @@ export function hash_to_field(msg: Uint8Array, count: number, options: htfOpts):
     for (let j = 0; j < options.m; j++) {
       const elm_offset = L * (j + i * options.m);
       const tv = pseudo_random_bytes.subarray(elm_offset, elm_offset + L);
-      e[j] = mod.mod(os2ip(tv), options.p);
+      e[j] = mod(os2ip(tv), options.p);
     }
     u[i] = e;
   }
   return u;
 }
 
-export function isogenyMap<T, F extends mod.Field<T>>(field: F, map: [T[], T[], T[], T[]]) {
+export function isogenyMap<T, F extends Field<T>>(field: F, map: [T[], T[], T[], T[]]) {
   // Make same order as in spec
   const COEFF = map.map((i) => Array.from(i).reverse());
   return (x: T, y: T) => {
@@ -175,3 +181,56 @@ export function isogenyMap<T, F extends mod.Field<T>>(field: F, map: [T[], T[],
     return { x, y };
   };
 }
+
+export interface H2CPoint<T> extends Group<H2CPoint<T>> {
+  add(rhs: H2CPoint<T>): H2CPoint<T>;
+  toAffine(iz?: bigint): AffinePoint<T>;
+  clearCofactor(): H2CPoint<T>;
+  assertValidity(): void;
+}
+
+export interface H2CPointConstructor<T> extends GroupConstructor<H2CPoint<T>> {
+  fromAffine(ap: AffinePoint<T>): H2CPoint<T>;
+}
+
+export type MapToCurve<T> = (scalar: bigint[]) => AffinePoint<T>;
+
+// Separated from initialization opts, so users won't accidentally change per-curve parameters (changing DST is ok!)
+export type htfBasicOpts = {
+  DST: string;
+};
+
+export function hashToCurve<T>(
+  Point: H2CPointConstructor<T>,
+  mapToCurve: MapToCurve<T>,
+  def: Opts
+) {
+  validateOpts(def);
+  if (typeof mapToCurve !== 'function')
+    throw new Error('hashToCurve: mapToCurve() has not been defined');
+
+  return {
+    // Encodes byte string to elliptic curve
+    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3
+    hashToCurve(msg: Hex, options?: htfBasicOpts) {
+      if (!mapToCurve) throw new Error('CURVE.mapToCurve() has not been defined');
+      msg = ensureBytes(msg);
+      const u = hash_to_field(msg, 2, { ...def, DST: def.DST, ...options } as Opts);
+      const P = Point.fromAffine(mapToCurve(u[0]))
+        .add(Point.fromAffine(mapToCurve(u[1])))
+        .clearCofactor();
+      P.assertValidity();
+      return P;
+    },
+
+    // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3
+    encodeToCurve(msg: Hex, options?: htfBasicOpts) {
+      if (!mapToCurve) throw new Error('CURVE.mapToCurve() has not been defined');
+      msg = ensureBytes(msg);
+      const u = hash_to_field(msg, 1, { ...def, DST: def.encodeDST, ...options } as Opts);
+      const P = Point.fromAffine(mapToCurve(u[0])).clearCofactor();
+      P.assertValidity();
+      return P;
+    },
+  };
+}

src/abstract/modular.ts

@@ -1,7 +1,14 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-// TODO: remove circular imports
-import * as utils from './utils.js';
 // Utilities for modular arithmetics and finite fields
+import {
+  bitMask,
+  numberToBytesBE,
+  numberToBytesLE,
+  bytesToNumberBE,
+  bytesToNumberLE,
+  ensureBytes,
+  validateObject,
+} from './utils.js';
 // prettier-ignore
 const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
 // prettier-ignore
@@ -34,7 +41,6 @@ export function pow(num: bigint, power: bigint, modulo: bigint): bigint {
 }
 
 // Does x ^ (2 ^ power) mod p. pow2(30, 4) == 30 ^ (2 ^ 4)
-// TODO: Fp version?
 export function pow2(x: bigint, power: bigint, modulo: bigint): bigint {
   let res = x;
   while (power-- > _0n) {
@@ -92,7 +98,7 @@ export function tonelliShanks(P: bigint) {
     const p1div4 = (P + _1n) / _4n;
     return function tonelliFast<T>(Fp: Field<T>, n: T) {
       const root = Fp.pow(n, p1div4);
-      if (!Fp.equals(Fp.square(root), n)) throw new Error('Cannot find square root');
+      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');
       return root;
     };
   }
@@ -101,24 +107,24 @@ export function tonelliShanks(P: bigint) {
   const Q1div2 = (Q + _1n) / _2n;
   return function tonelliSlow<T>(Fp: Field<T>, n: T): T {
     // Step 0: Check that n is indeed a square: (n | p) should not be ≡ -1
-    if (Fp.pow(n, legendreC) === Fp.negate(Fp.ONE)) throw new Error('Cannot find square root');
+    if (Fp.pow(n, legendreC) === Fp.neg(Fp.ONE)) throw new Error('Cannot find square root');
     let r = S;
     // TODO: will fail at Fp2/etc
     let g = Fp.pow(Fp.mul(Fp.ONE, Z), Q); // will update both x and b
     let x = Fp.pow(n, Q1div2); // first guess at the square root
     let b = Fp.pow(n, Q); // first guess at the fudge factor
 
-    while (!Fp.equals(b, Fp.ONE)) {
+    while (!Fp.eql(b, Fp.ONE)) {
-      if (Fp.equals(b, Fp.ZERO)) return Fp.ZERO; // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm (4. If t = 0, return r = 0)
+      if (Fp.eql(b, Fp.ZERO)) return Fp.ZERO; // https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm (4. If t = 0, return r = 0)
       // Find m such b^(2^m)==1
       let m = 1;
-      for (let t2 = Fp.square(b); m < r; m++) {
+      for (let t2 = Fp.sqr(b); m < r; m++) {
-        if (Fp.equals(t2, Fp.ONE)) break;
+        if (Fp.eql(t2, Fp.ONE)) break;
-        t2 = Fp.square(t2); // t2 *= t2
+        t2 = Fp.sqr(t2); // t2 *= t2
       }
       // NOTE: r-m-1 can be bigger than 32, need to convert to bigint before shift, otherwise there will be overflow
       const ge = Fp.pow(g, _1n << BigInt(r - m - 1)); // ge = 2^(r-m-1)
-      g = Fp.square(ge); // g = ge * ge
+      g = Fp.sqr(ge); // g = ge * ge
       x = Fp.mul(x, ge); // x *= ge
       b = Fp.mul(b, g); // b *= g
       r = m;
@@ -142,7 +148,7 @@ export function FpSqrt(P: bigint) {
     return function sqrt3mod4<T>(Fp: Field<T>, n: T) {
       const root = Fp.pow(n, p1div4);
       // Throw if root**2 != n
-      if (!Fp.equals(Fp.square(root), n)) throw new Error('Cannot find square root');
+      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');
       return root;
     };
   }
@@ -156,7 +162,7 @@ export function FpSqrt(P: bigint) {
       const nv = Fp.mul(n, v);
       const i = Fp.mul(Fp.mul(nv, _2n), v);
       const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));
-      if (!Fp.equals(Fp.square(root), n)) throw new Error('Cannot find square root');
+      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');
       return root;
     };
   }
@@ -206,13 +212,13 @@ export interface Field<T> {
   // 1-arg
   create: (num: T) => T;
   isValid: (num: T) => boolean;
-  isZero: (num: T) => boolean;
+  is0: (num: T) => boolean;
-  negate(num: T): T;
+  neg(num: T): T;
-  invert(num: T): T;
+  inv(num: T): T;
   sqrt(num: T): T;
-  square(num: T): T;
+  sqr(num: T): T;
   // 2-args
-  equals(lhs: T, rhs: T): boolean;
+  eql(lhs: T, rhs: T): boolean;
   add(lhs: T, rhs: T): T;
   sub(lhs: T, rhs: T): T;
   mul(lhs: T, rhs: T | bigint): T;
@@ -222,13 +228,13 @@ export interface Field<T> {
   addN(lhs: T, rhs: T): T;
   subN(lhs: T, rhs: T): T;
   mulN(lhs: T, rhs: T | bigint): T;
-  squareN(num: T): T;
+  sqrN(num: T): T;
 
   // Optional
   // Should be same as sgn0 function in https://datatracker.ietf.org/doc/draft-irtf-cfrg-hash-to-curve/
   // NOTE: sgn0 is 'negative in LE', which is same as odd. And negative in LE is kinda strange definition anyway.
   isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2
-  legendre?(num: T): T;
+  // legendre?(num: T): T;
   pow(lhs: T, power: bigint): T;
   invertBatch: (lst: T[]) => T[];
   toBytes(num: T): Uint8Array;
@@ -238,23 +244,22 @@ export interface Field<T> {
 }
 // prettier-ignore
 const FIELD_FIELDS = [
-  'create', 'isValid', 'isZero', 'negate', 'invert', 'sqrt', 'square',
+  'create', 'isValid', 'is0', 'neg', 'inv', 'sqrt', 'sqr',
-  'equals', 'add', 'sub', 'mul', 'pow', 'div',
+  'eql', 'add', 'sub', 'mul', 'pow', 'div',
-  'addN', 'subN', 'mulN', 'squareN'
+  'addN', 'subN', 'mulN', 'sqrN'
 ] as const;
 export function validateField<T>(field: Field<T>) {
-  for (const i of ['ORDER', 'MASK'] as const) {
+  const initial = {
-    if (typeof field[i] !== 'bigint')
+    ORDER: 'bigint',
-      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+    MASK: 'bigint',
-  }
+    BYTES: 'isSafeInteger',
-  for (const i of ['BYTES', 'BITS'] as const) {
+    BITS: 'isSafeInteger',
-    if (typeof field[i] !== 'number')
+  } as Record<string, string>;
-      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  const opts = FIELD_FIELDS.reduce((map, val: string) => {
-  }
+    map[val] = 'function';
-  for (const i of FIELD_FIELDS) {
+    return map;
-    if (typeof field[i] !== 'function')
+  }, initial);
-      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  return validateObject(field, opts);
-  }
 }
 
 // Generic field functions
@@ -268,7 +273,7 @@ export function FpPow<T>(f: Field<T>, num: T, power: bigint): T {
   let d = num;
   while (power > _0n) {
     if (power & _1n) p = f.mul(p, d);
-    d = f.square(d);
+    d = f.sqr(d);
     power >>= 1n;
   }
   return p;
@@ -278,15 +283,15 @@ export function FpInvertBatch<T>(f: Field<T>, nums: T[]): T[] {
   const tmp = new Array(nums.length);
   // Walk from first to last, multiply them by each other MOD p
   const lastMultiplied = nums.reduce((acc, num, i) => {
-    if (f.isZero(num)) return acc;
+    if (f.is0(num)) return acc;
     tmp[i] = acc;
     return f.mul(acc, num);
   }, f.ONE);
   // Invert last element
-  const inverted = f.invert(lastMultiplied);
+  const inverted = f.inv(lastMultiplied);
   // Walk from last to first, multiply them by inverted each other MOD p
   nums.reduceRight((acc, num, i) => {
-    if (f.isZero(num)) return acc;
+    if (f.is0(num)) return acc;
     tmp[i] = f.mul(acc, tmp[i]);
     return f.mul(acc, num);
   }, inverted);
@@ -294,7 +299,7 @@ export function FpInvertBatch<T>(f: Field<T>, nums: T[]): T[] {
 }
 
 export function FpDiv<T>(f: Field<T>, lhs: T, rhs: T | bigint): T {
-  return f.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, f.ORDER) : f.invert(rhs));
+  return f.mul(lhs, typeof rhs === 'bigint' ? invert(rhs, f.ORDER) : f.inv(rhs));
 }
 
 // This function returns True whenever the value x is a square in the field F.
@@ -302,10 +307,18 @@ export function FpIsSquare<T>(f: Field<T>) {
   const legendreConst = (f.ORDER - _1n) / _2n; // Integer arithmetic
   return (x: T): boolean => {
     const p = f.pow(x, legendreConst);
-    return f.equals(p, f.ZERO) || f.equals(p, f.ONE);
+    return f.eql(p, f.ZERO) || f.eql(p, f.ONE);
   };
 }
 
+// CURVE.n lengths
+export function nLength(n: bigint, nBitLength?: number) {
+  // Bit size, byte size of CURVE.n
+  const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;
+  const nByteLength = Math.ceil(_nBitLength / 8);
+  return { nBitLength: _nBitLength, nByteLength };
+}
+
 // NOTE: very fragile, always bench. Major performance points:
 // - NonNormalized ops
 // - Object.freeze
@@ -318,28 +331,28 @@ export function Fp(
   redef: Partial<Field<bigint>> = {}
 ): Readonly<FpField> {
   if (ORDER <= _0n) throw new Error(`Expected Fp ORDER > 0, got ${ORDER}`);
-  const { nBitLength: BITS, nByteLength: BYTES } = utils.nLength(ORDER, bitLen);
+  const { nBitLength: BITS, nByteLength: BYTES } = nLength(ORDER, bitLen);
   if (BYTES > 2048) throw new Error('Field lengths over 2048 bytes are not supported');
   const sqrtP = FpSqrt(ORDER);
   const f: Readonly<FpField> = Object.freeze({
     ORDER,
     BITS,
     BYTES,
-    MASK: utils.bitMask(BITS),
+    MASK: bitMask(BITS),
     ZERO: _0n,
     ONE: _1n,
     create: (num) => mod(num, ORDER),
     isValid: (num) => {
       if (typeof num !== 'bigint')
         throw new Error(`Invalid field element: expected bigint, got ${typeof num}`);
-      return _0n <= num && num < ORDER;
+      return _0n <= num && num < ORDER; // 0 is valid element, but it's not invertible
     },
-    isZero: (num) => num === _0n,
+    is0: (num) => num === _0n,
     isOdd: (num) => (num & _1n) === _1n,
-    negate: (num) => mod(-num, ORDER),
+    neg: (num) => mod(-num, ORDER),
-    equals: (lhs, rhs) => lhs === rhs,
+    eql: (lhs, rhs) => lhs === rhs,
 
-    square: (num) => mod(num * num, ORDER),
+    sqr: (num) => mod(num * num, ORDER),
     add: (lhs, rhs) => mod(lhs + rhs, ORDER),
     sub: (lhs, rhs) => mod(lhs - rhs, ORDER),
     mul: (lhs, rhs) => mod(lhs * rhs, ORDER),
@@ -347,24 +360,22 @@ export function Fp(
     div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),
 
     // Same as above, but doesn't normalize
-    squareN: (num) => num * num,
+    sqrN: (num) => num * num,
     addN: (lhs, rhs) => lhs + rhs,
     subN: (lhs, rhs) => lhs - rhs,
     mulN: (lhs, rhs) => lhs * rhs,
 
-    invert: (num) => invert(num, ORDER),
+    inv: (num) => invert(num, ORDER),
     sqrt: redef.sqrt || ((n) => sqrtP(f, n)),
     invertBatch: (lst) => FpInvertBatch(f, lst),
     // TODO: do we really need constant cmov?
     // We don't have const-time bigints anyway, so probably will be not very useful
     cmov: (a, b, c) => (c ? b : a),
-    toBytes: (num) =>
+    toBytes: (num) => (isLE ? numberToBytesLE(num, BYTES) : numberToBytesBE(num, BYTES)),
-      isLE ? utils.numberToBytesLE(num, BYTES) : utils.numberToBytesBE(num, BYTES),
-
     fromBytes: (bytes) => {
       if (bytes.length !== BYTES)
         throw new Error(`Fp.fromBytes: expected ${BYTES}, got ${bytes.length}`);
-      return isLE ? utils.bytesToNumberLE(bytes) : utils.bytesToNumberBE(bytes);
+      return isLE ? bytesToNumberLE(bytes) : bytesToNumberBE(bytes);
     },
   } as FpField);
   return Object.freeze(f);
@@ -373,11 +384,34 @@ export function Fp(
 export function FpSqrtOdd<T>(Fp: Field<T>, elm: T) {
   if (!Fp.isOdd) throw new Error(`Field doesn't have isOdd`);
   const root = Fp.sqrt(elm);
-  return Fp.isOdd(root) ? root : Fp.negate(root);
+  return Fp.isOdd(root) ? root : Fp.neg(root);
 }
 
 export function FpSqrtEven<T>(Fp: Field<T>, elm: T) {
   if (!Fp.isOdd) throw new Error(`Field doesn't have isOdd`);
   const root = Fp.sqrt(elm);
-  return Fp.isOdd(root) ? Fp.negate(root) : root;
+  return Fp.isOdd(root) ? Fp.neg(root) : root;
+}
+
+/**
+ * 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.
+ * 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
+ * @returns valid private scalar
+ */
+export function hashToPrivateScalar(
+  hash: string | Uint8Array,
+  groupOrder: bigint,
+  isLE = false
+): bigint {
+  hash = ensureBytes(hash);
+  const hashLen = hash.length;
+  const minLen = nLength(groupOrder).nByteLength + 8;
+  if (minLen < 24 || hashLen < minLen || hashLen > 1024)
+    throw new Error(`hashToPrivateScalar: expected ${minLen}-1024 bytes of input, got ${hashLen}`);
+  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
+  return mod(num, groupOrder - _1n) + _1n;
 }

src/abstract/montgomery.ts

@@ -1,14 +1,13 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import * as mod from './modular.js';
+import { mod, pow } from './modular.js';
-import { ensureBytes, numberToBytesLE, bytesToNumberLE, isPositiveInt } from './utils.js';
+import { bytesToNumberLE, ensureBytes, numberToBytesLE, validateObject } from './utils.js';
 
 const _0n = BigInt(0);
 const _1n = BigInt(1);
 type Hex = string | Uint8Array;
 
 export type CurveType = {
-  // Field over which we'll do calculations. Verify with:
+  P: bigint; // finite field prime
-  P: bigint;
   nByteLength: number;
   adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array;
   domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array;
@@ -27,26 +26,21 @@ export type CurveFn = {
 };
 
 function validateOpts(curve: CurveType) {
-  for (const i of ['a24'] as const) {
+  validateObject(
-    if (typeof curve[i] !== 'bigint')
+    curve,
-      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+    {
-  }
+      a24: 'bigint',
-  for (const i of ['montgomeryBits', 'nByteLength'] as const) {
+    },
-    if (curve[i] === undefined) continue; // Optional
+    {
-    if (!isPositiveInt(curve[i]))
+      montgomeryBits: 'isSafeInteger',
-      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
+      nByteLength: 'isSafeInteger',
-  }
+      adjustScalarBytes: 'function',
-  for (const fn of ['adjustScalarBytes', 'domain', 'powPminus2'] as const) {
+      domain: 'function',
-    if (curve[fn] === undefined) continue; // Optional
+      powPminus2: 'function',
-    if (typeof curve[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
+      Gu: 'string',
-  }
+    }
-  for (const i of ['Gu'] as const) {
+  );
-    if (curve[i] === undefined) continue; // Optional
-    if (typeof curve[i] !== 'string')
-      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
-  }
   // Set defaults
-  // ...nLength(curve.n, curve.nBitLength),
   return Object.freeze({ ...curve } as const);
 }
 
@@ -55,34 +49,14 @@ function validateOpts(curve: CurveType) {
 export function montgomery(curveDef: CurveType): CurveFn {
   const CURVE = validateOpts(curveDef);
   const { P } = CURVE;
-  const modP = (a: bigint) => mod.mod(a, P);
+  const modP = (a: bigint) => mod(a, P);
   const montgomeryBits = CURVE.montgomeryBits;
   const montgomeryBytes = Math.ceil(montgomeryBits / 8);
   const fieldLen = CURVE.nByteLength;
   const adjustScalarBytes = CURVE.adjustScalarBytes || ((bytes: Uint8Array) => bytes);
-  const powPminus2 = CURVE.powPminus2 || ((x: bigint) => mod.pow(x, P - BigInt(2), P));
+  const powPminus2 = CURVE.powPminus2 || ((x: bigint) => pow(x, P - BigInt(2), P));
 
-  /**
+  // cswap from RFC7748. But it is not from RFC7748!
-   * Checks for num to be in range:
-   * For strict == true:  `0 <  num < max`.
-   * For strict == false: `0 <= num < max`.
-   * Converts non-float safe numbers to bigints.
-   */
-  function normalizeScalar(num: number | bigint, max: bigint, strict = true): bigint {
-    if (!max) throw new TypeError('Specify max value');
-    if (typeof num === 'number' && Number.isSafeInteger(num)) num = BigInt(num);
-    if (typeof num === 'bigint' && num < max) {
-      if (strict) {
-        if (_0n < num) return num;
-      } else {
-        if (_0n <= num) return num;
-      }
-    }
-    throw new TypeError('Expected valid scalar: 0 < scalar < max');
-  }
-
-  // cswap from RFC7748
-  // NOTE: cswap is not from RFC7748!
   /*
     cswap(swap, x_2, x_3):
          dummy = mask(swap) AND (x_2 XOR x_3)
@@ -99,6 +73,11 @@ export function montgomery(curveDef: CurveType): CurveFn {
     return [x_2, x_3];
   }
 
+  function assertFieldElement(n: bigint): bigint {
+    if (typeof n === 'bigint' && _0n <= n && n < P) return n;
+    throw new Error('Expected valid scalar 0 < scalar < CURVE.P');
+  }
+
   // x25519 from 4
   /**
    *
@@ -107,11 +86,10 @@ export function montgomery(curveDef: CurveType): CurveFn {
    * @returns new Point on Montgomery curve
    */
   function montgomeryLadder(pointU: bigint, scalar: bigint): bigint {
-    const { P } = CURVE;
+    const u = assertFieldElement(pointU);
-    const u = normalizeScalar(pointU, P);
     // Section 5: Implementations MUST accept non-canonical values and process them as
     // if they had been reduced modulo the field prime.
-    const k = normalizeScalar(scalar, P);
+    const k = assertFieldElement(scalar);
     // The constant a24 is (486662 - 2) / 4 = 121665 for curve25519/X25519
     const a24 = CURVE.a24;
     const x_1 = u;
@@ -167,28 +145,20 @@ export function montgomery(curveDef: CurveType): CurveFn {
   }
 
   function decodeUCoordinate(uEnc: Hex): bigint {
-    const u = ensureBytes(uEnc, montgomeryBytes);
     // Section 5: When receiving such an array, implementations of X25519
     // MUST mask the most significant bit in the final byte.
     // This is very ugly way, but it works because fieldLen-1 is outside of bounds for X448, so this becomes NOOP
     // fieldLen - scalaryBytes = 1 for X448 and = 0 for X25519
+    const u = ensureBytes(uEnc, montgomeryBytes);
     u[fieldLen - 1] &= 127; // 0b0111_1111
     return bytesToNumberLE(u);
   }
-
   function decodeScalar(n: Hex): bigint {
     const bytes = ensureBytes(n);
     if (bytes.length !== montgomeryBytes && bytes.length !== fieldLen)
       throw new Error(`Expected ${montgomeryBytes} or ${fieldLen} bytes, got ${bytes.length}`);
     return bytesToNumberLE(adjustScalarBytes(bytes));
   }
-  /**
-   * Computes shared secret between private key "scalar" and public key's "u" (x) coordinate.
-   * We can get 'y' coordinate from 'u',
-   * but Point.fromHex also wants 'x' coordinate oddity flag,
-   * and we cannot get 'x' without knowing 'v'.
-   * Need to add generic conversion between twisted edwards and complimentary curve for JubJub.
-   */
   function scalarMult(scalar: Hex, u: Hex): Uint8Array {
     const pointU = decodeUCoordinate(u);
     const _scalar = decodeScalar(scalar);
@@ -198,12 +168,7 @@ export function montgomery(curveDef: CurveType): CurveFn {
     if (pu === _0n) throw new Error('Invalid private or public key received');
     return encodeUCoordinate(pu);
   }
-  /**
+  // Computes public key from private. By doing scalar multiplication of base point.
-   * Computes public key from private.
-   * Executes scalar multiplication of curve's base point by scalar.
-   * @param scalar private key
-   * @returns new public key
-   */
   function scalarMultBase(scalar: Hex): Uint8Array {
     return scalarMult(scalar, CURVE.Gu);
   }

src/abstract/poseidon.ts

@@ -0,0 +1,119 @@
+/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+// Poseidon Hash: https://eprint.iacr.org/2019/458.pdf, https://www.poseidon-hash.info
+import { Field, FpPow, validateField } from './modular.js';
+// We don't provide any constants, since different implementations use different constants.
+// For reference constants see './test/poseidon.test.js'.
+export type PoseidonOpts = {
+  Fp: Field<bigint>;
+  t: number;
+  roundsFull: number;
+  roundsPartial: number;
+  sboxPower?: number;
+  reversePartialPowIdx?: boolean; // Hack for stark
+  mds: bigint[][];
+  roundConstants: bigint[][];
+};
+
+export function validateOpts(opts: PoseidonOpts) {
+  const { Fp } = opts;
+  validateField(Fp);
+  for (const i of ['t', 'roundsFull', 'roundsPartial'] as const) {
+    if (typeof opts[i] !== 'number' || !Number.isSafeInteger(opts[i]))
+      throw new Error(`Poseidon: invalid param ${i}=${opts[i]} (${typeof opts[i]})`);
+  }
+  if (opts.reversePartialPowIdx !== undefined && typeof opts.reversePartialPowIdx !== 'boolean')
+    throw new Error(`Poseidon: invalid param reversePartialPowIdx=${opts.reversePartialPowIdx}`);
+  // Default is 5, but by some reasons stark uses 3
+  let sboxPower = opts.sboxPower;
+  if (sboxPower === undefined) sboxPower = 5;
+  if (typeof sboxPower !== 'number' || !Number.isSafeInteger(sboxPower))
+    throw new Error(`Poseidon wrong sboxPower=${sboxPower}`);
+
+  const _sboxPower = BigInt(sboxPower);
+  let sboxFn = (n: bigint) => FpPow(Fp, n, _sboxPower);
+  // Unwrapped sbox power for common cases (195->142μs)
+  if (sboxPower === 3) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(n), n);
+  else if (sboxPower === 5) sboxFn = (n: bigint) => Fp.mul(Fp.sqrN(Fp.sqrN(n)), n);
+
+  if (opts.roundsFull % 2 !== 0)
+    throw new Error(`Poseidon roundsFull is not even: ${opts.roundsFull}`);
+  const rounds = opts.roundsFull + opts.roundsPartial;
+
+  if (!Array.isArray(opts.roundConstants) || opts.roundConstants.length !== rounds)
+    throw new Error('Poseidon: wrong round constants');
+  const roundConstants = opts.roundConstants.map((rc) => {
+    if (!Array.isArray(rc) || rc.length !== opts.t)
+      throw new Error(`Poseidon wrong round constants: ${rc}`);
+    return rc.map((i) => {
+      if (typeof i !== 'bigint' || !Fp.isValid(i))
+        throw new Error(`Poseidon wrong round constant=${i}`);
+      return Fp.create(i);
+    });
+  });
+  // MDS is TxT matrix
+  if (!Array.isArray(opts.mds) || opts.mds.length !== opts.t)
+    throw new Error('Poseidon: wrong MDS matrix');
+  const mds = opts.mds.map((mdsRow) => {
+    if (!Array.isArray(mdsRow) || mdsRow.length !== opts.t)
+      throw new Error(`Poseidon MDS matrix row: ${mdsRow}`);
+    return mdsRow.map((i) => {
+      if (typeof i !== 'bigint') throw new Error(`Poseidon MDS matrix value=${i}`);
+      return Fp.create(i);
+    });
+  });
+  return Object.freeze({ ...opts, rounds, sboxFn, roundConstants, mds });
+}
+
+export function splitConstants(rc: bigint[], t: number) {
+  if (typeof t !== 'number') throw new Error('poseidonSplitConstants: wrong t');
+  if (!Array.isArray(rc) || rc.length % t) throw new Error('poseidonSplitConstants: wrong rc');
+  const res = [];
+  let tmp = [];
+  for (let i = 0; i < rc.length; i++) {
+    tmp.push(rc[i]);
+    if (tmp.length === t) {
+      res.push(tmp);
+      tmp = [];
+    }
+  }
+  return res;
+}
+
+export function poseidon(opts: PoseidonOpts) {
+  const { t, Fp, rounds, sboxFn, reversePartialPowIdx } = validateOpts(opts);
+  const halfRoundsFull = Math.floor(opts.roundsFull / 2);
+  const partialIdx = reversePartialPowIdx ? t - 1 : 0;
+  const poseidonRound = (values: bigint[], isFull: boolean, idx: number) => {
+    values = values.map((i, j) => Fp.add(i, opts.roundConstants[idx][j]));
+
+    if (isFull) values = values.map((i) => sboxFn(i));
+    else values[partialIdx] = sboxFn(values[partialIdx]);
+    // Matrix multiplication
+    values = opts.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: bigint[]) {
+    if (!Array.isArray(values) || values.length !== t)
+      throw new Error(`Poseidon: wrong values (expected array of bigints with length ${t})`);
+    values = values.map((i) => {
+      if (typeof i !== 'bigint') throw new Error(`Poseidon: wrong value=${i} (${typeof i})`);
+      return Fp.create(i);
+    });
+    let round = 0;
+    // Apply r_f/2 full rounds.
+    for (let i = 0; i < halfRoundsFull; i++) values = poseidonRound(values, true, round++);
+    // Apply r_p partial rounds.
+    for (let i = 0; i < opts.roundsPartial; i++) values = poseidonRound(values, false, round++);
+    // Apply r_f/2 full rounds.
+    for (let i = 0; i < halfRoundsFull; i++) values = poseidonRound(values, true, round++);
+
+    if (round !== rounds)
+      throw new Error(`Poseidon: wrong number of rounds: last round=${round}, total=${rounds}`);
+    return values;
+  };
+  // For verification in tests
+  poseidonHash.roundConstants = opts.roundConstants;
+  return poseidonHash;
+}

src/abstract/utils.ts

@@ -1,75 +1,28 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import * as mod from './modular.js';
 const _0n = BigInt(0);
 const _1n = BigInt(1);
 const _2n = BigInt(2);
+const u8a = (a: any): a is Uint8Array => a instanceof Uint8Array;
 
 // We accept hex strings besides Uint8Array for simplicity
 export type Hex = Uint8Array | string;
 // Very few implementations accept numbers, we do it to ease learning curve
-export type PrivKey = Hex | bigint | number;
+export type PrivKey = Hex | bigint;
 export type CHash = {
   (message: Uint8Array | string): Uint8Array;
   blockLen: number;
   outputLen: number;
   create(opts?: { dkLen?: number }): any; // For shake
 };
-
+export type FHash = (message: Uint8Array | string) => Uint8Array;
-// NOTE: these are generic, even if curve is on some polynominal field (bls), it will still have P/n/h
-// But generator can be different (Fp2/Fp6 for bls?)
-export type BasicCurve<T> = {
-  // Field over which we'll do calculations (Fp)
-  Fp: mod.Field<T>;
-  // Curve order, total count of valid points in the field
-  n: bigint;
-  // Bit/byte length of curve order
-  nBitLength?: number;
-  nByteLength?: number;
-  // Cofactor
-  // NOTE: we can assign default value of 1, but then users will just ignore it, without validating with spec
-  // Has not use for now, but nice to have in API
-  h: bigint;
-  hEff?: bigint; // Number to multiply to clear cofactor
-  // Base point (x, y) aka generator point
-  Gx: T;
-  Gy: T;
-  // Wrap private key by curve order (% CURVE.n instead of throwing error)
-  wrapPrivateKey?: boolean;
-  // Point at infinity is perfectly valid point, but not valid public key.
-  // Disabled by default because of compatibility reasons with @noble/secp256k1
-  allowInfinityPoint?: boolean;
-};
-
-// Bans floats and integers above 2^53-1
-export function isPositiveInt(num: any): num is number {
-  return typeof num === 'number' && Number.isSafeInteger(num) && num > 0;
-}
-
-export function validateOpts<FP, T>(curve: BasicCurve<FP> & T) {
-  mod.validateField(curve.Fp);
-  for (const i of ['n', 'h'] as const) {
-    const val = curve[i];
-    if (typeof val !== 'bigint') throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
-  }
-  if (!curve.Fp.isValid(curve.Gx)) throw new Error('Invalid generator X coordinate Fp element');
-  if (!curve.Fp.isValid(curve.Gy)) throw new Error('Invalid generator Y coordinate Fp element');
-
-  for (const i of ['nBitLength', 'nByteLength'] as const) {
-    const val = curve[i];
-    if (val === undefined) continue; // Optional
-    if (!isPositiveInt(val)) throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
-  }
-  // Set defaults
-  return Object.freeze({ ...nLength(curve.n, curve.nBitLength), ...curve } as const);
-}
 
 const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
-export function bytesToHex(uint8a: Uint8Array): string {
+export function bytesToHex(bytes: Uint8Array): string {
-  if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
+  if (!u8a(bytes)) throw new Error('Uint8Array expected');
   // pre-caching improves the speed 6x
   let hex = '';
-  for (let i = 0; i < uint8a.length; i++) {
+  for (let i = 0; i < bytes.length; i++) {
-    hex += hexes[uint8a[i]];
+    hex += hexes[bytes[i]];
   }
   return hex;
 }
@@ -80,25 +33,21 @@ export function numberToHexUnpadded(num: number | bigint): string {
 }
 
 export function hexToNumber(hex: string): bigint {
-  if (typeof hex !== 'string') {
+  if (typeof hex !== 'string') throw new Error('string expected, got ' + typeof hex);
-    throw new TypeError('hexToNumber: expected string, got ' + typeof hex);
-  }
   // Big Endian
   return BigInt(`0x${hex}`);
 }
 
 // Caching slows it down 2-3x
 export function hexToBytes(hex: string): Uint8Array {
-  if (typeof hex !== 'string') {
+  if (typeof hex !== 'string') throw new Error('string expected, got ' + typeof hex);
-    throw new TypeError('hexToBytes: expected string, got ' + typeof hex);
+  if (hex.length % 2) throw new Error('hex string is invalid: unpadded ' + hex.length);
-  }
-  if (hex.length % 2) throw new Error('hexToBytes: received invalid unpadded hex ' + hex.length);
   const array = new Uint8Array(hex.length / 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;
@@ -108,63 +57,36 @@ export function hexToBytes(hex: string): Uint8Array {
 export function bytesToNumberBE(bytes: Uint8Array): bigint {
   return hexToNumber(bytesToHex(bytes));
 }
-export function bytesToNumberLE(uint8a: Uint8Array): bigint {
+export function bytesToNumberLE(bytes: Uint8Array): bigint {
-  if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
+  if (!u8a(bytes)) throw new Error('Uint8Array expected');
-  return BigInt('0x' + bytesToHex(Uint8Array.from(uint8a).reverse()));
+  return hexToNumber(bytesToHex(Uint8Array.from(bytes).reverse()));
 }
 
 export const numberToBytesBE = (n: bigint, len: number) =>
   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 const numberToVarBytesBE = (n: bigint) => hexToBytes(numberToHexUnpadded(n));
 
 export function ensureBytes(hex: Hex, expectedLength?: number): Uint8Array {
   // Uint8Array.from() instead of hash.slice() because node.js Buffer
   // is instance of Uint8Array, and its slice() creates **mutable** copy
-  const bytes = hex instanceof Uint8Array ? Uint8Array.from(hex) : hexToBytes(hex);
+  const bytes = u8a(hex) ? Uint8Array.from(hex) : hexToBytes(hex);
   if (typeof expectedLength === 'number' && bytes.length !== expectedLength)
     throw new Error(`Expected ${expectedLength} bytes`);
   return bytes;
 }
 
 // Copies several Uint8Arrays into one.
-export function concatBytes(...arrays: Uint8Array[]): Uint8Array {
+export function concatBytes(...arrs: Uint8Array[]): Uint8Array {
-  if (!arrays.every((b) => b instanceof Uint8Array)) throw new Error('Uint8Array list expected');
+  const r = new Uint8Array(arrs.reduce((sum, a) => sum + a.length, 0));
-  if (arrays.length === 1) return arrays[0];
+  let pad = 0; // walk through each item, ensure they have proper type
-  const length = arrays.reduce((a, arr) => a + arr.length, 0);
+  arrs.forEach((a) => {
-  const result = new Uint8Array(length);
+    if (!u8a(a)) throw new Error('Uint8Array expected');
-  for (let i = 0, pad = 0; i < arrays.length; i++) {
+    r.set(a, pad);
-    const arr = arrays[i];
+    pad += a.length;
-    result.set(arr, pad);
+  });
-    pad += arr.length;
+  return r;
-  }
-  return result;
-}
-
-// CURVE.n lengths
-export function nLength(n: bigint, nBitLength?: number) {
-  // Bit size, byte size of CURVE.n
-  const _nBitLength = nBitLength !== undefined ? nBitLength : n.toString(2).length;
-  const nByteLength = Math.ceil(_nBitLength / 8);
-  return { nBitLength: _nBitLength, nByteLength };
-}
-
-/**
- * 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.
- * 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
- * @returns valid private scalar
- */
-export function hashToPrivateScalar(hash: Hex, groupOrder: bigint, isLE = false): bigint {
-  hash = ensureBytes(hash);
-  const hashLen = hash.length;
-  const minLen = nLength(groupOrder).nByteLength + 8;
-  if (minLen < 24 || hashLen < minLen || hashLen > 1024)
-    throw new Error(`hashToPrivateScalar: expected ${minLen}-1024 bytes of input, got ${hashLen}`);
-  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
-  return mod.mod(num, groupOrder - _1n) + _1n;
 }
 
 export function equalBytes(b1: Uint8Array, b2: Uint8Array) {
@@ -191,3 +113,32 @@ export const bitSet = (n: bigint, pos: number, value: boolean) =>
 // Return mask for N bits (Same as BigInt(`0b${Array(i).fill('1').join('')}`))
 // Not using ** operator with bigints for old engines.
 export const bitMask = (n: number) => (_2n << BigInt(n - 1)) - _1n;
+
+type ValMap = Record<string, string>;
+export function validateObject(object: object, validators: ValMap, optValidators: ValMap = {}) {
+  const validatorFns: Record<string, (val: any) => boolean> = {
+    bigint: (val) => typeof val === 'bigint',
+    function: (val) => typeof val === 'function',
+    boolean: (val) => typeof val === 'boolean',
+    string: (val) => typeof val === 'string',
+    isSafeInteger: (val) => Number.isSafeInteger(val),
+    array: (val) => Array.isArray(val),
+    field: (val) => (object as any).Fp.isValid(val),
+    hash: (val) => typeof val === 'function' && Number.isSafeInteger(val.outputLen),
+  };
+  // type Key = keyof typeof validators;
+  const checkField = (fieldName: string, type: string, isOptional: boolean) => {
+    const checkVal = validatorFns[type];
+    if (typeof checkVal !== 'function')
+      throw new Error(`Invalid validator "${type}", expected function`);
+
+    const val = object[fieldName as keyof typeof object];
+    if (isOptional && val === undefined) return;
+    if (!checkVal(val)) {
+      throw new Error(`Invalid param ${fieldName}=${val} (${typeof val}), expected ${type}`);
+    }
+  };
+  for (let [fieldName, type] of Object.entries(validators)) checkField(fieldName, type, false);
+  for (let [fieldName, type] of Object.entries(optValidators)) checkField(fieldName, type, true);
+  return object;
+}

src/bls12-381.ts

@@ -16,7 +16,7 @@ import { randomBytes } from '@noble/hashes/utils';
 import { bls, CurveFn } from './abstract/bls.js';
 import * as mod from './abstract/modular.js';
 import {
-  concatBytes,
+  concatBytes as concatB,
   ensureBytes,
   numberToBytesBE,
   bytesToNumberBE,
@@ -28,10 +28,10 @@ import {
 } from './abstract/utils.js';
 // Types
 import {
-  PointType,
+  ProjPointType,
-  ProjectivePointType,
+  ProjConstructor,
-  ProjectiveConstructor,
   mapToCurveSimpleSWU,
+  AffinePoint,
 } from './abstract/weierstrass.js';
 import { isogenyMap } from './abstract/hash-to-curve.js';
 
@@ -99,25 +99,24 @@ const Fp2: mod.Field<Fp2> & Fp2Utils = {
   ONE: { c0: Fp.ONE, c1: Fp.ZERO },
   create: (num) => num,
   isValid: ({ c0, c1 }) => typeof c0 === 'bigint' && typeof c1 === 'bigint',
-  isZero: ({ c0, c1 }) => Fp.isZero(c0) && Fp.isZero(c1),
+  is0: ({ c0, c1 }) => Fp.is0(c0) && Fp.is0(c1),
-  equals: ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => Fp.equals(c0, r0) && Fp.equals(c1, r1),
+  eql: ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => Fp.eql(c0, r0) && Fp.eql(c1, r1),
-  negate: ({ c0, c1 }) => ({ c0: Fp.negate(c0), c1: Fp.negate(c1) }),
+  neg: ({ c0, c1 }) => ({ c0: Fp.neg(c0), c1: Fp.neg(c1) }),
   pow: (num, power) => mod.FpPow(Fp2, num, power),
   invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums),
   // Normalized
   add: Fp2Add,
   sub: Fp2Subtract,
   mul: Fp2Multiply,
-  square: Fp2Square,
+  sqr: Fp2Square,
   // NonNormalized stuff
   addN: Fp2Add,
   subN: Fp2Subtract,
   mulN: Fp2Multiply,
-  squareN: Fp2Square,
+  sqrN: Fp2Square,
   // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context?
-  div: (lhs, rhs) =>
+  div: (lhs, rhs) => Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp2.inv(rhs)),
-    Fp2.mul(lhs, typeof rhs === 'bigint' ? Fp.invert(Fp.create(rhs)) : Fp2.invert(rhs)),
+  inv: ({ c0: a, c1: b }) => {
-  invert: ({ c0: a, c1: b }) => {
     // We wish to find the multiplicative inverse of a nonzero
     // element a + bu in Fp2. We leverage an identity
     //
@@ -131,11 +130,11 @@ const Fp2: mod.Field<Fp2> & Fp2Utils = {
     // 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 factor = Fp.invert(Fp.create(a * a + b * b));
+    const factor = Fp.inv(Fp.create(a * a + b * b));
     return { c0: Fp.mul(factor, Fp.create(a)), c1: Fp.mul(factor, Fp.create(-b)) };
   },
   sqrt: (num) => {
-    if (Fp2.equals(num, Fp2.ZERO)) return Fp2.ZERO; // Algo doesn't handles this case
+    if (Fp2.eql(num, Fp2.ZERO)) return Fp2.ZERO; // Algo doesn't handles this case
     // TODO: Optimize this line. It's extremely slow.
     // Speeding this up would boost aggregateSignatures.
     // https://eprint.iacr.org/2012/685.pdf applicable?
@@ -143,15 +142,15 @@ const Fp2: mod.Field<Fp2> & Fp2Utils = {
     // https://github.com/supranational/blst/blob/aae0c7d70b799ac269ff5edf29d8191dbd357876/src/exp2.c#L1
     // Inspired by https://github.com/dalek-cryptography/curve25519-dalek/blob/17698df9d4c834204f83a3574143abacb4fc81a5/src/field.rs#L99
     const candidateSqrt = Fp2.pow(num, (Fp2.ORDER + 8n) / 16n);
-    const check = Fp2.div(Fp2.square(candidateSqrt), num); // candidateSqrt.square().div(this);
+    const check = Fp2.div(Fp2.sqr(candidateSqrt), num); // candidateSqrt.square().div(this);
     const R = FP2_ROOTS_OF_UNITY;
-    const divisor = [R[0], R[2], R[4], R[6]].find((r) => Fp2.equals(r, check));
+    const divisor = [R[0], R[2], R[4], R[6]].find((r) => Fp2.eql(r, check));
     if (!divisor) throw new Error('No root');
     const index = R.indexOf(divisor);
     const root = R[index / 2];
     if (!root) throw new Error('Invalid root');
     const x1 = Fp2.div(candidateSqrt, root);
-    const x2 = Fp2.negate(x1);
+    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;
@@ -170,7 +169,7 @@ const Fp2: mod.Field<Fp2> & Fp2Utils = {
     if (b.length !== Fp2.BYTES) throw new Error(`fromBytes wrong length=${b.length}`);
     return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) };
   },
-  toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)),
+  toBytes: ({ c0, c1 }) => concatB(Fp.toBytes(c0), Fp.toBytes(c1)),
   cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
     c0: Fp.cmov(c0, r0, c),
     c1: Fp.cmov(c1, r1, c),
@@ -280,18 +279,15 @@ const Fp6Multiply = ({ c0, c1, c2 }: Fp6, rhs: Fp6 | bigint) => {
   };
 };
 const Fp6Square = ({ c0, c1, c2 }: Fp6) => {
-  let t0 = Fp2.square(c0); // c0²
+  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.square(c2); // c2²
+  let t4 = Fp2.sqr(c2); // c2²
   return {
     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(
+    c2: Fp2.sub(Fp2.sub(Fp2.add(Fp2.add(t1, Fp2.sqr(Fp2.add(Fp2.sub(c0, c1), c2))), t3), t0), t4),
-      Fp2.sub(Fp2.add(Fp2.add(t1, Fp2.square(Fp2.add(Fp2.sub(c0, c1), c2))), t3), t0),
-      t4
-    ),
   };
 };
 type Fp6Utils = {
@@ -312,35 +308,34 @@ const Fp6: mod.Field<Fp6> & Fp6Utils = {
   ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO },
   create: (num) => num,
   isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2),
-  isZero: ({ c0, c1, c2 }) => Fp2.isZero(c0) && Fp2.isZero(c1) && Fp2.isZero(c2),
+  is0: ({ c0, c1, c2 }) => Fp2.is0(c0) && Fp2.is0(c1) && Fp2.is0(c2),
-  negate: ({ c0, c1, c2 }) => ({ c0: Fp2.negate(c0), c1: Fp2.negate(c1), c2: Fp2.negate(c2) }),
+  neg: ({ c0, c1, c2 }) => ({ c0: Fp2.neg(c0), c1: Fp2.neg(c1), c2: Fp2.neg(c2) }),
-  equals: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) =>
+  eql: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) =>
-    Fp2.equals(c0, r0) && Fp2.equals(c1, r1) && Fp2.equals(c2, r2),
+    Fp2.eql(c0, r0) && Fp2.eql(c1, r1) && Fp2.eql(c2, r2),
   sqrt: () => {
     throw new Error('Not implemented');
   },
   // Do we need division by bigint at all? Should be done via order:
-  div: (lhs, rhs) =>
+  div: (lhs, rhs) => Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp6.inv(rhs)),
-    Fp6.mul(lhs, typeof rhs === 'bigint' ? Fp.invert(Fp.create(rhs)) : Fp6.invert(rhs)),
   pow: (num, power) => mod.FpPow(Fp6, num, power),
   invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums),
   // Normalized
   add: Fp6Add,
   sub: Fp6Subtract,
   mul: Fp6Multiply,
-  square: Fp6Square,
+  sqr: Fp6Square,
   // NonNormalized stuff
   addN: Fp6Add,
   subN: Fp6Subtract,
   mulN: Fp6Multiply,
-  squareN: Fp6Square,
+  sqrN: Fp6Square,
 
-  invert: ({ c0, c1, c2 }) => {
+  inv: ({ c0, c1, c2 }) => {
-    let t0 = Fp2.sub(Fp2.square(c0), Fp2.mulByNonresidue(Fp2.mul(c2, c1))); // c0² - c2 * c1 * (u + 1)
+    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.square(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
+    let t1 = Fp2.sub(Fp2.mulByNonresidue(Fp2.sqr(c2)), Fp2.mul(c0, c1)); // c2² * (u + 1) - c0 * c1
-    let t2 = Fp2.sub(Fp2.square(c1), Fp2.mul(c0, c2)); // c1² - c0 * c2
+    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.invert(
+    let t4 = Fp2.inv(
       Fp2.add(Fp2.mulByNonresidue(Fp2.add(Fp2.mul(c2, t1), Fp2.mul(c1, t2))), Fp2.mul(c0, t0))
     );
     return { c0: Fp2.mul(t4, t0), c1: Fp2.mul(t4, t1), c2: Fp2.mul(t4, t2) };
@@ -355,7 +350,7 @@ const Fp6: mod.Field<Fp6> & Fp6Utils = {
     };
   },
   toBytes: ({ c0, c1, c2 }): Uint8Array =>
-    concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),
+    concatB(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)),
   cmov: ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6, c) => ({
     c0: Fp2.cmov(c0, r0, c),
     c1: Fp2.cmov(c1, r1, c),
@@ -498,11 +493,11 @@ const Fp12Square = ({ c0, c1 }: Fp12) => {
   }; // AB + AB
 };
 function Fp4Square(a: Fp2, b: Fp2): { first: Fp2; second: Fp2 } {
-  const a2 = Fp2.square(a);
+  const a2 = Fp2.sqr(a);
-  const b2 = Fp2.square(b);
+  const b2 = Fp2.sqr(b);
   return {
     first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a²
-    second: Fp2.sub(Fp2.sub(Fp2.square(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
+    second: Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b²
   };
 }
 type Fp12Utils = {
@@ -525,30 +520,30 @@ const Fp12: mod.Field<Fp12> & Fp12Utils = {
   ONE: { c0: Fp6.ONE, c1: Fp6.ZERO },
   create: (num) => num,
   isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1),
-  isZero: ({ c0, c1 }) => Fp6.isZero(c0) && Fp6.isZero(c1),
+  is0: ({ c0, c1 }) => Fp6.is0(c0) && Fp6.is0(c1),
-  negate: ({ c0, c1 }) => ({ c0: Fp6.negate(c0), c1: Fp6.negate(c1) }),
+  neg: ({ c0, c1 }) => ({ c0: Fp6.neg(c0), c1: Fp6.neg(c1) }),
-  equals: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.equals(c0, r0) && Fp6.equals(c1, r1),
+  eql: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.eql(c0, r0) && Fp6.eql(c1, r1),
   sqrt: () => {
     throw new Error('Not implemented');
   },
-  invert: ({ c0, c1 }) => {
+  inv: ({ c0, c1 }) => {
-    let t = Fp6.invert(Fp6.sub(Fp6.square(c0), Fp6.mulByNonresidue(Fp6.square(c1)))); // 1 / (c0² - c1² * v)
+    let t = Fp6.inv(Fp6.sub(Fp6.sqr(c0), Fp6.mulByNonresidue(Fp6.sqr(c1)))); // 1 / (c0² - c1² * v)
-    return { c0: Fp6.mul(c0, t), c1: Fp6.negate(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
+    return { c0: Fp6.mul(c0, t), c1: Fp6.neg(Fp6.mul(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w
   },
   div: (lhs, rhs) =>
-    Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.invert(Fp.create(rhs)) : Fp12.invert(rhs)),
+    Fp12.mul(lhs, typeof rhs === 'bigint' ? Fp.inv(Fp.create(rhs)) : Fp12.inv(rhs)),
   pow: (num, power) => mod.FpPow(Fp12, num, power),
   invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums),
   // Normalized
   add: Fp12Add,
   sub: Fp12Subtract,
   mul: Fp12Multiply,
-  square: Fp12Square,
+  sqr: Fp12Square,
   // NonNormalized stuff
   addN: Fp12Add,
   subN: Fp12Subtract,
   mulN: Fp12Multiply,
-  squareN: Fp12Square,
+  sqrN: Fp12Square,
 
   // Bytes utils
   fromBytes: (b: Uint8Array): Fp12 => {
@@ -558,7 +553,7 @@ const Fp12: mod.Field<Fp12> & Fp12Utils = {
       c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)),
     };
   },
-  toBytes: ({ c0, c1 }): Uint8Array => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)),
+  toBytes: ({ c0, c1 }): Uint8Array => concatB(Fp6.toBytes(c0), Fp6.toBytes(c1)),
   cmov: ({ c0, c1 }, { c0: r0, c1: r1 }, c) => ({
     c0: Fp6.cmov(c0, r0, c),
     c1: Fp6.cmov(c1, r1, c),
@@ -602,7 +597,7 @@ const Fp12: mod.Field<Fp12> & Fp12Utils = {
     c0: Fp6.multiplyByFp2(c0, rhs),
     c1: Fp6.multiplyByFp2(c1, rhs),
   }),
-  conjugate: ({ c0, c1 }): Fp12 => ({ c0, c1: Fp6.negate(c1) }),
+  conjugate: ({ c0, c1 }): Fp12 => ({ c0, c1: Fp6.neg(c1) }),
 
   // A cyclotomic group is a subgroup of Fp^n defined by
   //   GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1}
@@ -886,7 +881,7 @@ function psi(x: Fp2, y: Fp2): [Fp2, Fp2] {
   return [x2, y2];
 }
 // Ψ endomorphism
-function G2psi(c: ProjectiveConstructor<Fp2>, P: ProjectivePointType<Fp2>) {
+function G2psi(c: ProjConstructor<Fp2>, P: ProjPointType<Fp2>) {
   const affine = P.toAffine();
   const p = psi(affine.x, affine.y);
   return new c(p[0], p[1], Fp2.ONE);
@@ -897,9 +892,9 @@ const PSI2_C1 =
   0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaacn;
 
 function psi2(x: Fp2, y: Fp2): [Fp2, Fp2] {
-  return [Fp2.mul(x, PSI2_C1), Fp2.negate(y)];
+  return [Fp2.mul(x, PSI2_C1), Fp2.neg(y)];
 }
-function G2psi2(c: ProjectiveConstructor<Fp2>, P: ProjectivePointType<Fp2>) {
+function G2psi2(c: ProjConstructor<Fp2>, P: ProjPointType<Fp2>) {
   const affine = P.toAffine();
   const p = psi2(affine.x, affine.y);
   return new c(p[0], p[1], Fp2.ONE);
@@ -920,6 +915,7 @@ const htfDefaults = {
   // defined in section 2.2.5
   // Use utils.getDSTLabel(), utils.setDSTLabel(value)
   DST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_',
+  encodeDST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_',
   // p: the characteristic of F
   //    where F is a finite field of characteristic p and order q = p^m
   p: Fp.ORDER,
@@ -989,7 +985,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
       // φ endomorphism
       const cubicRootOfUnityModP =
         0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffen;
-      const phi = new c(Fp.mul(point.x, cubicRootOfUnityModP), point.y, point.z);
+      const phi = new c(Fp.mul(point.px, cubicRootOfUnityModP), point.py, point.pz);
 
       // todo: unroll
       const xP = point.multiplyUnsafe(bls12_381.CURVE.x).negate(); // [x]P
@@ -1018,7 +1014,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
       const { x, y } = G1_SWU(Fp.create(scalars[0]));
       return isogenyMapG1(x, y);
     },
-    fromBytes: (bytes: Uint8Array): { x: Fp; y: Fp } => {
+    fromBytes: (bytes: Uint8Array): AffinePoint<Fp> => {
       if (bytes.length === 48) {
         const P = Fp.ORDER;
         const compressedValue = bytesToNumberBE(bytes);
@@ -1030,11 +1026,11 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
         let y = Fp.sqrt(right);
         if (!y) throw new Error('Invalid compressed G1 point');
         const aflag = bitGet(compressedValue, C_BIT_POS);
-        if ((y * 2n) / P !== aflag) y = Fp.negate(y);
+        if ((y * 2n) / P !== aflag) y = Fp.neg(y);
         return { x: Fp.create(x), y: Fp.create(y) };
       } else if (bytes.length === 96) {
         // Check if the infinity flag is set
-        if ((bytes[0] & (1 << 6)) !== 0) return bls12_381.G1.Point.ZERO;
+        if ((bytes[0] & (1 << 6)) !== 0) return bls12_381.G1.ProjectivePoint.ZERO.toAffine();
         const x = bytesToNumberBE(bytes.slice(0, Fp.BYTES));
         const y = bytesToNumberBE(bytes.slice(Fp.BYTES));
         return { x: Fp.create(x), y: Fp.create(y) };
@@ -1044,7 +1040,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
     },
     toBytes: (c, point, isCompressed) => {
       const isZero = point.equals(c.ZERO);
-      const { x, y } = point;
+      const { x, y } = point.toAffine();
       if (isCompressed) {
         if (isZero) return COMPRESSED_ZERO.slice();
         const P = Fp.ORDER;
@@ -1055,10 +1051,10 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
       } else {
         if (isZero) {
           // 2x PUBLIC_KEY_LENGTH
-          const x = concatBytes(new Uint8Array([0x40]), new Uint8Array(2 * Fp.BYTES - 1));
+          const x = concatB(new Uint8Array([0x40]), new Uint8Array(2 * Fp.BYTES - 1));
           return x;
         } else {
-          return concatBytes(numberToBytesBE(x, Fp.BYTES), numberToBytesBE(y, Fp.BYTES));
+          return concatB(numberToBytesBE(x, Fp.BYTES), numberToBytesBE(y, Fp.BYTES));
         }
       }
     },
@@ -1120,7 +1116,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
       const Q = t3.subtract(P);               // Ψ²(2P) - Ψ(P) + [x²]P - [x]Ψ(P) + [x]P - 1P
       return Q;                               // [x²-x-1]P + [x-1]Ψ(P) + Ψ²(2P)
     },
-    fromBytes: (bytes: Uint8Array): { x: Fp2; y: Fp2 } => {
+    fromBytes: (bytes: Uint8Array): AffinePoint<Fp2> => {
       const m_byte = bytes[0] & 0xe0;
       if (m_byte === 0x20 || m_byte === 0x60 || m_byte === 0xe0) {
         throw new Error('Invalid encoding flag: ' + m_byte);
@@ -1128,6 +1124,8 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
       const bitC = m_byte & 0x80; // compression bit
       const bitI = m_byte & 0x40; // point at infinity bit
       const bitS = m_byte & 0x20; // sign bit
+      const L = Fp.BYTES;
+      const slc = (b: Uint8Array, from: number, to?: number) => bytesToNumberBE(b.slice(from, to));
       if (bytes.length === 96 && bitC) {
         const { b } = bls12_381.CURVE.G2;
         const P = Fp.ORDER;
@@ -1140,23 +1138,23 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
           }
           return { x: Fp2.ZERO, y: Fp2.ZERO };
         }
-        const x_1 = bytesToNumberBE(bytes.slice(0, Fp.BYTES));
+        const x_1 = slc(bytes, 0, L);
-        const x_0 = bytesToNumberBE(bytes.slice(Fp.BYTES));
+        const x_0 = slc(bytes, L, 2 * L);
         const x = Fp2.create({ c0: Fp.create(x_0), c1: Fp.create(x_1) });
         const right = Fp2.add(Fp2.pow(x, 3n), b); // y² = x³ + 4 * (u+1) = x³ + b
         let y = Fp2.sqrt(right);
         const Y_bit = y.c1 === 0n ? (y.c0 * 2n) / P : (y.c1 * 2n) / P ? 1n : 0n;
-        y = bitS > 0 && Y_bit > 0 ? y : Fp2.negate(y);
+        y = bitS > 0 && Y_bit > 0 ? y : Fp2.neg(y);
         return { x, y };
       } else if (bytes.length === 192 && !bitC) {
         // Check if the infinity flag is set
         if ((bytes[0] & (1 << 6)) !== 0) {
           return { x: Fp2.ZERO, y: Fp2.ZERO };
         }
-        const x1 = bytesToNumberBE(bytes.slice(0, Fp.BYTES));
+        const x1 = slc(bytes, 0, L);
-        const x0 = bytesToNumberBE(bytes.slice(Fp.BYTES, 2 * Fp.BYTES));
+        const x0 = slc(bytes, L, 2 * L);
-        const y1 = bytesToNumberBE(bytes.slice(2 * Fp.BYTES, 3 * Fp.BYTES));
+        const y1 = slc(bytes, 2 * L, 3 * L);
-        const y0 = bytesToNumberBE(bytes.slice(3 * Fp.BYTES));
+        const y0 = slc(bytes, 3 * L, 4 * L);
         return { x: Fp2.fromBigTuple([x0, x1]), y: Fp2.fromBigTuple([y0, y1]) };
       } else {
         throw new Error('Invalid point G2, expected 96/192 bytes');
@@ -1164,20 +1162,20 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
     },
     toBytes: (c, point, isCompressed) => {
       const isZero = point.equals(c.ZERO);
-      const { x, y } = point;
+      const { x, y } = point.toAffine();
       if (isCompressed) {
         const P = Fp.ORDER;
-        if (isZero) return concatBytes(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES));
+        if (isZero) return concatB(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES));
         const flag = Boolean(y.c1 === 0n ? (y.c0 * 2n) / P : (y.c1 * 2n) / P);
         // set compressed & sign bits (looks like different offsets than for G1/Fp?)
         let x_1 = bitSet(x.c1, C_BIT_POS, flag);
         x_1 = bitSet(x_1, S_BIT_POS, true);
-        return concatBytes(numberToBytesBE(x_1, Fp.BYTES), numberToBytesBE(x.c0, Fp.BYTES));
+        return concatB(numberToBytesBE(x_1, Fp.BYTES), numberToBytesBE(x.c0, Fp.BYTES));
       } else {
-        if (isZero) return concatBytes(new Uint8Array([0x40]), new Uint8Array(4 * Fp.BYTES - 1)); // bytes[0] |= 1 << 6;
+        if (isZero) return concatB(new Uint8Array([0x40]), new Uint8Array(4 * Fp.BYTES - 1)); // bytes[0] |= 1 << 6;
         const { re: x0, im: x1 } = Fp2.reim(x);
         const { re: y0, im: y1 } = Fp2.reim(y);
-        return concatBytes(
+        return concatB(
           numberToBytesBE(x1, Fp.BYTES),
           numberToBytesBE(x0, Fp.BYTES),
           numberToBytesBE(y1, Fp.BYTES),
@@ -1187,7 +1185,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
     },
     Signature: {
       // TODO: Optimize, it's very slow because of sqrt.
-      decode(hex: Hex): PointType<Fp2> {
+      decode(hex: Hex): ProjPointType<Fp2> {
         hex = ensureBytes(hex);
         const P = Fp.ORDER;
         const half = hex.length / 2;
@@ -1197,7 +1195,7 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
         const z2 = bytesToNumberBE(hex.slice(half));
         // Indicates the infinity point
         const bflag1 = bitGet(z1, I_BIT_POS);
-        if (bflag1 === 1n) return bls12_381.G2.Point.ZERO;
+        if (bflag1 === 1n) return bls12_381.G2.ProjectivePoint.ZERO;
 
         const x1 = Fp.create(z1 & Fp.MASK);
         const x2 = Fp.create(z2);
@@ -1213,23 +1211,25 @@ export const bls12_381: CurveFn<Fp, Fp2, Fp6, Fp12> = bls({
         const aflag1 = bitGet(z1, 381);
         const isGreater = y1 > 0n && (y1 * 2n) / P !== aflag1;
         const isZero = y1 === 0n && (y0 * 2n) / P !== aflag1;
-        if (isGreater || isZero) y = Fp2.negate(y);
+        if (isGreater || isZero) y = Fp2.neg(y);
-        const point = new bls12_381.G2.Point(x, y);
+        const point = bls12_381.G2.ProjectivePoint.fromAffine({ x, y });
+        // console.log('Signature.decode', point);
         point.assertValidity();
         return point;
       },
-      encode(point: PointType<Fp2>) {
+      encode(point: ProjPointType<Fp2>) {
         // NOTE: by some reasons it was missed in bls12-381, looks like bug
         point.assertValidity();
-        if (point.equals(bls12_381.G2.Point.ZERO))
+        if (point.equals(bls12_381.G2.ProjectivePoint.ZERO))
-          return concatBytes(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES));
+          return concatB(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES));
-        const { re: x0, im: x1 } = Fp2.reim(point.x);
+        const a = point.toAffine();
-        const { re: y0, im: y1 } = Fp2.reim(point.y);
+        const { re: x0, im: x1 } = Fp2.reim(a.x);
+        const { re: y0, im: y1 } = Fp2.reim(a.y);
         const tmp = y1 > 0n ? y1 * 2n : y0 * 2n;
         const aflag1 = Boolean((tmp / Fp.ORDER) & 1n);
         const z1 = bitSet(bitSet(x1, 381, aflag1), S_BIT_POS, true);
         const z2 = x0;
-        return concatBytes(numberToBytesBE(z1, Fp.BYTES), numberToBytesBE(z2, Fp.BYTES));
+        return concatB(numberToBytesBE(z1, Fp.BYTES), numberToBytesBE(z2, Fp.BYTES));
       },
     },
   },

src/bn.ts

@@ -1,6 +1,6 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { weierstrass } from './abstract/weierstrass.js';
 import { sha256 } from '@noble/hashes/sha256';
+import { weierstrass } from './abstract/weierstrass.js';
 import { getHash } from './_shortw_utils.js';
 import { Fp } from './abstract/modular.js';
 /**

src/ed25519.ts

@@ -1,7 +1,7 @@
 /*! 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, ExtendedPointType } from './abstract/edwards.js';
+import { twistedEdwards, ExtPointType } from './abstract/edwards.js';
 import { montgomery } from './abstract/montgomery.js';
 import { mod, pow2, isNegativeLE, Fp as Field, FpSqrtEven } from './abstract/modular.js';
 import {
@@ -12,6 +12,7 @@ import {
   numberToBytesLE,
   Hex,
 } from './abstract/utils.js';
+import * as htf from './abstract/hash-to-curve.js';
 
 /**
  * ed25519 Twisted Edwards curve with following addons:
@@ -93,79 +94,6 @@ export const ED25519_TORSION_SUBGROUP = [
 
 const Fp = Field(ED25519_P, undefined, true);
 
-// Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)
-// NOTE: very important part is usage of FpSqrtEven for ELL2_C1_EDWARDS, since
-// SageMath returns different root first and everything falls apart
-
-const ELL2_C1 = (Fp.ORDER + BigInt(3)) / BigInt(8); // 1. c1 = (q + 3) / 8       # Integer arithmetic
-
-const ELL2_C2 = Fp.pow(_2n, ELL2_C1); // 2. c2 = 2^c1
-const ELL2_C3 = Fp.sqrt(Fp.negate(Fp.ONE)); // 3. c3 = sqrt(-1)
-const ELL2_C4 = (Fp.ORDER - BigInt(5)) / BigInt(8); // 4. c4 = (q - 5) / 8       # Integer arithmetic
-const ELL2_J = BigInt(486662);
-
-// prettier-ignore
-function map_to_curve_elligator2_curve25519(u: bigint) {
-  let tv1 = Fp.square(u);       //  1.  tv1 = u^2
-  tv1 = Fp.mul(tv1, _2n);       //  2.  tv1 = 2 * tv1
-  let xd = Fp.add(tv1, Fp.ONE); //  3.   xd = tv1 + 1         # Nonzero: -1 is square (mod p), tv1 is not
-  let x1n = Fp.negate(ELL2_J);  //  4.  x1n = -J              # x1 = x1n / xd = -J / (1 + 2 * u^2)
-  let tv2 = Fp.square(xd);      //  5.  tv2 = xd^2
-  let gxd = Fp.mul(tv2, xd);    //  6.  gxd = tv2 * xd        # gxd = xd^3
-  let gx1 = Fp.mul(tv1, ELL2_J); //  7.  gx1 = J * tv1         # x1n + J * xd
-  gx1 = Fp.mul(gx1, x1n);       //  8.  gx1 = gx1 * x1n       # x1n^2 + J * x1n * xd
-  gx1 = Fp.add(gx1, tv2);       //  9.  gx1 = gx1 + tv2       # x1n^2 + J * x1n * xd + xd^2
-  gx1 = Fp.mul(gx1, x1n);       //  10. gx1 = gx1 * x1n       # x1n^3 + J * x1n^2 * xd + x1n * xd^2
-  let tv3 = Fp.square(gxd);     //  11. tv3 = gxd^2
-  tv2 = Fp.square(tv3);         //  12. tv2 = tv3^2           # gxd^4
-  tv3 = Fp.mul(tv3, gxd);       //  13. tv3 = tv3 * gxd       # gxd^3
-  tv3 = Fp.mul(tv3, gx1);       //  14. tv3 = tv3 * gx1       # gx1 * gxd^3
-  tv2 = Fp.mul(tv2, tv3);       //  15. tv2 = tv2 * tv3       # gx1 * gxd^7
-  let y11 = Fp.pow(tv2, ELL2_C4); //  16. y11 = tv2^c4        # (gx1 * gxd^7)^((p - 5) / 8)
-  y11 = Fp.mul(y11, tv3);       //  17. y11 = y11 * tv3       # gx1*gxd^3*(gx1*gxd^7)^((p-5)/8)
-  let y12 = Fp.mul(y11, ELL2_C3); //  18. y12 = y11 * c3
-  tv2 = Fp.square(y11);         //  19. tv2 = y11^2
-  tv2 = Fp.mul(tv2, gxd);       //  20. tv2 = tv2 * gxd
-  let e1 = Fp.equals(tv2, gx1); //  21.  e1 = tv2 == gx1
-  let y1 = Fp.cmov(y12, y11, e1); //  22.  y1 = CMOV(y12, y11, e1)  # If g(x1) is square, this is its sqrt
-  let x2n = Fp.mul(x1n, tv1);   //  23. x2n = x1n * tv1       # x2 = x2n / xd = 2 * u^2 * x1n / xd
-  let y21 = Fp.mul(y11, u);     //  24. y21 = y11 * u
-  y21 = Fp.mul(y21, ELL2_C2);   //  25. y21 = y21 * c2
-  let y22 = Fp.mul(y21, ELL2_C3); //  26. y22 = y21 * c3
-  let gx2 = Fp.mul(gx1, tv1);   //  27. gx2 = gx1 * tv1       # g(x2) = gx2 / gxd = 2 * u^2 * g(x1)
-  tv2 = Fp.square(y21);         //  28. tv2 = y21^2
-  tv2 = Fp.mul(tv2, gxd);       //  29. tv2 = tv2 * gxd
-  let e2 = Fp.equals(tv2, gx2); //  30.  e2 = tv2 == gx2
-  let y2 = Fp.cmov(y22, y21, e2); //  31.  y2 = CMOV(y22, y21, e2)  # If g(x2) is square, this is its sqrt
-  tv2 = Fp.square(y1);          //  32. tv2 = y1^2
-  tv2 = Fp.mul(tv2, gxd);       //  33. tv2 = tv2 * gxd
-  let e3 = Fp.equals(tv2, gx1); //  34.  e3 = tv2 == gx1
-  let xn = Fp.cmov(x2n, x1n, e3); //  35.  xn = CMOV(x2n, x1n, e3)  # If e3, x = x1, else x = x2
-  let y = Fp.cmov(y2, y1, e3);  //  36.   y = CMOV(y2, y1, e3)    # If e3, y = y1, else y = y2
-  let e4 = Fp.isOdd(y);         //  37.  e4 = sgn0(y) == 1        # Fix sign of y
-  y = Fp.cmov(y, Fp.negate(y), e3 !== e4); //  38.   y = CMOV(y, -y, e3 XOR e4)
-  return { xMn: xn, xMd: xd, yMn: y, yMd: 1n }; //  39. return (xn, xd, y, 1)
-}
-
-const ELL2_C1_EDWARDS = FpSqrtEven(Fp, Fp.negate(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)
-  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
-  let yn = Fp.sub(xMn, xMd); //  5.  yn = xMn - xMd
-  let yd = Fp.add(xMn, xMd); //  6.  yd = xMn + xMd    # (n / d - 1) / (n / d + 1) = (n - d) / (n + d)
-  let tv1 = Fp.mul(xd, yd); //  7. tv1 = xd * yd
-  let e = Fp.equals(tv1, Fp.ZERO); //  8.   e = tv1 == 0
-  xn = Fp.cmov(xn, Fp.ZERO, e); //  9.  xn = CMOV(xn, 0, e)
-  xd = Fp.cmov(xd, Fp.ONE, e); //  10. xd = CMOV(xd, 1, e)
-  yn = Fp.cmov(yn, Fp.ONE, e); //  11. yn = CMOV(yn, 1, e)
-  yd = Fp.cmov(yd, Fp.ONE, e); //  12. yd = CMOV(yd, 1, e)
-
-  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 ED25519_DEF = {
   // Param: a
   a: BigInt(-1),
@@ -189,15 +117,6 @@ const ED25519_DEF = {
   // Ratio of u to v. Allows us to combine inversion and square root. Uses algo from RFC8032 5.1.3.
   // Constant-time, u/√v
   uvRatio,
-  htfDefaults: {
-    DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
-    p: Fp.ORDER,
-    m: 1,
-    k: 128,
-    expand: 'xmd',
-    hash: sha512,
-  },
-  mapToCurve: (scalars: bigint[]) => map_to_curve_elligator2_edwards25519(scalars[0]),
 } as const;
 
 export const ed25519 = twistedEdwards(ED25519_DEF);
@@ -232,8 +151,95 @@ export const x25519 = montgomery({
   adjustScalarBytes,
 });
 
+// Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)
+// NOTE: very important part is usage of FpSqrtEven for ELL2_C1_EDWARDS, since
+// SageMath returns different root first and everything falls apart
+
+const ELL2_C1 = (Fp.ORDER + BigInt(3)) / BigInt(8); // 1. c1 = (q + 3) / 8       # Integer arithmetic
+
+const ELL2_C2 = Fp.pow(_2n, ELL2_C1); // 2. c2 = 2^c1
+const ELL2_C3 = Fp.sqrt(Fp.neg(Fp.ONE)); // 3. c3 = sqrt(-1)
+const ELL2_C4 = (Fp.ORDER - BigInt(5)) / BigInt(8); // 4. c4 = (q - 5) / 8       # Integer arithmetic
+const ELL2_J = BigInt(486662);
+
+// prettier-ignore
+function map_to_curve_elligator2_curve25519(u: bigint) {
+  let tv1 = Fp.sqr(u);       //  1.  tv1 = u^2
+  tv1 = Fp.mul(tv1, _2n);       //  2.  tv1 = 2 * tv1
+  let xd = Fp.add(tv1, Fp.ONE); //  3.   xd = tv1 + 1         # Nonzero: -1 is square (mod p), tv1 is not
+  let x1n = Fp.neg(ELL2_J);  //  4.  x1n = -J              # x1 = x1n / xd = -J / (1 + 2 * u^2)
+  let tv2 = Fp.sqr(xd);      //  5.  tv2 = xd^2
+  let gxd = Fp.mul(tv2, xd);    //  6.  gxd = tv2 * xd        # gxd = xd^3
+  let gx1 = Fp.mul(tv1, ELL2_J); //  7.  gx1 = J * tv1         # x1n + J * xd
+  gx1 = Fp.mul(gx1, x1n);       //  8.  gx1 = gx1 * x1n       # x1n^2 + J * x1n * xd
+  gx1 = Fp.add(gx1, tv2);       //  9.  gx1 = gx1 + tv2       # x1n^2 + J * x1n * xd + xd^2
+  gx1 = Fp.mul(gx1, x1n);       //  10. gx1 = gx1 * x1n       # x1n^3 + J * x1n^2 * xd + x1n * xd^2
+  let tv3 = Fp.sqr(gxd);     //  11. tv3 = gxd^2
+  tv2 = Fp.sqr(tv3);         //  12. tv2 = tv3^2           # gxd^4
+  tv3 = Fp.mul(tv3, gxd);       //  13. tv3 = tv3 * gxd       # gxd^3
+  tv3 = Fp.mul(tv3, gx1);       //  14. tv3 = tv3 * gx1       # gx1 * gxd^3
+  tv2 = Fp.mul(tv2, tv3);       //  15. tv2 = tv2 * tv3       # gx1 * gxd^7
+  let y11 = Fp.pow(tv2, ELL2_C4); //  16. y11 = tv2^c4        # (gx1 * gxd^7)^((p - 5) / 8)
+  y11 = Fp.mul(y11, tv3);       //  17. y11 = y11 * tv3       # gx1*gxd^3*(gx1*gxd^7)^((p-5)/8)
+  let y12 = Fp.mul(y11, ELL2_C3); //  18. y12 = y11 * c3
+  tv2 = Fp.sqr(y11);         //  19. tv2 = y11^2
+  tv2 = Fp.mul(tv2, gxd);       //  20. tv2 = tv2 * gxd
+  let e1 = Fp.eql(tv2, gx1); //  21.  e1 = tv2 == gx1
+  let y1 = Fp.cmov(y12, y11, e1); //  22.  y1 = CMOV(y12, y11, e1)  # If g(x1) is square, this is its sqrt
+  let x2n = Fp.mul(x1n, tv1);   //  23. x2n = x1n * tv1       # x2 = x2n / xd = 2 * u^2 * x1n / xd
+  let y21 = Fp.mul(y11, u);     //  24. y21 = y11 * u
+  y21 = Fp.mul(y21, ELL2_C2);   //  25. y21 = y21 * c2
+  let y22 = Fp.mul(y21, ELL2_C3); //  26. y22 = y21 * c3
+  let gx2 = Fp.mul(gx1, tv1);   //  27. gx2 = gx1 * tv1       # g(x2) = gx2 / gxd = 2 * u^2 * g(x1)
+  tv2 = Fp.sqr(y21);         //  28. tv2 = y21^2
+  tv2 = Fp.mul(tv2, gxd);       //  29. tv2 = tv2 * gxd
+  let e2 = Fp.eql(tv2, gx2); //  30.  e2 = tv2 == gx2
+  let y2 = Fp.cmov(y22, y21, e2); //  31.  y2 = CMOV(y22, y21, e2)  # If g(x2) is square, this is its sqrt
+  tv2 = Fp.sqr(y1);          //  32. tv2 = y1^2
+  tv2 = Fp.mul(tv2, gxd);       //  33. tv2 = tv2 * gxd
+  let e3 = Fp.eql(tv2, gx1); //  34.  e3 = tv2 == gx1
+  let xn = Fp.cmov(x2n, x1n, e3); //  35.  xn = CMOV(x2n, x1n, e3)  # If e3, x = x1, else x = x2
+  let y = Fp.cmov(y2, y1, e3);  //  36.   y = CMOV(y2, y1, e3)    # If e3, y = y1, else y = y2
+  let e4 = Fp.isOdd(y);         //  37.  e4 = sgn0(y) == 1        # Fix sign of y
+  y = Fp.cmov(y, Fp.neg(y), e3 !== e4); //  38.   y = CMOV(y, -y, e3 XOR e4)
+  return { xMn: xn, xMd: xd, yMn: y, yMd: 1n }; //  39. return (xn, xd, y, 1)
+}
+
+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)
+  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
+  let yn = Fp.sub(xMn, xMd); //  5.  yn = xMn - xMd
+  let yd = Fp.add(xMn, xMd); //  6.  yd = xMn + xMd    # (n / d - 1) / (n / d + 1) = (n - d) / (n + d)
+  let tv1 = Fp.mul(xd, yd); //  7. tv1 = xd * yd
+  let e = Fp.eql(tv1, Fp.ZERO); //  8.   e = tv1 == 0
+  xn = Fp.cmov(xn, Fp.ZERO, e); //  9.  xn = CMOV(xn, 0, e)
+  xd = Fp.cmov(xd, Fp.ONE, e); //  10. xd = CMOV(xd, 1, e)
+  yn = Fp.cmov(yn, Fp.ONE, e); //  11. yn = CMOV(yn, 1, e)
+  yd = Fp.cmov(yd, Fp.ONE, e); //  12. yd = CMOV(yd, 1, e)
+
+  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.hashToCurve(
+  ed25519.ExtendedPoint,
+  (scalars: bigint[]) => map_to_curve_elligator2_edwards25519(scalars[0]),
+  {
+    DST: 'edwards25519_XMD:SHA-512_ELL2_RO_',
+    encodeDST: 'edwards25519_XMD:SHA-512_ELL2_NU_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 128,
+    expand: 'xmd',
+    hash: sha512,
+  }
+);
+export { hashToCurve, encodeToCurve };
+
 function assertRstPoint(other: unknown) {
-  if (!(other instanceof RistrettoPoint)) throw new TypeError('RistrettoPoint expected');
+  if (!(other instanceof RistrettoPoint)) throw new Error('RistrettoPoint expected');
 }
 // √(-1) aka √(a) aka 2^((p-1)/4)
 const SQRT_M1 = BigInt(
@@ -262,7 +268,7 @@ const MAX_255B = BigInt('0x7ffffffffffffffffffffffffffffffffffffffffffffffffffff
 const bytes255ToNumberLE = (bytes: Uint8Array) =>
   ed25519.CURVE.Fp.create(bytesToNumberLE(bytes) & MAX_255B);
 
-type ExtendedPoint = ExtendedPointType;
+type ExtendedPoint = ExtPointType;
 
 // Computes Elligator map for Ristretto
 // https://ristretto.group/formulas/elligator.html
@@ -355,7 +361,7 @@ export class RistrettoPoint {
    * https://ristretto.group/formulas/encoding.html
    */
   toRawBytes(): Uint8Array {
-    let { x, y, z, t } = this.ep;
+    let { ex: x, ey: y, ez: z, et: t } = this.ep;
     const P = ed25519.CURVE.Fp.ORDER;
     const mod = ed25519.CURVE.Fp.create;
     const u1 = mod(mod(z + y) * mod(z - y)); // 1
@@ -393,12 +399,12 @@ export class RistrettoPoint {
   // Compare one point to another.
   equals(other: RistrettoPoint): boolean {
     assertRstPoint(other);
-    const a = this.ep;
+    const { ex: X1, ey: Y1 } = this.ep;
-    const b = other.ep;
+    const { ex: X2, ey: Y2 } = this.ep;
     const mod = ed25519.CURVE.Fp.create;
     // (x1 * y2 == y1 * x2) | (y1 * y2 == x1 * x2)
-    const one = mod(a.x * b.y) === mod(a.y * b.x);
+    const one = mod(X1 * Y2) === mod(Y1 * X2);
-    const two = mod(a.y * b.y) === mod(a.x * b.x);
+    const two = mod(Y1 * Y2) === mod(X1 * X2);
     return one || two;
   }
 
@@ -412,11 +418,11 @@ export class RistrettoPoint {
     return new RistrettoPoint(this.ep.subtract(other.ep));
   }
 
-  multiply(scalar: number | bigint): RistrettoPoint {
+  multiply(scalar: bigint): RistrettoPoint {
     return new RistrettoPoint(this.ep.multiply(scalar));
   }
 
-  multiplyUnsafe(scalar: number | bigint): RistrettoPoint {
+  multiplyUnsafe(scalar: bigint): RistrettoPoint {
     return new RistrettoPoint(this.ep.multiplyUnsafe(scalar));
   }
 }

src/ed448.ts

@@ -4,6 +4,7 @@ import { concatBytes, randomBytes, utf8ToBytes, wrapConstructor } from '@noble/h
 import { twistedEdwards } from './abstract/edwards.js';
 import { mod, pow2, Fp as Field } from './abstract/modular.js';
 import { montgomery } from './abstract/montgomery.js';
+import * as htf from './abstract/hash-to-curve.js';
 
 /**
  * Edwards448 (not Ed448-Goldilocks) curve with following addons:
@@ -54,81 +55,6 @@ function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
 
 const Fp = Field(ed448P, 456, true);
 
-// Hash To Curve Elligator2 Map
-const ELL2_C1 = (Fp.ORDER - BigInt(3)) / BigInt(4); // 1. c1 = (q - 3) / 4         # Integer arithmetic
-const ELL2_J = BigInt(156326);
-function map_to_curve_elligator2_curve448(u: bigint) {
-  let tv1 = Fp.square(u); // 1.  tv1 = u^2
-  let e1 = Fp.equals(tv1, Fp.ONE); // 2.   e1 = tv1 == 1
-  tv1 = Fp.cmov(tv1, Fp.ZERO, e1); // 3.  tv1 = CMOV(tv1, 0, e1)  # If Z * u^2 == -1, set tv1 = 0
-  let xd = Fp.sub(Fp.ONE, tv1); // 4.   xd = 1 - tv1
-  let x1n = Fp.negate(ELL2_J); // 5.  x1n = -J
-  let tv2 = Fp.square(xd); // 6.  tv2 = xd^2
-  let gxd = Fp.mul(tv2, xd); // 7.  gxd = tv2 * xd          # gxd = xd^3
-  let gx1 = Fp.mul(tv1, Fp.negate(ELL2_J)); // 8.  gx1 = -J * tv1          # x1n + J * xd
-  gx1 = Fp.mul(gx1, x1n); // 9.  gx1 = gx1 * x1n         # x1n^2 + J * x1n * xd
-  gx1 = Fp.add(gx1, tv2); // 10. gx1 = gx1 + tv2         # x1n^2 + J * x1n * xd + xd^2
-  gx1 = Fp.mul(gx1, x1n); // 11. gx1 = gx1 * x1n         # x1n^3 + J * x1n^2 * xd + x1n * xd^2
-  let tv3 = Fp.square(gxd); // 12. tv3 = gxd^2
-  tv2 = Fp.mul(gx1, gxd); // 13. tv2 = gx1 * gxd         # gx1 * gxd
-  tv3 = Fp.mul(tv3, tv2); // 14. tv3 = tv3 * tv2         # gx1 * gxd^3
-  let y1 = Fp.pow(tv3, ELL2_C1); // 15.  y1 = tv3^c1            # (gx1 * gxd^3)^((p - 3) / 4)
-  y1 = Fp.mul(y1, tv2); // 16.  y1 = y1 * tv2          # gx1 * gxd * (gx1 * gxd^3)^((p - 3) / 4)
-  let x2n = Fp.mul(x1n, Fp.negate(tv1)); // 17. x2n = -tv1 * x1n        # x2 = x2n / xd = -1 * u^2 * x1n / xd
-  let y2 = Fp.mul(y1, u); // 18.  y2 = y1 * u
-  y2 = Fp.cmov(y2, Fp.ZERO, e1); // 19.  y2 = CMOV(y2, 0, e1)
-  tv2 = Fp.square(y1); // 20. tv2 = y1^2
-  tv2 = Fp.mul(tv2, gxd); // 21. tv2 = tv2 * gxd
-  let e2 = Fp.equals(tv2, gx1); // 22.  e2 = tv2 == gx1
-  let xn = Fp.cmov(x2n, x1n, e2); // 23.  xn = CMOV(x2n, x1n, e2)  # If e2, x = x1, else x = x2
-  let y = Fp.cmov(y2, y1, e2); // 24.   y = CMOV(y2, y1, e2)    # If e2, y = y1, else y = y2
-  let e3 = Fp.isOdd(y); // 25.  e3 = sgn0(y) == 1        # Fix sign of y
-  y = Fp.cmov(y, Fp.negate(y), e2 !== e3); // 26.   y = CMOV(y, -y, e2 XOR e3)
-  return { xn, xd, yn: y, yd: Fp.ONE }; // 27. return (xn, xd, y, 1)
-}
-function map_to_curve_elligator2_edwards448(u: bigint) {
-  let { xn, xd, yn, yd } = map_to_curve_elligator2_curve448(u); // 1. (xn, xd, yn, yd) = map_to_curve_elligator2_curve448(u)
-  let xn2 = Fp.square(xn); // 2.  xn2 = xn^2
-  let xd2 = Fp.square(xd); // 3.  xd2 = xd^2
-  let xd4 = Fp.square(xd2); // 4.  xd4 = xd2^2
-  let yn2 = Fp.square(yn); // 5.  yn2 = yn^2
-  let yd2 = Fp.square(yd); // 6.  yd2 = yd^2
-  let xEn = Fp.sub(xn2, xd2); // 7.  xEn = xn2 - xd2
-  let tv2 = Fp.sub(xEn, xd2); // 8.  tv2 = xEn - xd2
-  xEn = Fp.mul(xEn, xd2); // 9.  xEn = xEn * xd2
-  xEn = Fp.mul(xEn, yd); // 10. xEn = xEn * yd
-  xEn = Fp.mul(xEn, yn); // 11. xEn = xEn * yn
-  xEn = Fp.mul(xEn, 4n); // 12. xEn = xEn * 4
-  tv2 = Fp.mul(tv2, xn2); // 13. tv2 = tv2 * xn2
-  tv2 = Fp.mul(tv2, yd2); // 14. tv2 = tv2 * yd2
-  let tv3 = Fp.mul(yn2, 4n); // 15. tv3 = 4 * yn2
-  let tv1 = Fp.add(tv3, yd2); // 16. tv1 = tv3 + yd2
-  tv1 = Fp.mul(tv1, xd4); // 17. tv1 = tv1 * xd4
-  let xEd = Fp.add(tv1, tv2); // 18. xEd = tv1 + tv2
-  tv2 = Fp.mul(tv2, xn); // 19. tv2 = tv2 * xn
-  let tv4 = Fp.mul(xn, xd4); // 20. tv4 = xn * xd4
-  let yEn = Fp.sub(tv3, yd2); // 21. yEn = tv3 - yd2
-  yEn = Fp.mul(yEn, tv4); // 22. yEn = yEn * tv4
-  yEn = Fp.sub(yEn, tv2); // 23. yEn = yEn - tv2
-  tv1 = Fp.add(xn2, xd2); // 24. tv1 = xn2 + xd2
-  tv1 = Fp.mul(tv1, xd2); // 25. tv1 = tv1 * xd2
-  tv1 = Fp.mul(tv1, xd); // 26. tv1 = tv1 * xd
-  tv1 = Fp.mul(tv1, yn2); // 27. tv1 = tv1 * yn2
-  tv1 = Fp.mul(tv1, BigInt(-2)); // 28. tv1 = -2 * tv1
-  let yEd = Fp.add(tv2, tv1); // 29. yEd = tv2 + tv1
-  tv4 = Fp.mul(tv4, yd2); // 30. tv4 = tv4 * yd2
-  yEd = Fp.add(yEd, tv4); // 31. yEd = yEd + tv4
-  tv1 = Fp.mul(xEd, yEd); // 32. tv1 = xEd * yEd
-  let e = Fp.equals(tv1, Fp.ZERO); // 33.   e = tv1 == 0
-  xEn = Fp.cmov(xEn, Fp.ZERO, e); // 34. xEn = CMOV(xEn, 0, e)
-  xEd = Fp.cmov(xEd, Fp.ONE, e); // 35. xEd = CMOV(xEd, 1, e)
-  yEn = Fp.cmov(yEn, Fp.ONE, e); // 36. yEn = CMOV(yEn, 1, e)
-  yEd = Fp.cmov(yEd, Fp.ONE, e); // 37. yEd = CMOV(yEd, 1, e)
-
-  const inv = Fp.invertBatch([xEd, yEd]); // batch division
-  return { x: Fp.mul(xEn, inv[0]), y: Fp.mul(yEn, inv[1]) }; // 38. return (xEn, xEd, yEn, yEd)
-}
-
 const ED448_DEF = {
   // Param: a
   a: BigInt(1),
@@ -189,15 +115,6 @@ const ED448_DEF = {
     // square root exists, and the decoding fails.
     return { isValid: mod(x2 * v, P) === u, value: x };
   },
-  htfDefaults: {
-    DST: 'edwards448_XOF:SHAKE256_ELL2_RO_',
-    p: Fp.ORDER,
-    m: 1,
-    k: 224,
-    expand: 'xof',
-    hash: shake256,
-  },
-  mapToCurve: (scalars: bigint[]) => map_to_curve_elligator2_edwards448(scalars[0]),
 } as const;
 
 export const ed448 = twistedEdwards(ED448_DEF);
@@ -232,3 +149,93 @@ export const x448 = montgomery({
   //   return numberToBytesLE(u, 56);
   // },
 });
+
+// Hash To Curve Elligator2 Map
+const ELL2_C1 = (Fp.ORDER - BigInt(3)) / BigInt(4); // 1. c1 = (q - 3) / 4         # Integer arithmetic
+const ELL2_J = BigInt(156326);
+function map_to_curve_elligator2_curve448(u: bigint) {
+  let tv1 = Fp.sqr(u); // 1.  tv1 = u^2
+  let e1 = Fp.eql(tv1, Fp.ONE); // 2.   e1 = tv1 == 1
+  tv1 = Fp.cmov(tv1, Fp.ZERO, e1); // 3.  tv1 = CMOV(tv1, 0, e1)  # If Z * u^2 == -1, set tv1 = 0
+  let xd = Fp.sub(Fp.ONE, tv1); // 4.   xd = 1 - tv1
+  let x1n = Fp.neg(ELL2_J); // 5.  x1n = -J
+  let tv2 = Fp.sqr(xd); // 6.  tv2 = xd^2
+  let gxd = Fp.mul(tv2, xd); // 7.  gxd = tv2 * xd          # gxd = xd^3
+  let gx1 = Fp.mul(tv1, Fp.neg(ELL2_J)); // 8.  gx1 = -J * tv1          # x1n + J * xd
+  gx1 = Fp.mul(gx1, x1n); // 9.  gx1 = gx1 * x1n         # x1n^2 + J * x1n * xd
+  gx1 = Fp.add(gx1, tv2); // 10. gx1 = gx1 + tv2         # x1n^2 + J * x1n * xd + xd^2
+  gx1 = Fp.mul(gx1, x1n); // 11. gx1 = gx1 * x1n         # x1n^3 + J * x1n^2 * xd + x1n * xd^2
+  let tv3 = Fp.sqr(gxd); // 12. tv3 = gxd^2
+  tv2 = Fp.mul(gx1, gxd); // 13. tv2 = gx1 * gxd         # gx1 * gxd
+  tv3 = Fp.mul(tv3, tv2); // 14. tv3 = tv3 * tv2         # gx1 * gxd^3
+  let y1 = Fp.pow(tv3, ELL2_C1); // 15.  y1 = tv3^c1            # (gx1 * gxd^3)^((p - 3) / 4)
+  y1 = Fp.mul(y1, tv2); // 16.  y1 = y1 * tv2          # gx1 * gxd * (gx1 * gxd^3)^((p - 3) / 4)
+  let x2n = Fp.mul(x1n, Fp.neg(tv1)); // 17. x2n = -tv1 * x1n        # x2 = x2n / xd = -1 * u^2 * x1n / xd
+  let y2 = Fp.mul(y1, u); // 18.  y2 = y1 * u
+  y2 = Fp.cmov(y2, Fp.ZERO, e1); // 19.  y2 = CMOV(y2, 0, e1)
+  tv2 = Fp.sqr(y1); // 20. tv2 = y1^2
+  tv2 = Fp.mul(tv2, gxd); // 21. tv2 = tv2 * gxd
+  let e2 = Fp.eql(tv2, gx1); // 22.  e2 = tv2 == gx1
+  let xn = Fp.cmov(x2n, x1n, e2); // 23.  xn = CMOV(x2n, x1n, e2)  # If e2, x = x1, else x = x2
+  let y = Fp.cmov(y2, y1, e2); // 24.   y = CMOV(y2, y1, e2)    # If e2, y = y1, else y = y2
+  let e3 = Fp.isOdd(y); // 25.  e3 = sgn0(y) == 1        # Fix sign of y
+  y = Fp.cmov(y, Fp.neg(y), e2 !== e3); // 26.   y = CMOV(y, -y, e2 XOR e3)
+  return { xn, xd, yn: y, yd: Fp.ONE }; // 27. return (xn, xd, y, 1)
+}
+function map_to_curve_elligator2_edwards448(u: bigint) {
+  let { xn, xd, yn, yd } = map_to_curve_elligator2_curve448(u); // 1. (xn, xd, yn, yd) = map_to_curve_elligator2_curve448(u)
+  let xn2 = Fp.sqr(xn); // 2.  xn2 = xn^2
+  let xd2 = Fp.sqr(xd); // 3.  xd2 = xd^2
+  let xd4 = Fp.sqr(xd2); // 4.  xd4 = xd2^2
+  let yn2 = Fp.sqr(yn); // 5.  yn2 = yn^2
+  let yd2 = Fp.sqr(yd); // 6.  yd2 = yd^2
+  let xEn = Fp.sub(xn2, xd2); // 7.  xEn = xn2 - xd2
+  let tv2 = Fp.sub(xEn, xd2); // 8.  tv2 = xEn - xd2
+  xEn = Fp.mul(xEn, xd2); // 9.  xEn = xEn * xd2
+  xEn = Fp.mul(xEn, yd); // 10. xEn = xEn * yd
+  xEn = Fp.mul(xEn, yn); // 11. xEn = xEn * yn
+  xEn = Fp.mul(xEn, 4n); // 12. xEn = xEn * 4
+  tv2 = Fp.mul(tv2, xn2); // 13. tv2 = tv2 * xn2
+  tv2 = Fp.mul(tv2, yd2); // 14. tv2 = tv2 * yd2
+  let tv3 = Fp.mul(yn2, 4n); // 15. tv3 = 4 * yn2
+  let tv1 = Fp.add(tv3, yd2); // 16. tv1 = tv3 + yd2
+  tv1 = Fp.mul(tv1, xd4); // 17. tv1 = tv1 * xd4
+  let xEd = Fp.add(tv1, tv2); // 18. xEd = tv1 + tv2
+  tv2 = Fp.mul(tv2, xn); // 19. tv2 = tv2 * xn
+  let tv4 = Fp.mul(xn, xd4); // 20. tv4 = xn * xd4
+  let yEn = Fp.sub(tv3, yd2); // 21. yEn = tv3 - yd2
+  yEn = Fp.mul(yEn, tv4); // 22. yEn = yEn * tv4
+  yEn = Fp.sub(yEn, tv2); // 23. yEn = yEn - tv2
+  tv1 = Fp.add(xn2, xd2); // 24. tv1 = xn2 + xd2
+  tv1 = Fp.mul(tv1, xd2); // 25. tv1 = tv1 * xd2
+  tv1 = Fp.mul(tv1, xd); // 26. tv1 = tv1 * xd
+  tv1 = Fp.mul(tv1, yn2); // 27. tv1 = tv1 * yn2
+  tv1 = Fp.mul(tv1, BigInt(-2)); // 28. tv1 = -2 * tv1
+  let yEd = Fp.add(tv2, tv1); // 29. yEd = tv2 + tv1
+  tv4 = Fp.mul(tv4, yd2); // 30. tv4 = tv4 * yd2
+  yEd = Fp.add(yEd, tv4); // 31. yEd = yEd + tv4
+  tv1 = Fp.mul(xEd, yEd); // 32. tv1 = xEd * yEd
+  let e = Fp.eql(tv1, Fp.ZERO); // 33.   e = tv1 == 0
+  xEn = Fp.cmov(xEn, Fp.ZERO, e); // 34. xEn = CMOV(xEn, 0, e)
+  xEd = Fp.cmov(xEd, Fp.ONE, e); // 35. xEd = CMOV(xEd, 1, e)
+  yEn = Fp.cmov(yEn, Fp.ONE, e); // 36. yEn = CMOV(yEn, 1, e)
+  yEd = Fp.cmov(yEd, Fp.ONE, e); // 37. yEd = CMOV(yEd, 1, e)
+
+  const inv = Fp.invertBatch([xEd, yEd]); // batch division
+  return { x: Fp.mul(xEn, inv[0]), y: Fp.mul(yEn, inv[1]) }; // 38. return (xEn, xEd, yEn, yEd)
+}
+
+const { hashToCurve, encodeToCurve } = htf.hashToCurve(
+  ed448.ExtendedPoint,
+  (scalars: bigint[]) => map_to_curve_elligator2_edwards448(scalars[0]),
+  {
+    DST: 'edwards448_XOF:SHAKE256_ELL2_RO_',
+    encodeDST: 'edwards448_XOF:SHAKE256_ELL2_NU_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 224,
+    expand: 'xof',
+    hash: shake256,
+  }
+);
+export { hashToCurve, encodeToCurve };

src/jubjub.ts

@@ -39,7 +39,7 @@ export function groupHash(tag: Uint8Array, personalization: Uint8Array) {
   h.update(GH_FIRST_BLOCK);
   h.update(tag);
   // NOTE: returns ExtendedPoint, in case it will be multiplied later
-  let p = jubjub.ExtendedPoint.fromAffine(jubjub.Point.fromHex(h.digest()));
+  let p = jubjub.ExtendedPoint.fromHex(h.digest());
   // NOTE: cannot replace with isSmallOrder, returns Point*8
   p = p.multiply(jubjub.CURVE.h);
   if (p.equals(jubjub.ExtendedPoint.ZERO)) throw new Error('Point has small order');

src/p224.ts

@@ -10,7 +10,7 @@ export const P224 = createCurve(
     // Params: a, b
     a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe'),
     b: BigInt('0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4'),
-    // Field over which we'll do calculations; 2n**224n - 2n**96n + 1n
+    // Field over which we'll do calculations;
     Fp: Fp(BigInt('0xffffffffffffffffffffffffffffffff000000000000000000000001')),
     // Curve order, total count of valid points in the field
     n: BigInt('0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d'),

src/p256.ts

@@ -3,6 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha256 } from '@noble/hashes/sha256';
 import { Fp as Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+import * as htf from './abstract/hash-to-curve.js';
 
 // NIST secp256r1 aka P256
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256
@@ -31,16 +32,22 @@ export const P256 = createCurve(
     Gy: BigInt('0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5'),
     h: BigInt(1),
     lowS: false,
-    mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
-    htfDefaults: {
-      DST: 'P256_XMD:SHA-256_SSWU_RO_',
-      p: Fp.ORDER,
-      m: 1,
-      k: 128,
-      expand: 'xmd',
-      hash: sha256,
-    },
   } as const,
   sha256
 );
 export const secp256r1 = P256;
+
+const { hashToCurve, encodeToCurve } = htf.hashToCurve(
+  secp256r1.ProjectivePoint,
+  (scalars: bigint[]) => mapSWU(scalars[0]),
+  {
+    DST: 'P256_XMD:SHA-256_SSWU_RO_',
+    encodeDST: 'P256_XMD:SHA-256_SSWU_NU_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 128,
+    expand: 'xmd',
+    hash: sha256,
+  }
+);
+export { hashToCurve, encodeToCurve };

src/p384.ts

@@ -3,6 +3,7 @@ import { createCurve } from './_shortw_utils.js';
 import { sha384 } from '@noble/hashes/sha512';
 import { Fp as Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+import * as htf from './abstract/hash-to-curve.js';
 
 // NIST secp384r1 aka P384
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384
@@ -35,16 +36,22 @@ export const P384 = createCurve({
     Gy: BigInt('0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f'),
     h: BigInt(1),
     lowS: false,
-    mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
-    htfDefaults: {
-      DST: 'P384_XMD:SHA-384_SSWU_RO_',
-      p: Fp.ORDER,
-      m: 1,
-      k: 192,
-      expand: 'xmd',
-      hash: sha384,
-    },
   } as const,
   sha384
 );
 export const secp384r1 = P384;
+
+const { hashToCurve, encodeToCurve } = htf.hashToCurve(
+  secp384r1.ProjectivePoint,
+  (scalars: bigint[]) => mapSWU(scalars[0]),
+  {
+    DST: 'P384_XMD:SHA-384_SSWU_RO_',
+    encodeDST: 'P384_XMD:SHA-384_SSWU_NU_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 192,
+    expand: 'xmd',
+    hash: sha384,
+  }
+);
+export { hashToCurve, encodeToCurve };

src/p521.ts

@@ -1,9 +1,9 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { createCurve } from './_shortw_utils.js';
 import { sha512 } from '@noble/hashes/sha512';
-import { bytesToHex, PrivKey } from './abstract/utils.js';
 import { Fp as Field } from './abstract/modular.js';
 import { mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+import * as htf from './abstract/hash-to-curve.js';
 
 // NIST secp521r1 aka P521
 // Note that it's 521, which differs from 512 of its hash function.
@@ -37,25 +37,21 @@ export const P521 = createCurve({
   Gy: BigInt('0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650'),
   h: BigInt(1),
   lowS: false,
-  // P521 keys could be 130, 131, 132 bytes - which doesn't play nicely.
+  allowedPrivateKeyLengths: [130, 131, 132] // P521 keys are variable-length. Normalize to 132b
-  // We ensure all keys are 132 bytes.
+} as const, sha512);
-  // Does not replace validation; invalid keys would still be rejected.
+export const secp521r1 = P521;
-  normalizePrivateKey(key: PrivKey) {
+
-    if (typeof key === 'bigint') return key;
+const { hashToCurve, encodeToCurve } = htf.hashToCurve(
-    if (key instanceof Uint8Array) key = bytesToHex(key);
+  secp521r1.ProjectivePoint,
-    if (typeof key !== 'string' || !([130, 131, 132].includes(key.length))) {
+  (scalars: bigint[]) => mapSWU(scalars[0]),
-      throw new Error('Invalid key');
+  {
-    }
-    return key.padStart(66 * 2, '0');
-  },
-  mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
-  htfDefaults: {
     DST: 'P521_XMD:SHA-512_SSWU_RO_',
+    encodeDST: 'P521_XMD:SHA-512_SSWU_NU_',
     p: Fp.ORDER,
     m: 1,
     k: 256,
-      expand: 'xmd',
+    expand: 'xmd',
     hash: sha512,
-  },
+  }
-} as const, sha512);
+);
-export const secp521r1 = P521;
+export { hashToCurve, encodeToCurve };

src/secp256k1.ts

@@ -2,17 +2,17 @@
 import { sha256 } from '@noble/hashes/sha256';
 import { Fp as Field, mod, pow2 } from './abstract/modular.js';
 import { createCurve } from './_shortw_utils.js';
-import { PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js';
+import { ProjPointType as PointType, mapToCurveSimpleSWU } from './abstract/weierstrass.js';
 import {
   ensureBytes,
   concatBytes,
   Hex,
-  hexToBytes,
+  bytesToNumberBE as bytesToInt,
-  bytesToNumberBE,
   PrivKey,
+  numberToBytesBE,
 } from './abstract/utils.js';
 import { randomBytes } from '@noble/hashes/utils';
-import { isogenyMap } from './abstract/hash-to-curve.js';
+import * as htf from './abstract/hash-to-curve.js';
 
 /**
  * secp256k1 belongs to Koblitz curves: it has efficiently computable endomorphism.
@@ -29,10 +29,7 @@ const _2n = BigInt(2);
 const divNearest = (a: bigint, b: bigint) => (a + b / _2n) / b;
 
 /**
- * Allows to compute square root √y 2x faster.
+ * √n = n^((p+1)/4) for fields p = 3 mod 4. We unwrap the loop and multiply bit-by-bit.
- * To calculate √y, we need to exponentiate it to a very big number:
- * `y² = x³ + ax + b; y = y² ^ (p+1)/4`
- * We are unwrapping the loop and multiplying it bit-by-bit.
  * (P+1n/4n).toString(2) would produce bits [223x 1, 0, 22x 1, 4x 0, 11, 00]
  */
 function sqrtMod(y: bigint): bigint {
@@ -55,52 +52,13 @@ function sqrtMod(y: bigint): bigint {
   const t1 = (pow2(b223, _23n, P) * b22) % P;
   const t2 = (pow2(t1, _6n, P) * b2) % P;
   const root = pow2(t2, _2n, P);
-  if (!Fp.equals(Fp.square(root), y)) throw new Error('Cannot find square root');
+  if (!Fp.eql(Fp.sqr(root), y)) throw new Error('Cannot find square root');
   return root;
 }
 
 const Fp = Field(secp256k1P, undefined, undefined, { sqrt: sqrtMod });
 type Fp = bigint;
 
-const isoMap = isogenyMap(
-  Fp,
-  [
-    // xNum
-    [
-      '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',
-      '0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',
-      '0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',
-      '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',
-    ],
-    // xDen
-    [
-      '0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',
-      '0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',
-      '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
-    ],
-    // yNum
-    [
-      '0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',
-      '0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',
-      '0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',
-      '0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',
-    ],
-    // yDen
-    [
-      '0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',
-      '0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',
-      '0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',
-      '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
-    ],
-  ].map((i) => i.map((j) => BigInt(j))) as [Fp[], Fp[], Fp[], Fp[]]
-);
-
-const mapSWU = mapToCurveSimpleSWU(Fp, {
-  A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
-  B: BigInt('1771'),
-  Z: Fp.create(BigInt('-11')),
-});
-
 export const secp256k1 = createCurve(
   {
     // Params: a, b
@@ -143,52 +101,16 @@ export const secp256k1 = createCurve(
         return { k1neg, k1, k2neg, k2 };
       },
     },
-    mapToCurve: (scalars: bigint[]) => {
-      const { x, y } = mapSWU(Fp.create(scalars[0]));
-      return isoMap(x, y);
-    },
-    htfDefaults: {
-      DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
-      p: Fp.ORDER,
-      m: 1,
-      k: 128,
-      expand: 'xmd',
-      hash: sha256,
-    },
   },
   sha256
 );
 
-// Schnorr
+// Schnorr signatures are superior to ECDSA from above.
+// Below is Schnorr-specific code as per BIP0340.
+// https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki
 const _0n = BigInt(0);
-const numTo32b = secp256k1.utils._bigintToBytes;
+const fe = (x: bigint) => typeof x === 'bigint' && _0n < x && x < secp256k1P;
-const numTo32bStr = secp256k1.utils._bigintToString;
+const ge = (x: bigint) => typeof x === 'bigint' && _0n < x && x < secp256k1N;
-const normalizePrivateKey = secp256k1.utils._normalizePrivateKey;
-
-// TODO: export?
-function normalizePublicKey(publicKey: Hex | PointType<bigint>): PointType<bigint> {
-  if (publicKey instanceof secp256k1.Point) {
-    publicKey.assertValidity();
-    return publicKey;
-  } else {
-    const bytes = ensureBytes(publicKey);
-    // Schnorr is 32 bytes
-    if (bytes.length !== 32) throw new Error('Schnorr pubkeys must be 32 bytes');
-    const x = bytesToNumberBE(bytes);
-    if (!isValidFieldElement(x)) throw new Error('Point is not on curve');
-    const y2 = secp256k1.utils._weierstrassEquation(x); // y² = x³ + ax + b
-    let y = sqrtMod(y2); // y = y² ^ (p+1)/4
-    const isYOdd = (y & _1n) === _1n;
-    // Schnorr
-    if (isYOdd) y = secp256k1.CURVE.Fp.negate(y);
-    const point = new secp256k1.Point(x, y);
-    point.assertValidity();
-    return point;
-  }
-}
-
-const isWithinCurveOrder = secp256k1.utils._isWithinCurveOrder;
-const isValidFieldElement = secp256k1.utils._isValidFieldElement;
 
 const TAGS = {
   challenge: 'BIP0340/challenge',
@@ -198,7 +120,7 @@ const TAGS = {
 
 /** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */
 const TAGGED_HASH_PREFIXES: { [tag: string]: Uint8Array } = {};
-export function taggedHash(tag: string, ...messages: Uint8Array[]): Uint8Array {
+function taggedHash(tag: string, ...messages: Uint8Array[]): Uint8Array {
   let tagP = TAGGED_HASH_PREFIXES[tag];
   if (tagP === undefined) {
     const tagH = sha256(Uint8Array.from(tag, (c) => c.charCodeAt(0)));
@@ -208,73 +130,58 @@ export function taggedHash(tag: string, ...messages: Uint8Array[]): Uint8Array {
   return sha256(concatBytes(tagP, ...messages));
 }
 
-const toRawX = (point: PointType<bigint>) => point.toRawBytes(true).slice(1);
+const pointToBytes = (point: PointType<bigint>) => point.toRawBytes(true).slice(1);
-
+const numTo32b = (n: bigint) => numberToBytesBE(n, 32);
-// Schnorr signatures are superior to ECDSA from above.
+const modN = (x: bigint) => mod(x, secp256k1N);
-// Below is Schnorr-specific code as per BIP0340.
+const Point = secp256k1.ProjectivePoint;
-function schnorrChallengeFinalize(ch: Uint8Array): bigint {
+const GmulAdd = (Q: PointType<bigint>, a: bigint, b: bigint) =>
-  return mod(bytesToNumberBE(ch), secp256k1.CURVE.n);
+  Point.BASE.multiplyAndAddUnsafe(Q, a, b);
+const hex32ToInt = (key: Hex) => bytesToInt(ensureBytes(key, 32));
+function schnorrGetExtPubKey(priv: PrivKey) {
+  let d = typeof priv === 'bigint' ? priv : hex32ToInt(priv);
+  const point = Point.fromPrivateKey(d); // P = d'⋅G; 0 < d' < n check is done inside
+  const scalar = point.hasEvenY() ? d : modN(-d); // d = d' if has_even_y(P), otherwise d = n-d'
+  return { point, scalar, bytes: pointToBytes(point) };
 }
-// Do we need this at all for Schnorr?
+function lift_x(x: bigint): PointType<bigint> {
-class SchnorrSignature {
+  if (!fe(x)) throw new Error('bad x: need 0 < x < p'); // Fail if x ≥ p.
-  constructor(readonly r: bigint, readonly s: bigint) {
+  const c = mod(x * x * x + BigInt(7), secp256k1P); // Let c = x³ + 7 mod p.
-    this.assertValidity();
+  let y = sqrtMod(c); // Let y = c^(p+1)/4 mod p.
-  }
+  if (y % 2n !== 0n) y = mod(-y, secp256k1P); // Return the unique point P such that x(P) = x and
-  static fromHex(hex: Hex) {
+  const p = new Point(x, y, _1n); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
-    const bytes = ensureBytes(hex);
+  p.assertValidity();
-    const len = 32; // group length
+  return p;
-    if (bytes.length !== 2 * len)
+}
-      throw new TypeError(
+function challenge(...args: Uint8Array[]): bigint {
-        `SchnorrSignature.fromHex: expected ${2 * len} bytes, not ${bytes.length}`
+  return modN(bytesToInt(taggedHash(TAGS.challenge, ...args)));
-      );
-    const r = bytesToNumberBE(bytes.subarray(0, len));
-    const s = bytesToNumberBE(bytes.subarray(len, 2 * len));
-    return new SchnorrSignature(r, s);
-  }
-  assertValidity() {
-    const { r, s } = this;
-    if (!isValidFieldElement(r) || !isWithinCurveOrder(s)) throw new Error('Invalid signature');
-  }
-  toHex(): string {
-    return numTo32bStr(this.r) + numTo32bStr(this.s);
-  }
-  toRawBytes(): Uint8Array {
-    return hexToBytes(this.toHex());
-  }
 }
 
-function schnorrGetScalar(priv: bigint) {
+// Schnorr's pubkey is just `x` of Point (BIP340)
-  const point = secp256k1.Point.fromPrivateKey(priv);
+function schnorrGetPublicKey(privateKey: Hex): Uint8Array {
-  const scalar = point.hasEvenY() ? priv : secp256k1.CURVE.n - priv;
+  return schnorrGetExtPubKey(privateKey).bytes; // d'=int(sk). Fail if d'=0 or d'≥n. Ret bytes(d'⋅G)
-  return { point, scalar, x: toRawX(point) };
 }
-/**
+
- * Synchronously creates Schnorr signature. Improved security: verifies itself before
+// Creates Schnorr signature as per BIP340. Verifies itself before returning anything.
- * producing an output.
+// auxRand is optional and is not the sole source of k generation: bad CSPRNG won't be dangerous
- * @param msg message (not message hash)
- * @param privateKey private key
- * @param auxRand random bytes that would be added to k. Bad RNG won't break it.
- */
 function schnorrSign(
   message: Hex,
   privateKey: PrivKey,
   auxRand: Hex = randomBytes(32)
 ): Uint8Array {
-  if (message == null) throw new TypeError(`sign: Expected valid message, not "${message}"`);
+  if (message == null) throw new Error(`sign: Expected valid message, not "${message}"`);
-  const m = ensureBytes(message);
+  const m = ensureBytes(message); // checks for isWithinCurveOrder
-  // checks for isWithinCurveOrder
+  const { bytes: px, scalar: d } = schnorrGetExtPubKey(privateKey);
-  const { x: px, scalar: d } = schnorrGetScalar(normalizePrivateKey(privateKey));
+  const a = ensureBytes(auxRand, 32); // Auxiliary random data a: a 32-byte array
-  const rand = ensureBytes(auxRand);
+  const t = numTo32b(d ^ bytesToInt(taggedHash(TAGS.aux, a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
-  if (rand.length !== 32) throw new TypeError('sign: Expected 32 bytes of aux randomness');
+  const rand = taggedHash(TAGS.nonce, t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
-  const tag = taggedHash;
+  const k_ = modN(bytesToInt(rand)); // Let k' = int(rand) mod n
-  const t0h = tag(TAGS.aux, rand);
+  if (k_ === _0n) throw new Error('sign failed: k is zero'); // Fail if k' = 0.
-  const t = numTo32b(d ^ bytesToNumberBE(t0h));
+  const { point: R, bytes: rx, scalar: k } = schnorrGetExtPubKey(k_); // Let R = k'⋅G.
-  const k0h = tag(TAGS.nonce, t, px, m);
+  const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
-  const k0 = mod(bytesToNumberBE(k0h), secp256k1.CURVE.n);
+  const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
-  if (k0 === _0n) throw new Error('sign: Creation of signature failed. k is zero');
+  sig.set(numTo32b(R.px), 0);
-  const { point: R, x: rx, scalar: k } = schnorrGetScalar(k0);
+  sig.set(numTo32b(modN(k + e * d)), 32);
-  const e = schnorrChallengeFinalize(tag(TAGS.challenge, rx, px, m));
+  // If Verify(bytes(P), m, sig) (see below) returns failure, abort
-  const sig = new SchnorrSignature(R.x, mod(k + e * d, secp256k1.CURVE.n)).toRawBytes();
   if (!schnorrVerify(sig, m, px)) throw new Error('sign: Invalid signature produced');
   return sig;
 }
@@ -284,34 +191,88 @@ function schnorrSign(
  */
 function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
   try {
-    const raw = signature instanceof SchnorrSignature;
+    const P = lift_x(hex32ToInt(publicKey)); // P = lift_x(int(pk)); fail if that fails
-    const sig: SchnorrSignature = raw ? signature : SchnorrSignature.fromHex(signature);
+    const sig = ensureBytes(signature, 64);
-    if (raw) sig.assertValidity(); // just in case
+    const r = bytesToInt(sig.subarray(0, 32)); // Let r = int(sig[0:32]); fail if r ≥ p.
-
+    if (!fe(r)) return false;
-    const { r, s } = sig;
+    const s = bytesToInt(sig.subarray(32, 64)); // Let s = int(sig[32:64]); fail if s ≥ n.
+    if (!ge(s)) return false;
     const m = ensureBytes(message);
-    const P = normalizePublicKey(publicKey);
+    const e = challenge(numTo32b(r), pointToBytes(P), m); // int(challenge(bytes(r)||bytes(P)||m)) mod n
-    const e = schnorrChallengeFinalize(taggedHash(TAGS.challenge, numTo32b(r), toRawX(P), m));
+    const R = GmulAdd(P, s, modN(-e)); // R = s⋅G - e⋅P
-    // Finalize
+    if (!R || !R.hasEvenY() || R.toAffine().x !== r) return false; // -eP == (n-e)P
-    // R = s⋅G - e⋅P
+    return true; // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
-    // -eP == (n-e)P
-    const R = secp256k1.Point.BASE.multiplyAndAddUnsafe(
-      P,
-      normalizePrivateKey(s),
-      mod(-e, secp256k1.CURVE.n)
-    );
-    if (!R || !R.hasEvenY() || R.x !== r) return false;
-    return true;
   } catch (error) {
     return false;
   }
 }
 
 export const schnorr = {
-  Signature: SchnorrSignature,
+  getPublicKey: schnorrGetPublicKey,
-  // Schnorr's pubkey is just `x` of Point (BIP340)
-  getPublicKey: (privateKey: PrivKey): Uint8Array =>
-    toRawX(secp256k1.Point.fromPrivateKey(privateKey)),
   sign: schnorrSign,
   verify: schnorrVerify,
+  utils: {
+    getExtendedPublicKey: schnorrGetExtPubKey,
+    lift_x,
+    pointToBytes,
+    numberToBytesBE,
+    bytesToNumberBE: bytesToInt,
+    taggedHash,
+    mod,
+  },
 };
+
+const isoMap = htf.isogenyMap(
+  Fp,
+  [
+    // xNum
+    [
+      '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa8c7',
+      '0x7d3d4c80bc321d5b9f315cea7fd44c5d595d2fc0bf63b92dfff1044f17c6581',
+      '0x534c328d23f234e6e2a413deca25caece4506144037c40314ecbd0b53d9dd262',
+      '0x8e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38e38daaaaa88c',
+    ],
+    // xDen
+    [
+      '0xd35771193d94918a9ca34ccbb7b640dd86cd409542f8487d9fe6b745781eb49b',
+      '0xedadc6f64383dc1df7c4b2d51b54225406d36b641f5e41bbc52a56612a8c6d14',
+      '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
+    ],
+    // yNum
+    [
+      '0x4bda12f684bda12f684bda12f684bda12f684bda12f684bda12f684b8e38e23c',
+      '0xc75e0c32d5cb7c0fa9d0a54b12a0a6d5647ab046d686da6fdffc90fc201d71a3',
+      '0x29a6194691f91a73715209ef6512e576722830a201be2018a765e85a9ecee931',
+      '0x2f684bda12f684bda12f684bda12f684bda12f684bda12f684bda12f38e38d84',
+    ],
+    // yDen
+    [
+      '0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffff93b',
+      '0x7a06534bb8bdb49fd5e9e6632722c2989467c1bfc8e8d978dfb425d2685c2573',
+      '0x6484aa716545ca2cf3a70c3fa8fe337e0a3d21162f0d6299a7bf8192bfd2a76f',
+      '0x0000000000000000000000000000000000000000000000000000000000000001', // LAST 1
+    ],
+  ].map((i) => i.map((j) => BigInt(j))) as [Fp[], Fp[], Fp[], Fp[]]
+);
+const mapSWU = mapToCurveSimpleSWU(Fp, {
+  A: BigInt('0x3f8731abdd661adca08a5558f0f5d272e953d363cb6f0e5d405447c01a444533'),
+  B: BigInt('1771'),
+  Z: Fp.create(BigInt('-11')),
+});
+const { hashToCurve, encodeToCurve } = htf.hashToCurve(
+  secp256k1.ProjectivePoint,
+  (scalars: bigint[]) => {
+    const { x, y } = mapSWU(Fp.create(scalars[0]));
+    return isoMap(x, y);
+  },
+  {
+    DST: 'secp256k1_XMD:SHA-256_SSWU_RO_',
+    encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 128,
+    expand: 'xmd',
+    hash: sha256,
+  }
+);
+export { hashToCurve, encodeToCurve };

src/stark.ts

@@ -1,12 +1,14 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { keccak_256 } from '@noble/hashes/sha3';
 import { sha256 } from '@noble/hashes/sha256';
-import { weierstrass, ProjectivePointType } from './abstract/weierstrass.js';
+import { weierstrass, ProjPointType } from './abstract/weierstrass.js';
 import * as cutils from './abstract/utils.js';
-import { Fp } from './abstract/modular.js';
+import { Fp, mod, Field, validateField } from './abstract/modular.js';
 import { getHash } from './_shortw_utils.js';
+import * as poseidon from './abstract/poseidon.js';
+import { utf8ToBytes } from '@noble/hashes/utils';
 
-type ProjectivePoint = ProjectivePointType<bigint>;
+type ProjectivePoint = ProjPointType<bigint>;
 // Stark-friendly elliptic curve
 // https://docs.starkware.co/starkex/stark-curve.html
 
@@ -14,6 +16,15 @@ const CURVE_N = BigInt(
   '3618502788666131213697322783095070105526743751716087489154079457884512865583'
 );
 const nBitLength = 252;
+// Copy-pasted from weierstrass.ts
+function bits2int(bytes: Uint8Array): bigint {
+  const delta = bytes.length * 8 - nBitLength;
+  const num = cutils.bytesToNumberBE(bytes);
+  return delta > 0 ? num >> BigInt(delta) : num;
+}
+function bits2int_modN(bytes: Uint8Array): bigint {
+  return mod(bits2int(bytes), CURVE_N);
+}
 export const starkCurve = weierstrass({
   // Params: a, b
   a: BigInt(1),
@@ -31,31 +42,27 @@ export const starkCurve = weierstrass({
   // Default options
   lowS: false,
   ...getHash(sha256),
-  truncateHash: (hash: Uint8Array, truncateOnly = false): bigint => {
+  // Custom truncation routines for stark curve
-    // TODO: cleanup, ugly code
+  bits2int: (bytes: Uint8Array): bigint => {
-    // Fix truncation
+    while (bytes[0] === 0) bytes = bytes.subarray(1);
-    if (!truncateOnly) {
+    return bits2int(bytes);
-      let hashS = bytesToNumber0x(hash).toString(16);
+  },
-      if (hashS.length === 63) {
+  bits2int_modN: (bytes: Uint8Array): bigint => {
-        hashS += '0';
+    let hashS = cutils.bytesToNumberBE(bytes).toString(16);
-        hash = hexToBytes0x(hashS);
+    if (hashS.length === 63) {
-      }
+      hashS += '0';
+      bytes = hexToBytes0x(hashS);
     }
     // Truncate zero bytes on left (compat with elliptic)
-    while (hash[0] === 0) hash = hash.subarray(1);
+    while (bytes[0] === 0) bytes = bytes.subarray(1);
-    const byteLength = hash.length;
+    return bits2int_modN(bytes);
-    const delta = byteLength * 8 - nBitLength; // size of curve.n (252 bits)
-    let h = hash.length ? bytesToNumber0x(hash) : 0n;
-    if (delta > 0) h = h >> BigInt(delta);
-    if (!truncateOnly && h >= CURVE_N) h -= CURVE_N;
-    return h;
   },
 });
 
 // Custom Starknet type conversion functions that can handle 0x and unpadded hex
 function hexToBytes0x(hex: string): Uint8Array {
   if (typeof hex !== 'string') {
-    throw new TypeError('hexToBytes: expected string, got ' + typeof hex);
+    throw new Error('hexToBytes: expected string, got ' + typeof hex);
   }
   hex = strip0x(hex);
   if (hex.length & 1) hex = '0' + hex; // padding
@@ -72,7 +79,7 @@ function hexToBytes0x(hex: string): Uint8Array {
 }
 function hexToNumber0x(hex: string): bigint {
   if (typeof hex !== 'string') {
-    throw new TypeError('hexToNumber: expected string, got ' + typeof hex);
+    throw new Error('hexToNumber: expected string, got ' + typeof hex);
   }
   // Big Endian
   // TODO: strip vs no strip?
@@ -88,9 +95,9 @@ function ensureBytes0x(hex: Hex): Uint8Array {
 }
 
 function normalizePrivateKey(privKey: Hex) {
-  return cutils.bytesToHex(ensureBytes0x(privKey)).padStart(32 * 2, '0');
+  return cutils.bytesToHex(ensureBytes0x(privKey)).padStart(64, '0');
 }
-function getPublicKey0x(privKey: Hex, isCompressed?: boolean) {
+function getPublicKey0x(privKey: Hex, isCompressed = false) {
   return starkCurve.getPublicKey(normalizePrivateKey(privKey), isCompressed);
 }
 function getSharedSecret0x(privKeyA: Hex, pubKeyB: Hex) {
@@ -106,11 +113,10 @@ function verify0x(signature: Hex, msgHash: Hex, pubKey: Hex) {
   return starkCurve.verify(sig, ensureBytes0x(msgHash), ensureBytes0x(pubKey));
 }
 
-const { CURVE, Point, ProjectivePoint, Signature } = starkCurve;
+const { CURVE, ProjectivePoint, Signature } = starkCurve;
 export const utils = starkCurve.utils;
 export {
   CURVE,
-  Point,
   Signature,
   ProjectivePoint,
   getPublicKey0x as getPublicKey,
@@ -132,18 +138,18 @@ type Hex = Uint8Array | string;
 function hashKeyWithIndex(key: Uint8Array, index: number) {
   let indexHex = cutils.numberToHexUnpadded(index);
   if (indexHex.length & 1) indexHex = '0' + indexHex;
-  return bytesToNumber0x(sha256(cutils.concatBytes(key, hexToBytes0x(indexHex))));
+  return sha256Num(cutils.concatBytes(key, hexToBytes0x(indexHex)));
 }
 
 export function grindKey(seed: Hex) {
   const _seed = ensureBytes0x(seed);
   const sha256mask = 2n ** 256n;
-  const Fn = Fp(CURVE.n);
+
-  const limit = sha256mask - Fn.create(sha256mask);
+  const limit = sha256mask - mod(sha256mask, CURVE_N);
   for (let i = 0; ; i++) {
     const key = hashKeyWithIndex(_seed, i);
     // key should be in [0, limit)
-    if (key < limit) return Fn.create(key).toString(16);
+    if (key < limit) return mod(key, CURVE_N).toString(16);
   }
 }
 
@@ -165,37 +171,42 @@ export function getAccountPath(
   ethereumAddress: string,
   index: number
 ) {
-  const layerNum = int31(bytesToNumber0x(sha256(layer)));
+  const layerNum = int31(sha256Num(layer));
-  const applicationNum = int31(bytesToNumber0x(sha256(application)));
+  const applicationNum = int31(sha256Num(application));
   const eth = hexToNumber0x(ethereumAddress);
   return `m/2645'/${layerNum}'/${applicationNum}'/${int31(eth)}'/${int31(eth >> 31n)}'/${index}`;
 }
 
 // https://docs.starkware.co/starkex/pedersen-hash-function.html
 const PEDERSEN_POINTS_AFFINE = [
-  new Point(
+  new ProjectivePoint(
     2089986280348253421170679821480865132823066470938446095505822317253594081284n,
-    1713931329540660377023406109199410414810705867260802078187082345529207694986n
+    1713931329540660377023406109199410414810705867260802078187082345529207694986n,
+    1n
   ),
-  new Point(
+  new ProjectivePoint(
     996781205833008774514500082376783249102396023663454813447423147977397232763n,
-    1668503676786377725805489344771023921079126552019160156920634619255970485781n
+    1668503676786377725805489344771023921079126552019160156920634619255970485781n,
+    1n
   ),
-  new Point(
+  new ProjectivePoint(
     2251563274489750535117886426533222435294046428347329203627021249169616184184n,
-    1798716007562728905295480679789526322175868328062420237419143593021674992973n
+    1798716007562728905295480679789526322175868328062420237419143593021674992973n,
+    1n
   ),
-  new Point(
+  new ProjectivePoint(
     2138414695194151160943305727036575959195309218611738193261179310511854807447n,
-    113410276730064486255102093846540133784865286929052426931474106396135072156n
+    113410276730064486255102093846540133784865286929052426931474106396135072156n,
+    1n
   ),
-  new Point(
+  new ProjectivePoint(
     2379962749567351885752724891227938183011949129833673362440656643086021394946n,
-    776496453633298175483985398648758586525933812536653089401905292063708816422n
+    776496453633298175483985398648758586525933812536653089401905292063708816422n,
+    1n
   ),
 ];
 // for (const p of PEDERSEN_POINTS) p._setWindowSize(8);
-const PEDERSEN_POINTS = PEDERSEN_POINTS_AFFINE.map(ProjectivePoint.fromAffine);
+const PEDERSEN_POINTS = PEDERSEN_POINTS_AFFINE;
 
 function pedersenPrecompute(p1: ProjectivePoint, p2: ProjectivePoint): ProjectivePoint[] {
   const out: ProjectivePoint[] = [];
@@ -234,7 +245,7 @@ function pedersenSingle(point: ProjectivePoint, value: PedersenArg, constants: P
   let x = pedersenArg(value);
   for (let j = 0; j < 252; j++) {
     const pt = constants[j];
-    if (pt.x === point.x) throw new Error('Same point');
+    if (pt.px === point.px) throw new Error('Same point');
     if ((x & 1n) !== 0n) point = point.add(pt);
     x >>= 1n;
   }
@@ -246,7 +257,7 @@ export function pedersen(x: PedersenArg, y: PedersenArg) {
   let point: ProjectivePoint = PEDERSEN_POINTS[0];
   point = pedersenSingle(point, x, PEDERSEN_POINTS1);
   point = pedersenSingle(point, y, PEDERSEN_POINTS2);
-  return bytesToHexEth(point.toAffine().toRawBytes(true).slice(1));
+  return bytesToHexEth(point.toRawBytes(true).slice(1));
 }
 
 export function hashChain(data: PedersenArg[], fn = pedersen) {
@@ -261,5 +272,85 @@ export function hashChain(data: PedersenArg[], fn = pedersen) {
 export const computeHashOnElements = (data: PedersenArg[], fn = pedersen) =>
   [0, ...data, data.length].reduce((x, y) => fn(x, y));
 
-const MASK_250 = 2n ** 250n - 1n;
+const MASK_250 = cutils.bitMask(250);
-export const keccak = (data: Uint8Array) => bytesToNumber0x(keccak_256(data)) & MASK_250;
+export const keccak = (data: Uint8Array): bigint => bytesToNumber0x(keccak_256(data)) & MASK_250;
+const sha256Num = (data: Uint8Array | string): bigint => cutils.bytesToNumberBE(sha256(data));
+
+// Poseidon hash
+export const Fp253 = Fp(
+  BigInt('14474011154664525231415395255581126252639794253786371766033694892385558855681')
+); // 2^253 + 2^199 + 1
+export const Fp251 = Fp(
+  BigInt('3618502788666131213697322783095070105623107215331596699973092056135872020481')
+); // 2^251 + 17 * 2^192 + 1
+
+function poseidonRoundConstant(Fp: Field<bigint>, name: string, idx: number) {
+  const val = Fp.fromBytes(sha256(utf8ToBytes(`${name}${idx}`)));
+  return Fp.create(val);
+}
+
+// NOTE: doesn't check eiginvalues and possible can create unsafe matrix. But any filtration here will break compatibility with starknet
+// Please use only if you really know what you doing.
+// https://eprint.iacr.org/2019/458.pdf Section 2.3 (Avoiding Insecure Matrices)
+export function _poseidonMDS(Fp: Field<bigint>, name: string, m: number, attempt = 0) {
+  const x_values: bigint[] = [];
+  const y_values: bigint[] = [];
+  for (let i = 0; i < m; i++) {
+    x_values.push(poseidonRoundConstant(Fp, `${name}x`, attempt * m + i));
+    y_values.push(poseidonRoundConstant(Fp, `${name}y`, attempt * m + i));
+  }
+  if (new Set([...x_values, ...y_values]).size !== 2 * m)
+    throw new Error('X and Y values are not distinct');
+  return x_values.map((x) => y_values.map((y) => Fp.inv(Fp.sub(x, y))));
+}
+
+const MDS_SMALL = [
+  [3, 1, 1],
+  [1, -1, 1],
+  [1, 1, -2],
+].map((i) => i.map(BigInt));
+
+export type PoseidonOpts = {
+  Fp: Field<bigint>;
+  rate: number;
+  capacity: number;
+  roundsFull: number;
+  roundsPartial: number;
+};
+
+export function poseidonBasic(opts: PoseidonOpts, mds: bigint[][]) {
+  validateField(opts.Fp);
+  if (!Number.isSafeInteger(opts.rate) || !Number.isSafeInteger(opts.capacity))
+    throw new Error(`Wrong poseidon opts: ${opts}`);
+  const m = opts.rate + opts.capacity;
+  const rounds = opts.roundsFull + opts.roundsPartial;
+  const roundConstants = [];
+  for (let i = 0; i < rounds; i++) {
+    const row = [];
+    for (let j = 0; j < m; j++) row.push(poseidonRoundConstant(opts.Fp, 'Hades', m * i + j));
+    roundConstants.push(row);
+  }
+  return poseidon.poseidon({
+    ...opts,
+    t: m,
+    sboxPower: 3,
+    reversePartialPowIdx: true, // Why?!
+    mds,
+    roundConstants,
+  });
+}
+
+export function poseidonCreate(opts: PoseidonOpts, mdsAttempt = 0) {
+  const m = opts.rate + opts.capacity;
+  if (!Number.isSafeInteger(mdsAttempt)) throw new Error(`Wrong mdsAttempt=${mdsAttempt}`);
+  return poseidonBasic(opts, _poseidonMDS(opts.Fp, 'HadesMDS', m, mdsAttempt));
+}
+
+export const poseidonSmall = poseidonBasic(
+  { Fp: Fp251, rate: 2, capacity: 1, roundsFull: 8, roundsPartial: 83 },
+  MDS_SMALL
+);
+
+export function poseidonHash(x: bigint, y: bigint, fn = poseidonSmall) {
+  return fn([x, y, 2n])[0];
+}

test/basic.test.js

@@ -68,8 +68,8 @@ for (const c in FIELDS) {
           fc.property(FC_BIGINT, (num) => {
             const a = create(num);
             const b = create(num);
-            deepStrictEqual(Fp.equals(a, b), true);
+            deepStrictEqual(Fp.eql(a, b), true);
-            deepStrictEqual(Fp.equals(b, a), true);
+            deepStrictEqual(Fp.eql(b, a), true);
           })
         );
       });
@@ -78,8 +78,8 @@ for (const c in FIELDS) {
           fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
             const a = create(num1);
             const b = create(num2);
-            deepStrictEqual(Fp.equals(a, b), num1 === num2);
+            deepStrictEqual(Fp.eql(a, b), num1 === num2);
-            deepStrictEqual(Fp.equals(b, a), num1 === num2);
+            deepStrictEqual(Fp.eql(b, a), num1 === num2);
           })
         );
       });
@@ -124,8 +124,8 @@ for (const c in FIELDS) {
           fc.property(FC_BIGINT, (num1) => {
             const a = create(num1);
             const b = create(num1);
-            deepStrictEqual(Fp.sub(Fp.ZERO, a), Fp.negate(a));
+            deepStrictEqual(Fp.sub(Fp.ZERO, a), Fp.neg(a));
-            deepStrictEqual(Fp.sub(a, b), Fp.add(a, Fp.negate(b)));
+            deepStrictEqual(Fp.sub(a, b), Fp.add(a, Fp.neg(b)));
             deepStrictEqual(Fp.sub(a, b), Fp.add(a, Fp.mul(b, Fp.create(-1n))));
           })
         );
@@ -134,13 +134,13 @@ for (const c in FIELDS) {
         fc.assert(
           fc.property(FC_BIGINT, (num) => {
             const a = create(num);
-            deepStrictEqual(Fp.negate(a), Fp.sub(Fp.ZERO, a));
+            deepStrictEqual(Fp.neg(a), Fp.sub(Fp.ZERO, a));
-            deepStrictEqual(Fp.negate(a), Fp.mul(a, Fp.create(-1n)));
+            deepStrictEqual(Fp.neg(a), Fp.mul(a, Fp.create(-1n)));
           })
         );
       });
       should('negate(0)', () => {
-        deepStrictEqual(Fp.negate(Fp.ZERO), Fp.ZERO);
+        deepStrictEqual(Fp.neg(Fp.ZERO), Fp.ZERO);
       });
 
       should('multiply/commutativity', () => {
@@ -190,7 +190,7 @@ for (const c in FIELDS) {
         fc.assert(
           fc.property(FC_BIGINT, (num) => {
             const a = create(num);
-            deepStrictEqual(Fp.square(a), Fp.mul(a, a));
+            deepStrictEqual(Fp.sqr(a), Fp.mul(a, a));
           })
         );
       });
@@ -207,18 +207,18 @@ for (const c in FIELDS) {
       });
 
       should('square(0)', () => {
-        deepStrictEqual(Fp.square(Fp.ZERO), Fp.ZERO);
+        deepStrictEqual(Fp.sqr(Fp.ZERO), Fp.ZERO);
         deepStrictEqual(Fp.mul(Fp.ZERO, Fp.ZERO), Fp.ZERO);
       });
 
       should('square(1)', () => {
-        deepStrictEqual(Fp.square(Fp.ONE), Fp.ONE);
+        deepStrictEqual(Fp.sqr(Fp.ONE), Fp.ONE);
         deepStrictEqual(Fp.mul(Fp.ONE, Fp.ONE), Fp.ONE);
       });
 
       should('square(-1)', () => {
-        const minus1 = Fp.negate(Fp.ONE);
+        const minus1 = Fp.neg(Fp.ONE);
-        deepStrictEqual(Fp.square(minus1), Fp.ONE);
+        deepStrictEqual(Fp.sqr(minus1), Fp.ONE);
         deepStrictEqual(Fp.mul(minus1, minus1), Fp.ONE);
       });
 
@@ -237,8 +237,8 @@ for (const c in FIELDS) {
                 return;
               }
               deepStrictEqual(isSquare(a), true);
-              deepStrictEqual(Fp.equals(Fp.square(root), a), true, 'sqrt(a)^2 == a');
+              deepStrictEqual(Fp.eql(Fp.sqr(root), a), true, 'sqrt(a)^2 == a');
-              deepStrictEqual(Fp.equals(Fp.square(Fp.negate(root)), a), true, '(-sqrt(a))^2 == a');
+              deepStrictEqual(Fp.eql(Fp.sqr(Fp.neg(root)), a), true, '(-sqrt(a))^2 == a');
             })
           );
         });
@@ -247,7 +247,7 @@ for (const c in FIELDS) {
           deepStrictEqual(Fp.sqrt(Fp.ZERO), Fp.ZERO);
           const sqrt1 = Fp.sqrt(Fp.ONE);
           deepStrictEqual(
-            Fp.equals(sqrt1, Fp.ONE) || Fp.equals(sqrt1, Fp.negate(Fp.ONE)),
+            Fp.eql(sqrt1, Fp.ONE) || Fp.eql(sqrt1, Fp.neg(Fp.ONE)),
             true,
             'sqrt(1) = 1 or -1'
           );
@@ -258,7 +258,7 @@ for (const c in FIELDS) {
         fc.assert(
           fc.property(FC_BIGINT, (num) => {
             const a = create(num);
-            if (Fp.equals(a, Fp.ZERO)) return; // No division by zero
+            if (Fp.eql(a, Fp.ZERO)) return; // No division by zero
             deepStrictEqual(Fp.div(a, Fp.ONE), a);
             deepStrictEqual(Fp.div(a, a), Fp.ONE);
           })
@@ -287,7 +287,7 @@ for (const c in FIELDS) {
           fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
             const a = create(num1);
             const b = create(num2);
-            deepStrictEqual(Fp.div(a, b), Fp.mul(a, Fp.invert(b)));
+            deepStrictEqual(Fp.div(a, b), Fp.mul(a, Fp.inv(b)));
           })
         );
       });
@@ -313,12 +313,12 @@ const NUM_RUNS = 5;
 const getXY = (p) => ({ x: p.x, y: p.y });
 
 function equal(a, b, comment) {
-  deepStrictEqual(a.equals(b), true, 'eq(${comment})');
+  deepStrictEqual(a.equals(b), true, `eq(${comment})`);
   if (a.toAffine && b.toAffine) {
-    deepStrictEqual(getXY(a.toAffine()), getXY(b.toAffine()), 'eqToAffine(${comment})');
+    deepStrictEqual(getXY(a.toAffine()), getXY(b.toAffine()), `eqToAffine(${comment})`);
   } else if (!a.toAffine && !b.toAffine) {
     // Already affine
-    deepStrictEqual(getXY(a), getXY(b), 'eqAffine(${comment})');
+    deepStrictEqual(getXY(a), getXY(b), `eqAffine(${comment})`);
   } else throw new Error('Different point types');
 }
 
@@ -342,50 +342,50 @@ for (const name in CURVES) {
     if (!p) continue;
 
     const G = [p.ZERO, p.BASE];
-    for (let i = 2; i < 10; i++) G.push(G[1].multiply(i));
+    for (let i = 2n; i < 10n; i++) G.push(G[1].multiply(i));
     const title = `${name}/${pointName}`;
     describe(title, () => {
       describe('basic group laws', () => {
         // Here we check basic group laws, to verify that points works as group
-        should('(zero)', () => {
+        should('zero', () => {
           equal(G[0].double(), G[0], '(0*G).double() = 0');
           equal(G[0].add(G[0]), G[0], '0*G + 0*G = 0');
           equal(G[0].subtract(G[0]), G[0], '0*G - 0*G = 0');
           equal(G[0].negate(), G[0], '-0 = 0');
           for (let i = 0; i < G.length; i++) {
             const p = G[i];
-            equal(p, p.add(G[0]), '${i}*G + 0 = ${i}*G');
+            equal(p, p.add(G[0]), `${i}*G + 0 = ${i}*G`);
-            equal(G[0].multiply(i + 1), G[0], '${i + 1}*0 = 0');
+            equal(G[0].multiply(BigInt(i + 1)), G[0], `${i + 1}*0 = 0`);
           }
         });
-        should('(one)', () => {
+        should('one', () => {
           equal(G[1].double(), G[2], '(1*G).double() = 2*G');
           equal(G[1].subtract(G[1]), G[0], '1*G - 1*G = 0');
           equal(G[1].add(G[1]), G[2], '1*G + 1*G = 2*G');
         });
-        should('(sanity tests)', () => {
+        should('sanity tests', () => {
           equal(G[2].double(), G[4], '(2*G).double() = 4*G');
           equal(G[2].add(G[2]), G[4], '2*G + 2*G = 4*G');
           equal(G[7].add(G[3].negate()), G[4], '7*G - 3*G = 4*G');
         });
-        should('(addition commutativity)', () => {
+        should('add commutativity', () => {
           equal(G[4].add(G[3]), G[3].add(G[4]), '4*G + 3*G = 3*G + 4*G');
           equal(G[4].add(G[3]), G[3].add(G[2]).add(G[2]), '4*G + 3*G = 3*G + 2*G + 2*G');
         });
-        should('(double)', () => {
+        should('double', () => {
           equal(G[3].double(), G[6], '(3*G).double() = 6*G');
         });
-        should('(multiply)', () => {
+        should('multiply', () => {
-          equal(G[2].multiply(3), G[6], '(2*G).multiply(3) = 6*G');
+          equal(G[2].multiply(3n), G[6], '(2*G).multiply(3) = 6*G');
         });
-        should('(same point addition)', () => {
+        should('add same-point', () => {
           equal(G[3].add(G[3]), G[6], '3*G + 3*G = 6*G');
         });
-        should('(same point (negative) addition)', () => {
+        should('add same-point negative', () => {
           equal(G[3].add(G[3].negate()), G[0], '3*G + (- 3*G) = 0*G');
           equal(G[3].subtract(G[3]), G[0], '3*G - 3*G = 0*G');
         });
-        should('(curve order)', () => {
+        should('mul by curve order', () => {
           equal(G[1].multiply(CURVE_ORDER - 1n).add(G[1]), G[0], '(N-1)*G + G = 0');
           equal(G[1].multiply(CURVE_ORDER - 1n).add(G[2]), G[1], '(N-1)*G + 2*G = 1*G');
           equal(G[1].multiply(CURVE_ORDER - 2n).add(G[2]), G[0], '(N-2)*G + 2*G = 0');
@@ -393,7 +393,7 @@ for (const name in CURVES) {
           const carry = CURVE_ORDER % 2n === 1n ? G[1] : G[0];
           equal(G[1].multiply(half).double().add(carry), G[0], '((N/2) * G).double() = 0');
         });
-        should('(inversion)', () => {
+        should('inversion', () => {
           const a = 1234n;
           const b = 5678n;
           const c = a * b;
@@ -401,7 +401,7 @@ for (const name in CURVES) {
           const inv = mod.invert(b, CURVE_ORDER);
           equal(G[1].multiply(c).multiply(inv), G[1].multiply(a), 'c*G * (1/b)*G = a*G');
         });
-        should('(multiply, rand)', () =>
+        should('multiply, rand', () =>
           fc.assert(
             fc.property(FC_BIGINT, FC_BIGINT, (a, b) => {
               const c = mod.mod(a + b, CURVE_ORDER);
@@ -415,7 +415,7 @@ for (const name in CURVES) {
             { numRuns: NUM_RUNS }
           )
         );
-        should('(multiply2, rand)', () =>
+        should('multiply2, rand', () =>
           fc.assert(
             fc.property(FC_BIGINT, FC_BIGINT, (a, b) => {
               const c = mod.mod(a * b, CURVE_ORDER);
@@ -436,9 +436,16 @@ for (const name in CURVES) {
             throws(() => G[1][op](0n), '0n');
             G[1][op](G[2]);
             throws(() => G[1][op](CURVE_ORDER), 'CURVE_ORDER');
+            throws(() => G[1][op](-123n), '-123n');
+            throws(() => G[1][op](123), '123');
             throws(() => G[1][op](123.456), '123.456');
             throws(() => G[1][op](true), 'true');
+            throws(() => G[1][op](false), 'false');
+            throws(() => G[1][op](null), 'null');
+            throws(() => G[1][op](undefined), 'undefined');
             throws(() => G[1][op]('1'), "'1'");
+            throws(() => G[1][op]({ x: 1n, y: 1n }), '{ x: 1n, y: 1n }');
+            throws(() => G[1][op]({ x: 1n, y: 1n, z: 1n }), '{ x: 1n, y: 1n, z: 1n }');
             throws(
               () => G[1][op]({ x: 1n, y: 1n, z: 1n, t: 1n }),
               '{ x: 1n, y: 1n, z: 1n, t: 1n }'
@@ -447,8 +454,8 @@ for (const name in CURVES) {
             throws(() => G[1][op](new Uint8Array([0])), 'ui8a([0])');
             throws(() => G[1][op](new Uint8Array([1])), 'ui8a([1])');
             throws(() => G[1][op](new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])');
-            if (G[1].toAffine) throws(() => G[1][op](C.Point.BASE), 'Point ${op} ${pointName}');
+            // if (G[1].toAffine) throws(() => G[1][op](C.Point.BASE), `Point ${op} ${pointName}`);
-            throws(() => G[1][op](o.BASE), '${op}/other curve point');
+            throws(() => G[1][op](o.BASE), `${op}/other curve point`);
           });
         });
       }
@@ -468,7 +475,7 @@ for (const name in CURVES) {
         throws(() => G[1].equals(new Uint8Array([0])), 'ui8a([0])');
         throws(() => G[1].equals(new Uint8Array([1])), 'ui8a([1])');
         throws(() => G[1].equals(new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])');
-        if (G[1].toAffine) throws(() => G[1].equals(C.Point.BASE), 'Point.equals(${pointName})');
+        // if (G[1].toAffine) throws(() => G[1].equals(C.Point.BASE), 'Point.equals(${pointName})');
         throws(() => G[1].equals(o.BASE), 'other curve point');
       });
 
@@ -497,18 +504,18 @@ for (const name in CURVES) {
         });
       }
       // Complex point (Extended/Jacobian/Projective?)
-      if (p.BASE.toAffine) {
+      // if (p.BASE.toAffine && C.Point) {
-        should('toAffine()', () => {
+      //   should('toAffine()', () => {
-          equal(p.ZERO.toAffine(), C.Point.ZERO, '0 = 0');
+      //     equal(p.ZERO.toAffine(), C.Point.ZERO, '0 = 0');
-          equal(p.BASE.toAffine(), C.Point.BASE, '1 = 1');
+      //     equal(p.BASE.toAffine(), C.Point.BASE, '1 = 1');
-        });
+      //   });
-      }
+      // }
-      if (p.fromAffine) {
+      // if (p.fromAffine && C.Point) {
-        should('fromAffine()', () => {
+      //   should('fromAffine()', () => {
-          equal(p.ZERO, p.fromAffine(C.Point.ZERO), '0 = 0');
+      //     equal(p.ZERO, p.fromAffine(C.Point.ZERO), '0 = 0');
-          equal(p.BASE, p.fromAffine(C.Point.BASE), '1 = 1');
+      //     equal(p.BASE, p.fromAffine(C.Point.BASE), '1 = 1');
-        });
+      //   });
-      }
+      // }
       // toHex/fromHex (if available)
       if (p.fromHex && p.BASE.toHex) {
         should('fromHex(toHex()) roundtrip', () => {
@@ -524,20 +531,26 @@ for (const name in CURVES) {
   }
   describe(name, () => {
     // Generic complex things (getPublicKey/sign/verify/getSharedSecret)
-    should('getPublicKey type check', () => {
+    should('.getPublicKey() type check', () => {
       throws(() => C.getPublicKey(0), '0');
       throws(() => C.getPublicKey(0n), '0n');
-      throws(() => C.getPublicKey(false), 'false');
+      throws(() => C.getPublicKey(-123n), '-123n');
+      throws(() => C.getPublicKey(123), '123');
       throws(() => C.getPublicKey(123.456), '123.456');
       throws(() => C.getPublicKey(true), 'true');
+      throws(() => C.getPublicKey(false), 'false');
+      throws(() => C.getPublicKey(null), 'null');
+      throws(() => C.getPublicKey(undefined), 'undefined');
       throws(() => C.getPublicKey(''), "''");
       // NOTE: passes because of disabled hex padding checks for starknet, maybe enable?
-      //throws(() => C.getPublicKey('1'), "'1'");
+      // throws(() => C.getPublicKey('1'), "'1'");
       throws(() => C.getPublicKey('key'), "'key'");
+      throws(() => C.getPublicKey({}));
       throws(() => C.getPublicKey(new Uint8Array([])));
       throws(() => C.getPublicKey(new Uint8Array([0])));
       throws(() => C.getPublicKey(new Uint8Array([1])));
       throws(() => C.getPublicKey(new Uint8Array(4096).fill(1)));
+      throws(() => C.getPublicKey(Array(32).fill(1)));
     });
     should('.verify() should verify random signatures', () =>
       fc.assert(
@@ -557,15 +570,29 @@ for (const name in CURVES) {
     should('.sign() edge cases', () => {
       throws(() => C.sign());
       throws(() => C.sign(''));
+      throws(() => C.sign('', ''));
+      throws(() => C.sign(new Uint8Array(), new Uint8Array()));
     });
 
-    should('.verify() should not verify signature with wrong hash', () => {
+    describe('verify()', () => {
-      const MSG = '01'.repeat(32);
+      const msg = '01'.repeat(32);
-      const PRIV_KEY = 0x2n;
+      should('true for proper signatures', () => {
-      const WRONG_MSG = '11'.repeat(32);
+        const priv = C.utils.randomPrivateKey();
-      const signature = C.sign(MSG, PRIV_KEY);
+        const sig = C.sign(msg, priv);
-      const publicKey = C.getPublicKey(PRIV_KEY);
+        const pub = C.getPublicKey(priv);
-      deepStrictEqual(C.verify(signature, WRONG_MSG, publicKey), false);
+        deepStrictEqual(C.verify(sig, msg, pub), true);
+      });
+      should('false for wrong messages', () => {
+        const priv = C.utils.randomPrivateKey();
+        const sig = C.sign(msg, priv);
+        const pub = C.getPublicKey(priv);
+        deepStrictEqual(C.verify(sig, '11'.repeat(32), pub), false);
+      });
+      should('false for wrong keys', () => {
+        const priv = C.utils.randomPrivateKey();
+        const sig = C.sign(msg, priv);
+        deepStrictEqual(C.verify(sig, msg, C.getPublicKey(C.utils.randomPrivateKey())), false);
+      });
     });
     // NOTE: fails for ed, because of empty message. Since we convert it to scalar,
     // need to check what other implementations do. Empty message != new Uint8Array([0]), but what scalar should be in that case?
@@ -618,10 +645,10 @@ should('secp224k1 sqrt bug', () => {
     23621584063597419797792593680131996961517196803742576047493035507225n
   );
   deepStrictEqual(
-    Fp.negate(sqrtMinus1),
+    Fp.neg(sqrtMinus1),
     3338362603553219996874421406887633712040719456283732096017030791656n
   );
-  deepStrictEqual(Fp.square(sqrtMinus1), Fp.create(-1n));
+  deepStrictEqual(Fp.sqr(sqrtMinus1), Fp.create(-1n));
 });
 
 // ESM is broken.

test/ed25519.test.js

@@ -20,6 +20,7 @@ import { default as x25519vectors } from './wycheproof/x25519_test.json' assert
 describe('ed25519', () => {
   const ed = ed25519;
   const hex = bytesToHex;
+  const Point = ed.ExtendedPoint;
 
   function to32Bytes(numOrStr) {
     let hex = typeof numOrStr === 'string' ? numOrStr : numOrStr.toString(16);
@@ -28,7 +29,7 @@ describe('ed25519', () => {
 
   function utf8ToBytes(str) {
     if (typeof str !== 'string') {
-      throw new TypeError(`utf8ToBytes expected string, got ${typeof str}`);
+      throw new Error(`utf8ToBytes expected string, got ${typeof str}`);
     }
     return new TextEncoder().encode(str);
   }
@@ -78,6 +79,7 @@ describe('ed25519', () => {
     );
   });
   const privKey = to32Bytes('a665a45920422f9d417e4867ef');
+  const wrongPriv = to32Bytes('a675a45920422f9d417e4867ef');
   const msg = hexToBytes('874f9960c5d2b7a9b5fad383e1ba44719ebb743a');
   const wrongMsg = hexToBytes('589d8c7f1da0a24bc07b7381ad48b1cfc211af1c');
   describe('basic methods', () => {
@@ -86,16 +88,6 @@ describe('ed25519', () => {
       const signature = ed.sign(msg, privKey);
       deepStrictEqual(ed.verify(signature, msg, publicKey), true);
     });
-    should('not verify signature with wrong public key', () => {
-      const publicKey = ed.getPublicKey(12);
-      const signature = ed.sign(msg, privKey);
-      deepStrictEqual(ed.verify(signature, msg, publicKey), false);
-    });
-    should('not verify signature with wrong hash', () => {
-      const publicKey = ed.getPublicKey(privKey);
-      const signature = ed.sign(msg, privKey);
-      deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
-    });
   });
   describe('sync methods', () => {
     should('sign and verify', () => {
@@ -104,7 +96,7 @@ describe('ed25519', () => {
       deepStrictEqual(ed.verify(signature, msg, publicKey), true);
     });
     should('not verify signature with wrong public key', () => {
-      const publicKey = ed.getPublicKey(12);
+      const publicKey = ed.getPublicKey(wrongPriv);
       const signature = ed.sign(msg, privKey);
       deepStrictEqual(ed.verify(signature, msg, publicKey), false);
     });
@@ -114,55 +106,45 @@ describe('ed25519', () => {
       deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
     });
   });
-  // https://xmr.llcoins.net/addresstests.html
+  describe('BASE_POINT.multiply()', () => {
-  should(
+    // https://xmr.llcoins.net/addresstests.html
-    'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 1',
+    should('create right publicKey without SHA-512 hashing TEST 1', () => {
-    () => {
       const publicKey =
-        ed.Point.BASE.multiply(0x90af56259a4b6bfbc4337980d5d75fbe3c074630368ff3804d33028e5dbfa77n);
+        Point.BASE.multiply(0x90af56259a4b6bfbc4337980d5d75fbe3c074630368ff3804d33028e5dbfa77n);
       deepStrictEqual(
         publicKey.toHex(),
         '0f3b913371411b27e646b537e888f685bf929ea7aab93c950ed84433f064480d'
       );
-    }
+    });
-  );
+    should('create right publicKey without SHA-512 hashing TEST 2', () => {
-  should(
-    'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 2',
-    () => {
       const publicKey =
-        ed.Point.BASE.multiply(0x364e8711a60780382a5d57b061c126f039940f28a9e91fe039d4d3094d8b88n);
+        Point.BASE.multiply(0x364e8711a60780382a5d57b061c126f039940f28a9e91fe039d4d3094d8b88n);
       deepStrictEqual(
         publicKey.toHex(),
         'ad545340b58610f0cd62f17d55af1ab11ecde9c084d5476865ddb4dbda015349'
       );
-    }
+    });
-  );
+    should('create right publicKey without SHA-512 hashing TEST 3', () => {
-  should(
-    'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 3',
-    () => {
       const publicKey =
-        ed.Point.BASE.multiply(0xb9bf90ff3abec042752cac3a07a62f0c16cfb9d32a3fc2305d676ec2d86e941n);
+        Point.BASE.multiply(0xb9bf90ff3abec042752cac3a07a62f0c16cfb9d32a3fc2305d676ec2d86e941n);
       deepStrictEqual(
         publicKey.toHex(),
         'e097c4415fe85724d522b2e449e8fd78dd40d20097bdc9ae36fe8ec6fe12cb8c'
       );
-    }
+    });
-  );
+    should('create right publicKey without SHA-512 hashing TEST 4', () => {
-  should(
-    'ed25519/BASE_POINT.multiply()/should create right publicKey without SHA-512 hashing TEST 4',
-    () => {
       const publicKey =
-        ed.Point.BASE.multiply(0x69d896f02d79524c9878e080308180e2859d07f9f54454e0800e8db0847a46en);
+        Point.BASE.multiply(0x69d896f02d79524c9878e080308180e2859d07f9f54454e0800e8db0847a46en);
       deepStrictEqual(
         publicKey.toHex(),
         'f12cb7c43b59971395926f278ce7c2eaded9444fbce62ca717564cb508a0db1d'
       );
-    }
+    });
-  );
+    should('throw Point#multiply on TEST 5', () => {
-  should('ed25519/BASE_POINT.multiply()/should throw Point#multiply on TEST 5', () => {
+      for (const num of [0n, 0, -1n, -1, 1.1]) {
-    for (const num of [0n, 0, -1n, -1, 1.1]) {
+        throws(() => Point.BASE.multiply(num));
-      throws(() => ed.Point.BASE.multiply(num));
+      }
-    }
+    });
   });
 
   // https://ed25519.cr.yp.to/python/sign.py
@@ -184,7 +166,7 @@ describe('ed25519', () => {
       // Calculate
       const pub = ed.getPublicKey(to32Bytes(priv));
       deepStrictEqual(hex(pub), expectedPub);
-      deepStrictEqual(pub, ed.Point.fromHex(pub).toRawBytes());
+      deepStrictEqual(pub, Point.fromHex(pub).toRawBytes());
 
       const signature = hex(ed.sign(msg, priv));
       // console.log('vector', i);
@@ -382,7 +364,7 @@ describe('ed25519', () => {
       throws(() => RistrettoPoint.fromHex(b), badBytes);
     }
   });
-  should('ristretto255/should create right points from uniform hash', async () => {
+  should('ristretto255/should create right points from uniform hash', () => {
     const labels = [
       'Ristretto is traditionally a short shot of espresso coffee',
       'made with the normal amount of ground coffee but extracted with',
@@ -440,13 +422,14 @@ describe('ed25519', () => {
       } catch (e) {
         noble = false;
       }
-      deepStrictEqual(noble, v.valid_zip215);
+      deepStrictEqual(noble, v.valid_zip215, JSON.stringify(v));
     }
   });
   should('ZIP-215 compliance tests/disallows sig.s >= CURVE.n', () => {
-    const sig = new ed.Signature(ed.Point.BASE, 1n);
+    // sig.R = BASE, sig.s = N+1
-    sig.s = ed.CURVE.n + 1n;
+    const sig =
-    throws(() => ed.verify(sig, 'deadbeef', ed.Point.BASE));
+      '5866666666666666666666666666666666666666666666666666666666666666eed3f55c1a631258d69cf7a2def9de1400000000000000000000000000000010';
+    throws(() => ed.verify(sig, 'deadbeef', Point.BASE));
   });
 
   const rfc7748Mul = [
@@ -511,7 +494,7 @@ describe('ed25519', () => {
 
   // should('X25519: should convert base point to montgomery using fromPoint', () => {
   //   deepStrictEqual(
-  //     hex(ed.montgomeryCurve.UfromPoint(ed.Point.BASE)),
+  //     hex(ed.montgomeryCurve.UfromPoint(Point.BASE)),
   //     ed.montgomeryCurve.BASE_POINT_U
   //   );
   // });
@@ -655,16 +638,16 @@ describe('ed25519', () => {
   }
 
   should('X25519 base point', () => {
-    const { y } = ed25519.Point.BASE;
+    const { y } = ed25519.ExtendedPoint.BASE;
     const { Fp } = ed25519.CURVE;
-    const u = Fp.create((y + 1n) * Fp.invert(1n - y));
+    const u = Fp.create((y + 1n) * Fp.inv(1n - y));
     deepStrictEqual(hex(numberToBytesLE(u, 32)), x25519.Gu);
   });
 
   should('isTorsionFree()', () => {
     const orig = ed.utils.getExtendedPublicKey(ed.utils.randomPrivateKey()).point;
     for (const hex of ED25519_TORSION_SUBGROUP.slice(1)) {
-      const dirty = orig.add(ed.Point.fromHex(hex));
+      const dirty = orig.add(Point.fromHex(hex));
       const cleared = dirty.clearCofactor();
       strictEqual(orig.isTorsionFree(), true, `orig must be torsionFree: ${hex}`);
       strictEqual(dirty.isTorsionFree(), false, `dirty must not be torsionFree: ${hex}`);

test/ed448.test.js

@@ -11,9 +11,10 @@ describe('ed448', () => {
   const ed = ed448;
   const hex = bytesToHex;
   ed.utils.precompute(4);
+  const Point = ed.ExtendedPoint;
 
   should(`Basic`, () => {
-    const G1 = ed.Point.BASE;
+    const G1 = Point.BASE.toAffine();
     deepStrictEqual(
       G1.x,
       224580040295924300187604334099896036246789641632564134246125461686950415467406032909029192869357953282578032075146446173674602635247710n
@@ -22,7 +23,7 @@ describe('ed448', () => {
       G1.y,
       298819210078481492676017930443930673437544040154080242095928241372331506189835876003536878655418784733982303233503462500531545062832660n
     );
-    const G2 = ed.Point.BASE.multiply(2n);
+    const G2 = Point.BASE.multiply(2n).toAffine();
     deepStrictEqual(
       G2.x,
       484559149530404593699549205258669689569094240458212040187660132787056912146709081364401144455726350866276831544947397859048262938744149n
@@ -31,7 +32,7 @@ describe('ed448', () => {
       G2.y,
       494088759867433727674302672526735089350544552303727723746126484473087719117037293890093462157703888342865036477787453078312060500281069n
     );
-    const G3 = ed.Point.BASE.multiply(3n);
+    const G3 = Point.BASE.multiply(3n).toAffine();
     deepStrictEqual(
       G3.x,
       23839778817283171003887799738662344287085130522697782688245073320169861206004018274567429238677677920280078599146891901463786155880335n
@@ -43,12 +44,12 @@ describe('ed448', () => {
   });
 
   should('Basic/decompress', () => {
-    const G1 = ed.Point.BASE;
+    const G1 = Point.BASE;
-    const G2 = ed.Point.BASE.multiply(2n);
+    const G2 = Point.BASE.multiply(2n);
-    const G3 = ed.Point.BASE.multiply(3n);
+    const G3 = Point.BASE.multiply(3n);
     const points = [G1, G2, G3];
-    const getXY = (p) => ({ x: p.x, y: p.y });
+    const getXY = (p) => p.toAffine();
-    for (const p of points) deepStrictEqual(getXY(ed.Point.fromHex(p.toHex())), getXY(p));
+    for (const p of points) deepStrictEqual(getXY(Point.fromHex(p.toHex())), getXY(p));
   });
 
   const VECTORS_RFC8032 = [
@@ -315,16 +316,18 @@ describe('ed448', () => {
     },
   ];
 
-  for (let i = 0; i < VECTORS_RFC8032.length; i++) {
+  describe('RFC8032', () => {
-    const v = VECTORS_RFC8032[i];
+    for (let i = 0; i < VECTORS_RFC8032.length; i++) {
-    should(`RFC8032/${i}`, () => {
+      const v = VECTORS_RFC8032[i];
-      deepStrictEqual(hex(ed.getPublicKey(v.secretKey)), v.publicKey);
+      should(`${i}`, () => {
-      deepStrictEqual(hex(ed.sign(v.message, v.secretKey)), v.signature);
+        deepStrictEqual(hex(ed.getPublicKey(v.secretKey)), v.publicKey);
-      deepStrictEqual(ed.verify(v.signature, v.message, v.publicKey), true);
+        deepStrictEqual(hex(ed.sign(v.message, v.secretKey)), v.signature);
-    });
+        deepStrictEqual(ed.verify(v.signature, v.message, v.publicKey), true);
-  }
+      });
+    }
+  });
 
-  should('not accept >57byte private keys', async () => {
+  should('not accept >57byte private keys', () => {
     const invalidPriv =
       100000000000000000000000000000000000009000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000090000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000800073278156000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000n;
     throws(() => ed.getPublicKey(invalidPriv));
@@ -382,7 +385,24 @@ describe('ed448', () => {
       deepStrictEqual(ed.verify(signature, msg, publicKey), true);
     });
     should('not verify signature with wrong public key', () => {
-      const publicKey = ed.getPublicKey(12);
+      const publicKey = ed.getPublicKey(ed.utils.randomPrivateKey());
+      const signature = ed.sign(msg, privKey);
+      deepStrictEqual(ed.verify(signature, msg, publicKey), false);
+    });
+    should('not verify signature with wrong hash', () => {
+      const publicKey = ed.getPublicKey(privKey);
+      const signature = ed.sign(msg, privKey);
+      deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
+    });
+  });
+  describe('sync methods', () => {
+    should('sign and verify', () => {
+      const publicKey = ed.getPublicKey(privKey);
+      const signature = ed.sign(msg, privKey);
+      deepStrictEqual(ed.verify(signature, msg, publicKey), true);
+    });
+    should('not verify signature with wrong public key', () => {
+      const publicKey = ed.getPublicKey(ed.utils.randomPrivateKey());
       const signature = ed.sign(msg, privKey);
       deepStrictEqual(ed.verify(signature, msg, publicKey), false);
     });
@@ -393,27 +413,9 @@ describe('ed448', () => {
     });
   });
 
-  describe('sync methods', () => {
-    should('sign and verify', () => {
-      const publicKey = ed.getPublicKey(privKey);
-      const signature = ed.sign(msg, privKey);
-      deepStrictEqual(ed.verify(signature, msg, publicKey), true);
-    });
-    should('not verify signature with wrong public key', async () => {
-      const publicKey = ed.getPublicKey(12);
-      const signature = ed.sign(msg, privKey);
-      deepStrictEqual(ed.verify(signature, msg, publicKey), false);
-    });
-    should('not verify signature with wrong hash', async () => {
-      const publicKey = ed.getPublicKey(privKey);
-      const signature = ed.sign(msg, privKey);
-      deepStrictEqual(ed.verify(signature, wrongMsg, publicKey), false);
-    });
-  });
-
   should('BASE_POINT.multiply() throws in Point#multiply on TEST 5', () => {
     for (const num of [0n, 0, -1n, -1, 1.1]) {
-      throws(() => ed.Point.BASE.multiply(num));
+      throws(() => ed.ExtendedPoint.BASE.multiply(num));
     }
   });
 
@@ -437,14 +439,14 @@ describe('ed448', () => {
     }
   });
 
-  {
+  describe('wycheproof', () => {
     for (let g = 0; g < ed448vectors.testGroups.length; g++) {
       const group = ed448vectors.testGroups[g];
       const key = group.key;
-      should(`Wycheproof/ED448(${g}, public)`, () => {
+      should(`ED448(${g}, public)`, () => {
         deepStrictEqual(hex(ed.getPublicKey(key.sk)), key.pk);
       });
-      should(`Wycheproof/ED448`, () => {
+      should(`ED448`, () => {
         for (let i = 0; i < group.tests.length; i++) {
           const v = group.tests[i];
           const index = `${g}/${i} ${v.comment}`;
@@ -463,7 +465,7 @@ describe('ed448', () => {
         }
       });
     }
-  }
+  });
 
   // ECDH
   const rfc7748Mul = [
@@ -482,12 +484,14 @@ describe('ed448', () => {
         '884a02576239ff7a2f2f63b2db6a9ff37047ac13568e1e30fe63c4a7ad1b3ee3a5700df34321d62077e63633c575c1c954514e99da7c179d',
     },
   ];
-  for (let i = 0; i < rfc7748Mul.length; i++) {
+  describe('RFC7748', () => {
-    const v = rfc7748Mul[i];
+    for (let i = 0; i < rfc7748Mul.length; i++) {
-    should(`RFC7748: scalarMult (${i})`, () => {
+      const v = rfc7748Mul[i];
-      deepStrictEqual(hex(x448.scalarMult(v.scalar, v.u)), v.outputU);
+      should(`scalarMult (${i})`, () => {
-    });
+        deepStrictEqual(hex(x448.scalarMult(v.scalar, v.u)), v.outputU);
-  }
+      });
+    }
+  });
 
   const rfc7748Iter = [
     {
@@ -528,9 +532,9 @@ describe('ed448', () => {
     deepStrictEqual(hex(x448.scalarMult(bobPrivate, alicePublic)), shared);
   });
 
-  {
+  describe('wycheproof', () => {
     const group = x448vectors.testGroups[0];
-    should(`Wycheproof/X448`, () => {
+    should(`X448`, () => {
       for (let i = 0; i < group.tests.length; i++) {
         const v = group.tests[i];
         const index = `(${i}, ${v.result}) ${v.comment}`;
@@ -556,11 +560,11 @@ describe('ed448', () => {
         } else throw new Error('unknown test result');
       }
     });
-  }
+  });
 
   // should('X448: should convert base point to montgomery using fromPoint', () => {
   //   deepStrictEqual(
-  //     hex(ed.montgomeryCurve.UfromPoint(ed.Point.BASE)),
+  //     hex(ed.montgomeryCurve.UfromPoint(Point.BASE)),
   //     ed.montgomeryCurve.BASE_POINT_U
   //   );
   // });
@@ -655,7 +659,7 @@ describe('ed448', () => {
   }
 
   should('X448 base point', () => {
-    const { x, y } = ed448.Point.BASE;
+    const { x, y } = Point.BASE;
     const { Fp } = ed448.CURVE;
     // const invX = Fp.invert(x * x); // x²
     const u = Fp.div(Fp.create(y * y), Fp.create(x * x)); // (y²/x²)

test/hash-to-curve.test.js

@@ -5,12 +5,12 @@ import { bytesToHex } from '@noble/hashes/utils';
 import { sha256 } from '@noble/hashes/sha256';
 import { sha512 } from '@noble/hashes/sha512';
 import { shake128, shake256 } from '@noble/hashes/sha3';
-import { secp256r1 } from '../lib/esm/p256.js';
+import * as secp256r1 from '../lib/esm/p256.js';
-import { secp384r1 } from '../lib/esm/p384.js';
+import * as secp384r1 from '../lib/esm/p384.js';
-import { secp521r1 } from '../lib/esm/p521.js';
+import * as secp521r1 from '../lib/esm/p521.js';
-import { ed25519 } from '../lib/esm/ed25519.js';
+import * as ed25519 from '../lib/esm/ed25519.js';
-import { ed448 } from '../lib/esm/ed448.js';
+import * as ed448 from '../lib/esm/ed448.js';
-import { secp256k1 } from '../lib/esm/secp256k1.js';
+import * as secp256k1 from '../lib/esm/secp256k1.js';
 import { bls12_381 } from '../lib/esm/bls12-381.js';
 import {
   stringToBytes,
@@ -111,9 +111,11 @@ function testCurve(curve, ro, nu) {
     for (let i = 0; i < ro.vectors.length; i++) {
       const t = ro.vectors[i];
       should(`(${i})`, () => {
-        const p = curve.Point.hashToCurve(stringToBytes(t.msg), {
+        const p = curve
-          DST: ro.dst,
+          .hashToCurve(stringToBytes(t.msg), {
-        });
+            DST: ro.dst,
+          })
+          .toAffine();
         deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
         deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
       });
@@ -123,9 +125,11 @@ function testCurve(curve, ro, nu) {
     for (let i = 0; i < nu.vectors.length; i++) {
       const t = nu.vectors[i];
       should(`(${i})`, () => {
-        const p = curve.Point.encodeToCurve(stringToBytes(t.msg), {
+        const p = curve
-          DST: nu.dst,
+          .encodeToCurve(stringToBytes(t.msg), {
-        });
+            DST: nu.dst,
+          })
+          .toAffine();
         deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
         deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
       });
@@ -136,9 +140,8 @@ function testCurve(curve, ro, nu) {
 testCurve(secp256r1, p256_ro, p256_nu);
 testCurve(secp384r1, p384_ro, p384_nu);
 testCurve(secp521r1, p521_ro, p521_nu);
-// TODO: remove same tests from bls12
+testCurve(bls12_381.hashToCurve.G1, g1_ro, g1_nu);
-testCurve(bls12_381.G1, g1_ro, g1_nu);
+testCurve(bls12_381.hashToCurve.G2, g2_ro, g2_nu);
-testCurve(bls12_381.G2, g2_ro, g2_nu);
 testCurve(secp256k1, secp256k1_ro, secp256k1_nu);
 testCurve(ed25519, ed25519_ro, ed25519_nu);
 testCurve(ed448, ed448_ro, ed448_nu);

test/index.test.js

@@ -6,7 +6,7 @@ import './nist.test.js';
 import './ed448.test.js';
 import './ed25519.test.js';
 import './secp256k1.test.js';
-import './stark/stark.test.js';
+import './stark/index.test.js';
 import './jubjub.test.js';
 import './bls12-381.test.js';
 import './hash-to-curve.test.js';

test/jubjub.test.js

@@ -1,15 +1,15 @@
 import { jubjub, findGroupHash } from '../lib/esm/jubjub.js';
 import { describe, should } from 'micro-should';
 import { deepStrictEqual, throws } from 'assert';
-import { hexToBytes, bytesToHex } from '@noble/hashes/utils';
+const Point = jubjub.ExtendedPoint;
 
-const G_SPEND = new jubjub.ExtendedPoint(
+const G_SPEND = new Point(
   0x055f1f24f0f0512287e51c3c5a0a6903fc0baf8711de9eafd7c0e66f69d8d2dbn,
   0x566178b2505fdd52132a5007d80a04652842e78ffb376897588f406278214ed7n,
   0x0141fafa1f11088a3b2007c14d652375888f3b37838ba6bdffae096741ceddfen,
   0x12eada93c0b7d595f5f04f5ebfb4b7d033ef2884136475cab5e41ce17db5be9cn
 );
-const G_PROOF = new jubjub.ExtendedPoint(
+const G_PROOF = new Point(
   0x0174d54ce9fad258a2f8a86a1deabf15c7a2b51106b0fbcd9d29020f78936f71n,
   0x16871d6d877dcd222e4ec3bccb3f37cb1865a2d37dd3a5dcbc032a69b62b4445n,
   0x57a3cd31e496d82bd4aa78bd5ecd751cfb76d54a5d3f4560866379f9fc11c9b3n,
@@ -22,7 +22,7 @@ describe('jubjub', () => {
   should('toHex/fromHex', () => {
     // More than field
     throws(() =>
-      jubjub.Point.fromHex(
+      Point.fromHex(
         new Uint8Array([
           255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
           255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
@@ -31,14 +31,14 @@ describe('jubjub', () => {
     );
     // Multiplicative generator (sqrt == null), not on curve.
     throws(() =>
-      jubjub.Point.fromHex(
+      Point.fromHex(
         new Uint8Array([
           7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0,
         ])
       )
     );
-    const tmp = jubjub.Point.fromHex(
+    const tmp = Point.fromHex(
       new Uint8Array([
         0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
         0,
@@ -47,14 +47,14 @@ describe('jubjub', () => {
     deepStrictEqual(tmp.x, 0x8d51ccce760304d0ec030002760300000001000000000000n);
     deepStrictEqual(tmp.y, 0n);
 
-    const S = G_SPEND.toAffine().toRawBytes();
+    const S = G_SPEND.toRawBytes();
-    const S2 = G_SPEND.double().toAffine().toRawBytes();
+    const S2 = G_SPEND.double().toRawBytes();
-    const P = G_PROOF.toAffine().toRawBytes();
+    const P = G_PROOF.toRawBytes();
-    const P2 = G_PROOF.double().toAffine().toRawBytes();
+    const P2 = G_PROOF.double().toRawBytes();
-    const S_exp = jubjub.Point.fromHex(S);
+    const S_exp = Point.fromHex(S);
-    const S2_exp = jubjub.Point.fromHex(S2);
+    const S2_exp = Point.fromHex(S2);
-    const P_exp = jubjub.Point.fromHex(P);
+    const P_exp = Point.fromHex(P);
-    const P2_exp = jubjub.Point.fromHex(P2);
+    const P2_exp = Point.fromHex(P2);
     deepStrictEqual(getXY(G_SPEND.toAffine()), getXY(S_exp));
     deepStrictEqual(getXY(G_SPEND.double().toAffine()), getXY(S2_exp));
     deepStrictEqual(getXY(G_PROOF.toAffine()), getXY(P_exp));

test/nist.test.js

@@ -11,164 +11,11 @@ import { default as ecdsa } from './wycheproof/ecdsa_test.json' assert { type: '
 import { default as ecdh } from './wycheproof/ecdh_test.json' assert { type: 'json' };
 import { default as rfc6979 } from './fixtures/rfc6979.json' assert { type: 'json' };
 
-const hex = bytesToHex;
-
-// prettier-ignore
-const NIST = {
-  secp192r1, P192,
-  secp224r1, P224,
-  secp256r1, P256,
-  secp384r1, P384,
-  secp521r1, P521,
-  secp256k1,
-};
-
-should('Curve Fields', () => {
-  const vectors = {
-    secp192r1: 0xfffffffffffffffffffffffffffffffeffffffffffffffffn,
-    secp224r1: 0xffffffffffffffffffffffffffffffff000000000000000000000001n,
-    secp256r1: 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffffn,
-    secp256k1: 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fn,
-    secp384r1:
-      0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffffn,
-    secp521r1:
-      0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffn,
-  };
-  for (const n in vectors) deepStrictEqual(NIST[n].CURVE.Fp.ORDER, vectors[n]);
-});
-
-should('wychenproof ECDSA vectors', () => {
-  for (const group of ecdsa.testGroups) {
-    // Tested in secp256k1.test.js
-    if (group.key.curve === 'secp256k1') continue;
-    let CURVE = NIST[group.key.curve];
-    if (!CURVE) continue;
-    if (group.key.curve === 'secp224r1' && group.sha !== 'SHA-224') {
-      if (group.sha === 'SHA-256') CURVE = CURVE.create(sha256);
-    }
-    const pubKey = CURVE.Point.fromHex(group.key.uncompressed);
-    deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
-    deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
-    for (const test of group.tests) {
-      if (['Hash weaker than DL-group'].includes(test.comment)) {
-        continue;
-      }
-      const m = CURVE.CURVE.hash(hexToBytes(test.msg));
-      if (test.result === 'valid' || test.result === 'acceptable') {
-        try {
-          CURVE.Signature.fromDER(test.sig);
-        } catch (e) {
-          // Some test has invalid signature which we don't accept
-          if (e.message.includes('Invalid signature: incorrect length')) continue;
-          throw e;
-        }
-        const verified = CURVE.verify(test.sig, m, pubKey);
-        deepStrictEqual(verified, true, 'valid');
-      } else if (test.result === 'invalid') {
-        let failed = false;
-        try {
-          failed = !CURVE.verify(test.sig, m, pubKey);
-        } catch (error) {
-          failed = true;
-        }
-        deepStrictEqual(failed, true, 'invalid');
-      } else throw new Error('unknown test result');
-    }
-  }
-});
-
-should('wychenproof ECDH vectors', () => {
-  for (const group of ecdh.testGroups) {
-    // // Tested in secp256k1.test.js
-    // if (group.key.curve === 'secp256k1') continue;
-    // We don't have SHA-224
-    const CURVE = NIST[group.curve];
-    if (!CURVE) continue;
-    for (const test of group.tests) {
-      if (test.result === 'valid' || test.result === 'acceptable') {
-        try {
-          const pub = CURVE.Point.fromHex(test.public);
-        } catch (e) {
-          if (e.message.includes('Point.fromHex: received invalid point.')) continue;
-          throw e;
-        }
-        const shared = CURVE.getSharedSecret(test.private, test.public);
-        deepStrictEqual(shared, test.shared, 'valid');
-      } else if (test.result === 'invalid') {
-        let failed = false;
-        try {
-          CURVE.getSharedSecret(test.private, test.public);
-        } catch (error) {
-          failed = true;
-        }
-        deepStrictEqual(failed, true, 'invalid');
-      } else throw new Error('unknown test result');
-    }
-  }
-});
-
 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' };
 import { default as ecdh_secp256k1_test } from './wycheproof/ecdh_secp256k1_test.json' assert { type: 'json' };
 import { default as ecdh_secp384r1_test } from './wycheproof/ecdh_secp384r1_test.json' assert { type: 'json' };
 import { default as ecdh_secp521r1_test } from './wycheproof/ecdh_secp521r1_test.json' assert { type: 'json' };
-
-// More per curve tests
-const WYCHEPROOF_ECDH = {
-  P224: {
-    curve: P224,
-    tests: [ecdh_secp224r1_test],
-  },
-  P256: {
-    curve: P256,
-    tests: [ecdh_secp256r1_test],
-  },
-  secp256k1: {
-    curve: secp256k1,
-    tests: [ecdh_secp256k1_test],
-  },
-  P384: {
-    curve: P384,
-    tests: [ecdh_secp384r1_test],
-  },
-  P521: {
-    curve: P521,
-    tests: [ecdh_secp521r1_test],
-  },
-};
-
-for (const name in WYCHEPROOF_ECDH) {
-  const { curve, tests } = WYCHEPROOF_ECDH[name];
-  for (let i = 0; i < tests.length; i++) {
-    const test = tests[i];
-    for (let j = 0; j < test.testGroups.length; j++) {
-      const group = test.testGroups[j];
-      should(`Wycheproof/ECDH ${name} (${i}/${j})`, () => {
-        for (const test of group.tests) {
-          if (test.result === 'valid' || test.result === 'acceptable') {
-            try {
-              const pub = curve.Point.fromHex(test.public);
-            } catch (e) {
-              if (e.message.includes('Point.fromHex: received invalid point.')) continue;
-              throw e;
-            }
-            const shared = curve.getSharedSecret(test.private, test.public);
-            deepStrictEqual(hex(shared), test.shared, 'valid');
-          } else if (test.result === 'invalid') {
-            let failed = false;
-            try {
-              curve.getSharedSecret(test.private, test.public);
-            } catch (error) {
-              failed = true;
-            }
-            deepStrictEqual(failed, true, 'invalid');
-          } else throw new Error('unknown test result');
-        }
-      });
-    }
-  }
-}
-
 // Tests with custom hashes
 import { default as secp224r1_sha224_test } from './wycheproof/ecdsa_secp224r1_sha224_test.json' assert { type: 'json' };
 import { default as secp224r1_sha256_test } from './wycheproof/ecdsa_secp224r1_sha256_test.json' assert { type: 'json' };
@@ -199,6 +46,123 @@ import { sha3_224, sha3_256, sha3_384, sha3_512 } from '@noble/hashes/sha3';
 import { sha512, sha384 } from '@noble/hashes/sha512';
 import { sha224, sha256 } from '@noble/hashes/sha256';
 
+const hex = bytesToHex;
+
+// prettier-ignore
+const NIST = {
+  secp192r1, P192,
+  secp224r1, P224,
+  secp256r1, P256,
+  secp384r1, P384,
+  secp521r1, P521,
+  secp256k1,
+};
+
+describe('NIST curves', () => {});
+should('fields', () => {
+  const vectors = {
+    secp192r1: 0xfffffffffffffffffffffffffffffffeffffffffffffffffn,
+    secp224r1: 0xffffffffffffffffffffffffffffffff000000000000000000000001n,
+    secp256r1: 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffffn,
+    secp256k1: 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fn,
+    secp384r1:
+      0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffffn,
+    secp521r1:
+      0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffn,
+  };
+  for (const n in vectors) deepStrictEqual(NIST[n].CURVE.Fp.ORDER, vectors[n]);
+});
+
+describe('wycheproof ECDH', () => {
+  for (const group of ecdh.testGroups) {
+    // // Tested in secp256k1.test.js
+    // if (group.key.curve === 'secp256k1') continue;
+    // We don't have SHA-224
+    const CURVE = NIST[group.curve];
+    if (!CURVE) continue;
+    should(group.curve, () => {
+      for (const test of group.tests) {
+        if (test.result === 'valid' || test.result === 'acceptable') {
+          try {
+            const pub = CURVE.ProjectivePoint.fromHex(test.public);
+          } catch (e) {
+            // Our strict validation filter doesn't let weird-length DER vectors
+            if (e.message.startsWith('Point of length')) continue;
+            throw e;
+          }
+          const shared = CURVE.getSharedSecret(test.private, test.public);
+          deepStrictEqual(shared, test.shared, 'valid');
+        } else if (test.result === 'invalid') {
+          let failed = false;
+          try {
+            CURVE.getSharedSecret(test.private, test.public);
+          } catch (error) {
+            failed = true;
+          }
+          deepStrictEqual(failed, true, 'invalid');
+        } else throw new Error('unknown test result');
+      }
+    });
+  }
+
+  // More per curve tests
+  const WYCHEPROOF_ECDH = {
+    P224: {
+      curve: P224,
+      tests: [ecdh_secp224r1_test],
+    },
+    P256: {
+      curve: P256,
+      tests: [ecdh_secp256r1_test],
+    },
+    secp256k1: {
+      curve: secp256k1,
+      tests: [ecdh_secp256k1_test],
+    },
+    P384: {
+      curve: P384,
+      tests: [ecdh_secp384r1_test],
+    },
+    P521: {
+      curve: P521,
+      tests: [ecdh_secp521r1_test],
+    },
+  };
+
+  for (const name in WYCHEPROOF_ECDH) {
+    const { curve, tests } = WYCHEPROOF_ECDH[name];
+    for (let i = 0; i < tests.length; i++) {
+      const test = tests[i];
+      for (let j = 0; j < test.testGroups.length; j++) {
+        const group = test.testGroups[j];
+        should(`additional ${name} (${i}/${j})`, () => {
+          for (const test of group.tests) {
+            if (test.result === 'valid' || test.result === 'acceptable') {
+              try {
+                const pub = curve.ProjectivePoint.fromHex(test.public);
+              } catch (e) {
+                // Our strict validation filter doesn't let weird-length DER vectors
+                if (e.message.includes('Point of length')) continue;
+                throw e;
+              }
+              const shared = curve.getSharedSecret(test.private, test.public);
+              deepStrictEqual(hex(shared), test.shared, 'valid');
+            } else if (test.result === 'invalid') {
+              let failed = false;
+              try {
+                curve.getSharedSecret(test.private, test.public);
+              } catch (error) {
+                failed = true;
+              }
+              deepStrictEqual(failed, true, 'invalid');
+            } else throw new Error('unknown test result');
+          }
+        });
+      }
+    }
+  }
+});
+
 const WYCHEPROOF_ECDSA = {
   P224: {
     curve: P224,
@@ -232,7 +196,6 @@ const WYCHEPROOF_ECDSA = {
   secp256k1: {
     curve: secp256k1,
     hashes: {
-      // TODO: debug why fails, can be bug
       sha256: {
         hash: sha256,
         tests: [secp256k1_sha256_test],
@@ -309,31 +272,33 @@ const WYCHEPROOF_ECDSA = {
 };
 
 function runWycheproof(name, CURVE, group, index) {
-  const pubKey = CURVE.Point.fromHex(group.key.uncompressed);
+  const pubKey = CURVE.ProjectivePoint.fromHex(group.key.uncompressed);
   deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
   deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
+  const pubR = pubKey.toRawBytes();
   for (const test of group.tests) {
     const m = CURVE.CURVE.hash(hexToBytes(test.msg));
+    const { sig } = test;
 
     if (test.result === 'valid' || test.result === 'acceptable') {
       try {
-        CURVE.Signature.fromDER(test.sig);
+        CURVE.Signature.fromDER(sig);
       } catch (e) {
         // Some tests has invalid signature which we don't accept
         if (e.message.includes('Invalid signature: incorrect length')) continue;
         throw e;
       }
-      const verified = CURVE.verify(test.sig, m, pubKey);
+      const verified = CURVE.verify(sig, m, pubR);
       if (name === 'secp256k1') {
         // lowS: true for secp256k1
-        deepStrictEqual(verified, !CURVE.Signature.fromDER(test.sig).hasHighS(), `${index}: valid`);
+        deepStrictEqual(verified, !CURVE.Signature.fromDER(sig).hasHighS(), `${index}: valid`);
       } else {
         deepStrictEqual(verified, true, `${index}: valid`);
       }
     } else if (test.result === 'invalid') {
       let failed = false;
       try {
-        failed = !CURVE.verify(test.sig, m, pubKey);
+        failed = !CURVE.verify(sig, m, pubR);
       } catch (error) {
         failed = true;
       }
@@ -342,42 +307,85 @@ function runWycheproof(name, CURVE, group, index) {
   }
 }
 
-for (const name in WYCHEPROOF_ECDSA) {
+describe('wycheproof ECDSA', () => {
-  const { curve, hashes } = WYCHEPROOF_ECDSA[name];
+  should('generic', () => {
-  describe('Wycheproof/WYCHEPROOF_ECDSA', () => {
+    for (const group of ecdsa.testGroups) {
-    for (const hName in hashes) {
+      // Tested in secp256k1.test.js
-      const { hash, tests } = hashes[hName];
+      if (group.key.curve === 'secp256k1') continue;
-      const CURVE = curve.create(hash);
+      let CURVE = NIST[group.key.curve];
-      should(`${name}/${hName}`, () => {
+      if (!CURVE) continue;
-        for (let i = 0; i < tests.length; i++) {
+      if (group.key.curve === 'secp224r1' && group.sha !== 'SHA-224') {
-          const groups = tests[i].testGroups;
+        if (group.sha === 'SHA-256') CURVE = CURVE.create(sha256);
-          for (let j = 0; j < groups.length; j++) {
+      }
-            const group = groups[j];
+      const pubKey = CURVE.ProjectivePoint.fromHex(group.key.uncompressed);
-            runWycheproof(name, CURVE, group, `${i}/${j}`);
+      deepStrictEqual(pubKey.x, BigInt(`0x${group.key.wx}`));
-          }
+      deepStrictEqual(pubKey.y, BigInt(`0x${group.key.wy}`));
+      for (const test of group.tests) {
+        if (['Hash weaker than DL-group'].includes(test.comment)) {
+          continue;
         }
-      });
+        const m = CURVE.CURVE.hash(hexToBytes(test.msg));
+        if (test.result === 'valid' || test.result === 'acceptable') {
+          try {
+            CURVE.Signature.fromDER(test.sig);
+          } catch (e) {
+            // Some test has invalid signature which we don't accept
+            if (e.message.includes('Invalid signature: incorrect length')) continue;
+            throw e;
+          }
+          const verified = CURVE.verify(test.sig, m, pubKey.toHex());
+          deepStrictEqual(verified, true, 'valid');
+        } else if (test.result === 'invalid') {
+          let failed = false;
+          try {
+            failed = !CURVE.verify(test.sig, m, pubKey.toHex());
+          } catch (error) {
+            failed = true;
+          }
+          deepStrictEqual(failed, true, 'invalid');
+        } else throw new Error('unknown test result');
+      }
     }
   });
-}
+  for (const name in WYCHEPROOF_ECDSA) {
+    const { curve, hashes } = WYCHEPROOF_ECDSA[name];
+    describe(name, () => {
+      for (const hName in hashes) {
+        const { hash, tests } = hashes[hName];
+        const CURVE = curve.create(hash);
+        should(`${name}/${hName}`, () => {
+          for (let i = 0; i < tests.length; i++) {
+            const groups = tests[i].testGroups;
+            for (let j = 0; j < groups.length; j++) {
+              const group = groups[j];
+              runWycheproof(name, CURVE, group, `${i}/${j}`);
+            }
+          }
+        });
+      }
+    });
+  }
+});
 
 const hexToBigint = (hex) => BigInt(`0x${hex}`);
-should('RFC6979', () => {
+describe('RFC6979', () => {
   for (const v of rfc6979) {
-    const curve = NIST[v.curve];
+    should(v.curve, () => {
-    deepStrictEqual(curve.CURVE.n, hexToBigint(v.q));
+      const curve = NIST[v.curve];
-    const pubKey = curve.getPublicKey(v.private);
+      deepStrictEqual(curve.CURVE.n, hexToBigint(v.q));
-    const pubPoint = curve.Point.fromHex(pubKey);
+      const pubKey = curve.getPublicKey(v.private);
-    deepStrictEqual(pubPoint.x, hexToBigint(v.Ux));
+      const pubPoint = curve.ProjectivePoint.fromHex(pubKey);
-    deepStrictEqual(pubPoint.y, hexToBigint(v.Uy));
+      deepStrictEqual(pubPoint.x, hexToBigint(v.Ux));
-    for (const c of v.cases) {
+      deepStrictEqual(pubPoint.y, hexToBigint(v.Uy));
-      const h = curve.CURVE.hash(c.message);
+      for (const c of v.cases) {
-      const sigObj = curve.sign(h, v.private);
+        const h = curve.CURVE.hash(c.message);
-      deepStrictEqual(sigObj.r, hexToBigint(c.r), 'R');
+        const sigObj = curve.sign(h, v.private);
-      deepStrictEqual(sigObj.s, hexToBigint(c.s), 'S');
+        deepStrictEqual(sigObj.r, hexToBigint(c.r), 'R');
-      deepStrictEqual(curve.verify(sigObj.toDERRawBytes(), h, pubKey), true, 'verify(1)');
+        deepStrictEqual(sigObj.s, hexToBigint(c.s), 'S');
-      deepStrictEqual(curve.verify(sigObj, h, pubKey), true, 'verify(2)');
+        deepStrictEqual(curve.verify(sigObj.toDERRawBytes(), h, pubKey), true, 'verify(1)');
-    }
+        deepStrictEqual(curve.verify(sigObj, h, pubKey), true, 'verify(2)');
+      }
+    });
   }
 });
 

test/poseidon.test.js

@@ -0,0 +1,375 @@
+import { deepStrictEqual, throws } from 'assert';
+import { should, describe } from 'micro-should';
+import * as poseidon from '../lib/esm/abstract/poseidon.js';
+import * as stark from '../lib/esm/stark.js';
+import * as mod from '../lib/esm/abstract/modular.js';
+import { default as pvectors } from './vectors/poseidon.json' assert { type: 'json' };
+const { st1, st2, st3, st4 } = pvectors;
+
+describe('Stark', () => {
+  should('poseidonMdsMatrixUnsafe', () => {
+    const matrix = [
+      [
+        2778560475384578201077246683568670693743746494974613838537993780462451025202n,
+        1175299404131241652930097281601393692628174430208909163156444576599667748918n,
+        459930634481240293374476654621049426021644833445120509139335338093973616187n,
+      ],
+      [
+        2699370377471722242958186781613316939129713429759631049128040020458992590651n,
+        1488831960940040807419416081499284128899207850625157044437836107358246188803n,
+        3405112981980800875534081635548548562399171531483475155039499736396630179833n,
+      ],
+
+      [
+        1860070716810022053527433635909648527418980081585070357136946388030401399342n,
+        2606527819893847364468965441606872534271438365089422719512470850627617054272n,
+        2715867691630559973784374069384091521307896505826088878858115800121387149186n,
+      ],
+    ];
+    deepStrictEqual(stark._poseidonMDS(stark.Fp251, 'HadesMDS', 3, 0), matrix);
+  });
+
+  should('HadesPermutation', () => {
+    deepStrictEqual(
+      stark.poseidonSmall([
+        4379311784651118086770398084575492314150568148003994287303975907890254409956n,
+        5329163686893598957822497554130545759427567507701132391649270915797304266381n,
+        1081797873147645298856697595691862435558345225505029083672323747888463248125n,
+      ]),
+      [
+        1342232677189718451682683203787286758407058155581807117466384919996430343159n,
+        380853961496438693334706417244065195303131974442781224856980145160981376662n,
+        1919212703304954644851339421413808305076993030243665926017858381407659820613n,
+      ]
+    );
+  });
+  should('HadesPermutation (custom)', () => {
+    const h = stark.poseidonCreate({
+      Fp: stark.Fp251,
+      rate: 2,
+      capacity: 1,
+      roundsFull: 8,
+      roundsPartial: 83,
+    });
+    deepStrictEqual(
+      h([
+        4379311784651118086770398084575492314150568148003994287303975907890254409956n,
+        5329163686893598957822497554130545759427567507701132391649270915797304266381n,
+        1081797873147645298856697595691862435558345225505029083672323747888463248125n,
+      ]),
+      [
+        2864461397224564530993577865807718592436235694918699912757414692654057505365n,
+        1576206983934669422583425346343473837630736957734769961428118554039862202613n,
+        1607006208879950753054674913136990521997740361932184292107790666308092455675n,
+      ]
+    );
+  });
+  should('HadesPermutation (custom, Fp253)', () => {
+    const h = stark.poseidonCreate({
+      Fp: stark.Fp253,
+      rate: 2,
+      capacity: 1,
+      roundsFull: 8,
+      roundsPartial: 83,
+    });
+    deepStrictEqual(
+      h([
+        4379311784651118086770398084575492314150568148003994287303975907890254409956n,
+        5329163686893598957822497554130545759427567507701132391649270915797304266381n,
+        1081797873147645298856697595691862435558345225505029083672323747888463248125n,
+      ]),
+      [
+        11142411210283675631592374649001218595612035205233832049083369488791454026844n,
+        98304838055259883374145304326851527594402230455144399354815642835291000581n,
+        8643534790068701259242695637167859384191499281344739826454631748110172472997n,
+      ]
+    );
+  });
+  should('PoseidonHash', () => {
+    deepStrictEqual(
+      stark.poseidonHash(
+        4379311784651118086770398084575492314150568148003994287303975907890254409956n,
+        5329163686893598957822497554130545759427567507701132391649270915797304266381n
+      ),
+      2457757238178986673695038558497063891521456354791980183317105434323761563347n
+    );
+  });
+  should('PoseidonHash (custom)', () => {
+    const h = stark.poseidonCreate({
+      Fp: stark.Fp251,
+      rate: 2,
+      capacity: 1,
+      roundsFull: 8,
+      roundsPartial: 83,
+    });
+    deepStrictEqual(
+      stark.poseidonHash(
+        4379311784651118086770398084575492314150568148003994287303975907890254409956n,
+        5329163686893598957822497554130545759427567507701132391649270915797304266381n,
+        h
+      ),
+      654164301216498483748450956182386165976155551413834652546305861430119544536n
+    );
+  });
+  should('PoseidonHash (custom, Fp253)', () => {
+    const h = stark.poseidonCreate({
+      Fp: stark.Fp253,
+      rate: 2,
+      capacity: 1,
+      roundsFull: 8,
+      roundsPartial: 83,
+    });
+    deepStrictEqual(
+      stark.poseidonHash(
+        4379311784651118086770398084575492314150568148003994287303975907890254409956n,
+        5329163686893598957822497554130545759427567507701132391649270915797304266381n,
+        h
+      ),
+      9557424461253897982213839283192966960594440725760392861778010931094267239786n
+    );
+  });
+});
+// Official vectors: https://extgit.iaik.tugraz.at/krypto/hadeshash/-/blob/master/code/test_vectors.txt
+
+should('poseidonperm_x5_255_3', () => {
+  const Fp = mod.Fp(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001'));
+
+  const mds = [
+    [
+      0x3d955d6c02fe4d7cb500e12f2b55eff668a7b4386bd27413766713c93f2acfcdn,
+      0x3798866f4e6058035dcf8addb2cf1771fac234bcc8fc05d6676e77e797f224bfn,
+      0x2c51456a7bf2467eac813649f3f25ea896eac27c5da020dae54a6e640278fda2n,
+    ],
+    [
+      0x20088ca07bbcd7490a0218ebc0ecb31d0ea34840e2dc2d33a1a5adfecff83b43n,
+      0x1d04ba0915e7807c968ea4b1cb2d610c7f9a16b4033f02ebacbb948c86a988c3n,
+      0x5387ccd5729d7acbd09d96714d1d18bbd0eeaefb2ddee3d2ef573c9c7f953307n,
+    ],
+    [
+      0x1e208f585a72558534281562cad89659b428ec61433293a8d7f0f0e38a6726acn,
+      0x0455ebf862f0b60f69698e97d36e8aafd4d107cae2b61be1858b23a3363642e0n,
+      0x569e2c206119e89455852059f707370e2c1fc9721f6c50991cedbbf782daef54n,
+    ],
+  ];
+
+  const t = 3;
+
+  const roundConstants = poseidon.splitConstants(st1.map(BigInt), t);
+
+  const poseidon_x5_255_3 = poseidon.poseidon({
+    Fp,
+    t,
+    roundsFull: 8,
+    roundsPartial: 57,
+    mds,
+    roundConstants,
+  });
+  deepStrictEqual(
+    poseidon_x5_255_3([
+      0x0000000000000000000000000000000000000000000000000000000000000000n,
+      0x0000000000000000000000000000000000000000000000000000000000000001n,
+      0x0000000000000000000000000000000000000000000000000000000000000002n,
+    ]),
+    [
+      0x28ce19420fc246a05553ad1e8c98f5c9d67166be2c18e9e4cb4b4e317dd2a78an,
+      0x51f3e312c95343a896cfd8945ea82ba956c1118ce9b9859b6ea56637b4b1ddc4n,
+      0x3b2b69139b235626a0bfb56c9527ae66a7bf486ad8c11c14d1da0c69bbe0f79an,
+    ]
+  );
+});
+
+should('poseidonperm_x5_255_5', () => {
+  const Fp = mod.Fp(0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n);
+  const t = 5;
+
+  const mds = [
+    [
+      0x354423b163d1078b0dd645be56316e34a9b98e52dcf9f469be44b108be46c107n,
+      0x44778737e8bc1154aca1cd92054a1e5b83808403705f7d54da88bbd1920e1053n,
+      0x5872eefb5ab6b2946556524168a2aebb69afd513a2fff91e50167b1f6e4055e0n,
+      0x43dff85b25129835819bc8c95819f1a34136f6114e900cd3656e1b9e0e13f86an,
+      0x07803d2ffe72940596803f244ac090a9cf2d3616546520bc360c7eed0b81cbf8n,
+    ],
+    [
+      0x45d6bc4b818e2b9a53e0e2c0a08f70c34167fd8128e05ac800651ddfee0932d1n,
+      0x08317abbb9e5046b22dfb79e64c8184855107c1d95dddd2b63ca10dddea9ff1an,
+      0x1bb80eba77c5dcffafb55ccba4ae39ac8f94a054f2a0ee3006b362f709d5e470n,
+      0x038e75bdcf8be7fd3a1e844c4de7333531bbd5a8d2c3779627df88e7480e7c5cn,
+      0x2dd797a699e620ea6b31b91ba3fad4a82f40cffb3e8a30c0b7a546ff69a9002bn,
+    ],
+    [
+      0x4b906f9ee339b196e958e3541b555b4b53e540a113b2f1cabba627be16eb5608n,
+      0x605f0c707b82ef287f46431f9241fe4acf0b7ddb151803cbcf1e7bbd27c3e974n,
+      0x100c514bf38f6ff10df1c83bb428397789cfff7bb0b1280f52343861e8c8737en,
+      0x2d40ce8af8a252f5611701c3d6b1e517161d0549ef27f443570c81fcdfe3706bn,
+      0x3e6418bdf0313f59afc5f40b4450e56881110ea9a0532e8092efb06a12a8b0f1n,
+    ],
+    [
+      0x71788bf7f6c0cebae5627c5629d012d5fba52428d1f25cdaa0a7434e70e014d0n,
+      0x55cc73296f7e7d26d10b9339721d7983ca06145675255025ab00b34342557db7n,
+      0x0f043b29be2def73a6c6ec92168ea4b47bc9f434a5e6b5d48677670a7ca4d285n,
+      0x62ccc9cdfed859a610f103d74ea04dec0f6874a9b36f3b4e9b47fd73368d45b4n,
+      0x55fb349dd6200b34eaba53a67e74f47d08e473da139dc47e44df50a26423d2d1n,
+    ],
+    [
+      0x45bfbe5ed2f4a01c13b15f20bba00ff577b1154a81b3f318a6aff86369a66735n,
+      0x6a008906685587af05dce9ad2c65ea1d42b1ec32609597bd00c01f58443329efn,
+      0x004feebd0dbdb9b71176a1d43c9eb495e16419382cdf7864e4bce7b37440cd58n,
+      0x09f080180ce23a5aef3a07e60b28ffeb2cf1771aefbc565c2a3059b39ed82f43n,
+      0x2f7126ddc54648ab6d02493dbe9907f29f4ef3967ad8cd609f0d9467e1694607n,
+    ],
+  ];
+
+  const roundConstants = poseidon.splitConstants(st2.map(BigInt), t);
+
+  const poseidon_x5_255_5 = poseidon.poseidon({
+    Fp,
+    t,
+    roundsFull: 8,
+    roundsPartial: 60,
+    mds,
+    roundConstants,
+  });
+
+  deepStrictEqual(
+    poseidon_x5_255_5([
+      0x0000000000000000000000000000000000000000000000000000000000000000n,
+      0x0000000000000000000000000000000000000000000000000000000000000001n,
+      0x0000000000000000000000000000000000000000000000000000000000000002n,
+      0x0000000000000000000000000000000000000000000000000000000000000003n,
+      0x0000000000000000000000000000000000000000000000000000000000000004n,
+    ]),
+    [
+      0x2a918b9c9f9bd7bb509331c81e297b5707f6fc7393dcee1b13901a0b22202e18n,
+      0x65ebf8671739eeb11fb217f2d5c5bf4a0c3f210e3f3cd3b08b5db75675d797f7n,
+      0x2cc176fc26bc70737a696a9dfd1b636ce360ee76926d182390cdb7459cf585cen,
+      0x4dc4e29d283afd2a491fe6aef122b9a968e74eff05341f3cc23fda1781dcb566n,
+      0x03ff622da276830b9451b88b85e6184fd6ae15c8ab3ee25a5667be8592cce3b1n,
+    ]
+  );
+});
+
+should('poseidonperm_x5_254_3', () => {
+  const Fp = mod.Fp(0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001n);
+  const t = 3;
+
+  const mds = [
+    [
+      0x109b7f411ba0e4c9b2b70caf5c36a7b194be7c11ad24378bfedb68592ba8118bn,
+      0x16ed41e13bb9c0c66ae119424fddbcbc9314dc9fdbdeea55d6c64543dc4903e0n,
+      0x2b90bba00fca0589f617e7dcbfe82e0df706ab640ceb247b791a93b74e36736dn,
+    ],
+    [
+      0x2969f27eed31a480b9c36c764379dbca2cc8fdd1415c3dded62940bcde0bd771n,
+      0x2e2419f9ec02ec394c9871c832963dc1b89d743c8c7b964029b2311687b1fe23n,
+      0x101071f0032379b697315876690f053d148d4e109f5fb065c8aacc55a0f89bfan,
+    ],
+    [
+      0x143021ec686a3f330d5f9e654638065ce6cd79e28c5b3753326244ee65a1b1a7n,
+      0x176cc029695ad02582a70eff08a6fd99d057e12e58e7d7b6b16cdfabc8ee2911n,
+      0x19a3fc0a56702bf417ba7fee3802593fa644470307043f7773279cd71d25d5e0n,
+    ],
+  ];
+
+  const roundConstants = poseidon.splitConstants(st3.map(BigInt), t);
+
+  const poseidon_x5_254_3 = poseidon.poseidon({
+    Fp,
+    t,
+    roundsFull: 8,
+    roundsPartial: 57,
+    mds,
+    roundConstants,
+  });
+
+  deepStrictEqual(
+    poseidon_x5_254_3([
+      0x0000000000000000000000000000000000000000000000000000000000000000n,
+      0x0000000000000000000000000000000000000000000000000000000000000001n,
+      0x0000000000000000000000000000000000000000000000000000000000000002n,
+    ]),
+    [
+      0x115cc0f5e7d690413df64c6b9662e9cf2a3617f2743245519e19607a4417189an,
+      0x0fca49b798923ab0239de1c9e7a4a9a2210312b6a2f616d18b5a87f9b628ae29n,
+      0x0e7ae82e40091e63cbd4f16a6d16310b3729d4b6e138fcf54110e2867045a30cn,
+    ]
+  );
+});
+
+should('poseidonperm_x5_254_5', () => {
+  const Fp = mod.Fp(0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001n);
+  const t = 5;
+
+  const mds = [
+    [
+      0x251e7fdf99591080080b0af133b9e4369f22e57ace3cd7f64fc6fdbcf38d7da1n,
+      0x25fb50b65acf4fb047cbd3b1c17d97c7fe26ea9ca238d6e348550486e91c7765n,
+      0x293d617d7da72102355f39ebf62f91b06deb5325f367a4556ea1e31ed5767833n,
+      0x104d0295ab00c85e960111ac25da474366599e575a9b7edf6145f14ba6d3c1c4n,
+      0x0aaa35e2c84baf117dea3e336cd96a39792b3813954fe9bf3ed5b90f2f69c977n,
+    ],
+    [
+      0x2a70b9f1d4bbccdbc03e17c1d1dcdb02052903dc6609ea6969f661b2eb74c839n,
+      0x281154651c921e746315a9934f1b8a1bba9f92ad8ef4b979115b8e2e991ccd7an,
+      0x28c2be2f8264f95f0b53c732134efa338ccd8fdb9ee2b45fb86a894f7db36c37n,
+      0x21888041e6febd546d427c890b1883bb9b626d8cb4dc18dcc4ec8fa75e530a13n,
+      0x14ddb5fada0171db80195b9592d8cf2be810930e3ea4574a350d65e2cbff4941n,
+    ],
+    [
+      0x2f69a7198e1fbcc7dea43265306a37ed55b91bff652ad69aa4fa8478970d401dn,
+      0x001c1edd62645b73ad931ab80e37bbb267ba312b34140e716d6a3747594d3052n,
+      0x15b98ce93e47bc64ce2f2c96c69663c439c40c603049466fa7f9a4b228bfc32bn,
+      0x12c7e2adfa524e5958f65be2fbac809fcba8458b28e44d9265051de33163cf9cn,
+      0x2efc2b90d688134849018222e7b8922eaf67ce79816ef468531ec2de53bbd167n,
+    ],
+    [
+      0x0c3f050a6bf5af151981e55e3e1a29a13c3ffa4550bd2514f1afd6c5f721f830n,
+      0x0dec54e6dbf75205fa75ba7992bd34f08b2efe2ecd424a73eda7784320a1a36en,
+      0x1c482a25a729f5df20225815034b196098364a11f4d988fb7cc75cf32d8136fan,
+      0x2625ce48a7b39a4252732624e4ab94360812ac2fc9a14a5fb8b607ae9fd8514an,
+      0x07f017a7ebd56dd086f7cd4fd710c509ed7ef8e300b9a8bb9fb9f28af710251fn,
+    ],
+    [
+      0x2a20e3a4a0e57d92f97c9d6186c6c3ea7c5e55c20146259be2f78c2ccc2e3595n,
+      0x1049f8210566b51faafb1e9a5d63c0ee701673aed820d9c4403b01feb727a549n,
+      0x02ecac687ef5b4b568002bd9d1b96b4bef357a69e3e86b5561b9299b82d69c8en,
+      0x2d3a1aea2e6d44466808f88c9ba903d3bdcb6b58ba40441ed4ebcf11bbe1e37bn,
+      0x14074bb14c982c81c9ad171e4f35fe49b39c4a7a72dbb6d9c98d803bfed65e64n,
+    ],
+  ];
+
+  const roundConstants = poseidon.splitConstants(st4.map(BigInt), t);
+
+  const poseidon_x5_254_5 = poseidon.poseidon({
+    Fp,
+    t,
+    roundsFull: 8,
+    roundsPartial: 60,
+    mds,
+    roundConstants,
+  });
+
+  deepStrictEqual(
+    poseidon_x5_254_5([
+      0x0000000000000000000000000000000000000000000000000000000000000000n,
+      0x0000000000000000000000000000000000000000000000000000000000000001n,
+      0x0000000000000000000000000000000000000000000000000000000000000002n,
+      0x0000000000000000000000000000000000000000000000000000000000000003n,
+      0x0000000000000000000000000000000000000000000000000000000000000004n,
+    ]),
+    [
+      0x299c867db6c1fdd79dcefa40e4510b9837e60ebb1ce0663dbaa525df65250465n,
+      0x1148aaef609aa338b27dafd89bb98862d8bb2b429aceac47d86206154ffe053dn,
+      0x24febb87fed7462e23f6665ff9a0111f4044c38ee1672c1ac6b0637d34f24907n,
+      0x0eb08f6d809668a981c186beaf6110060707059576406b248e5d9cf6e78b3d3en,
+      0x07748bc6877c9b82c8b98666ee9d0626ec7f5be4205f79ee8528ef1c4a376fc7n,
+    ]
+  );
+});
+// Startadperm is unsupported, since it is non prime field
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/secp256k1.test.js

@@ -1,6 +1,7 @@
 import * as fc from 'fast-check';
 import { secp256k1, schnorr } from '../lib/esm/secp256k1.js';
 import { Fp } from '../lib/esm/abstract/modular.js';
+import { bytesToNumberBE, ensureBytes, numberToBytesBE } from '../lib/esm/abstract/utils.js';
 import { readFileSync } from 'fs';
 import { default as ecdsa } from './vectors/ecdsa.json' assert { type: 'json' };
 import { default as ecdh } from './vectors/ecdh.json' assert { type: 'json' };
@@ -13,6 +14,7 @@ import { hexToBytes, bytesToHex } from '@noble/hashes/utils';
 
 const hex = bytesToHex;
 const secp = secp256k1;
+const Point = secp.ProjectivePoint;
 const privatesTxt = readFileSync('./test/vectors/privates-2.txt', 'utf-8');
 const schCsv = readFileSync('./test/vectors/schnorr.csv', 'utf-8');
 
@@ -24,7 +26,7 @@ const toBEHex = (n) => n.toString(16).padStart(64, '0');
 
 function hexToNumber(hex) {
   if (typeof hex !== 'string') {
-    throw new TypeError('hexToNumber: expected string, got ' + typeof hex);
+    throw new Error('hexToNumber: expected string, got ' + typeof hex);
   }
   // Big Endian
   return BigInt(`0x${hex}`);
@@ -37,15 +39,15 @@ describe('secp256k1', () => {
       .filter((line) => line)
       .map((line) => line.split(':'));
     for (let [priv, x, y] of data) {
-      const point = secp.Point.fromPrivateKey(BigInt(priv));
+      const point = Point.fromPrivateKey(BigInt(priv));
       deepStrictEqual(toBEHex(point.x), x);
       deepStrictEqual(toBEHex(point.y), y);
 
-      const point2 = secp.Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv))));
+      const point2 = Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv))));
       deepStrictEqual(toBEHex(point2.x), x);
       deepStrictEqual(toBEHex(point2.y), y);
 
-      const point3 = secp.Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv)))));
+      const point3 = Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv)))));
       deepStrictEqual(toBEHex(point3.x), x);
       deepStrictEqual(toBEHex(point3.y), y);
     }
@@ -62,106 +64,108 @@ describe('secp256k1', () => {
       .filter((line) => line)
       .map((line) => line.split(':'));
     for (let [priv, x, y] of data) {
-      const point = secp.Point.fromPrivateKey(BigInt(priv));
+      const point = Point.fromPrivateKey(BigInt(priv));
       deepStrictEqual(toBEHex(point.x), x);
       deepStrictEqual(toBEHex(point.y), y);
 
-      const point2 = secp.Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv))));
+      const point2 = Point.fromHex(secp.getPublicKey(toBEHex(BigInt(priv))));
       deepStrictEqual(toBEHex(point2.x), x);
       deepStrictEqual(toBEHex(point2.y), y);
 
-      const point3 = secp.Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv)))));
+      const point3 = Point.fromHex(secp.getPublicKey(hexToBytes(toBEHex(BigInt(priv)))));
       deepStrictEqual(toBEHex(point3.x), x);
       deepStrictEqual(toBEHex(point3.y), y);
     }
   });
 
-  should('Point.isValidPoint()', () => {
+  describe('Point', () => {
-    for (const vector of points.valid.isPoint) {
+    should('fromHex() assertValidity', () => {
-      const { P, expected } = vector;
+      for (const vector of points.valid.isPoint) {
-      if (expected) {
+        const { P, expected } = vector;
-        secp.Point.fromHex(P);
+        if (expected) {
-      } else {
+          Point.fromHex(P);
-        throws(() => secp.Point.fromHex(P));
+        } else {
-      }
+          throws(() => Point.fromHex(P));
-    }
-  });
-
-  should('Point.fromPrivateKey()', () => {
-    for (const vector of points.valid.pointFromScalar) {
-      const { d, expected } = vector;
-      let p = secp.Point.fromPrivateKey(d);
-      deepStrictEqual(p.toHex(true), expected);
-    }
-  });
-
-  should('Point#toHex(compressed)', () => {
-    for (const vector of points.valid.pointCompress) {
-      const { P, compress, expected } = vector;
-      let p = secp.Point.fromHex(P);
-      deepStrictEqual(p.toHex(compress), expected);
-    }
-  });
-
-  should('Point#toHex() roundtrip (failed case)', () => {
-    const point1 =
-      secp.Point.fromPrivateKey(
-        88572218780422190464634044548753414301110513745532121983949500266768436236425n
-      );
-    // const hex = point1.toHex(true);
-    // deepStrictEqual(secp.Point.fromHex(hex).toHex(true), hex);
-  });
-
-  should('Point#toHex() roundtrip', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (x) => {
-        const point1 = secp.Point.fromPrivateKey(x);
-        const hex = point1.toHex(true);
-        deepStrictEqual(secp.Point.fromHex(hex).toHex(true), hex);
-      })
-    );
-  });
-
-  should('Point#add(other)', () => {
-    for (const vector of points.valid.pointAdd) {
-      const { P, Q, expected } = vector;
-      let p = secp.Point.fromHex(P);
-      let q = secp.Point.fromHex(Q);
-      if (expected) {
-        deepStrictEqual(p.add(q).toHex(true), expected);
-      } else {
-        if (!p.equals(q.negate())) {
-          throws(() => p.add(q).toHex(true));
         }
       }
-    }
+    });
-  });
 
-  should('Point#multiply(privateKey)', () => {
+    should('.fromPrivateKey()', () => {
-    for (const vector of points.valid.pointMultiply) {
+      for (const vector of points.valid.pointFromScalar) {
-      const { P, d, expected } = vector;
+        const { d, expected } = vector;
-      const p = secp.Point.fromHex(P);
+        let p = Point.fromPrivateKey(d);
-      if (expected) {
+        deepStrictEqual(p.toHex(true), expected);
-        deepStrictEqual(p.multiply(hexToNumber(d)).toHex(true), expected);
-      } else {
-        throws(() => {
-          p.multiply(hexToNumber(d)).toHex(true);
-        });
       }
-    }
+    });
 
-    for (const vector of points.invalid.pointMultiply) {
+    should('#toHex(compressed)', () => {
-      const { P, d } = vector;
+      for (const vector of points.valid.pointCompress) {
-      if (hexToNumber(d) < secp.CURVE.n) {
+        const { P, compress, expected } = vector;
-        throws(() => {
+        let p = Point.fromHex(P);
-          const p = secp.Point.fromHex(P);
+        deepStrictEqual(p.toHex(compress), expected);
-          p.multiply(hexToNumber(d)).toHex(true);
-        });
       }
-    }
+    });
-    for (const num of [0n, 0, -1n, -1, 1.1]) {
+
-      throws(() => secp.Point.BASE.multiply(num));
+    should('#toHex() roundtrip (failed case)', () => {
-    }
+      const point1 =
+        Point.fromPrivateKey(
+          88572218780422190464634044548753414301110513745532121983949500266768436236425n
+        );
+      // const hex = point1.toHex(true);
+      // deepStrictEqual(Point.fromHex(hex).toHex(true), hex);
+    });
+
+    should('#toHex() roundtrip', () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (x) => {
+          const point1 = Point.fromPrivateKey(x);
+          const hex = point1.toHex(true);
+          deepStrictEqual(Point.fromHex(hex).toHex(true), hex);
+        })
+      );
+    });
+
+    should('#add(other)', () => {
+      for (const vector of points.valid.pointAdd) {
+        const { P, Q, expected } = vector;
+        let p = Point.fromHex(P);
+        let q = Point.fromHex(Q);
+        if (expected) {
+          deepStrictEqual(p.add(q).toHex(true), expected);
+        } else {
+          if (!p.equals(q.negate())) {
+            throws(() => p.add(q).toHex(true));
+          }
+        }
+      }
+    });
+
+    should('#multiply(privateKey)', () => {
+      for (const vector of points.valid.pointMultiply) {
+        const { P, d, expected } = vector;
+        const p = Point.fromHex(P);
+        if (expected) {
+          deepStrictEqual(p.multiply(hexToNumber(d)).toHex(true), expected, P);
+        } else {
+          throws(() => {
+            p.multiply(hexToNumber(d)).toHex(true);
+          });
+        }
+      }
+
+      for (const vector of points.invalid.pointMultiply) {
+        const { P, d } = vector;
+        if (hexToNumber(d) < secp.CURVE.n) {
+          throws(() => {
+            const p = Point.fromHex(P);
+            p.multiply(hexToNumber(d)).toHex(true);
+          });
+        }
+      }
+      for (const num of [0n, 0, -1n, -1, 1.1]) {
+        throws(() => Point.BASE.multiply(num));
+      }
+    });
   });
 
   // multiply() should equal multiplyUnsafe()
@@ -175,262 +179,269 @@ describe('secp256k1', () => {
   //   console.log(p0.multiply(z));
   //   console.log(secp.ProjectivePoint.normalizeZ([p0.multiplyUnsafe(z)])[0])
   // });
+  describe('Signature', () => {
+    should('.fromCompactHex() roundtrip', () => {
+      fc.assert(
+        fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
+          const sig = new secp.Signature(r, s);
+          deepStrictEqual(secp.Signature.fromCompact(sig.toCompactHex()), sig);
+        })
+      );
+    });
 
-  should('Signature.fromCompactHex() roundtrip', () => {
+    should('.fromDERHex() roundtrip', () => {
-    fc.assert(
+      fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
+        fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
-        const sig = new secp.Signature(r, s);
+          const sig = new secp.Signature(r, s);
-        deepStrictEqual(secp.Signature.fromCompact(sig.toCompactHex()), sig);
+          deepStrictEqual(secp.Signature.fromDER(sig.toDERHex()), sig);
-      })
+        })
-    );
+      );
+    });
   });
 
-  should('Signature.fromDERHex() roundtrip', () => {
+  describe('sign()', () => {
-    fc.assert(
+    should('create deterministic signatures with RFC 6979', () => {
-      fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
+      for (const vector of ecdsa.valid) {
-        const sig = new secp.Signature(r, s);
+        let usig = secp.sign(vector.m, vector.d);
-        deepStrictEqual(secp.Signature.fromDER(sig.toDERHex()), sig);
+        let sig = usig.toCompactHex();
-      })
+        const vsig = vector.signature;
-    );
+        deepStrictEqual(sig.slice(0, 64), vsig.slice(0, 64));
-  });
+        deepStrictEqual(sig.slice(64, 128), vsig.slice(64, 128));
+      }
+    });
 
-  should('sign()/should create deterministic signatures with RFC 6979', () => {
+    should('not create invalid deterministic signatures with RFC 6979', () => {
-    for (const vector of ecdsa.valid) {
-      let usig = secp.sign(vector.m, vector.d);
-      let sig = usig.toCompactHex();
-      const vsig = vector.signature;
-      deepStrictEqual(sig.slice(0, 64), vsig.slice(0, 64));
-      deepStrictEqual(sig.slice(64, 128), vsig.slice(64, 128));
-    }
-  });
-
-  should(
-    'secp256k1.sign()/should not create invalid deterministic signatures with RFC 6979',
-    () => {
       for (const vector of ecdsa.invalid.sign) {
         throws(() => secp.sign(vector.m, vector.d));
       }
-    }
+    });
-  );
 
-  should('sign()/edge cases', () => {
+    should('edge cases', () => {
-    throws(() => secp.sign());
+      throws(() => secp.sign());
-    throws(() => secp.sign(''));
+      throws(() => secp.sign(''));
+    });
+
+    should('create correct DER encoding against libsecp256k1', () => {
+      const CASES = [
+        [
+          'd1a9dc8ed4e46a6a3e5e594615ca351d7d7ef44df1e4c94c1802f3592183794b',
+          '304402203de2559fccb00c148574997f660e4d6f40605acc71267ee38101abf15ff467af02200950abdf40628fd13f547792ba2fc544681a485f2fdafb5c3b909a4df7350e6b',
+        ],
+        [
+          '5f97983254982546d3976d905c6165033976ee449d300d0e382099fa74deaf82',
+          '3045022100c046d9ff0bd2845b9aa9dff9f997ecebb31e52349f80fe5a5a869747d31dcb88022011f72be2a6d48fe716b825e4117747b397783df26914a58139c3f4c5cbb0e66c',
+        ],
+        [
+          '0d7017a96b97cd9be21cf28aada639827b2814a654a478c81945857196187808',
+          '3045022100d18990bba7832bb283e3ecf8700b67beb39acc73f4200ed1c331247c46edccc602202e5c8bbfe47ae159512c583b30a3fa86575cddc62527a03de7756517ae4c6c73',
+        ],
+      ];
+      const privKey = hexToBytes(
+        '0101010101010101010101010101010101010101010101010101010101010101'
+      );
+      for (const [msg, exp] of CASES) {
+        const res = secp.sign(msg, privKey, { extraEntropy: undefined });
+        deepStrictEqual(res.toDERHex(), exp);
+        const rs = secp.Signature.fromDER(res.toDERHex()).toCompactHex();
+        deepStrictEqual(secp.Signature.fromCompact(rs).toDERHex(), exp);
+      }
+    });
+    should('handle {extraData} option', () => {
+      const ent1 = '0000000000000000000000000000000000000000000000000000000000000000';
+      const ent2 = '0000000000000000000000000000000000000000000000000000000000000001';
+      const ent3 = '6e723d3fd94ed5d2b6bdd4f123364b0f3ca52af829988a63f8afe91d29db1c33';
+      const ent4 = 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141';
+      const ent5 = 'ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff';
+
+      for (const e of ecdsa.extraEntropy) {
+        const sign = (extraEntropy) => {
+          const s = secp.sign(e.m, e.d, { extraEntropy }).toCompactHex();
+          return s;
+        };
+        deepStrictEqual(sign(), e.signature);
+        deepStrictEqual(sign(ent1), e.extraEntropy0);
+        deepStrictEqual(sign(ent2), e.extraEntropy1);
+        deepStrictEqual(sign(ent3), e.extraEntropyRand);
+        deepStrictEqual(sign(ent4), e.extraEntropyN);
+        deepStrictEqual(sign(ent5), e.extraEntropyMax);
+      }
+    });
   });
 
-  should('sign()/should create correct DER encoding against libsecp256k1', () => {
+  describe('verify()', () => {
-    const CASES = [
+    should('verify signature', () => {
-      [
+      const MSG = '01'.repeat(32);
-        'd1a9dc8ed4e46a6a3e5e594615ca351d7d7ef44df1e4c94c1802f3592183794b',
+      const PRIV_KEY = 0x2n;
-        '304402203de2559fccb00c148574997f660e4d6f40605acc71267ee38101abf15ff467af02200950abdf40628fd13f547792ba2fc544681a485f2fdafb5c3b909a4df7350e6b',
+      const signature = secp.sign(MSG, PRIV_KEY);
-      ],
+      const publicKey = secp.getPublicKey(PRIV_KEY);
-      [
+      deepStrictEqual(publicKey.length, 33);
-        '5f97983254982546d3976d905c6165033976ee449d300d0e382099fa74deaf82',
+      deepStrictEqual(secp.verify(signature, MSG, publicKey), true);
-        '3045022100c046d9ff0bd2845b9aa9dff9f997ecebb31e52349f80fe5a5a869747d31dcb88022011f72be2a6d48fe716b825e4117747b397783df26914a58139c3f4c5cbb0e66c',
+    });
-      ],
+    should(' not verify signature with wrong public key', () => {
-      [
+      const MSG = '01'.repeat(32);
-        '0d7017a96b97cd9be21cf28aada639827b2814a654a478c81945857196187808',
+      const PRIV_KEY = '01'.repeat(32);
-        '3045022100d18990bba7832bb283e3ecf8700b67beb39acc73f4200ed1c331247c46edccc602202e5c8bbfe47ae159512c583b30a3fa86575cddc62527a03de7756517ae4c6c73',
+      const WRONG_PRIV_KEY = '02'.repeat(32);
-      ],
+      const signature = secp.sign(MSG, PRIV_KEY);
-    ];
+      const publicKey = Point.fromPrivateKey(WRONG_PRIV_KEY).toHex();
-    const privKey = hexToBytes('0101010101010101010101010101010101010101010101010101010101010101');
+      deepStrictEqual(publicKey.length, 66);
-    for (const [msg, exp] of CASES) {
+      deepStrictEqual(secp.verify(signature, MSG, publicKey), false);
-      const res = secp.sign(msg, privKey, { extraEntropy: undefined });
+    });
-      deepStrictEqual(res.toDERHex(), exp);
+    should('not verify signature with wrong hash', () => {
-      const rs = secp.Signature.fromDER(res.toDERHex()).toCompactHex();
+      const MSG = '01'.repeat(32);
-      deepStrictEqual(secp.Signature.fromCompact(rs).toDERHex(), exp);
+      const PRIV_KEY = 0x2n;
-    }
+      const WRONG_MSG = '11'.repeat(32);
-  });
+      const signature = secp.sign(MSG, PRIV_KEY);
-  should('sign()/sign ecdsa extraData', () => {
+      const publicKey = secp.getPublicKey(PRIV_KEY);
-    const ent1 = '0000000000000000000000000000000000000000000000000000000000000000';
+      deepStrictEqual(publicKey.length, 33);
-    const ent2 = '0000000000000000000000000000000000000000000000000000000000000001';
+      deepStrictEqual(secp.verify(signature, WRONG_MSG, publicKey), false);
-    const ent3 = '6e723d3fd94ed5d2b6bdd4f123364b0f3ca52af829988a63f8afe91d29db1c33';
+    });
-    const ent4 = 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141';
+    should('verify random signatures', () =>
-    const ent5 = 'ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff';
+      fc.assert(
+        fc.property(FC_BIGINT, fc.hexaString({ minLength: 64, maxLength: 64 }), (privKey, msg) => {
+          const pub = secp.getPublicKey(privKey);
+          const sig = secp.sign(msg, privKey);
+          deepStrictEqual(secp.verify(sig, msg, pub), true);
+        })
+      )
+    );
+    should('not verify signature with invalid r/s', () => {
+      const msg = new Uint8Array([
+        0xbb, 0x5a, 0x52, 0xf4, 0x2f, 0x9c, 0x92, 0x61, 0xed, 0x43, 0x61, 0xf5, 0x94, 0x22, 0xa1,
+        0xe3, 0x00, 0x36, 0xe7, 0xc3, 0x2b, 0x27, 0x0c, 0x88, 0x07, 0xa4, 0x19, 0xfe, 0xca, 0x60,
+        0x50, 0x23,
+      ]);
+      const x = 100260381870027870612475458630405506840396644859280795015145920502443964769584n;
+      const y = 41096923727651821103518389640356553930186852801619204169823347832429067794568n;
+      const r = 1n;
+      const s = 115792089237316195423570985008687907852837564279074904382605163141518162728904n;
 
-    for (const e of ecdsa.extraEntropy) {
+      const pub = new Point(x, y, 1n).toRawBytes();
-      const sign = (extraEntropy) => {
+      const signature = new secp.Signature(2n, 2n);
-        const s = secp.sign(e.m, e.d, { extraEntropy }).toCompactHex();
+      signature.r = r;
-        return s;
+      signature.s = s;
-      };
-      deepStrictEqual(sign(), e.signature);
-      deepStrictEqual(sign(ent1), e.extraEntropy0);
-      deepStrictEqual(sign(ent2), e.extraEntropy1);
-      deepStrictEqual(sign(ent3), e.extraEntropyRand);
-      deepStrictEqual(sign(ent4), e.extraEntropyN);
-      deepStrictEqual(sign(ent5), e.extraEntropyMax);
-    }
-  });
 
-  should('verify()/should verify signature', () => {
+      const verified = secp.verify(signature, msg, pub);
-    const MSG = '01'.repeat(32);
+      // Verifies, but it shouldn't, because signature S > curve order
-    const PRIV_KEY = 0x2n;
+      deepStrictEqual(verified, false);
-    const signature = secp.sign(MSG, PRIV_KEY);
+    });
-    const publicKey = secp.getPublicKey(PRIV_KEY);
+    should('not verify msg = curve order', () => {
-    deepStrictEqual(publicKey.length, 65);
+      const msg = 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141';
-    deepStrictEqual(secp.verify(signature, MSG, publicKey), true);
+      const x = 55066263022277343669578718895168534326250603453777594175500187360389116729240n;
-  });
+      const y = 32670510020758816978083085130507043184471273380659243275938904335757337482424n;
-  should('verify()/should not verify signature with wrong public key', () => {
+      const r = 104546003225722045112039007203142344920046999340768276760147352389092131869133n;
-    const MSG = '01'.repeat(32);
+      const s = 96900796730960181123786672629079577025401317267213807243199432755332205217369n;
-    const PRIV_KEY = 0x2n;
+      const pub = new Point(x, y, 1n).toRawBytes();
-    const WRONG_PRIV_KEY = 0x22n;
+      const sig = new secp.Signature(r, s);
-    const signature = secp.sign(MSG, PRIV_KEY);
+      deepStrictEqual(secp.verify(sig, msg, pub), false);
-    const publicKey = secp.Point.fromPrivateKey(WRONG_PRIV_KEY).toHex();
+    });
-    deepStrictEqual(publicKey.length, 130);
+    should('verify non-strict msg bb5a...', () => {
-    deepStrictEqual(secp.verify(signature, MSG, publicKey), false);
+      const msg = 'bb5a52f42f9c9261ed4361f59422a1e30036e7c32b270c8807a419feca605023';
-  });
+      const x = 3252872872578928810725465493269682203671229454553002637820453004368632726370n;
-  should('verify()/should not verify signature with wrong hash', () => {
+      const y = 17482644437196207387910659778872952193236850502325156318830589868678978890912n;
-    const MSG = '01'.repeat(32);
+      const r = 432420386565659656852420866390673177323n;
-    const PRIV_KEY = 0x2n;
+      const s = 115792089237316195423570985008687907852837564279074904382605163141518161494334n;
-    const WRONG_MSG = '11'.repeat(32);
+      const pub = new Point(x, y, 1n).toRawBytes();
-    const signature = secp.sign(MSG, PRIV_KEY);
+      const sig = new secp.Signature(r, s);
-    const publicKey = secp.getPublicKey(PRIV_KEY);
+      deepStrictEqual(secp.verify(sig, msg, pub, { strict: false }), true);
-    deepStrictEqual(publicKey.length, 65);
+    });
-    deepStrictEqual(secp.verify(signature, WRONG_MSG, publicKey), false);
+    should('not verify invalid deterministic signatures with RFC 6979', () => {
-  });
-  should('verify()/should verify random signatures', () =>
-    fc.assert(
-      fc.property(FC_BIGINT, fc.hexaString({ minLength: 64, maxLength: 64 }), (privKey, msg) => {
-        const pub = secp.getPublicKey(privKey);
-        const sig = secp.sign(msg, privKey);
-        deepStrictEqual(secp.verify(sig, msg, pub), true);
-      })
-    )
-  );
-  should('verify()/should not verify signature with invalid r/s', () => {
-    const msg = new Uint8Array([
-      0xbb, 0x5a, 0x52, 0xf4, 0x2f, 0x9c, 0x92, 0x61, 0xed, 0x43, 0x61, 0xf5, 0x94, 0x22, 0xa1,
-      0xe3, 0x00, 0x36, 0xe7, 0xc3, 0x2b, 0x27, 0x0c, 0x88, 0x07, 0xa4, 0x19, 0xfe, 0xca, 0x60,
-      0x50, 0x23,
-    ]);
-    const x = 100260381870027870612475458630405506840396644859280795015145920502443964769584n;
-    const y = 41096923727651821103518389640356553930186852801619204169823347832429067794568n;
-    const r = 1n;
-    const s = 115792089237316195423570985008687907852837564279074904382605163141518162728904n;
-
-    const pub = new secp.Point(x, y);
-    const signature = new secp.Signature(2n, 2n);
-    signature.r = r;
-    signature.s = s;
-
-    const verified = secp.verify(signature, msg, pub);
-    // Verifies, but it shouldn't, because signature S > curve order
-    deepStrictEqual(verified, false);
-  });
-  should('verify()/should not verify msg = curve order', () => {
-    const msg = 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141';
-    const x = 55066263022277343669578718895168534326250603453777594175500187360389116729240n;
-    const y = 32670510020758816978083085130507043184471273380659243275938904335757337482424n;
-    const r = 104546003225722045112039007203142344920046999340768276760147352389092131869133n;
-    const s = 96900796730960181123786672629079577025401317267213807243199432755332205217369n;
-    const pub = new secp.Point(x, y);
-    const sig = new secp.Signature(r, s);
-    deepStrictEqual(secp.verify(sig, msg, pub), false);
-  });
-  should('verify()/should verify non-strict msg bb5a...', () => {
-    const msg = 'bb5a52f42f9c9261ed4361f59422a1e30036e7c32b270c8807a419feca605023';
-    const x = 3252872872578928810725465493269682203671229454553002637820453004368632726370n;
-    const y = 17482644437196207387910659778872952193236850502325156318830589868678978890912n;
-    const r = 432420386565659656852420866390673177323n;
-    const s = 115792089237316195423570985008687907852837564279074904382605163141518161494334n;
-    const pub = new secp.Point(x, y);
-    const sig = new secp.Signature(r, s);
-    deepStrictEqual(secp.verify(sig, msg, pub, { strict: false }), true);
-  });
-  should(
-    'secp256k1.verify()/should not verify invalid deterministic signatures with RFC 6979',
-    () => {
       for (const vector of ecdsa.invalid.verify) {
         const res = secp.verify(vector.signature, vector.m, vector.Q);
         deepStrictEqual(res, false);
       }
-    }
+    });
-  );
+  });
 
-  // index,secret key,public key,aux_rand,message,signature,verification result,comment
+  describe('schnorr.sign()', () => {
-  const vectors = schCsv
+    // index,secret key,public key,aux_rand,message,signature,verification result,comment
-    .split('\n')
+    const vectors = schCsv
-    .map((line) => line.split(','))
+      .split('\n')
-    .slice(1, -1);
+      .map((line) => line.split(','))
-  for (let vec of vectors) {
+      .slice(1, -1);
-    const [index, sec, pub, rnd, msg, expSig, passes, comment] = vec;
+    for (let vec of vectors) {
-    should(`sign with Schnorr scheme vector ${index}`, () => {
+      const [index, sec, pub, rnd, msg, expSig, passes, comment] = vec;
-      if (sec) {
+      should(`${comment || 'vector ' + index}`, () => {
-        deepStrictEqual(hex(schnorr.getPublicKey(sec)), pub.toLowerCase());
+        if (sec) {
-        const sig = schnorr.sign(msg, sec, rnd);
+          deepStrictEqual(hex(schnorr.getPublicKey(sec)), pub.toLowerCase());
-        deepStrictEqual(hex(sig), expSig.toLowerCase());
+          const sig = schnorr.sign(msg, sec, rnd);
-        deepStrictEqual(schnorr.verify(sig, msg, pub), true);
+          deepStrictEqual(hex(sig), expSig.toLowerCase());
-      } else {
+          deepStrictEqual(schnorr.verify(sig, msg, pub), true);
-        const passed = schnorr.verify(expSig, msg, pub);
+        } else {
-        deepStrictEqual(passed, passes === 'TRUE');
+          const passed = schnorr.verify(expSig, msg, pub);
+          deepStrictEqual(passed, passes === 'TRUE');
+        }
+      });
+    }
+  });
+
+  describe('recoverPublicKey()', () => {
+    should('recover public key from recovery bit', () => {
+      const message = '00000000000000000000000000000000000000000000000000000000deadbeef';
+      const privateKey = 123456789n;
+      const publicKey = Point.fromHex(secp.getPublicKey(privateKey)).toHex(false);
+      const sig = secp.sign(message, privateKey);
+      const recoveredPubkey = sig.recoverPublicKey(message);
+      // const recoveredPubkey = secp.recoverPublicKey(message, signature, recovery);
+      deepStrictEqual(recoveredPubkey !== null, true);
+      deepStrictEqual(recoveredPubkey.toHex(false), publicKey);
+      deepStrictEqual(secp.verify(sig, message, publicKey), true);
+    });
+    should('not recover zero points', () => {
+      const msgHash = '6b8d2c81b11b2d699528dde488dbdf2f94293d0d33c32e347f255fa4a6c1f0a9';
+      const sig =
+        '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f817986b8d2c81b11b2d699528dde488dbdf2f94293d0d33c32e347f255fa4a6c1f0a9';
+      const recovery = 0;
+      throws(() => secp.recoverPublicKey(msgHash, sig, recovery));
+    });
+    should('handle all-zeros msghash', () => {
+      const privKey = secp.utils.randomPrivateKey();
+      const pub = secp.getPublicKey(privKey);
+      const zeros = '0000000000000000000000000000000000000000000000000000000000000000';
+      const sig = secp.sign(zeros, privKey);
+      const recoveredKey = sig.recoverPublicKey(zeros);
+      deepStrictEqual(recoveredKey.toRawBytes(), pub);
+    });
+    should('handle RFC 6979 vectors', () => {
+      for (const vector of ecdsa.valid) {
+        let usig = secp.sign(vector.m, vector.d);
+        let sig = usig.toDERHex();
+        const vpub = secp.getPublicKey(vector.d);
+        const recovered = usig.recoverPublicKey(vector.m);
+        deepStrictEqual(recovered.toHex(), hex(vpub));
       }
     });
-  }
-
-  should('recoverPublicKey()/should recover public key from recovery bit', () => {
-    const message = '00000000000000000000000000000000000000000000000000000000deadbeef';
-    const privateKey = 123456789n;
-    const publicKey = secp.Point.fromHex(secp.getPublicKey(privateKey)).toHex(false);
-    const sig = secp.sign(message, privateKey);
-    const recoveredPubkey = sig.recoverPublicKey(message);
-    // const recoveredPubkey = secp.recoverPublicKey(message, signature, recovery);
-    deepStrictEqual(recoveredPubkey !== null, true);
-    deepStrictEqual(recoveredPubkey.toHex(false), publicKey);
-    deepStrictEqual(secp.verify(sig, message, publicKey), true);
-  });
-  should('recoverPublicKey()/should not recover zero points', () => {
-    const msgHash = '6b8d2c81b11b2d699528dde488dbdf2f94293d0d33c32e347f255fa4a6c1f0a9';
-    const sig =
-      '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f817986b8d2c81b11b2d699528dde488dbdf2f94293d0d33c32e347f255fa4a6c1f0a9';
-    const recovery = 0;
-    throws(() => secp.recoverPublicKey(msgHash, sig, recovery));
-  });
-  should('recoverPublicKey()/should handle all-zeros msghash', () => {
-    const privKey = secp.utils.randomPrivateKey();
-    const pub = secp.getPublicKey(privKey);
-    const zeros = '0000000000000000000000000000000000000000000000000000000000000000';
-    const sig = secp.sign(zeros, privKey, { recovered: true });
-    const recoveredKey = sig.recoverPublicKey(zeros);
-    deepStrictEqual(recoveredKey.toRawBytes(), pub);
-  });
-  should('recoverPublicKey()/should handle RFC 6979 vectors', () => {
-    for (const vector of ecdsa.valid) {
-      let usig = secp.sign(vector.m, vector.d);
-      let sig = usig.toDERHex();
-      const vpub = secp.getPublicKey(vector.d);
-      const recovered = usig.recoverPublicKey(vector.m);
-      deepStrictEqual(recovered.toHex(), hex(vpub));
-    }
   });
 
-  // TODO: Real implementation.
+  describe('getSharedSecret()', () => {
-  function derToPub(der) {
+    // TODO: Real implementation.
-    return der.slice(46);
+    function derToPub(der) {
-  }
+      return der.slice(46);
-  should('getSharedSecret()/should produce correct results', () => {
-    // TODO: Once der is there, run all tests.
-    for (const vector of ecdh.testGroups[0].tests.slice(0, 230)) {
-      if (vector.result === 'invalid' || vector.private.length !== 64) {
-        throws(() => {
-          secp.getSharedSecret(vector.private, derToPub(vector.public), true);
-        });
-      } else if (vector.result === 'valid') {
-        const res = secp.getSharedSecret(vector.private, derToPub(vector.public), true);
-        deepStrictEqual(hex(res.slice(1)), `${vector.shared}`);
-      }
     }
-  });
+    should('produce correct results', () => {
-  should('getSharedSecret()/priv/pub order matters', () => {
+      // TODO: Once der is there, run all tests.
-    for (const vector of ecdh.testGroups[0].tests.slice(0, 100)) {
+      for (const vector of ecdh.testGroups[0].tests.slice(0, 230)) {
-      if (vector.result === 'valid') {
+        if (vector.result === 'invalid' || vector.private.length !== 64) {
-        let priv = vector.private;
+          throws(() => {
-        priv = priv.length === 66 ? priv.slice(2) : priv;
+            secp.getSharedSecret(vector.private, derToPub(vector.public), true);
-        throws(() => secp.getSharedSecret(derToPub(vector.public), priv, true));
+          });
+        } else if (vector.result === 'valid') {
+          const res = secp.getSharedSecret(vector.private, derToPub(vector.public), true);
+          deepStrictEqual(hex(res.slice(1)), `${vector.shared}`);
+        }
       }
-    }
+    });
-  });
+    should('priv/pub order matters', () => {
-  should('getSharedSecret()/rejects invalid keys', () => {
+      for (const vector of ecdh.testGroups[0].tests.slice(0, 100)) {
-    throws(() => secp.getSharedSecret('01', '02'));
+        if (vector.result === 'valid') {
+          let priv = vector.private;
+          priv = priv.length === 66 ? priv.slice(2) : priv;
+          throws(() => secp.getSharedSecret(derToPub(vector.public), priv, true));
+        }
+      }
+    });
+    should('reject invalid keys', () => {
+      throws(() => secp.getSharedSecret('01', '02'));
+    });
   });
 
   should('utils.isValidPrivateKey()', () => {
@@ -442,82 +453,77 @@ describe('secp256k1', () => {
   should('have proper curve equation in assertValidity()', () => {
     throws(() => {
       const { Fp } = secp.CURVE;
-      let point = new secp.Point(Fp.create(-2n), Fp.create(-1n));
+      let point = new Point(Fp.create(-2n), Fp.create(-1n), Fp.create(1n));
       point.assertValidity();
     });
   });
 
-  const Fn = Fp(secp.CURVE.n);
+  describe('tweak utilities (legacy)', () => {
-  const normal = secp.utils._normalizePrivateKey;
+    const Fn = Fp(secp.CURVE.n);
-  const tweakUtils = {
+    const normal = secp.utils._normalizePrivateKey;
-    privateAdd: (privateKey, tweak) => {
+    const tweakUtils = {
-      const p = normal(privateKey);
+      privateAdd: (privateKey, tweak) => {
-      const t = normal(tweak);
+        return numberToBytesBE(Fn.add(normal(privateKey), normal(tweak)), 32);
-      return secp.utils._bigintToBytes(Fn.create(p + t));
+      },
-    },
 
-    privateNegate: (privateKey) => {
+      privateNegate: (privateKey) => {
-      const p = normal(privateKey);
+        return numberToBytesBE(Fn.neg(normal(privateKey)), 32);
-      return secp.utils._bigintToBytes(Fn.negate(p));
+      },
-    },
 
-    pointAddScalar: (p, tweak, isCompressed) => {
+      pointAddScalar: (p, tweak, isCompressed) => {
-      const P = secp.Point.fromHex(p);
+        // Will throw if tweaked point is at infinity
-      const t = normal(tweak);
+        return Point.fromHex(p).add(Point.fromPrivateKey(tweak)).toRawBytes(isCompressed);
-      const Q = secp.Point.BASE.multiplyAndAddUnsafe(P, t, 1n);
+      },
-      if (!Q) throw new Error('Tweaked point at infinity');
-      return Q.toRawBytes(isCompressed);
-    },
 
-    pointMultiply: (p, tweak, isCompressed) => {
+      pointMultiply: (p, tweak, isCompressed) => {
-      const P = secp.Point.fromHex(p);
+        const t = bytesToNumberBE(ensureBytes(tweak));
-      const h = typeof tweak === 'string' ? tweak : bytesToHex(tweak);
+        return Point.fromHex(p).multiply(t).toRawBytes(isCompressed);
-      const t = BigInt(`0x${h}`);
+      },
-      return P.multiply(t).toRawBytes(isCompressed);
+    };
-    },
-  };
 
-  should('privateAdd()', () => {
+    should('privateAdd()', () => {
-    for (const vector of privates.valid.add) {
+      for (const vector of privates.valid.add) {
-      const { a, b, expected } = vector;
+        const { a, b, expected } = vector;
-      deepStrictEqual(bytesToHex(tweakUtils.privateAdd(a, b)), expected);
+        deepStrictEqual(bytesToHex(tweakUtils.privateAdd(a, b)), expected);
-    }
+      }
-  });
+    });
-  should('privateNegate()', () => {
+    should('privateNegate()', () => {
-    for (const vector of privates.valid.negate) {
+      for (const vector of privates.valid.negate) {
-      const { a, expected } = vector;
+        const { a, expected } = vector;
-      deepStrictEqual(bytesToHex(tweakUtils.privateNegate(a)), expected);
+        deepStrictEqual(bytesToHex(tweakUtils.privateNegate(a)), expected);
-    }
+      }
-  });
+    });
-  should('pointAddScalar()', () => {
+    should('pointAddScalar()', () => {
-    for (const vector of points.valid.pointAddScalar) {
+      for (const vector of points.valid.pointAddScalar) {
-      const { description, P, d, expected } = vector;
+        const { description, P, d, expected } = vector;
-      const compressed = !!expected && expected.length === 66; // compressed === 33 bytes
+        const compressed = !!expected && expected.length === 66; // compressed === 33 bytes
-      deepStrictEqual(bytesToHex(tweakUtils.pointAddScalar(P, d, compressed)), expected);
+        deepStrictEqual(bytesToHex(tweakUtils.pointAddScalar(P, d, compressed)), expected);
-    }
+      }
-  });
+    });
-  should('pointAddScalar() invalid', () => {
+    should('pointAddScalar() invalid', () => {
-    for (const vector of points.invalid.pointAddScalar) {
+      for (const vector of points.invalid.pointAddScalar) {
-      const { P, d, exception } = vector;
+        const { P, d, exception } = vector;
-      throws(() => tweakUtils.pointAddScalar(P, d));
+        throws(() => tweakUtils.pointAddScalar(P, d));
-    }
+      }
-  });
+    });
-  should('pointMultiply()', () => {
+    should('pointMultiply()', () => {
-    for (const vector of points.valid.pointMultiply) {
+      for (const vector of points.valid.pointMultiply) {
-      const { P, d, expected } = vector;
+        const { P, d, expected } = vector;
-      deepStrictEqual(bytesToHex(tweakUtils.pointMultiply(P, d, true)), expected);
+        deepStrictEqual(bytesToHex(tweakUtils.pointMultiply(P, d, true)), expected);
-    }
+      }
-  });
+    });
-  should('pointMultiply() invalid', () => {
+    should('pointMultiply() invalid', () => {
-    for (const vector of points.invalid.pointMultiply) {
+      for (const vector of points.invalid.pointMultiply) {
-      const { P, d, exception } = vector;
+        const { P, d, exception } = vector;
-      throws(() => tweakUtils.pointMultiply(P, d));
+        throws(() => tweakUtils.pointMultiply(P, d));
-    }
+      }
+    });
   });
 
-  should('wychenproof vectors', () => {
+  should('wycheproof vectors', () => {
     for (let group of wp.testGroups) {
-      const pubKey = secp.Point.fromHex(group.key.uncompressed);
+      // const pubKey = Point.fromHex().toRawBytes();
+      const pubKey = group.key.uncompressed;
       for (let test of group.tests) {
         const m = secp.CURVE.hash(hexToBytes(test.msg));
         if (test.result === 'valid' || test.result === 'acceptable') {

test/stark/basic.test.js

@@ -1,198 +1,199 @@
 import { deepStrictEqual, throws } from 'assert';
-import { should } from 'micro-should';
+import { describe, should } from 'micro-should';
 import * as starknet from '../../lib/esm/stark.js';
 import { default as issue2 } from './fixtures/issue2.json' assert { type: 'json' };
-
-should('Basic elliptic sanity check', () => {
-  const g1 = starknet.Point.BASE;
-  deepStrictEqual(
-    g1.x.toString(16),
-    '1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca'
-  );
-  deepStrictEqual(
-    g1.y.toString(16),
-    '5668060aa49730b7be4801df46ec62de53ecd11abe43a32873000c36e8dc1f'
-  );
-  const g2 = g1.double();
-  deepStrictEqual(
-    g2.x.toString(16),
-    '759ca09377679ecd535a81e83039658bf40959283187c654c5416f439403cf5'
-  );
-  deepStrictEqual(
-    g2.y.toString(16),
-    '6f524a3400e7708d5c01a28598ad272e7455aa88778b19f93b562d7a9646c41'
-  );
-  const g3 = g2.add(g1);
-  deepStrictEqual(
-    g3.x.toString(16),
-    '411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20'
-  );
-  deepStrictEqual(
-    g3.y.toString(16),
-    '7e1b3ebac08924d2c26f409549191fcf94f3bf6f301ed3553e22dfb802f0686'
-  );
-  const g32 = g1.multiply(3);
-  deepStrictEqual(
-    g32.x.toString(16),
-    '411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20'
-  );
-  deepStrictEqual(
-    g32.y.toString(16),
-    '7e1b3ebac08924d2c26f409549191fcf94f3bf6f301ed3553e22dfb802f0686'
-  );
-  const minus1 = g1.multiply(starknet.CURVE.n - 1n);
-  deepStrictEqual(
-    minus1.x.toString(16),
-    '1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca'
-  );
-  deepStrictEqual(
-    minus1.y.toString(16),
-    '7a997f9f55b68e04841b7fe20b9139d21ac132ee541bc5cd78cfff3c91723e2'
-  );
-});
-
-should('Pedersen', () => {
-  deepStrictEqual(
-    starknet.pedersen(2, 3),
-    '0x5774fa77b3d843ae9167abd61cf80365a9b2b02218fc2f628494b5bdc9b33b8'
-  );
-  deepStrictEqual(
-    starknet.pedersen(1, 2),
-    '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
-  );
-  deepStrictEqual(
-    starknet.pedersen(3, 4),
-    '0x262697b88544f733e5c6907c3e1763131e9f14c51ee7951258abbfb29415fbf'
-  );
-});
-
-should('Hash chain', () => {
-  deepStrictEqual(
-    starknet.hashChain([1, 2, 3]),
-    '0x5d9d62d4040b977c3f8d2389d494e4e89a96a8b45c44b1368f1cc6ec5418915'
-  );
-});
-
-should('Pedersen hash edgecases', () => {
-  // >>> pedersen_hash(0,0)
-  const zero = '0x49ee3eba8c1600700ee1b87eb599f16716b0b1022947733551fde4050ca6804';
-  deepStrictEqual(starknet.pedersen(0, 0), zero);
-  deepStrictEqual(starknet.pedersen(0n, 0n), zero);
-  deepStrictEqual(starknet.pedersen('0', '0'), zero);
-  deepStrictEqual(starknet.pedersen('0x0', '0x0'), zero);
-  // >>> pedersen_hash(3618502788666131213697322783095070105623107215331596699973092056135872020475,3618502788666131213697322783095070105623107215331596699973092056135872020475)
-  // 3226051580231087455100099637526672350308978851161639703631919449959447036451
-  const big = 3618502788666131213697322783095070105623107215331596699973092056135872020475n;
-  const bigExp = '0x721e167a36655994e88efa865e2ed8a0488d36db4d988fec043cda755728223';
-  deepStrictEqual(starknet.pedersen(big, big), bigExp);
-  // >= FIELD
-  const big2 = 36185027886661312136973227830950701056231072153315966999730920561358720204751n;
-  throws(() => starknet.pedersen(big2, big2), 'big2');
-
-  // FIELD -1
-  const big3 = 3618502788666131213697322783095070105623107215331596699973092056135872020480n;
-  const big3exp = '0x7258fccaf3371fad51b117471d9d888a1786c5694c3e6099160477b593a576e';
-  deepStrictEqual(starknet.pedersen(big3, big3), big3exp, 'big3');
-  // FIELD
-  const big4 = 3618502788666131213697322783095070105623107215331596699973092056135872020481n;
-  throws(() => starknet.pedersen(big4, big4), 'big4');
-  throws(() => starknet.pedersen(-1, -1), 'neg');
-  throws(() => starknet.pedersen(false, false), 'false');
-  throws(() => starknet.pedersen(true, true), 'true');
-  throws(() => starknet.pedersen(10.1, 10.1), 'float');
-});
-
-should('hashChain edgecases', () => {
-  deepStrictEqual(starknet.hashChain([32312321312321312312312321n]), '0x1aba6672c014b4838cc201');
-  deepStrictEqual(
-    starknet.hashChain([1n, 2n]),
-    '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
-  );
-  deepStrictEqual(
-    starknet.hashChain([1, 2]),
-    '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
-  );
-  throws(() => starknet.hashChain([]));
-  throws(() => starknet.hashChain('123'));
-  deepStrictEqual(
-    starknet.hashChain([1, 2]),
-    '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
-  );
-});
-
-should('Pedersen hash, issue #2', () => {
-  // Verified with starnet.js
-  deepStrictEqual(
-    starknet.computeHashOnElements(issue2),
-    '0x22064462ea33a6ce5272a295e0f551c5da3834f80d8444e7a4df68190b1bc42'
-  );
-  deepStrictEqual(
-    starknet.computeHashOnElements([]),
-    '0x49ee3eba8c1600700ee1b87eb599f16716b0b1022947733551fde4050ca6804'
-  );
-  deepStrictEqual(
-    starknet.computeHashOnElements([1]),
-    '0x78d74f61aeaa8286418fd34b3a12a610445eba11d00ecc82ecac2542d55f7a4'
-  );
-});
-
 import * as bip32 from '@scure/bip32';
 import * as bip39 from '@scure/bip39';
 
-should('Seed derivation (example)', () => {
+describe('starknet basic', () => {
-  const layer = 'starkex';
+  should('Basic elliptic sanity check', () => {
-  const application = 'starkdeployement';
+    const g1 = starknet.ProjectivePoint.BASE;
-  const mnemonic =
+    deepStrictEqual(
-    'range mountain blast problem vibrant void vivid doctor cluster enough melody ' +
+      g1.toAffine().x.toString(16),
-    'salt layer language laptop boat major space monkey unit glimpse pause change vibrant';
+      '1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca'
-  const ethAddress = '0xa4864d977b944315389d1765ffa7e66F74ee8cd7';
+    );
-  const hdKey = bip32.HDKey.fromMasterSeed(bip39.mnemonicToSeedSync(mnemonic)).derive(
+    deepStrictEqual(
-    starknet.getAccountPath(layer, application, ethAddress, 0)
+      g1.toAffine().y.toString(16),
-  );
+      '5668060aa49730b7be4801df46ec62de53ecd11abe43a32873000c36e8dc1f'
-  deepStrictEqual(
+    );
-    starknet.grindKey(hdKey.privateKey),
+    const g2 = g1.double();
-    '6cf0a8bf113352eb863157a45c5e5567abb34f8d32cddafd2c22aa803f4892c'
+    deepStrictEqual(
-  );
+      g2.toAffine().x.toString(16),
-});
+      '759ca09377679ecd535a81e83039658bf40959283187c654c5416f439403cf5'
+    );
+    deepStrictEqual(
+      g2.toAffine().y.toString(16),
+      '6f524a3400e7708d5c01a28598ad272e7455aa88778b19f93b562d7a9646c41'
+    );
+    const g3 = g2.add(g1);
+    deepStrictEqual(
+      g3.toAffine().x.toString(16),
+      '411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20'
+    );
+    deepStrictEqual(
+      g3.toAffine().y.toString(16),
+      '7e1b3ebac08924d2c26f409549191fcf94f3bf6f301ed3553e22dfb802f0686'
+    );
+    const g32 = g1.multiply(3n);
+    deepStrictEqual(
+      g32.toAffine().x.toString(16),
+      '411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20'
+    );
+    deepStrictEqual(
+      g32.toAffine().y.toString(16),
+      '7e1b3ebac08924d2c26f409549191fcf94f3bf6f301ed3553e22dfb802f0686'
+    );
+    const minus1 = g1.multiply(starknet.CURVE.n - 1n);
+    deepStrictEqual(
+      minus1.toAffine().x.toString(16),
+      '1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca'
+    );
+    deepStrictEqual(
+      minus1.toAffine().y.toString(16),
+      '7a997f9f55b68e04841b7fe20b9139d21ac132ee541bc5cd78cfff3c91723e2'
+    );
+  });
 
-should('Compressed keys', () => {
+  should('Pedersen', () => {
-  const G = starknet.Point.BASE;
+    deepStrictEqual(
-  const half = starknet.CURVE.n / 2n;
+      starknet.pedersen(2, 3),
-  const last = starknet.CURVE.n;
+      '0x5774fa77b3d843ae9167abd61cf80365a9b2b02218fc2f628494b5bdc9b33b8'
-  const vectors = [
+    );
-    1,
+    deepStrictEqual(
-    2,
+      starknet.pedersen(1, 2),
-    3,
+      '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
-    4,
+    );
-    5,
+    deepStrictEqual(
-    half - 5n,
+      starknet.pedersen(3, 4),
-    half - 4n,
+      '0x262697b88544f733e5c6907c3e1763131e9f14c51ee7951258abbfb29415fbf'
-    half - 3n,
+    );
-    half - 2n,
+  });
-    half - 1n,
-    half,
-    half + 1n,
-    half + 2n,
-    half + 3n,
-    half + 4n,
-    half + 5n,
-    last - 5n,
-    last - 4n,
-    last - 3n,
-    last - 2n,
-    last - 1n,
-  ].map((i) => G.multiply(i));
-  const fixPoint = (pt) => ({ ...pt, _WINDOW_SIZE: undefined });
-  for (const v of vectors) {
-    const uncompressed = v.toHex();
-    const compressed = v.toHex(true);
-    const exp = fixPoint(v);
-    deepStrictEqual(fixPoint(starknet.Point.fromHex(uncompressed)), exp);
-    deepStrictEqual(fixPoint(starknet.Point.fromHex(compressed)), exp);
-    deepStrictEqual(starknet.Point.fromHex(compressed).toHex(), uncompressed);
-  }
-});
 
+  should('Hash chain', () => {
+    deepStrictEqual(
+      starknet.hashChain([1, 2, 3]),
+      '0x5d9d62d4040b977c3f8d2389d494e4e89a96a8b45c44b1368f1cc6ec5418915'
+    );
+  });
+
+  should('Pedersen hash edgecases', () => {
+    // >>> pedersen_hash(0,0)
+    const zero = '0x49ee3eba8c1600700ee1b87eb599f16716b0b1022947733551fde4050ca6804';
+    deepStrictEqual(starknet.pedersen(0, 0), zero);
+    deepStrictEqual(starknet.pedersen(0n, 0n), zero);
+    deepStrictEqual(starknet.pedersen('0', '0'), zero);
+    deepStrictEqual(starknet.pedersen('0x0', '0x0'), zero);
+    // >>> pedersen_hash(3618502788666131213697322783095070105623107215331596699973092056135872020475,3618502788666131213697322783095070105623107215331596699973092056135872020475)
+    // 3226051580231087455100099637526672350308978851161639703631919449959447036451
+    const big = 3618502788666131213697322783095070105623107215331596699973092056135872020475n;
+    const bigExp = '0x721e167a36655994e88efa865e2ed8a0488d36db4d988fec043cda755728223';
+    deepStrictEqual(starknet.pedersen(big, big), bigExp);
+    // >= FIELD
+    const big2 = 36185027886661312136973227830950701056231072153315966999730920561358720204751n;
+    throws(() => starknet.pedersen(big2, big2), 'big2');
+
+    // FIELD -1
+    const big3 = 3618502788666131213697322783095070105623107215331596699973092056135872020480n;
+    const big3exp = '0x7258fccaf3371fad51b117471d9d888a1786c5694c3e6099160477b593a576e';
+    deepStrictEqual(starknet.pedersen(big3, big3), big3exp, 'big3');
+    // FIELD
+    const big4 = 3618502788666131213697322783095070105623107215331596699973092056135872020481n;
+    throws(() => starknet.pedersen(big4, big4), 'big4');
+    throws(() => starknet.pedersen(-1, -1), 'neg');
+    throws(() => starknet.pedersen(false, false), 'false');
+    throws(() => starknet.pedersen(true, true), 'true');
+    throws(() => starknet.pedersen(10.1, 10.1), 'float');
+  });
+
+  should('hashChain edgecases', () => {
+    deepStrictEqual(starknet.hashChain([32312321312321312312312321n]), '0x1aba6672c014b4838cc201');
+    deepStrictEqual(
+      starknet.hashChain([1n, 2n]),
+      '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
+    );
+    deepStrictEqual(
+      starknet.hashChain([1, 2]),
+      '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
+    );
+    throws(() => starknet.hashChain([]));
+    throws(() => starknet.hashChain('123'));
+    deepStrictEqual(
+      starknet.hashChain([1, 2]),
+      '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
+    );
+  });
+
+  should('Pedersen hash, issue #2', () => {
+    // Verified with starnet.js
+    deepStrictEqual(
+      starknet.computeHashOnElements(issue2),
+      '0x22064462ea33a6ce5272a295e0f551c5da3834f80d8444e7a4df68190b1bc42'
+    );
+    deepStrictEqual(
+      starknet.computeHashOnElements([]),
+      '0x49ee3eba8c1600700ee1b87eb599f16716b0b1022947733551fde4050ca6804'
+    );
+    deepStrictEqual(
+      starknet.computeHashOnElements([1]),
+      '0x78d74f61aeaa8286418fd34b3a12a610445eba11d00ecc82ecac2542d55f7a4'
+    );
+  });
+
+
+  should('Seed derivation (example)', () => {
+    const layer = 'starkex';
+    const application = 'starkdeployement';
+    const mnemonic =
+      'range mountain blast problem vibrant void vivid doctor cluster enough melody ' +
+      'salt layer language laptop boat major space monkey unit glimpse pause change vibrant';
+    const ethAddress = '0xa4864d977b944315389d1765ffa7e66F74ee8cd7';
+    const hdKey = bip32.HDKey.fromMasterSeed(bip39.mnemonicToSeedSync(mnemonic)).derive(
+      starknet.getAccountPath(layer, application, ethAddress, 0)
+    );
+    deepStrictEqual(
+      starknet.grindKey(hdKey.privateKey),
+      '6cf0a8bf113352eb863157a45c5e5567abb34f8d32cddafd2c22aa803f4892c'
+    );
+  });
+
+  should('Compressed keys', () => {
+    const G = starknet.ProjectivePoint.BASE;
+    const half = starknet.CURVE.n / 2n;
+    const last = starknet.CURVE.n;
+    const vectors = [
+      1n,
+      2n,
+      3n,
+      4n,
+      5n,
+      half - 5n,
+      half - 4n,
+      half - 3n,
+      half - 2n,
+      half - 1n,
+      half,
+      half + 1n,
+      half + 2n,
+      half + 3n,
+      half + 4n,
+      half + 5n,
+      last - 5n,
+      last - 4n,
+      last - 3n,
+      last - 2n,
+      last - 1n,
+    ].map((i) => G.multiply(i));
+    const fixPoint = (pt) => pt.toAffine();
+    for (const v of vectors) {
+      const uncompressed = v.toHex();
+      const compressed = v.toHex(true);
+      const exp = fixPoint(v);
+      deepStrictEqual(fixPoint(starknet.ProjectivePoint.fromHex(uncompressed)), exp);
+      deepStrictEqual(fixPoint(starknet.ProjectivePoint.fromHex(compressed)), exp);
+      deepStrictEqual(starknet.ProjectivePoint.fromHex(compressed).toHex(), uncompressed);
+    }
+  });
+});
 // ESM is broken.
 import url from 'url';
 if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {

test/stark/index.test.js

@@ -1,5 +1,4 @@
-
 import './basic.test.js';
 import './stark.test.js';
 import './property.test.js';
-
+import './poseidon.test.js';

test/stark/poseidon.test.js

@@ -0,0 +1,114 @@
+import { deepStrictEqual, throws } from 'assert';
+import { describe, should } from 'micro-should';
+import * as starknet from '../../lib/esm/stark.js';
+import * as fs from 'fs';
+
+function parseTest(path) {
+  let data = fs.readFileSync(path, 'ascii');
+  // Remove whitespaces
+  data = data.replace(/[ |\t]/g, '');
+  const pattern =
+    'Rate=(\\d+)\n' +
+    'Capacity=(\\d+)\n' +
+    'FullRounds=(\\d+)\n' +
+    'PartialRounds=(\\d+)\n' +
+    'MDS=\\[(.+)\\]\n' +
+    'RoundKeys=\\(?\n?\\[\n?(.+)\n?\\]\n?\\)?';
+  const r = data.match(new RegExp(pattern, 'ms'));
+
+  function parseArray(s) {
+    // Remove new lines
+    s = s.replace(/\n/gms, '');
+    return s.match(/(\[.+?\])/g).map((i) =>
+      i
+        .replace(/^\[(.+)\]$/, '$1')
+        .split(',')
+        .filter((i) => !!i)
+    );
+  }
+  const res = {
+    rate: +r[1],
+    capacity: +r[2],
+    roundsFull: +r[3],
+    roundsPartial: +r[4],
+    MDS: parseArray(r[5]).map((i) => i.map((j) => BigInt(j))),
+    roundConstants: parseArray(r[6]).map((i) => i.map((j) => BigInt(j))),
+  };
+  return res;
+}
+
+function mapPoseidon(parsed) {
+  return starknet.poseidonBasic(
+    {
+      Fp: starknet.Fp251,
+      rate: parsed.rate,
+      capacity: parsed.capacity,
+      roundsFull: parsed.roundsFull,
+      roundsPartial: parsed.roundsPartial,
+    },
+    parsed.MDS
+  );
+}
+
+const parsed = {
+  poseidon3: parseTest('./test/stark/poseidon/poseidon3.txt'),
+  poseidon4: parseTest('./test/stark/poseidon/poseidon4.txt'),
+  poseidon5: parseTest('./test/stark/poseidon/poseidon5.txt'),
+  poseidon9: parseTest('./test/stark/poseidon/poseidon9.txt'),
+};
+
+function poseidonTest(name, parsed) {
+  should(`${name}`, () => {
+    const fn = mapPoseidon(parsed);
+    deepStrictEqual(fn.roundConstants, parsed.roundConstants);
+  });
+}
+
+describe('poseidon txt vectors', () => {
+  poseidonTest('poseidon3', parsed.poseidon3);
+  poseidonTest('poseidon4', parsed.poseidon4);
+  poseidonTest('poseidon5', parsed.poseidon5);
+  poseidonTest('poseidon9', parsed.poseidon9);
+});
+
+should('Poseidon examples', () => {
+  const p3 = mapPoseidon(parsed.poseidon3);
+  deepStrictEqual(p3([0n, 0n, 0n]), [
+    3446325744004048536138401612021367625846492093718951375866996507163446763827n,
+    1590252087433376791875644726012779423683501236913937337746052470473806035332n,
+    867921192302518434283879514999422690776342565400001269945778456016268852423n,
+  ]);
+  const p4 = mapPoseidon(parsed.poseidon4);
+  deepStrictEqual(p4([0n, 0n, 0n, 0n]), [
+    535071095200566880914603862188010633478042591441142518549720701573192347548n,
+    3567335813488551850156302853280844225974867890860330236555401145692518003968n,
+    229995103310401763929738317978722680640995513996113588430855556460153357543n,
+    3513983790849716360905369754287999509206472929684378838050290392634812839312n,
+  ]);
+  const p5 = mapPoseidon(parsed.poseidon5);
+  deepStrictEqual(p5([0n, 0n, 0n, 0n, 0n]), [
+    2337689130971531876049206831496963607805116499042700598724344149414565980684n,
+    3230969295497815870174763682436655274044379544854667759151474216427142025631n,
+    3297330512217530111610698859408044542971696143761201570393504997742535648562n,
+    2585480844700786541432072704002477919020588246983274666988914431019064343941n,
+    3595308260654382824623573767385493361624474708214823462901432822513585995028n,
+  ]);
+  const p9 = mapPoseidon(parsed.poseidon9);
+  deepStrictEqual(p9([0n, 0n, 0n, 0n, 0n, 0n, 0n, 0n, 0n]), [
+    1534116856660032929112709488204491699743182428465681149262739677337223235050n,
+    1710856073207389764546990138116985223517553616229641666885337928044617114700n,
+    3165864635055638516987240200217592641540231237468651257819894959934472989427n,
+    1003007637710164252047715558598366312649052908276423203724288341354608811559n,
+    68117303579957054409211824649914588822081700129416361923518488718489651489n,
+    1123395637839379807713801282868237406546107732595903195840754789810160564711n,
+    478590974834311070537087181212389392308746075734019180430422247431982932503n,
+    835322726024358888065061514739954009068852229059154336727219387089732433787n,
+    3129703030204995742174502162918848446737407262178341733578946634564864233056n,
+  ]);
+});
+
+// ESM is broken.
+import url from 'url';
+if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {
+  should.run();
+}

test/stark/poseidon/LICENSE

@@ -0,0 +1,201 @@
+                                 Apache License
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+                        http://www.apache.org/licenses/
+
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test/stark/poseidon/README.md

@@ -0,0 +1,35 @@
+# StarkWare's Poseidon Hash
+
+[Poseidon](https://www.poseidon-hash.info/) is a family of hash functions designed for being very efficient as algebraic circuits.
+As such, they may be very useful in ZK proving systems such as STARKs and others.
+
+This repository provides the official parameters of StarkWare's Poseidon hash implementations.
+
+All the instances are over the prime field:
+p = 2^251 + 17 * 2^192 + 1 = 3618502788666131213697322783095070105623107215331596699973092056135872020481
+
+A few examples hash results with the different parameters:
+
+```
+Poseidon3([0,0,0]) = [3446325744004048536138401612021367625846492093718951375866996507163446763827,
+       1590252087433376791875644726012779423683501236913937337746052470473806035332,
+       867921192302518434283879514999422690776342565400001269945778456016268852423]
+Poseidon4([0,0,0,0]) = [535071095200566880914603862188010633478042591441142518549720701573192347548,
+       3567335813488551850156302853280844225974867890860330236555401145692518003968,
+       229995103310401763929738317978722680640995513996113588430855556460153357543,
+       3513983790849716360905369754287999509206472929684378838050290392634812839312]
+Poseidon5([0,0,0,0,0]) = [2337689130971531876049206831496963607805116499042700598724344149414565980684,
+       3230969295497815870174763682436655274044379544854667759151474216427142025631,
+       3297330512217530111610698859408044542971696143761201570393504997742535648562,
+       2585480844700786541432072704002477919020588246983274666988914431019064343941,
+       3595308260654382824623573767385493361624474708214823462901432822513585995028]
+Poseidon9([0,0,0,0,0,0,0,0,0]) = [1534116856660032929112709488204491699743182428465681149262739677337223235050,
+       1710856073207389764546990138116985223517553616229641666885337928044617114700,
+       3165864635055638516987240200217592641540231237468651257819894959934472989427,
+       1003007637710164252047715558598366312649052908276423203724288341354608811559,
+       68117303579957054409211824649914588822081700129416361923518488718489651489,
+       1123395637839379807713801282868237406546107732595903195840754789810160564711,
+       478590974834311070537087181212389392308746075734019180430422247431982932503,
+       835322726024358888065061514739954009068852229059154336727219387089732433787,
+       3129703030204995742174502162918848446737407262178341733578946634564864233056]
+```

test/stark/poseidon/poseidon3.txt

@@ -0,0 +1,462 @@
+Rate = 2
+Capacity = 1
+FullRounds = 8
+PartialRounds = 83
+MDS = [[3, 1, 1], [1, -1, 1], [1, 1, -2]]
+RoundKeys = [
+    [
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+    ],
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test/stark/poseidon/poseidon4.txt

@@ -0,0 +1,559 @@
+Rate = 3
+Capacity = 1
+FullRounds = 8
+PartialRounds = 84
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test/stark/poseidon/poseidon5.txt

@@ -0,0 +1,651 @@
+Rate = 4
+Capacity = 1
+FullRounds = 8
+PartialRounds = 84
+MDS = [[3, 1, 1, 1, 1], [1, 2, 1, 1, 1], [1, 1, 1, 1, 1], [1, 1, 1, -1, 1], [1, 1, 1, 1, -2]]
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+        584353160413525267849669053228533951552602295860601556035386665117717227391,
+        752038702160385294706011538400822066722189014251268673051846350397729870418,
+        3594041683498798688197194521326299097635429790757880308152971477196489335154,
+        1367902435756906062215608264424138718742854099315395230911274560900857414183,
+        1828549068951502746189364466794037234789986878381694857475972053743463890779,
+    ],
+    [
+        488172495141237210878388657234137733008417573114482400652274985829148564248,
+        962906242461930394022372340919543491337923491322497419797555620396501785566,
+        2275418085010046236619290386129138234541669589549771944697082317642065048898,
+        1966395064658902622886154686288219600816893261614483533899715888994623208964,
+        3496095878293416917311185659829821476802828534554531050412634978086916288609,
+    ],
+    [
+        3368478822390537245916137403277928093536087427951052230723275731232142463388,
+        3397410259276620127103231993277518800970669191016277541098821699302368873803,
+        2662600899665871010006649609856695263727220473364611552472965243032255906029,
+        2854831720595596992200155718152374313555878203864206470581502555480894633975,
+        2417859092561967752135741161218626374900182454089059862468108240576782064037,
+    ],
+    [
+        1064506915903089299531724594973601253341866933071158266140674053459433520889,
+        243845138053687262800349059300355289745206315347524675450796070948867090098,
+        1952653154963756062322124110012629666160000286707762177032475477295929736283,
+        2760979128531476595658428672038276216079708408852493051222686009638650156041,
+        3341178930260137001230946104398194306290005446746057811731360203227371301716,
+    ],
+    [
+        1033242545866274439991875444609632860132556714736615395036273942261573810479,
+        3567973410830779135148598005871071456943945697865168835204985462698751038238,
+        23014034649293369426970379738102323014738017168969687350330825050016457105,
+        1146720508452451012445869043641390200263192255569203352823376998708972325392,
+        2553707028642376593497768606567528232999203496079990242456254686325586089356,
+    ],
+    [
+        269729857648436699208023125596593246149228245518586029792966091405383426269,
+        276912682886955358118649215147238115764108757952690361549816619060658800027,
+        2367180947887796341722261610916728725977893583923967218630363334645641817362,
+        2398694802751362950028137620758033447242325333923222365760836442417755445092,
+        984868389243025029364428136317275892280780834039611841422502834917752411391,
+    ],
+    [
+        861353329558771468244040268521983016756775808329676883407171471251365927595,
+        2498672969617384807617108262141800974986393948110233099680635130601163654234,
+        1336236634145657673540555267430353130305889434115514586892320600753700983325,
+        980337801407886250576371882962628290239239581416378379141354256717803603922,
+        2308558359523317875952657835109605515063994805873180719205156915762120497245,
+    ],
+    [
+        2116737905426837141304542819940293184404010538896700217242374222514653607487,
+        2143995283326808680518644927890182524580312777400009071739277407358043120199,
+        3038758768133404431511594054950351369492648883179154555267474054094234927849,
+        981824005865625678985009911415023115269386212492064371040001594972137748141,
+        2427990511715778580869565219059895697855813782250850855111162965998948386792,
+    ],
+    [
+        1987498156785173719076522405088076990979859292718600184358583152317049836167,
+        1633834915134208237423144264187482951766302060112099587851513525797020813799,
+        2895454976388515752029424688351979030650325184941524820409482023485820781526,
+        941019661238578826272324221721825852217063629464317974190162904813488515671,
+        2529926057929249454763690180607677568685011502604470585585763159431333258299,
+    ],
+    [
+        2604831509257756199338105380847564711923112853239827243306562341166492672823,
+        2300475954087415591738767759767032267163723345312082546282694920273655145455,
+        1954000528502201000509342111010021527425422549437946241062907964768089317082,
+        1179936151696782249912570883839105595634344582873818018332922940963046083567,
+        3077707030301573630126144767923697288658782137457660869231140049571827937228,
+    ],
+    [
+        1062324397142900251844488719868780667589966366756786302007970554437994421840,
+        353718609497993885193404630053532608155520921625518104461520254335222009911,
+        770557645309607171206012551080400276506165720184677119001983749356594531977,
+        3043628430985247363392058521341757139056029350680498644930013342982472853636,
+        1694968537785457252742656255724723357998402478572600479401200420305593921487,
+    ],
+    [
+        539865665379093791531434211889371819368504193082947002067781562776138072582,
+        3473466148775696692731190426971123680342615414200262605154732883324298196699,
+        482783534456196983135936103604928650836406142744767857356485953118411089098,
+        2389101033971236780034779577432189630800997581132154923233144722790749715251,
+        845264223568475649981141803833883014312596504303895519674002924871878791033,
+    ],
+    [
+        3027004059915270231142566724881373969831662022738947178800901294120992473905,
+        2169574859350740480088697859610203373582027214052754592019828328614087431593,
+        3515527080764222354309565181793838292349410992793070639041305826153436624160,
+        1817926918350512904327755405973355211358017834277255662858654992240629698587,
+        1999148133619270973098477176176178514394558202995832714883251820350860287223,
+    ],
+    [
+        1203131300029280096510929599113528018338088236684405405384757591977164161039,
+        336815403657101171302040383579077521911288747438919304948637997306314852594,
+        986661060847815533035934253464295060766339947679669645818832311132001095573,
+        2291116974939980228917916563988261327966840303336559854772343651559589512651,
+        3421243089992476528970346847858594146122972226790673723411896208702859892637,
+    ],
+    [
+        1015505198663386486420800821559060487156096175034250154764824837183581949724,
+        1165880582987807286271819576391581724550686829511475839624601920297855380101,
+        904232961143172831178860280790910264843503022179578981166030973682571903458,
+        261322216292849827900157598748641385787016033372999683866859675894253115357,
+        3060676319159217735181388708455879854358158161989877552543698103915296690395,
+    ],
+    [
+        1175560144527845912984609340783959238735643215413930887771084560168082442967,
+        2813871258576082360085006002528268796351819524936446195552260262614692343332,
+        1841341101531851399935829271555098629075809587212843292354556374386667658235,
+        3076135575511709688509914361447080149794919016880133063891720256749999834767,
+        753111801049754117414662684453226478940731922961768343984187479992842213733,
+    ],
+    [
+        1405657437118503342762241742745888533114216548278983907019917904938403345580,
+        3111186124713876864436867307979940633543281080828379725576742174555539054855,
+        3404463650394703220454952017098727360005393139199301323890695570346564876407,
+        2024087816190101179456573591359233695334184711688920998987373624570170649371,
+        2770035625774572095496575568588054654502991645588385802705097377675051032967,
+    ],
+    [
+        437058215235292632621847481185406671372191763951486300610124033096831557414,
+        1345792773780982398809956395232061067669190682958320579442454533085407626029,
+        925357273912625669941681596445839316566672314870287993638671283923476231904,
+        3288133122086768300615066039539687885053110015077924175836976549020438910830,
+        666190075990703867784232802074474372379358766701681865975596503982238839889,
+    ],
+    [
+        2664898601165892062970298960258838238925231697327906221693001926762280012052,
+        2075648691532387787722427044464731934171216054855867223374228487601569118337,
+        3173725544188532489243684991828985285646224157242834030308807120745121062293,
+        1517474443612606408422643323550409253700128234157734252330869178582583531320,
+        1593950878945144789965609248470060076911813704207225832606804796819386297511,
+    ],
+    [
+        141195541167651298813588829225208004611326987855926870823948793274702167509,
+        2990187949585642302497822222637786229364740008175968941859105979392907839776,
+        2893807105405820282316438050347503569385510241526138409321358916388308586443,
+        1379719211597875648759619903854862028510320482486109668868067715175935658353,
+        2702780364788282233075255946852944970202849869091427738791947810055591218061,
+    ],
+    [
+        1825815734419326277729273926504439575157952821379179501821641713286627304656,
+        1481344458867016048625916723816339719872443766684158199301690902395849166360,
+        2014084774259125722186109781197998076881266739680534358898592778318128968629,
+        2612744185006548312909661512508122065214170543806989291921289897662387203493,
+        2486291022451231582267428921150634472835925206862678364689227838329114330247,
+    ],
+]

test/stark/property.test.js

@@ -1,49 +1,51 @@
 import { deepStrictEqual, throws } from 'assert';
-import { should } from 'micro-should';
+import { describe, should } from 'micro-should';
 import * as starknet from '../../lib/esm/stark.js';
 import * as fc from 'fast-check';
 
 const FC_BIGINT = fc.bigInt(1n + 1n, starknet.CURVE.n - 1n);
 
-should('Point#toHex() roundtrip', () => {
+describe('starknet property', () => {
-  fc.assert(
+  should('Point#toHex() roundtrip', () => {
-    fc.property(FC_BIGINT, (x) => {
+    fc.assert(
-      const point1 = starknet.Point.fromPrivateKey(x);
+      fc.property(FC_BIGINT, (x) => {
-      const hex = point1.toHex(true);
+        const point1 = starknet.ProjectivePoint.fromPrivateKey(x);
-      deepStrictEqual(starknet.Point.fromHex(hex).toHex(true), hex);
+        const hex = point1.toHex(true);
-    })
+        deepStrictEqual(starknet.ProjectivePoint.fromHex(hex).toHex(true), hex);
+      })
+    );
+  });
+
+  should('Signature.fromCompactHex() roundtrip', () => {
+    fc.assert(
+      fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
+        const sig = new starknet.Signature(r, s);
+        deepStrictEqual(starknet.Signature.fromCompact(sig.toCompactHex()), sig);
+      })
+    );
+  });
+
+  should('Signature.fromDERHex() roundtrip', () => {
+    fc.assert(
+      fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
+        const sig = new starknet.Signature(r, s);
+        deepStrictEqual(starknet.Signature.fromDER(sig.toDERHex()), sig);
+      })
+    );
+  });
+
+  should('verify()/should verify random signatures', () =>
+    fc.assert(
+      fc.property(FC_BIGINT, fc.hexaString({ minLength: 64, maxLength: 64 }), (privNum, msg) => {
+        const privKey = privNum.toString(16).padStart(64, '0');
+        const pub = starknet.getPublicKey(privKey);
+        const sig = starknet.sign(msg, privKey);
+        deepStrictEqual(starknet.verify(sig, msg, pub), true);
+      })
+    )
   );
 });
 
-should('Signature.fromCompactHex() roundtrip', () => {
-  fc.assert(
-    fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
-      const sig = new starknet.Signature(r, s);
-      deepStrictEqual(starknet.Signature.fromCompact(sig.toCompactHex()), sig);
-    })
-  );
-});
-
-should('Signature.fromDERHex() roundtrip', () => {
-  fc.assert(
-    fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
-      const sig = new starknet.Signature(r, s);
-      deepStrictEqual(starknet.Signature.fromDER(sig.toDERHex()), sig);
-    })
-  );
-});
-
-should('verify()/should verify random signatures', () =>
-  fc.assert(
-    fc.asyncProperty(FC_BIGINT, fc.hexaString({ minLength: 64, maxLength: 64 }), (privNum, msg) => {
-      const privKey = privNum.toString(16).padStart(64, '0');
-      const pub = starknet.getPublicKey(privKey);
-      const sig = starknet.sign(msg, privKey);
-      deepStrictEqual(starknet.verify(sig, msg, pub), true);
-    })
-  )
-);
-
 // ESM is broken.
 import url from 'url';
 if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {

test/stark/stark.test.js

@@ -1,5 +1,5 @@
 import { deepStrictEqual, throws } from 'assert';
-import { should } from 'micro-should';
+import { describe, should } from 'micro-should';
 import { hex, utf8 } from '@scure/base';
 import * as bip32 from '@scure/bip32';
 import * as bip39 from '@scure/bip39';
@@ -7,277 +7,279 @@ import * as starknet from '../../lib/esm/stark.js';
 import { default as sigVec } from './fixtures/rfc6979_signature_test_vector.json' assert { type: 'json' };
 import { default as precomputedKeys } from './fixtures/keys_precomputed.json' assert { type: 'json' };
 
-should('Starknet keccak', () => {
+describe('starknet', () => {
-  const value = starknet.keccak(utf8.decode('hello'));
+  should('custom keccak', () => {
-  deepStrictEqual(value, 0x8aff950685c2ed4bc3174f3472287b56d9517b9c948127319a09a7a36deac8n);
+    const value = starknet.keccak(utf8.decode('hello'));
-  deepStrictEqual(value < 2n ** 250n, true);
+    deepStrictEqual(value, 0x8aff950685c2ed4bc3174f3472287b56d9517b9c948127319a09a7a36deac8n);
-});
+    deepStrictEqual(value < 2n ** 250n, true);
+  });
 
-should('RFC6979', () => {
+  should('RFC6979', () => {
-  for (const msg of sigVec.messages) {
+    for (const msg of sigVec.messages) {
-    const { r, s } = starknet.sign(msg.hash, sigVec.private_key);
+      const { r, s } = starknet.sign(msg.hash, sigVec.private_key);
-    // const { r, s } = starknet.Signature.fromDER(sig);
+      // const { r, s } = starknet.Signature.fromDER(sig);
-    deepStrictEqual(r.toString(10), msg.r);
+      deepStrictEqual(r.toString(10), msg.r);
-    deepStrictEqual(s.toString(10), msg.s);
+      deepStrictEqual(s.toString(10), msg.s);
-  }
+    }
-});
+  });
 
-should('Signatures', () => {
+  should('Signatures', () => {
-  const vectors = [
+    const vectors = [
-    {
+      {
-      // Message hash of length 61.
+        // Message hash of length 61.
-      msg: 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47',
+        msg: 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47',
-      r: '5f496f6f210b5810b2711c74c15c05244dad43d18ecbbdbe6ed55584bc3b0a2',
+        r: '5f496f6f210b5810b2711c74c15c05244dad43d18ecbbdbe6ed55584bc3b0a2',
-      s: '4e8657b153787f741a67c0666bad6426c3741b478c8eaa3155196fc571416f3',
+        s: '4e8657b153787f741a67c0666bad6426c3741b478c8eaa3155196fc571416f3',
-    },
+      },
-    {
+      {
-      // Message hash of length 61, with leading zeros.
+        // Message hash of length 61, with leading zeros.
-      msg: '00c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47',
+        msg: '00c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47',
-      r: '5f496f6f210b5810b2711c74c15c05244dad43d18ecbbdbe6ed55584bc3b0a2',
+        r: '5f496f6f210b5810b2711c74c15c05244dad43d18ecbbdbe6ed55584bc3b0a2',
-      s: '4e8657b153787f741a67c0666bad6426c3741b478c8eaa3155196fc571416f3',
+        s: '4e8657b153787f741a67c0666bad6426c3741b478c8eaa3155196fc571416f3',
-    },
+      },
-    {
+      {
-      // Message hash of length 62.
+        // Message hash of length 62.
-      msg: 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47a',
+        msg: 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47a',
-      r: '233b88c4578f0807b4a7480c8076eca5cfefa29980dd8e2af3c46a253490e9c',
+        r: '233b88c4578f0807b4a7480c8076eca5cfefa29980dd8e2af3c46a253490e9c',
-      s: '28b055e825bc507349edfb944740a35c6f22d377443c34742c04e0d82278cf1',
+        s: '28b055e825bc507349edfb944740a35c6f22d377443c34742c04e0d82278cf1',
-    },
+      },
-    {
+      {
-      // Message hash of length 63.
+        // Message hash of length 63.
-      msg: '7465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47a1',
+        msg: '7465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47a1',
-      r: 'b6bee8010f96a723f6de06b5fa06e820418712439c93850dd4e9bde43ddf',
+        r: 'b6bee8010f96a723f6de06b5fa06e820418712439c93850dd4e9bde43ddf',
-      s: '1a3d2bc954ed77e22986f507d68d18115fa543d1901f5b4620db98e2f6efd80',
+        s: '1a3d2bc954ed77e22986f507d68d18115fa543d1901f5b4620db98e2f6efd80',
-    },
+      },
-  ];
+    ];
-  const privateKey = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
+    const privateKey = '2dccce1da22003777062ee0870e9881b460a8b7eca276870f57c601f182136c';
-  const publicKey = starknet.getPublicKey(privateKey);
+    const publicKey = starknet.getPublicKey(privateKey);
-  for (const v of vectors) {
+    for (const v of vectors) {
-    const sig = starknet.sign(v.msg, privateKey);
+      const sig = starknet.sign(v.msg, privateKey);
+      const { r, s } = sig;
+      // const { r, s } = starknet.Signature.fromDER(sig);
+      deepStrictEqual(r.toString(16), v.r, 'r equality');
+      deepStrictEqual(s.toString(16), v.s, 's equality');
+      deepStrictEqual(starknet.verify(sig, v.msg, publicKey), true, 'verify');
+    }
+  });
+
+  should('Invalid signatures', () => {
+    /*
+
+    it('should not verify invalid signature inputs lengths', () => {
+      const ecOrder = starkwareCrypto.ec.n;
+      const {maxEcdsaVal} = starkwareCrypto;
+      const maxMsgHash = maxEcdsaVal.sub(oneBn);
+      const maxR = maxEcdsaVal.sub(oneBn);
+      const maxS = ecOrder.sub(oneBn).sub(oneBn);
+      const maxStarkKey = maxEcdsaVal.sub(oneBn);
+
+      // Test invalid message length.
+      expect(() =>
+        starkwareCrypto.verify(maxStarkKey, maxMsgHash.add(oneBn).toString(16), {
+          r: maxR,
+          s: maxS
+        })
+      ).to.throw('Message not signable, invalid msgHash length.');
+      // Test invalid r length.
+      expect(() =>
+        starkwareCrypto.verify(maxStarkKey, maxMsgHash.toString(16), {
+          r: maxR.add(oneBn),
+          s: maxS
+        })
+      ).to.throw('Message not signable, invalid r length.');
+      // Test invalid w length.
+      expect(() =>
+        starkwareCrypto.verify(maxStarkKey, maxMsgHash.toString(16), {
+          r: maxR,
+          s: maxS.add(oneBn)
+        })
+      ).to.throw('Message not signable, invalid w length.');
+      // Test invalid s length.
+      expect(() =>
+        starkwareCrypto.verify(maxStarkKey, maxMsgHash.toString(16), {
+          r: maxR,
+          s: maxS.add(oneBn).add(oneBn)
+        })
+      ).to.throw('Message not signable, invalid s length.');
+    });
+
+    it('should not verify invalid signatures', () => {
+      const privKey = generateRandomStarkPrivateKey();
+      const keyPair = starkwareCrypto.ec.keyFromPrivate(privKey, 'hex');
+      const keyPairPub = starkwareCrypto.ec.keyFromPublic(
+        keyPair.getPublic(),
+        'BN'
+      );
+      const msgHash = new BN(randomHexString(61));
+      const msgSignature = starkwareCrypto.sign(keyPair, msgHash);
+
+      // Test invalid public key.
+      const invalidKeyPairPub = starkwareCrypto.ec.keyFromPublic(
+        {x: keyPairPub.pub.getX().add(oneBn), y: keyPairPub.pub.getY()},
+        'BN'
+      );
+      expect(
+        starkwareCrypto.verify(
+          invalidKeyPairPub,
+          msgHash.toString(16),
+          msgSignature
+        )
+      ).to.be.false;
+      // Test invalid message.
+      expect(
+        starkwareCrypto.verify(
+          keyPair,
+          msgHash.add(oneBn).toString(16),
+          msgSignature
+        )
+      ).to.be.false;
+      expect(
+        starkwareCrypto.verify(
+          keyPairPub,
+          msgHash.add(oneBn).toString(16),
+          msgSignature
+        )
+      ).to.be.false;
+      // Test invalid r.
+      msgSignature.r.iadd(oneBn);
+      expect(starkwareCrypto.verify(keyPair, msgHash.toString(16), msgSignature))
+        .to.be.false;
+      expect(
+        starkwareCrypto.verify(keyPairPub, msgHash.toString(16), msgSignature)
+      ).to.be.false;
+      // Test invalid s.
+      msgSignature.r.isub(oneBn);
+      msgSignature.s.iadd(oneBn);
+      expect(starkwareCrypto.verify(keyPair, msgHash.toString(16), msgSignature))
+        .to.be.false;
+      expect(
+        starkwareCrypto.verify(keyPairPub, msgHash.toString(16), msgSignature)
+      ).to.be.false;
+    });
+  });
+    */
+  });
+
+  should('Pedersen', () => {
+    deepStrictEqual(
+      starknet.pedersen(
+        '0x3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
+        '0x208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a'
+      ),
+      '0x30e480bed5fe53fa909cc0f8c4d99b8f9f2c016be4c41e13a4848797979c662'
+    );
+    deepStrictEqual(
+      starknet.pedersen(
+        '0x58f580910a6ca59b28927c08fe6c43e2e303ca384badc365795fc645d479d45',
+        '0x78734f65a067be9bdb39de18434d71e79f7b6466a4b66bbd979ab9e7515fe0b'
+      ),
+      '0x68cc0b76cddd1dd4ed2301ada9b7c872b23875d5ff837b3a87993e0d9996b87'
+    );
+  });
+
+  should('Hash chain', () => {
+    deepStrictEqual(starknet.hashChain([1, 2, 3]), starknet.pedersen(1, starknet.pedersen(2, 3)));
+  });
+
+  should('Key grinding', () => {
+    deepStrictEqual(
+      starknet.grindKey('86F3E7293141F20A8BAFF320E8EE4ACCB9D4A4BF2B4D295E8CEE784DB46E0519'),
+      '5c8c8683596c732541a59e03007b2d30dbbbb873556fe65b5fb63c16688f941'
+    );
+    // Loops more than once (verified manually)
+    deepStrictEqual(
+      starknet.grindKey('94F3E7293141F20A8BAFF320E8EE4ACCB9D4A4BF2B4D295E8CEE784DB46E0595'),
+      '33880b9aba464c1c01c9f8f5b4fc1134698f9b0a8d18505cab6cdd34d93dc02'
+    );
+  });
+
+  should('Private to stark key', () => {
+    deepStrictEqual(
+      starknet.getStarkKey('0x178047D3869489C055D7EA54C014FFB834A069C9595186ABE04EA4D1223A03F'),
+      '0x1895a6a77ae14e7987b9cb51329a5adfb17bd8e7c638f92d6892d76e51cebcf'
+    );
+    for (const [privKey, expectedPubKey] of Object.entries(precomputedKeys)) {
+      deepStrictEqual(starknet.getStarkKey(privKey), expectedPubKey);
+    }
+  });
+
+  should('Private stark key from eth signature', () => {
+    const ethSignature =
+      '0x21fbf0696d5e0aa2ef41a2b4ffb623bcaf070461d61cf7251c74161f82fec3a43' +
+      '70854bc0a34b3ab487c1bc021cd318c734c51ae29374f2beb0e6f2dd49b4bf41c';
+    deepStrictEqual(
+      starknet.ethSigToPrivate(ethSignature),
+      '766f11e90cd7c7b43085b56da35c781f8c067ac0d578eabdceebc4886435bda'
+    );
+  });
+
+  should('Key derivation', () => {
+    const layer = 'starkex';
+    const application = 'starkdeployement';
+    const mnemonic =
+      'range mountain blast problem vibrant void vivid doctor cluster enough melody ' +
+      'salt layer language laptop boat major space monkey unit glimpse pause change vibrant';
+    const ethAddress = '0xa4864d977b944315389d1765ffa7e66F74ee8cd7';
+    const VECTORS = [
+      {
+        index: 0,
+        path: "m/2645'/579218131'/891216374'/1961790679'/2135936222'/0",
+        privateKey: '6cf0a8bf113352eb863157a45c5e5567abb34f8d32cddafd2c22aa803f4892c',
+      },
+      {
+        index: 7,
+        path: "m/2645'/579218131'/891216374'/1961790679'/2135936222'/7",
+        privateKey: '341751bdc42841da35ab74d13a1372c1f0250617e8a2ef96034d9f46e6847af',
+      },
+      {
+        index: 598,
+        path: "m/2645'/579218131'/891216374'/1961790679'/2135936222'/598",
+        privateKey: '41a4d591a868353d28b7947eb132aa4d00c4a022743689ffd20a3628d6ca28c',
+      },
+    ];
+    const hd = bip32.HDKey.fromMasterSeed(bip39.mnemonicToSeedSync(mnemonic));
+    for (const { index, path, privateKey } of VECTORS) {
+      const realPath = starknet.getAccountPath(layer, application, ethAddress, index);
+      deepStrictEqual(realPath, path);
+      deepStrictEqual(starknet.grindKey(hd.derive(realPath).privateKey), privateKey);
+    }
+  });
+
+  // Verified against starknet.js
+  should('Starknet.js cross-tests', () => {
+    const privateKey = '0x019800ea6a9a73f94aee6a3d2edf018fc770443e90c7ba121e8303ec6b349279';
+    // NOTE: there is no compressed keys here, getPubKey returns stark-key (which is schnorr-like X coordinate)
+    // But it is not used in signing/verifying
+    deepStrictEqual(
+      starknet.getStarkKey(privateKey),
+      '0x33f45f07e1bd1a51b45fc24ec8c8c9908db9e42191be9e169bfcac0c0d99745'
+    );
+    const msgHash = '0x6d1706bd3d1ba7c517be2a2a335996f63d4738e2f182144d078a1dd9997062e';
+    const sig = starknet.sign(msgHash, privateKey);
     const { r, s } = sig;
-    // const { r, s } = starknet.Signature.fromDER(sig);
-    deepStrictEqual(r.toString(16), v.r, 'r equality');
-    deepStrictEqual(s.toString(16), v.s, 's equality');
-    deepStrictEqual(starknet.verify(sig, v.msg, publicKey), true, 'verify');
-  }
-});
 
-should('Invalid signatures', () => {
+    deepStrictEqual(
-  /*
+      r.toString(),
-
+      '1427981024487605678086498726488552139932400435436186597196374630267616399345'
-  it('should not verify invalid signature inputs lengths', () => {
-    const ecOrder = starkwareCrypto.ec.n;
-    const {maxEcdsaVal} = starkwareCrypto;
-    const maxMsgHash = maxEcdsaVal.sub(oneBn);
-    const maxR = maxEcdsaVal.sub(oneBn);
-    const maxS = ecOrder.sub(oneBn).sub(oneBn);
-    const maxStarkKey = maxEcdsaVal.sub(oneBn);
-
-    // Test invalid message length.
-    expect(() =>
-      starkwareCrypto.verify(maxStarkKey, maxMsgHash.add(oneBn).toString(16), {
-        r: maxR,
-        s: maxS
-      })
-    ).to.throw('Message not signable, invalid msgHash length.');
-    // Test invalid r length.
-    expect(() =>
-      starkwareCrypto.verify(maxStarkKey, maxMsgHash.toString(16), {
-        r: maxR.add(oneBn),
-        s: maxS
-      })
-    ).to.throw('Message not signable, invalid r length.');
-    // Test invalid w length.
-    expect(() =>
-      starkwareCrypto.verify(maxStarkKey, maxMsgHash.toString(16), {
-        r: maxR,
-        s: maxS.add(oneBn)
-      })
-    ).to.throw('Message not signable, invalid w length.');
-    // Test invalid s length.
-    expect(() =>
-      starkwareCrypto.verify(maxStarkKey, maxMsgHash.toString(16), {
-        r: maxR,
-        s: maxS.add(oneBn).add(oneBn)
-      })
-    ).to.throw('Message not signable, invalid s length.');
-  });
-
-  it('should not verify invalid signatures', () => {
-    const privKey = generateRandomStarkPrivateKey();
-    const keyPair = starkwareCrypto.ec.keyFromPrivate(privKey, 'hex');
-    const keyPairPub = starkwareCrypto.ec.keyFromPublic(
-      keyPair.getPublic(),
-      'BN'
     );
-    const msgHash = new BN(randomHexString(61));
+    deepStrictEqual(
-    const msgSignature = starkwareCrypto.sign(keyPair, msgHash);
+      s.toString(),
-
+      '1853664302719670721837677288395394946745467311923401353018029119631574115563'
-    // Test invalid public key.
-    const invalidKeyPairPub = starkwareCrypto.ec.keyFromPublic(
-      {x: keyPairPub.pub.getX().add(oneBn), y: keyPairPub.pub.getY()},
-      'BN'
     );
-    expect(
+    const hashMsg2 = starknet.pedersen(
-      starkwareCrypto.verify(
+      '0x33f45f07e1bd1a51b45fc24ec8c8c9908db9e42191be9e169bfcac0c0d99745',
-        invalidKeyPairPub,
+      '1'
-        msgHash.toString(16),
+    );
-        msgSignature
+    deepStrictEqual(hashMsg2, '0x2b0d4d43acce8ff68416f667f92ec7eab2b96f1d2224abd4d9d4d1e7fa4bb00');
-      )
+    const pubKey =
-    ).to.be.false;
+      '04033f45f07e1bd1a51b45fc24ec8c8c9908db9e42191be9e169bfcac0c0d997450319d0f53f6ca077c4fa5207819144a2a4165daef6ee47a7c1d06c0dcaa3e456';
-    // Test invalid message.
+    const sig2 = new starknet.Signature(
-    expect(
+      558858382392827003930138586379728730695763862039474863361948210004201119180n,
-      starkwareCrypto.verify(
+      2440689354481625417078677634625227600823892606910345662891037256374285369343n
-        keyPair,
+    );
-        msgHash.add(oneBn).toString(16),
+    deepStrictEqual(starknet.verify(sig2.toDERHex(), hashMsg2, pubKey), true);
-        msgSignature
-      )
-    ).to.be.false;
-    expect(
-      starkwareCrypto.verify(
-        keyPairPub,
-        msgHash.add(oneBn).toString(16),
-        msgSignature
-      )
-    ).to.be.false;
-    // Test invalid r.
-    msgSignature.r.iadd(oneBn);
-    expect(starkwareCrypto.verify(keyPair, msgHash.toString(16), msgSignature))
-      .to.be.false;
-    expect(
-      starkwareCrypto.verify(keyPairPub, msgHash.toString(16), msgSignature)
-    ).to.be.false;
-    // Test invalid s.
-    msgSignature.r.isub(oneBn);
-    msgSignature.s.iadd(oneBn);
-    expect(starkwareCrypto.verify(keyPair, msgHash.toString(16), msgSignature))
-      .to.be.false;
-    expect(
-      starkwareCrypto.verify(keyPairPub, msgHash.toString(16), msgSignature)
-    ).to.be.false;
   });
 });
-  */
-});
-
-should('Pedersen', () => {
-  deepStrictEqual(
-    starknet.pedersen(
-      '0x3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
-      '0x208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a'
-    ),
-    '0x30e480bed5fe53fa909cc0f8c4d99b8f9f2c016be4c41e13a4848797979c662'
-  );
-  deepStrictEqual(
-    starknet.pedersen(
-      '0x58f580910a6ca59b28927c08fe6c43e2e303ca384badc365795fc645d479d45',
-      '0x78734f65a067be9bdb39de18434d71e79f7b6466a4b66bbd979ab9e7515fe0b'
-    ),
-    '0x68cc0b76cddd1dd4ed2301ada9b7c872b23875d5ff837b3a87993e0d9996b87'
-  );
-});
-
-should('Hash chain', () => {
-  deepStrictEqual(starknet.hashChain([1, 2, 3]), starknet.pedersen(1, starknet.pedersen(2, 3)));
-});
-
-should('Key grinding', () => {
-  deepStrictEqual(
-    starknet.grindKey('86F3E7293141F20A8BAFF320E8EE4ACCB9D4A4BF2B4D295E8CEE784DB46E0519'),
-    '5c8c8683596c732541a59e03007b2d30dbbbb873556fe65b5fb63c16688f941'
-  );
-  // Loops more than once (verified manually)
-  deepStrictEqual(
-    starknet.grindKey('94F3E7293141F20A8BAFF320E8EE4ACCB9D4A4BF2B4D295E8CEE784DB46E0595'),
-    '33880b9aba464c1c01c9f8f5b4fc1134698f9b0a8d18505cab6cdd34d93dc02'
-  );
-});
-
-should('Private to stark key', () => {
-  deepStrictEqual(
-    starknet.getStarkKey('0x178047D3869489C055D7EA54C014FFB834A069C9595186ABE04EA4D1223A03F'),
-    '0x1895a6a77ae14e7987b9cb51329a5adfb17bd8e7c638f92d6892d76e51cebcf'
-  );
-  for (const [privKey, expectedPubKey] of Object.entries(precomputedKeys)) {
-    deepStrictEqual(starknet.getStarkKey(privKey), expectedPubKey);
-  }
-});
-
-should('Private stark key from eth signature', () => {
-  const ethSignature =
-    '0x21fbf0696d5e0aa2ef41a2b4ffb623bcaf070461d61cf7251c74161f82fec3a43' +
-    '70854bc0a34b3ab487c1bc021cd318c734c51ae29374f2beb0e6f2dd49b4bf41c';
-  deepStrictEqual(
-    starknet.ethSigToPrivate(ethSignature),
-    '766f11e90cd7c7b43085b56da35c781f8c067ac0d578eabdceebc4886435bda'
-  );
-});
-
-should('Key derivation', () => {
-  const layer = 'starkex';
-  const application = 'starkdeployement';
-  const mnemonic =
-    'range mountain blast problem vibrant void vivid doctor cluster enough melody ' +
-    'salt layer language laptop boat major space monkey unit glimpse pause change vibrant';
-  const ethAddress = '0xa4864d977b944315389d1765ffa7e66F74ee8cd7';
-  const VECTORS = [
-    {
-      index: 0,
-      path: "m/2645'/579218131'/891216374'/1961790679'/2135936222'/0",
-      privateKey: '6cf0a8bf113352eb863157a45c5e5567abb34f8d32cddafd2c22aa803f4892c',
-    },
-    {
-      index: 7,
-      path: "m/2645'/579218131'/891216374'/1961790679'/2135936222'/7",
-      privateKey: '341751bdc42841da35ab74d13a1372c1f0250617e8a2ef96034d9f46e6847af',
-    },
-    {
-      index: 598,
-      path: "m/2645'/579218131'/891216374'/1961790679'/2135936222'/598",
-      privateKey: '41a4d591a868353d28b7947eb132aa4d00c4a022743689ffd20a3628d6ca28c',
-    },
-  ];
-  const hd = bip32.HDKey.fromMasterSeed(bip39.mnemonicToSeedSync(mnemonic));
-  for (const { index, path, privateKey } of VECTORS) {
-    const realPath = starknet.getAccountPath(layer, application, ethAddress, index);
-    deepStrictEqual(realPath, path);
-    deepStrictEqual(starknet.grindKey(hd.derive(realPath).privateKey), privateKey);
-  }
-});
-
-// Verified against starknet.js
-should('Starknet.js cross-tests', () => {
-  const privateKey = '0x019800ea6a9a73f94aee6a3d2edf018fc770443e90c7ba121e8303ec6b349279';
-  // NOTE: there is no compressed keys here, getPubKey returns stark-key (which is schnorr-like X coordinate)
-  // But it is not used in signing/verifying
-  deepStrictEqual(
-    starknet.getStarkKey(privateKey),
-    '0x33f45f07e1bd1a51b45fc24ec8c8c9908db9e42191be9e169bfcac0c0d99745'
-  );
-  const msgHash = '0x6d1706bd3d1ba7c517be2a2a335996f63d4738e2f182144d078a1dd9997062e';
-  const sig = starknet.sign(msgHash, privateKey);
-  const { r, s } = (sig);
-
-  deepStrictEqual(
-    r.toString(),
-    '1427981024487605678086498726488552139932400435436186597196374630267616399345'
-  );
-  deepStrictEqual(
-    s.toString(),
-    '1853664302719670721837677288395394946745467311923401353018029119631574115563'
-  );
-  const hashMsg2 = starknet.pedersen(
-    '0x33f45f07e1bd1a51b45fc24ec8c8c9908db9e42191be9e169bfcac0c0d99745',
-    '1'
-  );
-  deepStrictEqual(hashMsg2, '0x2b0d4d43acce8ff68416f667f92ec7eab2b96f1d2224abd4d9d4d1e7fa4bb00');
-  const pubKey =
-    '04033f45f07e1bd1a51b45fc24ec8c8c9908db9e42191be9e169bfcac0c0d997450319d0f53f6ca077c4fa5207819144a2a4165daef6ee47a7c1d06c0dcaa3e456';
-  const sig2 = new starknet.Signature(
-    558858382392827003930138586379728730695763862039474863361948210004201119180n,
-    2440689354481625417078677634625227600823892606910345662891037256374285369343n
-  );
-  deepStrictEqual(starknet.verify(sig2.toDERHex(), hashMsg2, pubKey), true);
-});
 
 // ESM is broken.
 import url from 'url';