Release 0.6.0.

README.md

@@ -6,9 +6,11 @@ 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
-- 🔻 Tree-shaking-friendly: there is no entry point, which ensures small size of your app
+- Auditable
+- 🏎 [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:
 
@@ -24,7 +26,6 @@ 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.
 
 ### This library belongs to _noble_ crypto
 
@@ -84,11 +85,13 @@ To define a custom curve, check out API below.
 ## API
 
 - [Overview](#overview)
-- [abstract/edwards: Twisted Edwards curve](#abstract/edwards-twisted-edwards-curve)
+- [abstract/edwards: Twisted Edwards curve](#abstractedwards-twisted-edwards-curve)
-- [abstract/montgomery: Montgomery curve](#abstract/montgomery-montgomery-curve)
+- [abstract/montgomery: Montgomery curve](#abstractmontgomery-montgomery-curve)
-- [abstract/weierstrass: Short Weierstrass curve](#abstract/weierstrass-short-weierstrass-curve)
+- [abstract/weierstrass: Short Weierstrass curve](#abstractweierstrass-short-weierstrass-curve)
-- [abstract/modular](#abstract/modular)
+- [abstract/hash-to-curve: Hashing strings to curve points](#abstracthash-to-curve-hashing-strings-to-curve-points)
-- [abstract/utils](#abstract/utils)
+- [abstract/poseidon: Poseidon hash](#abstractposeidon-poseidon-hash)
+- [abstract/modular](#abstractmodular)
+- [abstract/utils](#abstractutils)
 
 ### Overview
 
@@ -200,8 +203,6 @@ export type CurveFn = {
   ExtendedPoint: ExtendedPointConstructor;
   Signature: SignatureConstructor;
   utils: {
-    mod: (a: bigint, b?: bigint) => bigint;
-    invert: (number: bigint, modulo?: bigint) => bigint;
     randomPrivateKey: () => Uint8Array;
     getExtendedPublicKey: (key: PrivKey) => {
       head: Uint8Array;
@@ -303,20 +304,18 @@ 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;
   verify: (
     signature: Hex | SignatureType,
     msgHash: Hex,
-    publicKey: PubKey,
+    publicKey: Hex,
     opts?: { lowS?: boolean }
   ) => boolean;
   Point: PointConstructor;
   ProjectivePoint: ProjectivePointConstructor;
   Signature: SignatureConstructor;
   utils: {
-    mod: (a: bigint) => bigint;
-    invert: (number: bigint) => bigint;
     isValidPrivateKey(privateKey: PrivKey): boolean;
     hashToPrivateKey: (hash: Hex) => Uint8Array;
     randomPrivateKey: () => Uint8Array;
@@ -324,20 +323,94 @@ export type CurveFn = {
 };
 ```
 
+### abstract/hash-to-curve: Hashing strings to curve points
+
+The module allows to hash arbitrary strings to elliptic curve points.
+
+- `expand_message_xmd` [(spec)](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.4.1) produces a uniformly random byte string using a cryptographic hash function H that outputs b bits..
+
+    ```ts
+    function expand_message_xmd(
+      msg: Uint8Array, DST: Uint8Array, lenInBytes: number, H: CHash
+    ): Uint8Array;
+    function expand_message_xof(
+      msg: Uint8Array, DST: Uint8Array, lenInBytes: number, k: number, H: CHash
+    ): Uint8Array;
+    ```
+
+- `hash_to_field(msg, count, options)` [(spec)](https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.3)
+hashes arbitrary-length byte strings to a list of one or more elements of a finite field F.
+    * `msg` a byte string containing the message to hash
+    * `count` the number of elements of F to output
+    * `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.
+
+    ```ts
+    function hash_to_field(msg: Uint8Array, count: number, options: htfOpts): bigint[][];
+    type htfOpts = {
+      // DST: a domain separation tag
+      // defined in section 2.2.5
+      DST: string;
+      // p: the characteristic of F
+      //    where F is a finite field of characteristic p and order q = p^m
+      p: bigint;
+      // m: the extension degree of F, m >= 1
+      //     where F is a finite field of characteristic p and order q = p^m
+      m: number;
+      // k: the target security level for the suite in bits
+      // defined in section 5.1
+      k: number;
+      // option to use a message that has already been processed by
+      // expand_message_xmd
+      expand?: 'xmd' | 'xof';
+      // Hash functions for: expand_message_xmd is appropriate for use with a
+      // wide range of hash functions, including SHA-2, SHA-3, BLAKE2, and others.
+      // BBS+ uses blake2: https://github.com/hyperledger/aries-framework-go/issues/2247
+      // TODO: verify that hash is shake if expand==='xof' via types
+      hash: CHash;
+    };
+    ```
+
+### 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.
 
 ```typescript
-import { mod, invert, div, invertBatch, sqrt, Fp } from '@noble/curves/abstract/modular';
+import { Fp, mod, invert, div, invertBatch, sqrt } from '@noble/curves/abstract/modular';
+const fp = Fp(2n ** 255n - 19n); // Finite field over 2^255-19
+fp.mul(591n, 932n);
+fp.pow(481n, 11024858120n);
+
+// Generic non-FP utils are also available
 mod(21n, 10n); // 21 mod 10 == 1n; fixed version of 21 % 10
 invert(17n, 10n); // invert(17) mod 10; modular multiplicative inverse
 div(5n, 17n, 10n); // 5/17 mod 10 == 5 * invert(17) mod 10; division
 invertBatch([1n, 2n, 4n], 21n); // => [1n, 11n, 16n] in one inversion
 sqrt(21n, 73n); // √21 mod 73; square root
-const fp = Fp(2n ** 255n - 19n); // Finite field over 2^255-19
-fp.mul(591n, 932n);
-fp.pow(481n, 11024858120n);
 ```
 
 ### abstract/utils
@@ -411,6 +484,25 @@ verify
   noble x 698 ops/sec @ 1ms/op
 ```
 
+## Upgrading
+
+Differences from @noble/secp256k1 1.7:
+
+1. Different double() formula (but same addition)
+2. Different sqrt() function
+3. DRBG supports outputLen bigger than outputLen of hmac
+4. Support for different hash functions
+
+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
+
+
 ## Contributing & testing
 
 1. Clone the repository

benchmark/index.js

@@ -44,9 +44,8 @@ const G2_VECTORS = readFileSync('../test/bls12-381/bls12-381-g2-test-vectors.txt
 let p1, p2, oldp1, oldp2;
 // /BLS
 
-for (let item of [secp256k1, ed25519, ed448, P256, P384, P521, old_secp, noble_ed25519]) {
+for (let item of [secp256k1, ed25519, ed448, P256, P384, P521]) item.utils.precompute(8);
-  item.utils.precompute(8);
+for (let item of [old_secp, noble_ed25519]) item.utils.precompute(8);
-}
 
 const ONLY_NOBLE = process.argv[2] === 'noble';
 
@@ -76,7 +75,7 @@ export const CURVES = {
     sign: {
       samples: 5000,
       secp256k1_old: ({ msg, priv }) => old_secp.signSync(msg, priv),
-      secp256k1: ({ msg, priv }) => secp256k1.sign(msg, priv),
+      secp256k1: ({ msg, priv }) => secp256k1.sign(msg, priv).toCompactRawBytes(),
     },
     verify: {
       samples: 1000,
@@ -96,6 +95,10 @@ export const CURVES = {
         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: () => {
@@ -124,6 +127,10 @@ export const CURVES = {
       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: () => {
@@ -145,6 +152,10 @@ export const CURVES = {
       samples: 500,
       noble: ({ sig, msg, pub }) => ed448.verify(sig, msg, pub),
     },
+    // hashToCurve: {
+    //   samples: 500,
+    //   noble: () => ed448.Point.hashToCurve('abcd'),
+    // },
   },
   nist: {
     data: () => {
@@ -168,6 +179,12 @@ export const CURVES = {
       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: () => {
@@ -201,6 +218,15 @@ export const CURVES = {
         );
       },
     },
+    poseidon: {
+      samples: 2000,
+      noble: () => {
+        return stark.poseidonHash(
+          0x3d937c035c878245caf64531a5756109c53068da139362728feb561405371cbn,
+          0x208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31an
+        );
+      },
+    },
     verify: {
       samples: 500,
       old: ({ publicKeyStark, msgHash, keyPair }) => {
@@ -259,11 +285,11 @@ export const CURVES = {
       },
       noble: () => {
         p1 =
-          bls.G1.Point.BASE.multiply(
+          bls.G1.ProjectivePoint.BASE.multiply(
             0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
           );
         p2 =
-          bls.G2.Point.BASE.multiply(
+          bls.G2.ProjectivePoint.BASE.multiply(
             0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
           );
         bls.pairing(p1, p2);
@@ -304,16 +330,16 @@ export const CURVES = {
       old: () => old_bls.pairing(oldp1, oldp2),
       noble: () => bls.pairing(p1, p2),
     },
-    'hashToCurve/G1': {
+    // 'hashToCurve/G1': {
-      samples: 500,
+    //   samples: 500,
-      old: () => old_bls.PointG1.hashToCurve('abcd'),
+    //   old: () => old_bls.PointG1.hashToCurve('abcd'),
-      noble: () => bls.G1.Point.hashToCurve('abcd'),
+    //   noble: () => bls.hashToCurve.G1.hashToCurve('abcd'),
-    },
+    // },
-    'hashToCurve/G2': {
+    // 'hashToCurve/G2': {
-      samples: 200,
+    //   samples: 200,
-      old: () => old_bls.PointG2.hashToCurve('abcd'),
+    //   old: () => old_bls.PointG2.hashToCurve('abcd'),
-      noble: () => bls.G2.Point.hashToCurve('abcd'),
+    //   noble: () => bls.hashToCurve.G2.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));
@@ -326,22 +352,22 @@ export const CURVES = {
     '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)),
+      noble: ({ pub32 }) => bls.aggregatePublicKeys(pub32.map(bls.G1.ProjectivePoint.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)),
+      noble: ({ pub128 }) => bls.aggregatePublicKeys(pub128.map(bls.G1.ProjectivePoint.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)),
+      noble: ({ pub512 }) => bls.aggregatePublicKeys(pub512.map(bls.G1.ProjectivePoint.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)),
+      noble: ({ pub2048 }) => bls.aggregatePublicKeys(pub2048.map(bls.G1.ProjectivePoint.fromHex)),
     },
     'aggregateSignatures/8': {
       samples: 50,

benchmark/package.json

@@ -12,13 +12,15 @@
     "author": "",
     "license": "MIT",
     "devDependencies": {
-        "micro-bmark": "0.2.0"
+        "micro-bmark": "0.2.1"
     },
     "dependencies": {
         "@noble/bls12-381": "^1.4.0",
         "@noble/ed25519": "^1.7.1",
         "@noble/hashes": "^1.1.5",
         "@noble/secp256k1": "^1.7.0",
-        "@starkware-industries/starkware-crypto-utils": "^0.0.2"
+        "@starkware-industries/starkware-crypto-utils": "^0.0.2",
+        "calculate-correlation": "^1.2.3",
+        "elliptic": "^6.5.4"
     }
 }

package.json

@@ -1,12 +1,12 @@
 {
   "name": "@noble/curves",
-  "version": "0.5.0",
+  "version": "0.6.0",
   "description": "Minimal, auditable JS implementation of elliptic curve cryptography",
   "files": [
     "lib"
   ],
   "scripts": {
-    "bench": "node benchmark/index.js",
+    "bench": "cd benchmark; node index.js",
     "build": "tsc && tsc -p tsconfig.esm.json",
     "build:release": "rollup -c rollup.config.js",
     "lint": "prettier --check 'src/**/*.{js,ts}' 'test/*.js'",
@@ -31,8 +31,8 @@
     "@types/node": "18.11.3",
     "fast-check": "3.0.0",
     "micro-bmark": "0.2.0",
-    "micro-should": "0.2.0",
+    "micro-should": "0.3.0",
-    "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",

src/abstract/bls.ts

@@ -1,93 +1,110 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-// Barreto-Lynn-Scott Curves. A family of pairing friendly curves, with embedding degree = 12 or 24
+/**
-// NOTE: only 12 supported for now
+ * BLS (Barreto-Lynn-Scott) family of pairing-friendly curves.
-// Constructed from pair of weierstrass curves, based pairing logic
+ * Implements BLS (Boneh-Lynn-Shacham) signatures.
-import * as mod from './modular.js';
+ * Consists of two curves: G1 and G2:
-import { ensureBytes, numberToBytesBE, bytesToNumberBE, bitLen, bitGet } from './utils.js';
+ * - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4.
-import * as utils from './utils.js';
+ * - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1
-// Types
+ * - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in
-import { hexToBytes, bytesToHex, Hex, PrivKey } from './utils.js';
+ *   Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not.
-import { htfOpts, stringToBytes, hash_to_field, expand_message_xmd } from './hash-to-curve.js';
+ * Pairing is used to aggregate and verify signatures.
-import { CurvePointsType, PointType, CurvePointsRes, weierstrassPoints } from './weierstrass.js';
+ * 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 { AffinePoint } from './curve.js';
+import { Field, hashToPrivateScalar } from './modular.js';
+import { Hex, PrivKey, CHash, bitLen, bitGet, hexToBytes, bytesToHex } from './utils.js';
+import * as htf from './hash-to-curve.js';
+import {
+  CurvePointsType,
+  ProjPointType as ProjPointType,
+  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: utils.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: {
-    bytesToHex: typeof utils.bytesToHex;
+    stringToBytes: typeof htf.stringToBytes;
-    hexToBytes: typeof utils.hexToBytes;
+    hashToField: typeof htf.hash_to_field;
-    stringToBytes: typeof stringToBytes;
+    expandMessageXMD: typeof htf.expand_message_xmd;
-    hashToField: typeof hash_to_field;
-    expandMessageXMD: typeof expand_message_xmd;
-    mod: typeof mod.mod;
-    getDSTLabel: () => string;
-    setDSTLabel(newLabel: string): void;
   };
 };
 
@@ -95,16 +112,14 @@ export function bls<Fp2, Fp6, Fp12>(
   CURVE: CurveType<Fp, 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 = CURVE.Fp;
+  const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE;
-  const Fr = CURVE.Fr;
-  const Fp2 = CURVE.Fp2;
-  const Fp6 = CURVE.Fp6;
-  const Fp12 = CURVE.Fp12;
   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
@@ -112,18 +127,18 @@ 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 (bitGet(CURVE.x, i)) {
         // Addition
@@ -131,13 +146,13 @@ export function bls<Fp2, Fp6, Fp12>(
         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
@@ -147,102 +162,49 @@ export function bls<Fp2, Fp6, Fp12>(
   }
 
   function millerLoop(ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]): Fp12 {
+    const { x } = CURVE;
     const Px = g1[0];
     const Py = g1[1];
     let f12 = Fp12.ONE;
     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 (bitGet(CURVE.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);
   }
 
-  // bls12-381 is a construction of two curves:
-  // 1. Fp: (x, y)
-  // 2. Fp₂: ((x₁, x₂+i), (y₁, y₂+i)) - (complex numbers)
-  //
-  // Bilinear Pairing (ate pairing) is used to combine both elements into a paired one:
-  //   Fp₁₂ = e(Fp, Fp2)
-  //   where Fp₁₂ = 12-degree polynomial
-  // Pairing is used to verify signatures.
-  //
-  // 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.
-
-  const htfDefaults = { ...CURVE.htfDefaults };
-
-  function isWithinCurveOrder(num: bigint): boolean {
-    return 0 < num && num < CURVE.r;
-  }
-
   const utils = {
     hexToBytes: hexToBytes,
     bytesToHex: bytesToHex,
-    mod: mod.mod,
+    stringToBytes: htf.stringToBytes,
-    stringToBytes,
     // TODO: do we need to export it here?
-    hashToField: (msg: Uint8Array, count: number, options: Partial<typeof htfDefaults> = {}) =>
+    hashToField: (
-      hash_to_field(msg, count, { ...CURVE.htfDefaults, ...options }),
+      msg: Uint8Array,
+      count: number,
+      options: Partial<typeof CURVE.htfDefaults> = {}
+    ) => htf.hash_to_field(msg, count, { ...CURVE.htfDefaults, ...options }),
     expandMessageXMD: (msg: Uint8Array, DST: Uint8Array, lenInBytes: number, H = CURVE.hash) =>
-      expand_message_xmd(msg, DST, lenInBytes, H),
+      htf.expand_message_xmd(msg, DST, lenInBytes, H),
-
+    hashToPrivateKey: (hash: Hex): Uint8Array => Fr.toBytes(hashToPrivateScalar(hash, CURVE.r)),
-    /**
+    randomBytes: (bytesLength: number = groupLen): Uint8Array => CURVE.randomBytes(bytesLength),
-     * Can take 40 or more bytes of uniform input e.g. from CSPRNG or KDF
+    randomPrivateKey: (): Uint8Array => utils.hashToPrivateKey(utils.randomBytes(groupLen + 8)),
-     * and convert them into private key, with the modulo bias being negligible.
-     * As per FIPS 186 B.1.1.
-     * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
-     * @param hash hash output from sha512, or a similar function
-     * @returns valid private key
-     */
-    hashToPrivateKey: (hash: Hex): Uint8Array => {
-      hash = ensureBytes(hash);
-      if (hash.length < 40 || hash.length > 1024)
-        throw new Error('Expected 40-1024 bytes of private key as per FIPS 186');
-      //     hashToPrivateScalar(hash, CURVE.r)
-      // NOTE: doesn't add +/-1
-      const num = mod.mod(bytesToNumberBE(hash), CURVE.r);
-      // This should never happen
-      if (num === 0n || num === 1n) throw new Error('Invalid private key');
-      return numberToBytesBE(num, 32);
-    },
-
-    randomBytes: (bytesLength: number = 32): Uint8Array => CURVE.randomBytes(bytesLength),
-    // NIST SP 800-56A rev 3, section 5.6.1.2.2
-    // https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
-    randomPrivateKey: (): Uint8Array => utils.hashToPrivateKey(utils.randomBytes(40)),
-    getDSTLabel: () => 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');
-      }
-      htfDefaults.DST = newLabel;
-    },
   };
 
-  function normalizePrivKey(key: PrivKey): bigint {
-    let int: bigint;
-    if (key instanceof Uint8Array && key.length === 32) int = bytesToNumberBE(key);
-    else if (typeof key === 'string' && key.length === 64) int = BigInt(`0x${key}`);
-    else if (typeof key === 'number' && key > 0 && Number.isSafeInteger(key)) int = BigInt(key);
-    else if (typeof key === 'bigint' && key > 0n) int = key;
-    else throw new TypeError('Expected valid private key');
-    int = mod.mod(int, CURVE.r);
-    if (!isWithinCurveOrder(int)) throw new Error('Private key must be 0 < key < CURVE.r');
-    return int;
-  }
-
   // Point on G1 curve: (x, y)
   const G1 = weierstrassPoints({
     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?
@@ -250,83 +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(normalizePrivKey(privateKey));
+    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.
@@ -335,11 +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;
     }
@@ -352,11 +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;
     }
@@ -365,12 +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 = [];
@@ -378,23 +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,
@@ -407,6 +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 +1,31 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 // Abelian group utilities
+import { Field, validateField, nLength } from './modular.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 +134,52 @@ 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 AbstractCurve<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
+  wrapPrivateKey?: boolean; // bls12-381 requires mod(n) instead of rejecting keys >= n
+  allowInfinityPoint?: boolean; // bls12-381 requires it. ZERO point is valid, but invalid pubkey
+};
+
+export function validateAbsOpts<FP, T>(curve: AbstractCurve<FP> & T) {
+  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 (!Number.isSafeInteger(val)) throw new Error(`Invalid param ${i}=${val} (${typeof val})`);
+  }
+  // Set defaults
+  return Object.freeze({ ...nLength(curve.n, curve.nBitLength), ...curve } as const);
+}

src/abstract/edwards.ts

@@ -1,29 +1,23 @@
 /*! 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. Different field element lengths in ed448:
-//   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 too (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 {
   bytesToHex,
+  bytesToNumberLE,
   concatBytes,
   ensureBytes,
-  numberToBytesLE,
+  FHash,
-  bytesToNumberLE,
-  hashToPrivateScalar,
-  BasicCurve,
-  validateOpts as utilOpts,
   Hex,
-  PrivKey,
+  numberToBytesLE,
-} from './utils.js'; // TODO: import * as u from './utils.js'?
+} from './utils.js';
-import { Group, GroupConstructor, wNAF } from './group.js';
+import {
-import { hash_to_field, htfOpts, validateHTFOpts } from './hash-to-curve.js';
+  Group,
+  GroupConstructor,
+  wNAF,
+  AbstractCurve,
+  validateAbsOpts,
+  AffinePoint,
+} from './curve.js';
 
 // Be friendly to bad ECMAScript parsers by not using bigint literals like 123n
 const _0n = BigInt(0);
@@ -31,204 +25,171 @@ const _1n = BigInt(1);
 const _2n = BigInt(2);
 const _8n = BigInt(8);
 
-export type CHash = {
+// Edwards curves must declare params a & d.
-  (message: Uint8Array | string): Uint8Array;
+export type CurveType = AbstractCurve<bigint> & {
-  blockLen: number;
+  a: bigint; // curve param a
-  outputLen: number;
+  d: bigint; // curve param d
-  create(): any;
+  hash: FHash; // Hashing
+  randomBytes: (bytesLength?: number) => Uint8Array; // CSPRNG
+  adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array; // clears bits to get valid field elemtn
+  domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array; // Used for hashing
+  uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint }; // Ratio √(u/v)
+  preHash?: FHash; // RFC 8032 pre-hashing of messages to sign() / verify()
+  mapToCurve?: (scalar: bigint[]) => AffinePoint<bigint>; // for hash-to-curve standard
 };
 
-export type CurveType = BasicCurve<bigint> & {
-  // Params: a, d
-  a: bigint;
-  d: bigint;
-  // Hashes
-  hash: CHash; // Because we need outputLen for DRBG
-  randomBytes: (bytesLength?: number) => Uint8Array;
-  adjustScalarBytes?: (bytes: Uint8Array) => Uint8Array;
-  domain?: (data: Uint8Array, ctx: Uint8Array, phflag: boolean) => Uint8Array;
-  uvRatio?: (u: bigint, v: bigint) => { isValid: boolean; value: bigint };
-  preHash?: CHash;
-  clearCofactor?: (c: ExtendedPointConstructor, point: ExtendedPointType) => ExtendedPointType;
-  // Hash to field opts
-  htfDefaults?: htfOpts;
-  mapToCurve?: (scalar: bigint[]) => { x: bigint; y: bigint };
-};
-
-// Should be separate from overrides, since overrides can use information about curve (for example nBits)
 function validateOpts(curve: CurveType) {
-  const opts = utilOpts(curve);
+  const opts = validateAbsOpts(curve);
-  if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
+  if (typeof opts.hash !== 'function') throw new Error('Invalid hash function');
-    throw new Error('Invalid hash function');
   for (const i of ['a', 'd'] as const) {
-    if (typeof opts[i] !== 'bigint')
+    const val = opts[i];
-      throw new Error(`Invalid curve param ${i}=${opts[i]} (${typeof opts[i]})`);
+    if (typeof val !== 'bigint') throw new Error(`Invalid curve param ${i}=${val} (${typeof val})`);
   }
   for (const fn of ['randomBytes'] as const) {
     if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
   }
-  for (const fn of [
+  for (const fn of ['adjustScalarBytes', 'domain', 'uvRatio', 'mapToCurve'] as const) {
-    'adjustScalarBytes',
-    'domain',
-    'uvRatio',
-    'mapToCurve',
-    'clearCofactor',
-  ] as const) {
     if (opts[fn] === undefined) continue; // Optional
     if (typeof opts[fn] !== 'function') throw new Error(`Invalid ${fn} function`);
   }
-  if (opts.htfDefaults !== undefined) validateHTFOpts(opts.htfDefaults);
   // Set defaults
   return Object.freeze({ ...opts } as const);
 }
 
-// Instance
+// Instance of Extended Point with coordinates in X, Y, Z, T
-export interface SignatureType {
+export interface ExtPointType extends Group<ExtPointType> {
-  readonly r: PointType;
+  readonly ex: bigint;
-  readonly s: bigint;
+  readonly ey: bigint;
-  assertValidity(): SignatureType;
+  readonly ez: bigint;
-  toRawBytes(): Uint8Array;
+  readonly et: bigint;
-  toHex(): string;
+  assertValidity(): void;
-}
+  multiply(scalar: bigint): ExtPointType;
-// Static methods
+  multiplyUnsafe(scalar: bigint): ExtPointType;
-export type SignatureConstructor = {
-  new (r: PointType, s: bigint): SignatureType;
-  fromHex(hex: Hex): SignatureType;
-};
-
-// Instance
-export interface ExtendedPointType extends Group<ExtendedPointType> {
-  readonly x: bigint;
-  readonly y: bigint;
-  readonly z: bigint;
-  readonly t: bigint;
-  multiply(scalar: number | bigint, affinePoint?: PointType): ExtendedPointType;
-  multiplyUnsafe(scalar: number | bigint): ExtendedPointType;
   isSmallOrder(): boolean;
   isTorsionFree(): boolean;
-  toAffine(invZ?: bigint): PointType;
+  clearCofactor(): ExtPointType;
-  clearCofactor(): ExtendedPointType;
+  toAffine(iz?: bigint): AffinePoint<bigint>;
 }
-// Static methods
+// 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; // TODO: remove
 }
 
-// Instance
-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
-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: {
-    mod: (a: bigint) => bigint;
-    invert: (number: bigint) => bigint;
     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 as mod.Field<bigint>;
+  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 fieldLen = Fp.BYTES; // 32 (length of one field element)
+  const modP = Fp.create; // Function overrides
-  if (fieldLen > 2048) throw new Error('Field lengths over 2048 are not supported');
-  const groupLen = CURVE.nByteLength;
-  // (2n ** 256n).toString(16);
-  const maxGroupElement = _2n ** BigInt(groupLen * 8); // previous POW_2_256
-
-  // Function overrides
-  const { randomBytes } = CURVE;
-  const modP = Fp.create;
 
   // sqrt(u/v)
-  function _uvRatio(u: bigint, v: bigint) {
+  const uvRatio =
+    CURVE.uvRatio ||
+    ((u: bigint, v: bigint) => {
       try {
-      const value = Fp.sqrt(u * Fp.invert(v));
+        return { isValid: true, value: Fp.sqrt(u * Fp.inv(v)) };
-      return { isValid: true, value };
       } catch (e) {
         return { isValid: false, value: _0n };
       }
-  }
+    });
-  const uvRatio = CURVE.uvRatio || _uvRatio;
+  const adjustScalarBytes = CURVE.adjustScalarBytes || ((bytes: Uint8Array) => bytes); // NOOP
-
+  const domain =
-  const _adjustScalarBytes = (bytes: Uint8Array) => bytes; // NOOP
+    CURVE.domain ||
-  const adjustScalarBytes = CURVE.adjustScalarBytes || _adjustScalarBytes;
+    ((data: Uint8Array, ctx: Uint8Array, phflag: boolean) => {
-  function _domain(data: Uint8Array, ctx: Uint8Array, phflag: boolean) {
       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}`);
   }
-  const domain = CURVE.domain || _domain; // NOOP
+  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);
@@ -236,17 +197,21 @@ 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
@@ -260,17 +225,17 @@ 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.
@@ -289,7 +254,7 @@ 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
@@ -304,401 +269,190 @@ 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.
-    // Allows scalar bigger than curve order, but less than 2^256
+    multiplyUnsafe(scalar: bigint): Point {
-    multiplyUnsafe(scalar: number | bigint): ExtendedPoint {
+      let n = assertGE0(scalar);
-      let n = normalizeScalar(scalar, CURVE_ORDER, false);
+      if (n === _0n) return I;
-      const G = ExtendedPoint.BASE;
+      if (this.equals(I) || n === _1n) return this;
-      const P0 = ExtendedPoint.ZERO;
+      if (this.equals(G)) return this.wNAF(n).p;
-      if (n === _0n) return P0;
-      if (this.equals(P0) || n === _1n) return this;
-      if (this.equals(G)) return this.wNAF(n);
       return wnaf.unsafeLadder(this, n);
     }
 
+    // Checks if point is of small order.
+    // If you add something to small order point, you will have "dirty"
+    // 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 a very big scalar 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 this.multiplyUnsafe(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 {
-      if (CURVE.h === _1n) return this; // Fast-path
-      // clear_cofactor(P) := h_eff * P
-      // hEff = h for ed25519/ed448. Maybe worth moving to params?
-      if (CURVE.clearCofactor) return CURVE.clearCofactor(ExtendedPoint, this) as ExtendedPoint;
-      return this.multiplyUnsafe(CURVE.h);
-    }
-  }
-  const wnaf = wNAF(ExtendedPoint, groupLen * 8);
 
-  function assertExtPoint(other: unknown) {
+    clearCofactor(): Point {
-    if (!(other instanceof ExtendedPoint)) throw new TypeError('ExtendedPoint expected');
+      const { h: cofactor } = CURVE;
-  }
+      if (cofactor === _1n) return this;
-  // Stores precomputed values for points.
+      return this.multiplyUnsafe(cofactor);
-  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;
-      hex = ensureBytes(hex, fieldLen);
+      const len = Fp.BYTES;
-      // 1.  First, interpret the string as an integer in little-endian
+      hex = ensureBytes(hex, len); // copy hex to a new array
-      // representation. Bit 255 of this number is the least significant
+      const normed = hex.slice(); // copy again, we'll manipulate it
-      // bit of the x-coordinate and denote this value x_0.  The
+      const lastByte = hex[len - 1]; // select last byte
-      // y-coordinate is recovered simply by clearing this bit.  If the
+      normed[len - 1] = lastByte & ~0x80; // clear last bit
-      // resulting value is >= p, decoding fails.
-      const normed = hex.slice();
-      const lastByte = hex[fieldLen - 1];
-      normed[fieldLen - 1] = lastByte & ~0x80;
       const y = 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 < 2**256');
-
-      // 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 = numberToBytesLE(this.y, fieldLen);
-      bytes[fieldLen - 1] |= this.x & _1n ? 0x80 : 0;
-      return bytes;
-    }
-
-    // Same as toRawBytes, but returns string.
-    toHex(): string {
-      return bytesToHex(this.toRawBytes());
-    }
-
-    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>) {
-      if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve');
-      msg = ensureBytes(msg);
-      const u = hash_to_field(msg, 2, { ...CURVE.htfDefaults, ...options } as htfOpts);
-      const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]);
-      const { x: x1, y: y1 } = CURVE.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>) {
-      if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve');
-      msg = ensureBytes(msg);
-      const u = hash_to_field(msg, 1, { ...CURVE.htfDefaults, ...options } as htfOpts);
-      const { x, y } = CURVE.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 bytes = ensureBytes(hex, 2 * fieldLen);
-      const r = Point.fromHex(bytes.slice(0, fieldLen), false);
-      const s = bytesToNumberLE(bytes.slice(fieldLen, 2 * fieldLen));
-      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 concatBytes(this.r.toRawBytes(), numberToBytesLE(this.s, fieldLen));
-    }
-
-    toHex() {
-      return bytesToHex(this.toRawBytes());
-    }
-  }
-
-  // Little-endian SHA512 with modulo n
-  function modlLE(hash: Uint8Array): bigint {
-    return mod.mod(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 (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;
+        // 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)
-    throw new TypeError('Expected valid scalar: 0 < scalar < max');
       }
 
-  function checkPrivateKey(key: PrivKey) {
+      // Ed25519: x² = (y²-1)/(dy²+1) mod p. Ed448: x² = (y²-1)/(dy²-1) mod p. Generic case:
-    // Normalize bigint / number / string to Uint8Array
+      // ax²+y²=1+dx²y² => y²-1=dx²y²-ax² => y²-1=x²(dy²-a) => x²=(y²-1)/(dy²-a)
-    key =
+      const y2 = modP(y * y); // denominator is always non-0 mod p.
-      typeof key === 'bigint' || typeof key === 'number'
+      const u = modP(y2 - _1n); // u = y² - 1
-        ? numberToBytesLE(normalizeScalar(key, maxGroupElement), groupLen)
+      const v = modP(d * y2 - a); // v = d y² + 1.
-        : ensureBytes(key);
+      let { isValid, value: x } = uvRatio(u, v); // √(u/v)
-    if (key.length !== groupLen) throw new Error(`Expected ${groupLen} bytes, got ${key.length}`);
+      if (!isValid) throw new Error('Point.fromHex: invalid y coordinate');
-    return key;
+      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 });
     }
+    static fromPrivateKey(privKey: Hex) {
+      return getExtendedPublicKey(privKey).point;
+    }
+    toRawBytes(): Uint8Array {
+      const { x, y } = this.toAffine();
+      const bytes = 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 bytesToHex(this.toRawBytes()); // Same as toRawBytes, but returns string.
+    }
+  }
+  const { BASE: G, ZERO: I } = Point;
+  const wnaf = wNAF(Point, nByteLength * 8);
 
-  // Takes 64 bytes
+  function modN(a: bigint) {
-  function getKeyFromHash(hashed: Uint8Array) {
+    return mod(a, CURVE_ORDER);
-    // First 32 bytes of 64b uniformingly random input are taken,
+  }
-    // clears 3 bits of it to produce a random field element.
+  // Little-endian SHA512 with modulo n
-    const head = adjustScalarBytes(hashed.slice(0, groupLen));
+  function modN_LE(hash: Uint8Array): bigint {
-    // Second 32 bytes is called key prefix (5.1.6)
+    return modN(bytesToNumberLE(hash));
-    const prefix = hashed.slice(groupLen, 2 * groupLen);
+  }
-    // The actual private scalar
+  function isHex(item: Hex, err: string) {
-    const scalar = modlLE(head);
+    if (typeof item !== 'string' && !(item instanceof Uint8Array))
-    // Point on Edwards curve aka public key
+      throw new Error(`${err} must be hex string or Uint8Array`);
-    const point = Point.BASE.multiply(scalar);
-    const pointBytes = point.toRawBytes();
-    return { head, prefix, scalar, point, pointBytes };
   }
 
   /** Convenience method that creates public key and other stuff. RFC8032 5.1.5 */
-  function getExtendedPublicKey(key: PrivKey) {
+  function getExtendedPublicKey(key: Hex) {
-    return getKeyFromHash(CURVE.hash(checkPrivateKey(key)));
+    isHex(key, 'private key');
+    const len = nByteLength;
+    // Hash private key with curve's hash function to produce uniformingly random input
+    // Check byte lengths: ensure(64, h(ensure(32, key)))
+    const hashed = ensureBytes(cHash(ensureBytes(key, len)), 2 * len);
+    const head = adjustScalarBytes(hashed.slice(0, len)); // clear first half bits, produce FE
+    const prefix = hashed.slice(len, 2 * len); // second half is called key prefix (5.1.6)
+    const scalar = modN_LE(head); // The actual private scalar
+    const point = G.multiply(scalar); // Point on Edwards curve aka public key
+    const pointBytes = point.toRawBytes(); // Uint8Array representation
+    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 = concatBytes(...msgs);
-    return modlLE(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(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(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 = concatBytes(R, 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 = 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(
-      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).multiplyUnsafe(CURVE.h).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,
-    mod: modP,
+    // ed25519 private keys are uniform 32b. No need to check for modulo bias, like in secp256k1.
-    invert: Fp.invert,
+    randomPrivateKey: (): Uint8Array => randomBytes(Fp.BYTES),
-
-    /**
-     * Not needed for ed25519 private keys. Needed if you use scalars directly (rare).
-     */
-    hashToPrivateScalar: (hash: Hex): bigint => 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(fieldLen),
 
     /**
      * We're doing scalar multiplication (used in getPublicKey etc) with precomputed BASE_POINT
@@ -706,11 +460,10 @@ 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;
     },
   };
 
@@ -719,9 +472,7 @@ 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;
@@ -17,29 +19,35 @@ export type htfOpts = {
   k: number;
   // option to use a message that has already been processed by
   // expand_message_xmd
-  expand: boolean;
+  expand?: 'xmd' | 'xof';
   // Hash functions for: expand_message_xmd is appropriate for use with a
   // wide range of hash functions, including SHA-2, SHA-3, BLAKE2, and others.
   // BBS+ uses blake2: https://github.com/hyperledger/aries-framework-go/issues/2247
+  // TODO: verify that hash is shake if expand==='xof' via types
   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');
   if (typeof opts.k !== 'number') throw new Error('Invalid htf/k');
-  if (typeof opts.expand !== 'boolean') throw new Error('Invalid htf/expand');
+  if (opts.expand !== 'xmd' && opts.expand !== 'xof' && opts.expand !== undefined)
+    throw new Error('Invalid htf/expand');
   if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
     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 TypeError(`utf8ToBytes expected string, got ${typeof str}`);
+  }
+  return new TextEncoder().encode(str);
 }
 
 // Octet Stream to Integer (bytesToNumberBE)
@@ -101,14 +109,41 @@ export function expand_message_xmd(
   return pseudo_random_bytes.slice(0, lenInBytes);
 }
 
-// hashes arbitrary-length byte strings to a list of one or more elements of a finite field F
+export function expand_message_xof(
-// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.3
+  msg: Uint8Array,
-// Inputs:
+  DST: Uint8Array,
-// msg - a byte string containing the message to hash.
+  lenInBytes: number,
-// count - the number of elements of F to output.
+  k: number,
-// Outputs:
+  H: CHash
-// [u_0, ..., u_(count - 1)], a list of field elements.
+): Uint8Array {
-export function hash_to_field(msg: Uint8Array, count: number, options: htfOpts): bigint[][] {
+  // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-5.3.3
+  // DST = H('H2C-OVERSIZE-DST-' || a_very_long_DST, Math.ceil((lenInBytes * k) / 8));
+  if (DST.length > 255) {
+    const dkLen = Math.ceil((2 * k) / 8);
+    DST = H.create({ dkLen }).update(stringToBytes('H2C-OVERSIZE-DST-')).update(DST).digest();
+  }
+  if (lenInBytes > 65535 || DST.length > 255)
+    throw new Error('expand_message_xof: invalid lenInBytes');
+  return (
+    H.create({ dkLen: lenInBytes })
+      .update(msg)
+      .update(i2osp(lenInBytes, 2))
+      // 2. DST_prime = DST || I2OSP(len(DST), 1)
+      .update(DST)
+      .update(i2osp(DST.length, 1))
+      .digest()
+  );
+}
+
+/**
+ * Hashes arbitrary-length byte strings to a list of one or more elements of a finite field F
+ * https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.3
+ * @param msg a byte string containing the message to hash
+ * @param count the number of elements of F to output
+ * @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: 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;
@@ -116,8 +151,10 @@ export function hash_to_field(msg: Uint8Array, count: number, options: htfOpts):
   const len_in_bytes = count * options.m * L;
   const DST = stringToBytes(options.DST);
   let pseudo_random_bytes = msg;
-  if (options.expand) {
+  if (options.expand === 'xmd') {
     pseudo_random_bytes = expand_message_xmd(msg, DST, len_in_bytes, options.hash);
+  } else if (options.expand === 'xof') {
+    pseudo_random_bytes = expand_message_xof(msg, DST, len_in_bytes, options.k, options.hash);
   }
   const u = new Array(count);
   for (let i = 0; i < count; i++) {
@@ -125,14 +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) => {
@@ -144,3 +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

@@ -1,10 +1,17 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import * as utils from './utils.js';
 // Utilities for modular arithmetics and finite fields
+import {
+  bitMask,
+  numberToBytesBE,
+  numberToBytesLE,
+  bytesToNumberBE,
+  bytesToNumberLE,
+  ensureBytes,
+} from './utils.js';
 // prettier-ignore
 const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
 // prettier-ignore
-const _4n = BigInt(4), _5n = BigInt(5), _7n = BigInt(7), _8n = BigInt(8);
+const _4n = BigInt(4), _5n = BigInt(5), _8n = BigInt(8);
 // prettier-ignore
 const _9n = BigInt(9), _16n = BigInt(16);
 
@@ -54,6 +61,7 @@ export function invert(number: bigint, modulo: bigint): bigint {
   // prettier-ignore
   let x = _0n, y = _1n, u = _1n, v = _0n;
   while (a !== _0n) {
+    // JIT applies optimization if those two lines follow each other
     const q = b / a;
     const r = b % a;
     const m = x - u * q;
@@ -66,26 +74,68 @@ export function invert(number: bigint, modulo: bigint): bigint {
   return mod(x, modulo);
 }
 
-/**
+// Tonelli-Shanks algorithm
- * Calculates Legendre symbol (a | p), which denotes the value of a^((p-1)/2) (mod p).
+// Paper 1: https://eprint.iacr.org/2012/685.pdf (page 12)
- * * (a | p) ≡ 1    if a is a square (mod p)
+// Paper 2: Square Roots from 1; 24, 51, 10 to Dan Shanks
- * * (a | p) ≡ -1   if a is not a square (mod p)
+export function tonelliShanks(P: bigint) {
- * * (a | p) ≡ 0    if a ≡ 0 (mod p)
+  // Legendre constant: used to calculate Legendre symbol (a | p),
- */
+  // which denotes the value of a^((p-1)/2) (mod p).
-export function legendre(num: bigint, fieldPrime: bigint): bigint {
+  // (a | p) ≡ 1    if a is a square (mod p)
-  return pow(num, (fieldPrime - _1n) / _2n, fieldPrime);
+  // (a | p) ≡ -1   if a is not a square (mod p)
+  // (a | p) ≡ 0    if a ≡ 0 (mod p)
+  const legendreC = (P - _1n) / _2n;
+
+  let Q: bigint, S: number, Z: bigint;
+  // Step 1: By factoring out powers of 2 from p - 1,
+  // find q and s such that p - 1 = q*(2^s) with q odd
+  for (Q = P - _1n, S = 0; Q % _2n === _0n; Q /= _2n, S++);
+
+  // Step 2: Select a non-square z such that (z | p) ≡ -1 and set c ≡ zq
+  for (Z = _2n; Z < P && pow(Z, legendreC, P) !== P - _1n; Z++);
+
+  // Fast-path
+  if (S === 1) {
+    const p1div4 = (P + _1n) / _4n;
+    return function tonelliFast<T>(Fp: Field<T>, n: T) {
+      const root = Fp.pow(n, p1div4);
+      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');
+      return root;
+    };
+  }
+
+  // Slow-path
+  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.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.eql(b, Fp.ONE)) {
+      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.sqr(b); m < r; m++) {
+        if (Fp.eql(t2, Fp.ONE)) break;
+        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.sqr(ge); // g = ge * ge
+      x = Fp.mul(x, ge); // x *= ge
+      b = Fp.mul(b, g); // b *= g
+      r = m;
+    }
+    return x;
+  };
 }
 
-/**
+export function FpSqrt(P: bigint) {
- * Calculates square root of a number in a finite field.
+  // NOTE: different algorithms can give different roots, it is up to user to decide which one they want.
- * √a mod P
+  // For example there is FpSqrtOdd/FpSqrtEven to choice root based on oddness (used for hash-to-curve).
- */
-// TODO: rewrite as generic Fp function && remove bls versions
-export function sqrt(number: bigint, modulo: bigint): bigint {
-  // prettier-ignore
-  const n = number;
-  const P = modulo;
-  const p1div4 = (P + _1n) / _4n;
 
   // P ≡ 3 (mod 4)
   // √n = n^((P+1)/4)
@@ -94,48 +144,54 @@ export function sqrt(number: bigint, modulo: bigint): bigint {
     // const ORDER =
     //   0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;
     // const NUM = 72057594037927816n;
-    // TODO: fix sqrtMod in secp256k1
+    const p1div4 = (P + _1n) / _4n;
-    const root = pow(n, p1div4, P);
+    return function sqrt3mod4<T>(Fp: Field<T>, n: T) {
-    if (mod(root * root, modulo) !== number) throw new Error('Cannot find square root');
+      const root = Fp.pow(n, p1div4);
+      // Throw if root**2 != n
+      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');
       return root;
+    };
   }
 
-  // P ≡ 5 (mod 8)
+  // Atkin algorithm for q ≡ 5 (mod 8), https://eprint.iacr.org/2012/685.pdf (page 10)
   if (P % _8n === _5n) {
-    const n2 = mod(n * _2n, P);
+    const c1 = (P - _5n) / _8n;
-    const v = pow(n2, (P - _5n) / _8n, P);
+    return function sqrt5mod8<T>(Fp: Field<T>, n: T) {
-    const nv = mod(n * v, P);
+      const n2 = Fp.mul(n, _2n);
-    const i = mod(_2n * nv * v, P);
+      const v = Fp.pow(n2, c1);
-    const r = mod(nv * (i - _1n), P);
+      const nv = Fp.mul(n, v);
-    return r;
+      const i = Fp.mul(Fp.mul(nv, _2n), v);
+      const root = Fp.mul(nv, Fp.sub(i, Fp.ONE));
+      if (!Fp.eql(Fp.sqr(root), n)) throw new Error('Cannot find square root');
+      return root;
+    };
+  }
+
+  // P ≡ 9 (mod 16)
+  if (P % _16n === _9n) {
+    // NOTE: tonelli is too slow for bls-Fp2 calculations even on start
+    // Means we cannot use sqrt for constants at all!
+    //
+    // const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
+    // const c2 = Fp.sqrt(c1);                //  2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F
+    // const c3 = Fp.sqrt(Fp.negate(c1));     //  3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F
+    // const c4 = (P + _7n) / _16n;           //  4. c4 = (q + 7) / 16        # Integer arithmetic
+    // sqrt = (x) => {
+    //   let tv1 = Fp.pow(x, c4);             //  1. tv1 = x^c4
+    //   let tv2 = Fp.mul(c1, tv1);           //  2. tv2 = c1 * tv1
+    //   const tv3 = Fp.mul(c2, tv1);         //  3. tv3 = c2 * tv1
+    //   let tv4 = Fp.mul(c3, tv1);           //  4. tv4 = c3 * tv1
+    //   const e1 = Fp.equals(Fp.square(tv2), x); //  5.  e1 = (tv2^2) == x
+    //   const e2 = Fp.equals(Fp.square(tv3), x); //  6.  e2 = (tv3^2) == x
+    //   tv1 = Fp.cmov(tv1, tv2, e1); //  7. tv1 = CMOV(tv1, tv2, e1)  # Select tv2 if (tv2^2) == x
+    //   tv2 = Fp.cmov(tv4, tv3, e2); //  8. tv2 = CMOV(tv4, tv3, e2)  # Select tv3 if (tv3^2) == x
+    //   const e3 = Fp.equals(Fp.square(tv2), x); //  9.  e3 = (tv2^2) == x
+    //   return Fp.cmov(tv1, tv2, e3); //  10.  z = CMOV(tv1, tv2, e3)  # Select the sqrt from tv1 and tv2
+    // }
   }
 
   // Other cases: Tonelli-Shanks algorithm
-  if (legendre(n, P) !== _1n) throw new Error('Cannot find square root');
+  return tonelliShanks(P);
-  let q: bigint, s: number, z: bigint;
-  for (q = P - _1n, s = 0; q % _2n === _0n; q /= _2n, s++);
-  if (s === 1) return pow(n, p1div4, P);
-  for (z = _2n; z < P && legendre(z, P) !== P - _1n; z++);
-
-  let c = pow(z, q, P);
-  let r = pow(n, (q + _1n) / _2n, P);
-  let t = pow(n, q, P);
-
-  let t2 = _0n;
-  while (mod(t - _1n, P) !== _0n) {
-    t2 = mod(t * t, P);
-    let i;
-    for (i = 1; i < s; i++) {
-      if (mod(t2 - _1n, P) === _0n) break;
-      t2 = mod(t2 * t2, P);
-    }
-    let b = pow(c, BigInt(1 << (s - i - 1)), P);
-    r = mod(r * b, P);
-    c = mod(b * b, P);
-    t = mod(t * c, P);
-    s = i;
-  }
-  return r;
 }
 
 // Little-endian check for first LE bit (last BE bit);
@@ -156,13 +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;
@@ -172,12 +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;
@@ -187,9 +244,9 @@ 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) {
@@ -217,7 +274,7 @@ 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;
@@ -227,15 +284,15 @@ 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);
@@ -243,42 +300,60 @@ 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.
+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.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
 // - same shape of object (don't add/remove keys)
+type FpField = Field<bigint> & Required<Pick<Field<bigint>, 'isOdd'>>;
 export function Fp(
   ORDER: bigint,
   bitLen?: number,
   isLE = false,
   redef: Partial<Field<bigint>> = {}
-): Readonly<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 = (num: bigint) => sqrt(num, ORDER);
+  const sqrtP = FpSqrt(ORDER);
-  const f: Field<bigint> = Object.freeze({
+  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),
@@ -286,106 +361,58 @@ 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 || sqrtP,
+    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 Field<bigint>);
+  } as FpField);
   return Object.freeze(f);
 }
 
-// TODO: re-use in bls/generic sqrt for field/etc?
+export function FpSqrtOdd<T>(Fp: Field<T>, elm: T) {
-// Something like sqrtUnsafe which always returns value, but sqrt throws exception if non-square
+  if (!Fp.isOdd) throw new Error(`Field doesn't have isOdd`);
-// From draft-irtf-cfrg-hash-to-curve-16
+  const root = Fp.sqrt(elm);
-export function FpSqrt<T>(Fp: Field<T>) {
+  return Fp.isOdd(root) ? root : Fp.neg(root);
-  // NOTE: it requires another sqrt for constant precomputes, but no need for roots of unity,
+}
-  // probably we can simply bls code using it
+
-  const q = Fp.ORDER;
+export function FpSqrtEven<T>(Fp: Field<T>, elm: T) {
-  const squareConst = (q - _1n) / _2n;
+  if (!Fp.isOdd) throw new Error(`Field doesn't have isOdd`);
-  // is_square(x) := { True,  if x^((q - 1) / 2) is 0 or 1 in F;
+  const root = Fp.sqrt(elm);
-  //                 { False, otherwise.
+  return Fp.isOdd(root) ? Fp.neg(root) : root;
-  let isSquare: (x: T) => boolean = (x) => {
+}
-    const p = Fp.pow(x, squareConst);
+
-    return Fp.equals(p, Fp.ZERO) || Fp.equals(p, Fp.ONE);
+/**
-  };
+ * FIPS 186 B.4.1-compliant "constant-time" private key generation utility.
-  // Constant-time Tonelli-Shanks algorithm
+ * Can take (n+8) or more bytes of uniform input e.g. from CSPRNG or KDF
-  let l = _0n;
+ * and convert them into private scalar, with the modulo bias being neglible.
-  for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;
+ * Needs at least 40 bytes of input for 32-byte private key.
-  const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
+ * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
-  const c2 = (q - _1n) / _2n ** c1; // 2. c2 = (q - 1) / (2^c1)        # Integer arithmetic
+ * @param hash hash output from SHA3 or a similar function
-  const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic
+ * @returns valid private scalar
-  //  4. c4, a non-square value in F
+ */
-  //  5. c5 = c4^c2 in F
+export function hashToPrivateScalar(
-  let c4 = Fp.ONE;
+  hash: string | Uint8Array,
-  while (isSquare(c4)) c4 = Fp.add(c4, Fp.ONE);
+  groupOrder: bigint,
-  const c5 = Fp.pow(c4, c2);
+  isLE = false
-
+): bigint {
-  let sqrt: (x: T) => T = (x) => {
+  hash = ensureBytes(hash);
-    let z = Fp.pow(x, c3); // 1.  z = x^c3
+  const hashLen = hash.length;
-    let t = Fp.square(z); // 2.  t = z * z
+  const minLen = nLength(groupOrder).nByteLength + 8;
-    t = Fp.mul(t, x); // 3.  t = t * x
+  if (minLen < 24 || hashLen < minLen || hashLen > 1024)
-    z = Fp.mul(z, x); // 4.  z = z * x
+    throw new Error(`hashToPrivateScalar: expected ${minLen}-1024 bytes of input, got ${hashLen}`);
-    let b = t; // 5.  b = t
+  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
-    let c = c5; // 6.  c = c5
+  return mod(num, groupOrder - _1n) + _1n;
-    // 7.  for i in (c1, c1 - 1, ..., 2):
-    for (let i = c1; i > 1; i--) {
-      // 8.    for j in (1, 2, ..., i - 2):
-      // 9.      b = b * b
-      for (let j = _1n; j < i - _1n; i++) b = Fp.square(b);
-      const e = Fp.equals(b, Fp.ONE); // 10.   e = b == 1
-      const zt = Fp.mul(z, c); // 11.   zt = z * c
-      z = Fp.cmov(zt, z, e); // 12.   z = CMOV(zt, z, e)
-      c = Fp.square(c); // 13.   c = c * c
-      let tt = Fp.mul(t, c); // 14.   tt = t * c
-      t = Fp.cmov(tt, t, e); // 15.   t = CMOV(tt, t, e)
-      b = t; // 16.   b = t
-    }
-    return z; // 17. return z
-  };
-  if (q % _4n === _3n) {
-    const c1 = (q + _1n) / _4n; // 1. c1 = (q + 1) / 4     # Integer arithmetic
-    sqrt = (x) => Fp.pow(x, c1);
-  } else if (q % _8n === _5n) {
-    const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
-    const c2 = (q + _3n) / _8n; //  2. c2 = (q + 3) / 8     # Integer arithmetic
-    sqrt = (x) => {
-      let tv1 = Fp.pow(x, c2); //  1. tv1 = x^c2
-      let tv2 = Fp.mul(tv1, c1); //  2. tv2 = tv1 * c1
-      let e = Fp.equals(Fp.square(tv1), x); //  3.   e = (tv1^2) == x
-      return Fp.cmov(tv2, tv1, e); //  4.   z = CMOV(tv2, tv1, e)
-    };
-  } else if (Fp.ORDER % _16n === _9n) {
-    const c1 = Fp.sqrt(Fp.negate(Fp.ONE)); //  1. c1 = sqrt(-1) in F, i.e., (c1^2) == -1 in F
-    const c2 = Fp.sqrt(c1); //  2. c2 = sqrt(c1) in F, i.e., (c2^2) == c1 in F
-    const c3 = Fp.sqrt(Fp.negate(c1)); //  3. c3 = sqrt(-c1) in F, i.e., (c3^2) == -c1 in F
-    const c4 = (Fp.ORDER + _7n) / _16n; //  4. c4 = (q + 7) / 16         # Integer arithmetic
-    sqrt = (x) => {
-      let tv1 = Fp.pow(x, c4); //  1. tv1 = x^c4
-      let tv2 = Fp.mul(c1, tv1); //  2. tv2 = c1 * tv1
-      const tv3 = Fp.mul(c2, tv1); //  3. tv3 = c2 * tv1
-      let tv4 = Fp.mul(c3, tv1); //  4. tv4 = c3 * tv1
-      const e1 = Fp.equals(Fp.square(tv2), x); //  5.  e1 = (tv2^2) == x
-      const e2 = Fp.equals(Fp.square(tv3), x); //  6.  e2 = (tv3^2) == x
-      tv1 = Fp.cmov(tv1, tv2, e1); //  7. tv1 = CMOV(tv1, tv2, e1)  # Select tv2 if (tv2^2) == x
-      tv2 = Fp.cmov(tv4, tv3, e2); //  8. tv2 = CMOV(tv4, tv3, e2)  # Select tv3 if (tv3^2) == x
-      const e3 = Fp.equals(Fp.square(tv2), x); //  9.  e3 = (tv2^2) == x
-      return Fp.cmov(tv1, tv2, e3); //  10.  z = CMOV(tv1, tv2, e3)  # Select the sqrt from tv1 and tv2
-    };
-  }
-  return { sqrt, isSquare };
 }

src/abstract/montgomery.ts

@@ -1,11 +1,6 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import * as mod from './modular.js';
+import { mod, pow } from './modular.js';
-import {
+import { ensureBytes, numberToBytesLE, bytesToNumberLE } from './utils.js';
-  ensureBytes,
-  numberToBytesLE,
-  bytesToNumberLE,
-  // nLength,
-} from './utils.js';
 
 const _0n = BigInt(0);
 const _1n = BigInt(1);
@@ -51,7 +46,6 @@ function validateOpts(curve: CurveType) {
       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);
 }
 
@@ -60,12 +54,12 @@ 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));
 
   /**
    * Checks for num to be in range:
@@ -73,7 +67,7 @@ export function montgomery(curveDef: CurveType): CurveFn {
    * For strict == false: `0 <= num < max`.
    * Converts non-float safe numbers to bigints.
    */
-  function normalizeScalar(num: number | bigint, max: bigint, strict = true): bigint {
+  function normalizeScalar(num: 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) {

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, validateField, FpPow } 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

@@ -1,70 +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(): any;
+  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;
-};
-
-export function validateOpts<FP, T>(curve: BasicCurve<FP> & T) {
-  mod.validateField(curve.Fp);
-  for (const i of ['n', 'h'] as const) {
-    if (typeof curve[i] !== 'bigint')
-      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
-  }
-  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) {
-    if (curve[i] === undefined) continue; // Optional
-    if (!Number.isSafeInteger(curve[i]))
-      throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`);
-  }
-  // 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('Expected Uint8Array');
   // 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;
 }
@@ -75,18 +33,14 @@ export function numberToHexUnpadded(num: number | bigint): string {
 }
 
 export function hexToNumber(hex: string): bigint {
-  if (typeof hex !== 'string') {
+  if (typeof hex !== 'string') throw new Error('hexToNumber: expected string, 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('hexToBytes: expected string, got ' + typeof hex);
-    throw new TypeError('hexToBytes: expected string, got ' + typeof hex);
-  }
   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++) {
@@ -103,19 +57,25 @@ 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('Expected Uint8Array');
-  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) => {
+  let hex = n.toString(16);
+  if (hex.length & 1) hex = '0' + hex;
+  return hexToBytes(hex);
+};
 
 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;
@@ -123,7 +83,7 @@ export function ensureBytes(hex: Hex, expectedLength?: number): Uint8Array {
 
 // Copies several Uint8Arrays into one.
 export function concatBytes(...arrays: Uint8Array[]): Uint8Array {
-  if (!arrays.every((b) => b instanceof Uint8Array)) throw new Error('Uint8Array list expected');
+  if (!arrays.every((b) => u8a(b))) throw new Error('Uint8Array list expected');
   if (arrays.length === 1) return arrays[0];
   const length = arrays.reduce((a, arr) => a + arr.length, 0);
   const result = new Uint8Array(length);
@@ -135,32 +95,6 @@ export function concatBytes(...arrays: Uint8Array[]): Uint8Array {
   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 };
-}
-
-/**
- * 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.
- * As per FIPS 186 B.4.1.
- * https://research.kudelskisecurity.com/2020/07/28/the-definitive-guide-to-modulo-bias-and-how-to-avoid-it/
- * @param hash hash output from sha512, or a similar function
- * @returns valid private scalar
- */
-export function hashToPrivateScalar(hash: Hex, CURVE_ORDER: bigint, isLE = false): bigint {
-  hash = ensureBytes(hash);
-  const orderLen = nLength(CURVE_ORDER).nByteLength;
-  const minLen = orderLen + 8;
-  if (orderLen < 16 || hash.length < minLen || hash.length > 1024)
-    throw new Error('Expected valid bytes of private key as per FIPS 186');
-  const num = isLE ? bytesToNumberLE(hash) : bytesToNumberBE(hash);
-  return mod.mod(num, CURVE_ORDER - _1n) + _1n;
-}
-
 export function equalBytes(b1: Uint8Array, b2: Uint8Array) {
   // We don't care about timing attacks here
   if (b1.length !== b2.length) return false;

src/bls12-381.ts

@@ -1,10 +1,22 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+
+// The pairing-friendly Barreto-Lynn-Scott elliptic curve construction allows to:
+// - Construct zk-SNARKs at the 128-bit security
+// - Use threshold signatures, which allows a user to sign lots of messages with one signature and verify them swiftly in a batch, using Boneh-Lynn-Shacham signature scheme.
+// Differences from @noble/bls12-381 1.4:
+// - PointG1 -> G1.Point
+// - PointG2 -> G2.Point
+// - PointG2.fromSignature -> Signature.decode
+// - PointG2.toSignature ->  Signature.encode
+// - Fixed Fp2 ORDER
+// - Points now have only two coordinates
+
 import { sha256 } from '@noble/hashes/sha256';
 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,
@@ -16,21 +28,13 @@ 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';
 
-// Differences from bls12-381:
-// - PointG1 -> G1.Point
-// - PointG2 -> G2.Point
-// - PointG2.fromSignature -> Signature.decode
-// - PointG2.toSignature ->  Signature.encode
-// - Fixed Fp2 ORDER
-// Points now have only two coordinates
-
 // CURVE FIELDS
 // Finite field over p.
 const Fp =
@@ -95,25 +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
     //
@@ -127,10 +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.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?
@@ -138,15 +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;
@@ -165,7 +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),
@@ -275,18 +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 = {
@@ -307,35 +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) };
@@ -350,7 +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),
@@ -493,11 +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 = {
@@ -520,30 +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 => {
@@ -553,7 +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),
@@ -597,7 +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}
@@ -881,7 +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);
@@ -892,9 +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);
@@ -915,6 +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,
@@ -926,12 +927,12 @@ const htfDefaults = {
   k: 128,
   // option to use a message that has already been processed by
   // expand_message_xmd
-  expand: true,
+  expand: 'xmd',
   // Hash functions for: expand_message_xmd is appropriate for use with a
   // wide range of hash functions, including SHA-2, SHA-3, BLAKE2, and others.
   // BBS+ uses blake2: https://github.com/hyperledger/aries-framework-go/issues/2247
   hash: sha256,
-};
+} as const;
 
 // Encoding utils
 // Point on G1 curve: (x, y)
@@ -984,7 +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
@@ -1013,7 +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);
@@ -1025,11 +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) };
@@ -1039,7 +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;
@@ -1050,10 +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));
         }
       }
     },
@@ -1115,7 +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);
@@ -1123,6 +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;
@@ -1135,23 +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');
@@ -1159,20 +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),
@@ -1182,7 +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;
@@ -1192,7 +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);
@@ -1208,23 +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

@@ -1,9 +1,9 @@
 /*! 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 } from './abstract/modular.js';
+import { mod, pow2, isNegativeLE, Fp as Field, FpSqrtEven } from './abstract/modular.js';
 import {
   ensureBytes,
   equalBytes,
@@ -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:
@@ -91,7 +92,7 @@ export const ED25519_TORSION_SUBGROUP = [
   'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa',
 ];
 
-const Fp = Field(ED25519_P);
+const Fp = Field(ED25519_P, undefined, true);
 
 const ED25519_DEF = {
   // Param: a
@@ -116,19 +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: true,
-    hash: sha512,
-  },
-  mapToCurve: (scalars: bigint[]): { x: bigint; y: bigint } => {
-    throw new Error('Not supported yet');
-    // const { x, y } = calcElligatorRistrettoMap(scalars[0]).toAffine();
-    // return { x, y };
-  },
 } as const;
 
 export const ed25519 = twistedEdwards(ED25519_DEF);
@@ -163,8 +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(
@@ -191,16 +266,16 @@ const invertSqrt = (number: bigint) => uvRatio(_1n, number);
 
 const MAX_255B = BigInt('0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff');
 const bytes255ToNumberLE = (bytes: Uint8Array) =>
-  ed25519.utils.mod(bytesToNumberLE(bytes) & MAX_255B);
+  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
 function calcElligatorRistrettoMap(r0: bigint): ExtendedPoint {
   const { d } = ed25519.CURVE;
   const P = ed25519.CURVE.Fp.ORDER;
-  const { mod } = ed25519.utils;
+  const mod = ed25519.CURVE.Fp.create;
   const r = mod(SQRT_M1 * r0 * r0); // 1
   const Ns = mod((r + _1n) * ONE_MINUS_D_SQ); // 2
   let c = BigInt(-1); // 3
@@ -258,7 +333,7 @@ export class RistrettoPoint {
     hex = ensureBytes(hex, 32);
     const { a, d } = ed25519.CURVE;
     const P = ed25519.CURVE.Fp.ORDER;
-    const { mod } = ed25519.utils;
+    const mod = ed25519.CURVE.Fp.create;
     const emsg = 'RistrettoPoint.fromHex: the hex is not valid encoding of RistrettoPoint';
     const s = bytes255ToNumberLE(hex);
     // 1. Check that s_bytes is the canonical encoding of a field element, or else abort.
@@ -286,9 +361,9 @@ 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.utils;
+    const mod = ed25519.CURVE.Fp.create;
     const u1 = mod(mod(z + y) * mod(z - y)); // 1
     const u2 = mod(x * y); // 2
     // Square root always exists
@@ -324,12 +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.utils;
+    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;
   }
 
@@ -343,11 +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

@@ -2,8 +2,9 @@
 import { shake256 } from '@noble/hashes/sha3';
 import { concatBytes, randomBytes, utf8ToBytes, wrapConstructor } from '@noble/hashes/utils';
 import { twistedEdwards } from './abstract/edwards.js';
-import { mod, pow2, Fp } from './abstract/modular.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:
@@ -52,6 +53,8 @@ function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
   return bytes;
 }
 
+const Fp = Field(ed448P, 456, true);
+
 const ED448_DEF = {
   // Param: a
   a: BigInt(1),
@@ -60,8 +63,9 @@ const ED448_DEF = {
     '726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018326358'
   ),
   // Finite field 𝔽p over which we'll do calculations; 2n ** 448n - 2n ** 224n - 1n
-  Fp: Fp(ed448P, 456),
+  Fp,
-  // Subgroup order: how many points ed448 has; 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
+  // Subgroup order: how many points curve has;
+  // 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
   n: BigInt(
     '181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779'
   ),
@@ -145,3 +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

@@ -1,5 +1,5 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-import { sha256 } from '@noble/hashes/sha256';
+import { sha512 } from '@noble/hashes/sha512';
 import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';
 import { twistedEdwards } from './abstract/edwards.js';
 import { blake2s } from '@noble/hashes/blake2s';
@@ -8,6 +8,7 @@ import { Fp } from './abstract/modular.js';
 /**
  * jubjub Twisted Edwards curve.
  * https://neuromancer.sk/std/other/JubJub
+ * jubjub does not use EdDSA, so `hash`/sha512 params are passed because interface expects them.
  */
 
 export const jubjub = twistedEdwards({
@@ -15,16 +16,16 @@ export const jubjub = twistedEdwards({
   a: BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000'),
   d: BigInt('0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1'),
   // Finite field 𝔽p over which we'll do calculations
+  // Same value as bls12-381 Fr (not Fp)
   Fp: Fp(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001')),
-  // Subgroup order: how many points ed25519 has
+  // Subgroup order: how many points curve has
-  // 2n ** 252n + 27742317777372353535851937790883648493n;
   n: BigInt('0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7'),
   // Cofactor
   h: BigInt(8),
   // Base point (x, y) aka generator point
   Gx: BigInt('0x11dafe5d23e1218086a365b99fbf3d3be72f6afd7d1f72623e6b071492d1122b'),
   Gy: BigInt('0x1d523cf1ddab1a1793132e78c866c0c33e26ba5cc220fed7cc3f870e59d292aa'),
-  hash: sha256,
+  hash: sha512,
   randomBytes,
 } as const);
 
@@ -38,7 +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/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: true,
-      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: true,
-      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

@@ -4,6 +4,7 @@ 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.
@@ -37,8 +38,7 @@ 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.
+  // P521 keys could be 130, 131, 132 bytes. We normalize to 132 bytes.
-  // We ensure all keys are 132 bytes.
   // Does not replace validation; invalid keys would still be rejected.
   normalizePrivateKey(key: PrivKey) {
     if (typeof key === 'bigint') return key;
@@ -46,16 +46,22 @@ export const P521 = createCurve({
     if (typeof key !== 'string' || !([130, 131, 132].includes(key.length))) {
       throw new Error('Invalid key');
     }
-    return key.padStart(66 * 2, '0');
+    return key.padStart(66 * 2, '0'); // ensure it's always 132 bytes
-  },
-  mapToCurve: (scalars: bigint[]) => mapSWU(scalars[0]),
-  htfDefaults: {
-    DST: 'P521_XMD:SHA-512_SSWU_RO_',
-    p: Fp.ORDER,
-    m: 1,
-    k: 256,
-    expand: true,
-    hash: sha512,
   },
 } as const, sha512);
 export const secp521r1 = P521;
+
+const { hashToCurve, encodeToCurve } = htf.hashToCurve(
+  secp521r1.ProjectivePoint,
+  (scalars: bigint[]) => mapSWU(scalars[0]),
+  {
+    DST: 'P521_XMD:SHA-512_SSWU_RO_',
+    encodeDST: 'P521_XMD:SHA-512_SSWU_NU_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 256,
+    expand: 'xmd',
+    hash: sha512,
+  }
+);
+export { hashToCurve, encodeToCurve };

src/secp256k1.ts

@@ -2,23 +2,21 @@
 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 bytesToNum,
-  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
+ * secp256k1 belongs to Koblitz curves: it has efficiently computable endomorphism.
- * efficiently computable Frobenius endomorphism.
+ * Endomorphism uses 2x less RAM, speeds up precomputation by 2x and ECDH / key recovery by 20%.
- * Endomorphism improves efficiency:
- * Uses 2x less RAM, speeds up precomputation by 2x and ECDH / sign key recovery by 20%.
  * Should always be used for Projective's double-and-add multiplication.
  * For affines cached multiplication, it trades off 1/2 init time & 1/3 ram for 20% perf hit.
  * https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
@@ -31,10 +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 {
@@ -56,13 +51,175 @@ function sqrtMod(y: bigint): bigint {
   const b223 = (pow2(b220, _3n, P) * b3) % P;
   const t1 = (pow2(b223, _23n, P) * b22) % P;
   const t2 = (pow2(t1, _6n, P) * b2) % P;
-  return pow2(t2, _2n, P);
+  const root = pow2(t2, _2n, P);
+  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(
+export const secp256k1 = createCurve(
+  {
+    // Params: a, b
+    // Seem to be rigid https://bitcointalk.org/index.php?topic=289795.msg3183975#msg3183975
+    a: BigInt(0),
+    b: BigInt(7),
+    // Field over which we'll do calculations;
+    // 2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n
+    Fp,
+    // Curve order, total count of valid points in the field
+    n: secp256k1N,
+    // Base point (x, y) aka generator point
+    Gx: BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
+    Gy: BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424'),
+    h: BigInt(1),
+    // Alllow only low-S signatures by default in sign() and verify()
+    lowS: true,
+    endo: {
+      // Params taken from https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
+      beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
+      splitScalar: (k: bigint) => {
+        const n = secp256k1N;
+        const a1 = BigInt('0x3086d221a7d46bcde86c90e49284eb15');
+        const b1 = -_1n * BigInt('0xe4437ed6010e88286f547fa90abfe4c3');
+        const a2 = BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8');
+        const b2 = a1;
+        const POW_2_128 = BigInt('0x100000000000000000000000000000000'); // (2n**128n).toString(16)
+
+        const c1 = divNearest(b2 * k, n);
+        const c2 = divNearest(-b1 * k, n);
+        let k1 = mod(k - c1 * a1 - c2 * a2, n);
+        let k2 = mod(-c1 * b1 - c2 * b2, n);
+        const k1neg = k1 > POW_2_128;
+        const k2neg = k2 > POW_2_128;
+        if (k1neg) k1 = n - k1;
+        if (k2neg) k2 = n - k2;
+        if (k1 > POW_2_128 || k2 > POW_2_128) {
+          throw new Error('splitScalar: Endomorphism failed, k=' + k);
+        }
+        return { k1neg, k1, k2neg, k2 };
+      },
+    },
+  },
+  sha256
+);
+
+// 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 fe = (x: bigint) => typeof x === 'bigint' && _0n < x && x < secp256k1P;
+const ge = (x: bigint) => typeof x === 'bigint' && _0n < x && x < secp256k1N;
+
+const TAGS = {
+  challenge: 'BIP0340/challenge',
+  aux: 'BIP0340/aux',
+  nonce: 'BIP0340/nonce',
+} as const;
+
+/** An object mapping tags to their tagged hash prefix of [SHA256(tag) | SHA256(tag)] */
+const TAGGED_HASH_PREFIXES: { [tag: string]: 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)));
+    tagP = concatBytes(tagH, tagH);
+    TAGGED_HASH_PREFIXES[tag] = tagP;
+  }
+  return sha256(concatBytes(tagP, ...messages));
+}
+
+const toRawX = (point: PointType<bigint>) => point.toRawBytes(true).slice(1);
+const numTo32b = (n: bigint) => numberToBytesBE(n, 32);
+const modN = (x: bigint) => mod(x, secp256k1N);
+const _Point = secp256k1.ProjectivePoint;
+const Gmul = (priv: PrivKey) => _Point.fromPrivateKey(priv);
+const GmulAdd = (Q: PointType<bigint>, a: bigint, b: bigint) =>
+  _Point.BASE.multiplyAndAddUnsafe(Q, a, b);
+function schnorrGetScalar(priv: bigint) {
+  // Let d' = int(sk)
+  // Fail if d' = 0 or d' ≥ n
+  // Let P = d'⋅G
+  // Let d = d' if has_even_y(P), otherwise let d = n - d' .
+  const point = Gmul(priv);
+  const scalar = point.hasEvenY() ? priv : modN(-priv);
+  return { point, scalar, x: toRawX(point) };
+}
+function lift_x(x: bigint): PointType<bigint> {
+  if (!fe(x)) throw new Error('bad x: need 0 < x < p'); // Fail if x ≥ p.
+  const c = mod(x * x * x + BigInt(7), secp256k1P); // Let c = x³ + 7 mod p.
+  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
+  const p = new _Point(x, y, _1n); // y(P) = y if y mod 2 = 0 or y(P) = p-y otherwise.
+  p.assertValidity();
+  return p;
+}
+function challenge(...args: Uint8Array[]): bigint {
+  return modN(bytesToNum(taggedHash(TAGS.challenge, ...args)));
+}
+function schnorrGetPublicKey(privateKey: PrivKey): Uint8Array {
+  return toRawX(Gmul(privateKey)); // Let d' = int(sk). Fail if d' = 0 or d' ≥ n. Return bytes(d'⋅G)
+}
+/**
+ * Synchronously creates Schnorr signature. Improved security: verifies itself before
+ * producing an output.
+ * @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: Hex, auxRand: Hex = randomBytes(32)): Uint8Array {
+  if (message == null) throw new Error(`sign: Expected valid message, not "${message}"`);
+  const m = ensureBytes(message);
+  // checks for isWithinCurveOrder
+
+  const { x: px, scalar: d } = schnorrGetScalar(bytesToNum(ensureBytes(privateKey, 32)));
+  const a = ensureBytes(auxRand, 32); // Auxiliary random data a: a 32-byte array
+  // TODO: replace with proper xor?
+  const t = numTo32b(d ^ bytesToNum(taggedHash(TAGS.aux, a))); // Let t be the byte-wise xor of bytes(d) and hash/aux(a)
+  const rand = taggedHash(TAGS.nonce, t, px, m); // Let rand = hash/nonce(t || bytes(P) || m)
+  const k_ = modN(bytesToNum(rand)); // Let k' = int(rand) mod n
+  if (k_ === _0n) throw new Error('sign failed: k is zero'); // Fail if k' = 0.
+  const { point: R, x: rx, scalar: k } = schnorrGetScalar(k_); // Let R = k'⋅G.
+  const e = challenge(rx, px, m); // Let e = int(hash/challenge(bytes(R) || bytes(P) || m)) mod n.
+  const sig = new Uint8Array(64); // Let sig = bytes(R) || bytes((k + ed) mod n).
+  sig.set(numTo32b(R.px), 0);
+  sig.set(numTo32b(modN(k + e * d)), 32);
+  // If Verify(bytes(P), m, sig) (see below) returns failure, abort
+  if (!schnorrVerify(sig, m, px)) throw new Error('sign: Invalid signature produced');
+  return sig;
+}
+
+/**
+ * Verifies Schnorr signature synchronously.
+ */
+function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
+  try {
+    const P = lift_x(bytesToNum(ensureBytes(publicKey, 32))); // P = lift_x(int(pk)); fail if that fails
+    const sig = ensureBytes(signature, 64);
+    const r = bytesToNum(sig.subarray(0, 32)); // Let r = int(sig[0:32]); fail if r ≥ p.
+    if (!fe(r)) return false;
+    const s = bytesToNum(sig.subarray(32, 64)); // Let s = int(sig[32:64]); fail if s ≥ n.
+    if (!ge(s)) return false;
+    const m = ensureBytes(message);
+    const e = challenge(numTo32b(r), toRawX(P), m); // int(challenge(bytes(r)||bytes(P)||m)) mod n
+    const R = GmulAdd(P, s, modN(-e)); // R = s⋅G - e⋅P
+    if (!R || !R.hasEvenY() || R.toAffine().x !== r) return false; // -eP == (n-e)P
+    return true; // Fail if is_infinite(R) / not has_even_y(R) / x(R) ≠ r.
+  } catch (error) {
+    return false;
+  }
+}
+
+export const schnorr = {
+  // Schnorr's pubkey is just `x` of Point (BIP340)
+  getPublicKey: schnorrGetPublicKey,
+  sign: schnorrSign,
+  verify: schnorrVerify,
+  utils: { lift_x, int: bytesToNum, taggedHash },
+};
+
+const isoMap = htf.isogenyMap(
   Fp,
   [
     // xNum
@@ -94,224 +251,25 @@ const isoMap = isogenyMap(
     ],
   ].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(
-export const secp256k1 = createCurve(
+  secp256k1.ProjectivePoint,
-  {
+  (scalars: bigint[]) => {
-    // Params: a, b
-    // Seem to be rigid https://bitcointalk.org/index.php?topic=289795.msg3183975#msg3183975
-    a: BigInt(0),
-    b: BigInt(7),
-    // Field over which we'll do calculations;
-    // 2n**256n - 2n**32n - 2n**9n - 2n**8n - 2n**7n - 2n**6n - 2n**4n - 1n
-    Fp,
-    // Curve order, total count of valid points in the field
-    n: secp256k1N,
-    // Base point (x, y) aka generator point
-    Gx: BigInt('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
-    Gy: BigInt('32670510020758816978083085130507043184471273380659243275938904335757337482424'),
-    h: BigInt(1),
-    // Alllow only low-S signatures by default in sign() and verify()
-    lowS: true,
-    endo: {
-      // Params taken from https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
-      beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
-      splitScalar: (k: bigint) => {
-        const n = secp256k1N;
-        const a1 = BigInt('0x3086d221a7d46bcde86c90e49284eb15');
-        const b1 = -_1n * BigInt('0xe4437ed6010e88286f547fa90abfe4c3');
-        const a2 = BigInt('0x114ca50f7a8e2f3f657c1108d9d44cfd8');
-        const b2 = a1;
-        const POW_2_128 = BigInt('0x100000000000000000000000000000000');
-
-        const c1 = divNearest(b2 * k, n);
-        const c2 = divNearest(-b1 * k, n);
-        let k1 = mod(k - c1 * a1 - c2 * a2, n);
-        let k2 = mod(-c1 * b1 - c2 * b2, n);
-        const k1neg = k1 > POW_2_128;
-        const k2neg = k2 > POW_2_128;
-        if (k1neg) k1 = n - k1;
-        if (k2neg) k2 = n - k2;
-        if (k1 > POW_2_128 || k2 > POW_2_128) {
-          throw new Error('splitScalar: Endomorphism failed, k=' + k);
-        }
-        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_',
+    encodeDST: 'secp256k1_XMD:SHA-256_SSWU_NU_',
     p: Fp.ORDER,
     m: 1,
     k: 128,
-      expand: true,
+    expand: 'xmd',
     hash: sha256,
-    },
+  }
-  },
-  sha256
 );
-
+export { hashToCurve, encodeToCurve };
-// Schnorr
-const _0n = BigInt(0);
-const numTo32b = secp256k1.utils._bigintToBytes;
-const numTo32bStr = secp256k1.utils._bigintToString;
-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) {
-      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;
-    }
-    // Do we need that in schnorr at all?
-    return secp256k1.Point.fromHex(publicKey);
-  }
-}
-
-const isWithinCurveOrder = secp256k1.utils._isWithinCurveOrder;
-const isValidFieldElement = secp256k1.utils._isValidFieldElement;
-
-const TAGS = {
-  challenge: 'BIP0340/challenge',
-  aux: 'BIP0340/aux',
-  nonce: 'BIP0340/nonce',
-} as const;
-
-/** 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 {
-  let tagP = TAGGED_HASH_PREFIXES[tag];
-  if (tagP === undefined) {
-    const tagH = sha256(Uint8Array.from(tag, (c) => c.charCodeAt(0)));
-    tagP = concatBytes(tagH, tagH);
-    TAGGED_HASH_PREFIXES[tag] = tagP;
-  }
-  return sha256(concatBytes(tagP, ...messages));
-}
-
-const toRawX = (point: PointType<bigint>) => point.toRawBytes(true).slice(1);
-
-// Schnorr signatures are superior to ECDSA from above.
-// Below is Schnorr-specific code as per BIP0340.
-function schnorrChallengeFinalize(ch: Uint8Array): bigint {
-  return mod(bytesToNumberBE(ch), secp256k1.CURVE.n);
-}
-// Do we need this at all for Schnorr?
-class SchnorrSignature {
-  constructor(readonly r: bigint, readonly s: bigint) {
-    this.assertValidity();
-  }
-  static fromHex(hex: Hex) {
-    const bytes = ensureBytes(hex);
-    if (bytes.length !== 64)
-      throw new TypeError(`SchnorrSignature.fromHex: expected 64 bytes, not ${bytes.length}`);
-    const r = bytesToNumberBE(bytes.subarray(0, 32));
-    const s = bytesToNumberBE(bytes.subarray(32, 64));
-    return new SchnorrSignature(r, s);
-  }
-  assertValidity() {
-    const { r, s } = this;
-    if (!isValidFieldElement(r) || !isWithinCurveOrder(s)) throw new Error('Invalid signature');
-  }
-  toHex(): string {
-    return numTo32bStr(this.r) + numTo32bStr(this.s);
-  }
-  toRawBytes(): Uint8Array {
-    return hexToBytes(this.toHex());
-  }
-}
-
-function schnorrGetScalar(priv: bigint) {
-  const point = secp256k1.Point.fromPrivateKey(priv);
-  const scalar = point.hasEvenY() ? priv : secp256k1.CURVE.n - priv;
-  return { point, scalar, x: toRawX(point) };
-}
-/**
- * Synchronously creates Schnorr signature. Improved security: verifies itself before
- * producing an output.
- * @param msg message (not message hash)
- * @param privateKey private key
- * @param auxRand random bytes that would be added to k. Bad RNG won't break it.
- */
-function schnorrSign(
-  message: Hex,
-  privateKey: PrivKey,
-  auxRand: Hex = randomBytes(32)
-): Uint8Array {
-  if (message == null) throw new TypeError(`sign: Expected valid message, not "${message}"`);
-  const m = ensureBytes(message);
-  // checks for isWithinCurveOrder
-  const { x: px, scalar: d } = schnorrGetScalar(normalizePrivateKey(privateKey));
-  const rand = ensureBytes(auxRand);
-  if (rand.length !== 32) throw new TypeError('sign: Expected 32 bytes of aux randomness');
-  const tag = taggedHash;
-  const t0h = tag(TAGS.aux, rand);
-  const t = numTo32b(d ^ bytesToNumberBE(t0h));
-  const k0h = tag(TAGS.nonce, t, px, m);
-  const k0 = mod(bytesToNumberBE(k0h), secp256k1.CURVE.n);
-  if (k0 === _0n) throw new Error('sign: Creation of signature failed. k is zero');
-  const { point: R, x: rx, scalar: k } = schnorrGetScalar(k0);
-  const e = schnorrChallengeFinalize(tag(TAGS.challenge, rx, px, m));
-  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;
-}
-
-/**
- * Verifies Schnorr signature synchronously.
- */
-function schnorrVerify(signature: Hex, message: Hex, publicKey: Hex): boolean {
-  try {
-    const raw = signature instanceof SchnorrSignature;
-    const sig: SchnorrSignature = raw ? signature : SchnorrSignature.fromHex(signature);
-    if (raw) sig.assertValidity(); // just in case
-
-    const { r, s } = sig;
-    const m = ensureBytes(message);
-    const P = normalizePublicKey(publicKey);
-    const e = schnorrChallengeFinalize(taggedHash(TAGS.challenge, numTo32b(r), toRawX(P), m));
-    // Finalize
-    // R = s⋅G - e⋅P
-    // -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,
-  // Schnorr's pubkey is just `x` of Point (BIP340)
-  getPublicKey: (privateKey: PrivKey): Uint8Array =>
-    toRawX(secp256k1.Point.fromPrivateKey(privateKey)),
-  sign: schnorrSign,
-  verify: schnorrVerify,
-};

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);
+  },
+  bits2int_modN: (bytes: Uint8Array): bigint => {
+    let hashS = cutils.bytesToNumberBE(bytes).toString(16);
     if (hashS.length === 63) {
       hashS += '0';
-        hash = hexToBytes0x(hashS);
+      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?
@@ -88,7 +95,7 @@ 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) {
   return starkCurve.getPublicKey(normalizePrivateKey(privKey), isCompressed);
@@ -97,7 +104,7 @@ function getSharedSecret0x(privKeyA: Hex, pubKeyB: Hex) {
   return starkCurve.getSharedSecret(normalizePrivateKey(privKeyA), pubKeyB);
 }
 
-function sign0x(msgHash: Hex, privKey: Hex, opts: any) {
+function sign0x(msgHash: Hex, privKey: Hex, opts?: any) {
   if (typeof privKey === 'string') privKey = strip0x(privKey).padStart(64, '0');
   return starkCurve.sign(ensureBytes0x(msgHash), normalizePrivateKey(privKey), opts);
 }
@@ -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,
@@ -132,17 +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 limit = sha256mask - starkCurve.utils.mod(sha256mask, starkCurve.CURVE.n);
+
+  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 starkCurve.utils.mod(key, starkCurve.CURVE.n).toString(16);
+    if (key < limit) return mod(key, CURVE_N).toString(16);
   }
 }
 
@@ -164,37 +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[] = [];
@@ -203,6 +215,8 @@ function pedersenPrecompute(p1: ProjectivePoint, p2: ProjectivePoint): Projectiv
     out.push(p);
     p = p.double();
   }
+  // NOTE: we cannot use wNAF here, because last 4 bits will require full 248 bits multiplication
+  // We can add support for this to wNAF, but it will complicate wNAF.
   p = p2;
   for (let i = 0; i < 4; i++) {
     out.push(p);
@@ -231,7 +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;
   }
@@ -243,7 +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) {
@@ -258,5 +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

@@ -1,7 +1,8 @@
 import { deepStrictEqual, throws } from 'assert';
-import { should } from 'micro-should';
+import { should, describe } from 'micro-should';
 import * as fc from 'fast-check';
 import * as mod from '../lib/esm/abstract/modular.js';
+import { bytesToHex as toHex } from '../lib/esm/abstract/utils.js';
 // Generic tests for all curves in package
 import { secp192r1 } from '../lib/esm/p192.js';
 import { secp224r1 } from '../lib/esm/p224.js';
@@ -15,7 +16,286 @@ import { starkCurve } from '../lib/esm/stark.js';
 import { pallas, vesta } from '../lib/esm/pasta.js';
 import { bn254 } from '../lib/esm/bn.js';
 import { jubjub } from '../lib/esm/jubjub.js';
+import { bls12_381 } from '../lib/esm/bls12-381.js';
 
+// Fields tests
+const FIELDS = {
+  secp192r1: { Fp: [secp192r1.CURVE.Fp] },
+  secp224r1: { Fp: [secp224r1.CURVE.Fp] },
+  secp256r1: { Fp: [secp256r1.CURVE.Fp] },
+  secp521r1: { Fp: [secp521r1.CURVE.Fp] },
+  secp256k1: { Fp: [secp256k1.CURVE.Fp] },
+  stark: { Fp: [starkCurve.CURVE.Fp] },
+  jubjub: { Fp: [jubjub.CURVE.Fp] },
+  ed25519: { Fp: [ed25519.CURVE.Fp] },
+  ed448: { Fp: [ed448.CURVE.Fp] },
+  bn254: { Fp: [bn254.CURVE.Fp] },
+  pallas: { Fp: [pallas.CURVE.Fp] },
+  vesta: { Fp: [vesta.CURVE.Fp] },
+  bls12: {
+    Fp: [bls12_381.CURVE.Fp],
+    Fp2: [
+      bls12_381.CURVE.Fp2,
+      fc.array(fc.bigInt(1n, bls12_381.CURVE.Fp.ORDER - 1n), {
+        minLength: 2,
+        maxLength: 2,
+      }),
+      (Fp2, num) => Fp2.fromBigTuple([num[0], num[1]]),
+    ],
+    // Fp6: [bls12_381.CURVE.Fp6],
+    Fp12: [
+      bls12_381.CURVE.Fp12,
+      fc.array(fc.bigInt(1n, bls12_381.CURVE.Fp.ORDER - 1n), {
+        minLength: 12,
+        maxLength: 12,
+      }),
+      (Fp12, num) => Fp12.fromBigTwelve(num),
+    ],
+  },
+};
+
+for (const c in FIELDS) {
+  const curve = FIELDS[c];
+  for (const f in curve) {
+    const Fp = curve[f][0];
+    const name = `${c}/${f}:`;
+    const FC_BIGINT = curve[f][1] ? curve[f][1] : fc.bigInt(1n, Fp.ORDER - 1n);
+
+    const create = curve[f][2] ? curve[f][2].bind(null, Fp) : (num) => Fp.create(num);
+    describe(name, () => {
+      should('equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            const b = create(num);
+            deepStrictEqual(Fp.eql(a, b), true);
+            deepStrictEqual(Fp.eql(b, a), true);
+          })
+        );
+      });
+      should('non-equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
+            const a = create(num1);
+            const b = create(num2);
+            deepStrictEqual(Fp.eql(a, b), num1 === num2);
+            deepStrictEqual(Fp.eql(b, a), num1 === num2);
+          })
+        );
+      });
+      should('add/subtract/commutativity', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
+            const a = create(num1);
+            const b = create(num2);
+            deepStrictEqual(Fp.add(a, b), Fp.add(b, a));
+          })
+        );
+      });
+      should('add/subtract/associativity', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
+            const a = create(num1);
+            const b = create(num2);
+            const c = create(num3);
+            deepStrictEqual(Fp.add(a, Fp.add(b, c)), Fp.add(Fp.add(a, b), c));
+          })
+        );
+      });
+      should('add/subtract/x+0=x', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            deepStrictEqual(Fp.add(a, Fp.ZERO), a);
+          })
+        );
+      });
+      should('add/subtract/x-0=x', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            deepStrictEqual(Fp.sub(a, Fp.ZERO), a);
+            deepStrictEqual(Fp.sub(a, a), Fp.ZERO);
+          })
+        );
+      });
+      should('add/subtract/negate equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num1) => {
+            const a = create(num1);
+            const b = create(num1);
+            deepStrictEqual(Fp.sub(Fp.ZERO, a), Fp.neg(a));
+            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))));
+          })
+        );
+      });
+      should('add/subtract/negate', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            deepStrictEqual(Fp.neg(a), Fp.sub(Fp.ZERO, a));
+            deepStrictEqual(Fp.neg(a), Fp.mul(a, Fp.create(-1n)));
+          })
+        );
+      });
+      should('negate(0)', () => {
+        deepStrictEqual(Fp.neg(Fp.ZERO), Fp.ZERO);
+      });
+
+      should('multiply/commutativity', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
+            const a = create(num1);
+            const b = create(num2);
+            deepStrictEqual(Fp.mul(a, b), Fp.mul(b, a));
+          })
+        );
+      });
+      should('multiply/associativity', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
+            const a = create(num1);
+            const b = create(num2);
+            const c = create(num3);
+            deepStrictEqual(Fp.mul(a, Fp.mul(b, c)), Fp.mul(Fp.mul(a, b), c));
+          })
+        );
+      });
+      should('multiply/distributivity', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
+            const a = create(num1);
+            const b = create(num2);
+            const c = create(num3);
+            deepStrictEqual(Fp.mul(a, Fp.add(b, c)), Fp.add(Fp.mul(b, a), Fp.mul(c, a)));
+          })
+        );
+      });
+      should('multiply/add equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            deepStrictEqual(Fp.mul(a, 0n), Fp.ZERO);
+            deepStrictEqual(Fp.mul(a, Fp.ZERO), Fp.ZERO);
+            deepStrictEqual(Fp.mul(a, 1n), a);
+            deepStrictEqual(Fp.mul(a, Fp.ONE), a);
+            deepStrictEqual(Fp.mul(a, 2n), Fp.add(a, a));
+            deepStrictEqual(Fp.mul(a, 3n), Fp.add(Fp.add(a, a), a));
+            deepStrictEqual(Fp.mul(a, 4n), Fp.add(Fp.add(Fp.add(a, a), a), a));
+          })
+        );
+      });
+      should('multiply/square equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            deepStrictEqual(Fp.sqr(a), Fp.mul(a, a));
+          })
+        );
+      });
+      should('multiply/pow equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            deepStrictEqual(Fp.pow(a, 0n), Fp.ONE);
+            deepStrictEqual(Fp.pow(a, 1n), a);
+            deepStrictEqual(Fp.pow(a, 2n), Fp.mul(a, a));
+            deepStrictEqual(Fp.pow(a, 3n), Fp.mul(Fp.mul(a, a), a));
+          })
+        );
+      });
+
+      should('square(0)', () => {
+        deepStrictEqual(Fp.sqr(Fp.ZERO), Fp.ZERO);
+        deepStrictEqual(Fp.mul(Fp.ZERO, Fp.ZERO), Fp.ZERO);
+      });
+
+      should('square(1)', () => {
+        deepStrictEqual(Fp.sqr(Fp.ONE), Fp.ONE);
+        deepStrictEqual(Fp.mul(Fp.ONE, Fp.ONE), Fp.ONE);
+      });
+
+      should('square(-1)', () => {
+        const minus1 = Fp.neg(Fp.ONE);
+        deepStrictEqual(Fp.sqr(minus1), Fp.ONE);
+        deepStrictEqual(Fp.mul(minus1, minus1), Fp.ONE);
+      });
+
+      const isSquare = mod.FpIsSquare(Fp);
+      // Not implemented
+      if (Fp !== bls12_381.CURVE.Fp12) {
+        should('multiply/sqrt', () => {
+          fc.assert(
+            fc.property(FC_BIGINT, (num) => {
+              const a = create(num);
+              let root;
+              try {
+                root = Fp.sqrt(a);
+              } catch (e) {
+                deepStrictEqual(isSquare(a), false);
+                return;
+              }
+              deepStrictEqual(isSquare(a), true);
+              deepStrictEqual(Fp.eql(Fp.sqr(root), a), true, 'sqrt(a)^2 == a');
+              deepStrictEqual(Fp.eql(Fp.sqr(Fp.neg(root)), a), true, '(-sqrt(a))^2 == a');
+            })
+          );
+        });
+
+        should('sqrt(0)', () => {
+          deepStrictEqual(Fp.sqrt(Fp.ZERO), Fp.ZERO);
+          const sqrt1 = Fp.sqrt(Fp.ONE);
+          deepStrictEqual(
+            Fp.eql(sqrt1, Fp.ONE) || Fp.eql(sqrt1, Fp.neg(Fp.ONE)),
+            true,
+            'sqrt(1) = 1 or -1'
+          );
+        });
+      }
+
+      should('div/division by one equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            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);
+          })
+        );
+      });
+      should('zero division equality', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, (num) => {
+            const a = create(num);
+            deepStrictEqual(Fp.div(Fp.ZERO, a), Fp.ZERO);
+          })
+        );
+      });
+      should('div/division distributivity', () => {
+        fc.assert(
+          fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
+            const a = create(num1);
+            const b = create(num2);
+            const c = create(num3);
+            deepStrictEqual(Fp.div(Fp.add(a, b), c), Fp.add(Fp.div(a, c), Fp.div(b, c)));
+          })
+        );
+      });
+      should('div/division and multiplication equality', () => {
+        fc.assert(
+          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.inv(b)));
+          })
+        );
+      });
+    });
+  }
+}
+
+// Group tests
 // prettier-ignore
 const CURVES = {
   secp192r1, secp224r1, secp256r1, secp384r1, secp521r1,
@@ -29,6 +309,7 @@ const CURVES = {
 };
 
 const NUM_RUNS = 5;
+
 const getXY = (p) => ({ x: p.x, y: p.y });
 
 function equal(a, b, comment) {
@@ -61,9 +342,12 @@ 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(`${name}/${pointName}/Basic group laws (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');
@@ -71,37 +355,37 @@ for (const name in CURVES) {
           for (let i = 0; i < G.length; i++) {
             const p = G[i];
             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], `${i + 1}*0 = 0`);
           }
         });
-    should(`${name}/${pointName}/Basic group laws (one)`, () => {
+        should('one', () => {
           equal(G[1].double(), G[2], '(1*G).double() = 2*G');
           equal(G[1].subtract(G[1]), G[0], '1*G - 1*G = 0');
           equal(G[1].add(G[1]), G[2], '1*G + 1*G = 2*G');
         });
-    should(`${name}/${pointName}/Basic group laws (sanity tests)`, () => {
+        should('sanity tests', () => {
-      equal(G[2].double(), G[4], `(2*G).double() = 4*G`);
+          equal(G[2].double(), G[4], '(2*G).double() = 4*G');
-      equal(G[2].add(G[2]), G[4], `2*G + 2*G = 4*G`);
+          equal(G[2].add(G[2]), G[4], '2*G + 2*G = 4*G');
-      equal(G[7].add(G[3].negate()), G[4], `7*G - 3*G = 4*G`);
+          equal(G[7].add(G[3].negate()), G[4], '7*G - 3*G = 4*G');
         });
-    should(`${name}/${pointName}/Basic group laws (addition commutativity)`, () => {
+        should('add commutativity', () => {
-      equal(G[4].add(G[3]), G[3].add(G[4]), `4*G + 3*G = 3*G + 4*G`);
+          equal(G[4].add(G[3]), G[3].add(G[4]), '4*G + 3*G = 3*G + 4*G');
-      equal(G[4].add(G[3]), G[3].add(G[2]).add(G[2]), `4*G + 3*G = 3*G + 2*G + 2*G`);
+          equal(G[4].add(G[3]), G[3].add(G[2]).add(G[2]), '4*G + 3*G = 3*G + 2*G + 2*G');
         });
-    should(`${name}/${pointName}/Basic group laws (double)`, () => {
+        should('double', () => {
           equal(G[3].double(), G[6], '(3*G).double() = 6*G');
         });
-    should(`${name}/${pointName}/Basic group laws (multiply)`, () => {
+        should('multiply', () => {
-      equal(G[2].multiply(3), G[6], '(2*G).multiply(3) = 6*G');
+          equal(G[2].multiply(3n), G[6], '(2*G).multiply(3) = 6*G');
         });
-    should(`${name}/${pointName}/Basic group laws (same point addition)`, () => {
+        should('add same-point', () => {
-      equal(G[3].add(G[3]), G[6], `3*G + 3*G = 6*G`);
+          equal(G[3].add(G[3]), G[6], '3*G + 3*G = 6*G');
         });
-    should(`${name}/${pointName}/Basic group laws (same point (negative) addition)`, () => {
+        should('add same-point negative', () => {
           equal(G[3].add(G[3].negate()), G[0], '3*G + (- 3*G) = 0*G');
           equal(G[3].subtract(G[3]), G[0], '3*G - 3*G = 0*G');
         });
-    should(`${name}/${pointName}/Basic group laws (curve order)`, () => {
+        should('mul by curve order', () => {
           equal(G[1].multiply(CURVE_ORDER - 1n).add(G[1]), G[0], '(N-1)*G + G = 0');
           equal(G[1].multiply(CURVE_ORDER - 1n).add(G[2]), G[1], '(N-1)*G + 2*G = 1*G');
           equal(G[1].multiply(CURVE_ORDER - 2n).add(G[2]), G[0], '(N-2)*G + 2*G = 0');
@@ -109,7 +393,7 @@ for (const name in CURVES) {
           const carry = CURVE_ORDER % 2n === 1n ? G[1] : G[0];
           equal(G[1].multiply(half).double().add(carry), G[0], '((N/2) * G).double() = 0');
         });
-    should(`${name}/${pointName}/Basic group laws (inversion)`, () => {
+        should('inversion', () => {
           const a = 1234n;
           const b = 5678n;
           const c = a * b;
@@ -117,7 +401,7 @@ for (const name in CURVES) {
           const inv = mod.invert(b, CURVE_ORDER);
           equal(G[1].multiply(c).multiply(inv), G[1].multiply(a), 'c*G * (1/b)*G = a*G');
         });
-    should(`${name}/${pointName}/Basic group laws (multiply, rand)`, () =>
+        should('multiply, rand', () =>
           fc.assert(
             fc.property(FC_BIGINT, FC_BIGINT, (a, b) => {
               const c = mod.mod(a + b, CURVE_ORDER);
@@ -125,27 +409,29 @@ for (const name in CURVES) {
               const pA = G[1].multiply(a);
               const pB = G[1].multiply(b);
               const pC = G[1].multiply(c);
-          equal(pA.add(pB), pB.add(pA), `pA + pB = pB + pA`);
+              equal(pA.add(pB), pB.add(pA), 'pA + pB = pB + pA');
-          equal(pA.add(pB), pC, `pA + pB = pC`);
+              equal(pA.add(pB), pC, 'pA + pB = pC');
             }),
             { numRuns: NUM_RUNS }
           )
         );
-    should(`${name}/${pointName}/Basic group laws (multiply2, rand)`, () =>
+        should('multiply2, rand', () =>
           fc.assert(
             fc.property(FC_BIGINT, FC_BIGINT, (a, b) => {
               const c = mod.mod(a * b, CURVE_ORDER);
               const pA = G[1].multiply(a);
               const pB = G[1].multiply(b);
-          equal(pA.multiply(b), pB.multiply(a), `b*pA = a*pB`);
+              equal(pA.multiply(b), pB.multiply(a), 'b*pA = a*pB');
-          equal(pA.multiply(b), G[1].multiply(c), `b*pA = c*G`);
+              equal(pA.multiply(b), G[1].multiply(c), 'b*pA = c*G');
             }),
             { numRuns: NUM_RUNS }
           )
         );
+      });
 
       for (const op of ['add', 'subtract']) {
-      should(`${name}/${pointName}/${op} type check`, () => {
+        describe(op, () => {
+          should('type check', () => {
             throws(() => G[1][op](0), '0');
             throws(() => G[1][op](0n), '0n');
             G[1][op](G[2]);
@@ -153,17 +439,21 @@ for (const name in CURVES) {
             throws(() => G[1][op](123.456), '123.456');
             throws(() => G[1][op](true), 'true');
             throws(() => G[1][op]('1'), "'1'");
-        throws(() => G[1][op]({ x: 1n, y: 1n, z: 1n, t: 1n }), '{ x: 1n, y: 1n, z: 1n, t: 1n }');
+            throws(
+              () => G[1][op]({ x: 1n, y: 1n, z: 1n, t: 1n }),
+              '{ x: 1n, y: 1n, z: 1n, t: 1n }'
+            );
             throws(() => G[1][op](new Uint8Array([])), 'ui8a([])');
             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`);
           });
+        });
       }
 
-    should(`${name}/${pointName}/equals type check`, () => {
+      should('equals type check', () => {
         throws(() => G[1].equals(0), '0');
         throws(() => G[1].equals(0n), '0n');
         deepStrictEqual(G[1].equals(G[2]), false, '1*G != 2*G');
@@ -178,13 +468,14 @@ 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');
       });
 
       for (const op of ['multiply', 'multiplyUnsafe']) {
         if (!p.BASE[op]) continue;
-      should(`${name}/${pointName}/${op} type check`, () => {
+        describe(op, () => {
+          should('type check', () => {
             if (op !== 'multiplyUnsafe') {
               throws(() => G[1][op](0), '0');
               throws(() => G[1][op](0n), '0n');
@@ -203,23 +494,24 @@ for (const name in CURVES) {
             throws(() => G[1][op](new Uint8Array(4096).fill(1)), 'ui8a(4096*[1])');
             throws(() => G[1][op](o.BASE), 'other curve point');
           });
+        });
       }
       // Complex point (Extended/Jacobian/Projective?)
-    if (p.BASE.toAffine) {
+      // if (p.BASE.toAffine && C.Point) {
-      should(`${name}/${pointName}/toAffine()`, () => {
+      //   should('toAffine()', () => {
-        equal(p.ZERO.toAffine(), C.Point.ZERO, `0 = 0`);
+      //     equal(p.ZERO.toAffine(), C.Point.ZERO, '0 = 0');
-        equal(p.BASE.toAffine(), C.Point.BASE, `1 = 1`);
+      //     equal(p.BASE.toAffine(), C.Point.BASE, '1 = 1');
-      });
+      //   });
-    }
+      // }
-    if (p.fromAffine) {
+      // if (p.fromAffine && C.Point) {
-      should(`${name}/${pointName}/fromAffine()`, () => {
+      //   should('fromAffine()', () => {
-        equal(p.ZERO, p.fromAffine(C.Point.ZERO), `0 = 0`);
+      //     equal(p.ZERO, p.fromAffine(C.Point.ZERO), '0 = 0');
-        equal(p.BASE, p.fromAffine(C.Point.BASE), `1 = 1`);
+      //     equal(p.BASE, p.fromAffine(C.Point.BASE), '1 = 1');
-      });
+      //   });
-    }
+      // }
       // toHex/fromHex (if available)
       if (p.fromHex && p.BASE.toHex) {
-      should(`${name}/${pointName}/fromHex(toHex()) roundtrip`, () => {
+        should('fromHex(toHex()) roundtrip', () => {
           fc.assert(
             fc.property(FC_BIGINT, (x) => {
               const hex = p.BASE.multiply(x).toHex();
@@ -228,50 +520,73 @@ for (const name in CURVES) {
           );
         });
       }
+    });
   }
+  describe(name, () => {
     // Generic complex things (getPublicKey/sign/verify/getSharedSecret)
-  should(`${name}/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(123), '123');
       throws(() => C.getPublicKey(123.456), '123.456');
       throws(() => C.getPublicKey(true), 'true');
       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(`${name}.verify()/should verify random signatures`, () =>
+    should('.verify() should verify random signatures', () =>
       fc.assert(
         fc.property(fc.hexaString({ minLength: 64, maxLength: 64 }), (msg) => {
           const priv = C.utils.randomPrivateKey();
           const pub = C.getPublicKey(priv);
           const sig = C.sign(msg, priv);
-        deepStrictEqual(C.verify(sig, msg, pub), true);
+          deepStrictEqual(
+            C.verify(sig, msg, pub),
+            true,
+            'priv=${toHex(priv)},pub=${toHex(pub)},msg=${msg}'
+          );
         }),
         { numRuns: NUM_RUNS }
       )
     );
-  should(`${name}.sign()/edge cases`, () => {
+    should('.sign() edge cases', () => {
       throws(() => C.sign());
       throws(() => C.sign(''));
     });
 
-  should(`${name}.verify()/should not verify signature with wrong hash`, () => {
+    describe('verify()', () => {
-    const MSG = '01'.repeat(32);
+      should('true for proper signatures', () => {
-    const PRIV_KEY = 0x2n;
+        const msg = '01'.repeat(32);
-    const WRONG_MSG = '11'.repeat(32);
+        const priv = C.utils.randomPrivateKey();
-    const signature = C.sign(MSG, PRIV_KEY);
+        const sig = C.sign(msg, priv);
-    const publicKey = C.getPublicKey(PRIV_KEY);
+        const pub = C.getPublicKey(priv);
-    deepStrictEqual(C.verify(signature, WRONG_MSG, publicKey), false);
+        deepStrictEqual(C.verify(sig, msg, pub), true);
+      });
+      should('false for wrong messages', () => {
+        const msg = '01'.repeat(32);
+        const priv = C.utils.randomPrivateKey();
+        const sig = C.sign(msg, priv);
+        const pub = C.getPublicKey(priv);
+        deepStrictEqual(C.verify(sig, '11'.repeat(32), pub), false);
+      });
+      should('false for wrong keys', () => {
+        const msg = '01'.repeat(32);
+        const priv = C.utils.randomPrivateKey();
+        const sig = C.sign(msg, priv);
+        deepStrictEqual(C.verify(sig, msg, C.getPublicKey(C.utils.randomPrivateKey())), false);
+      });
     });
     // NOTE: fails for ed, because of empty message. Since we convert it to scalar,
     // need to check what other implementations do. Empty message != new Uint8Array([0]), but what scalar should be in that case?
-  // should(`${name}/should not verify signature with wrong message`, () => {
+    // should('should not verify signature with wrong message', () => {
     //   fc.assert(
     //     fc.property(
     //       fc.array(fc.integer({ min: 0x00, max: 0xff })),
@@ -293,7 +608,7 @@ for (const name in CURVES) {
     // });
 
     if (C.getSharedSecret) {
-    should(`${name}/getSharedSecret() should be commutative`, () => {
+      should('getSharedSecret() should be commutative', () => {
         for (let i = 0; i < NUM_RUNS; i++) {
           const asec = C.utils.randomPrivateKey();
           const apub = C.getPublicKey(asec);
@@ -308,7 +623,24 @@ for (const name in CURVES) {
         }
       });
     }
+  });
 }
+
+should('secp224k1 sqrt bug', () => {
+  const { Fp } = secp224r1.CURVE;
+  const sqrtMinus1 = Fp.sqrt(-1n);
+  // Verified against sage
+  deepStrictEqual(
+    sqrtMinus1,
+    23621584063597419797792593680131996961517196803742576047493035507225n
+  );
+  deepStrictEqual(
+    Fp.neg(sqrtMinus1),
+    3338362603553219996874421406887633712040719456283732096017030791656n
+  );
+  deepStrictEqual(Fp.sqr(sqrtMinus1), Fp.create(-1n));
+});
+
 // ESM is broken.
 import url from 'url';
 if (import.meta.url === url.pathToFileURL(process.argv[1]).href) {

test/ed25519.test.js

@@ -1,7 +1,14 @@
-import { deepStrictEqual, throws } from 'assert';
+import { deepEqual, deepStrictEqual, strictEqual, throws } from 'assert';
-import { should } from 'micro-should';
+import { describe, should } from 'micro-should';
 import * as fc from 'fast-check';
-import { ed25519, ed25519ctx, ed25519ph, x25519, RistrettoPoint } from '../lib/esm/ed25519.js';
+import {
+  ed25519,
+  ed25519ctx,
+  ed25519ph,
+  x25519,
+  RistrettoPoint,
+  ED25519_TORSION_SUBGROUP,
+} from '../lib/esm/ed25519.js';
 import { readFileSync } from 'fs';
 import { default as zip215 } from './ed25519/zip215.json' assert { type: 'json' };
 import { hexToBytes, bytesToHex, randomBytes } from '@noble/hashes/utils';
@@ -10,29 +17,31 @@ import { sha512 } from '@noble/hashes/sha512';
 import { default as ed25519vectors } from './wycheproof/eddsa_test.json' assert { type: 'json' };
 import { default as x25519vectors } from './wycheproof/x25519_test.json' assert { type: 'json' };
 
-const ed = ed25519;
+describe('ed25519', () => {
-const hex = bytesToHex;
+  const ed = ed25519;
+  const hex = bytesToHex;
+  const Point = ed.ExtendedPoint;
 
-function to32Bytes(numOrStr) {
+  function to32Bytes(numOrStr) {
     let hex = typeof numOrStr === 'string' ? numOrStr : numOrStr.toString(16);
     return hexToBytes(hex.padStart(64, '0'));
-}
+  }
 
-function utf8ToBytes(str) {
+  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);
-}
+  }
 
-ed.utils.precompute(8);
+  ed.utils.precompute(8);
 
-should('ed25519/should not accept >32byte private keys', () => {
+  should('not accept >32byte private keys', () => {
     const invalidPriv =
       100000000000000000000000000000000000009000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000090000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000800073278156000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000n;
     throws(() => ed.getPublicKey(invalidPriv));
-});
+  });
-should('ed25519/should verify recent signature', () => {
+  should('verify recent signature', () => {
     fc.assert(
       fc.property(
         fc.hexaString({ minLength: 2, maxLength: 32 }),
@@ -47,8 +56,8 @@ should('ed25519/should verify recent signature', () => {
       ),
       { numRuns: 5 }
     );
-});
+  });
-should('ed25519/should not verify signature with wrong message', () => {
+  should('not verify signature with wrong message', () => {
     fc.assert(
       fc.property(
         fc.array(fc.integer({ min: 0x00, max: 0xff })),
@@ -68,101 +77,84 @@ should('ed25519/should not verify signature with wrong message', () => {
       ),
       { numRuns: 5 }
     );
-});
+  });
-const privKey = to32Bytes('a665a45920422f9d417e4867ef');
+  const privKey = to32Bytes('a665a45920422f9d417e4867ef');
-const msg = hexToBytes('874f9960c5d2b7a9b5fad383e1ba44719ebb743a');
+  const wrongPriv = to32Bytes('a675a45920422f9d417e4867ef');
-const wrongMsg = hexToBytes('589d8c7f1da0a24bc07b7381ad48b1cfc211af1c');
+  const msg = hexToBytes('874f9960c5d2b7a9b5fad383e1ba44719ebb743a');
-should('ed25519/basic methods/should sign and verify', () => {
+  const wrongMsg = hexToBytes('589d8c7f1da0a24bc07b7381ad48b1cfc211af1c');
+  describe('basic methods', () => {
+    should('sign and verify', () => {
       const publicKey = ed.getPublicKey(privKey);
       const signature = ed.sign(msg, privKey);
       deepStrictEqual(ed.verify(signature, msg, publicKey), true);
-});
+    });
-should('ed25519/basic methods/should not verify signature with wrong public key', () => {
+  });
-  const publicKey = ed.getPublicKey(12);
+  describe('sync methods', () => {
-  const signature = ed.sign(msg, privKey);
+    should('sign and verify', () => {
-  deepStrictEqual(ed.verify(signature, msg, publicKey), false);
-});
-should('ed25519/basic methods/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);
-});
-
-should('ed25519/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('ed25519/sync methods/should not verify signature with wrong public key', () => {
+    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);
-});
+    });
-should('ed25519/sync methods/should not verify signature with wrong hash', () => {
+    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);
-});
+    });
-
+  });
-// 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]) {
-    throws(() => ed.Point.BASE.multiply(num));
+        throws(() => Point.BASE.multiply(num));
       }
-});
+    });
+  });
 
-// https://ed25519.cr.yp.to/python/sign.py
+  // https://ed25519.cr.yp.to/python/sign.py
-// https://ed25519.cr.yp.to/python/sign.input
+  // https://ed25519.cr.yp.to/python/sign.input
-const data = readFileSync('./test/ed25519/vectors.txt', 'utf-8');
+  const data = readFileSync('./test/ed25519/vectors.txt', 'utf-8');
-const vectors = data
+  const vectors = data
     .trim()
     .split('\n')
     .map((line) => line.split(':'));
-should('ed25519 official vectors/should match 1024 official vectors', () => {
+  should('ed25519 official vectors/should match 1024 official vectors', () => {
     for (let i = 0; i < vectors.length; i++) {
       const vector = vectors[i];
       // Extract.
@@ -174,17 +166,17 @@ should('ed25519 official vectors/should match 1024 official vectors', () => {
       // 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);
       // expect(pub).toBe(expectedPub);
       deepStrictEqual(signature, expectedSignature);
     }
-});
+  });
 
-// https://tools.ietf.org/html/rfc8032#section-7
+  // https://tools.ietf.org/html/rfc8032#section-7
-should('rfc8032 vectors/should create right signature for 0x9d and empty string', () => {
+  should('rfc8032 vectors/should create right signature for 0x9d and empty string', () => {
     const privateKey = '9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60';
     const publicKey = ed.getPublicKey(privateKey);
     const message = '';
@@ -197,8 +189,8 @@ should('rfc8032 vectors/should create right signature for 0x9d and empty string'
       hex(signature),
       'e5564300c360ac729086e2cc806e828a84877f1eb8e5d974d873e065224901555fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b'
     );
-});
+  });
-should('rfc8032 vectors/should create right signature for 0x4c and 72', () => {
+  should('rfc8032 vectors/should create right signature for 0x4c and 72', () => {
     const privateKey = '4ccd089b28ff96da9db6c346ec114e0f5b8a319f35aba624da8cf6ed4fb8a6fb';
     const publicKey = ed.getPublicKey(privateKey);
     const message = '72';
@@ -211,8 +203,8 @@ should('rfc8032 vectors/should create right signature for 0x4c and 72', () => {
       hex(signature),
       '92a009a9f0d4cab8720e820b5f642540a2b27b5416503f8fb3762223ebdb69da085ac1e43e15996e458f3613d0f11d8c387b2eaeb4302aeeb00d291612bb0c00'
     );
-});
+  });
-should('rfc8032 vectors/should create right signature for 0x00 and 5a', () => {
+  should('rfc8032 vectors/should create right signature for 0x00 and 5a', () => {
     const privateKey = '002fdd1f7641793ab064bb7aa848f762e7ec6e332ffc26eeacda141ae33b1783';
     const publicKey = ed.getPublicKey(privateKey);
     const message =
@@ -226,8 +218,8 @@ should('rfc8032 vectors/should create right signature for 0x00 and 5a', () => {
       hex(signature),
       '0df3aa0d0999ad3dc580378f52d152700d5b3b057f56a66f92112e441e1cb9123c66f18712c87efe22d2573777296241216904d7cdd7d5ea433928bd2872fa0c'
     );
-});
+  });
-should('rfc8032 vectors/should create right signature for 0xf5 and long msg', () => {
+  should('rfc8032 vectors/should create right signature for 0xf5 and long msg', () => {
     const privateKey = 'f5e5767cf153319517630f226876b86c8160cc583bc013744c6bf255f5cc0ee5';
     const publicKey = ed.getPublicKey(privateKey);
     const message =
@@ -241,66 +233,66 @@ should('rfc8032 vectors/should create right signature for 0xf5 and long msg', ()
       hex(signature),
       '0aab4c900501b3e24d7cdf4663326a3a87df5e4843b2cbdb67cbf6e460fec350aa5371b1508f9f4528ecea23c436d94b5e8fcd4f681e30a6ac00a9704a188a03'
     );
-});
+  });
 
-// const PRIVATE_KEY = 0xa665a45920422f9d417e4867efn;
+  // const PRIVATE_KEY = 0xa665a45920422f9d417e4867efn;
-// const MESSAGE = ripemd160(new Uint8Array([97, 98, 99, 100, 101, 102, 103]));
+  // const MESSAGE = ripemd160(new Uint8Array([97, 98, 99, 100, 101, 102, 103]));
-// prettier-ignore
+  // prettier-ignore
-// const MESSAGE = new Uint8Array([
+  // const MESSAGE = new Uint8Array([
-//   135, 79, 153, 96, 197, 210, 183, 169, 181, 250, 211, 131, 225, 186, 68, 113, 158, 187, 116, 58,
+  //   135, 79, 153, 96, 197, 210, 183, 169, 181, 250, 211, 131, 225, 186, 68, 113, 158, 187, 116, 58,
-// ]);
+  // ]);
-// const WRONG_MESSAGE = ripemd160(new Uint8Array([98, 99, 100, 101, 102, 103]));
+  // const WRONG_MESSAGE = ripemd160(new Uint8Array([98, 99, 100, 101, 102, 103]));
-// prettier-ignore
+  // prettier-ignore
-// const WRONG_MESSAGE = new Uint8Array([
+  // const WRONG_MESSAGE = new Uint8Array([
-//   88, 157, 140, 127, 29, 160, 162, 75, 192, 123, 115, 129, 173, 72, 177, 207, 194, 17, 175, 28,
+  //   88, 157, 140, 127, 29, 160, 162, 75, 192, 123, 115, 129, 173, 72, 177, 207, 194, 17, 175, 28,
-// ]);
+  // ]);
-// // it("should verify just signed message", async () => {
+  // // it("should verify just signed message", async () => {
-// //   await fc.assert(fc.asyncProperty(
+  // //   await fc.assert(fc.asyncProperty(
-// //     fc.hexa(),
+  // //     fc.hexa(),
-// //     fc.bigInt(2n, ristretto25519.PRIME_ORDER),
+  // //     fc.bigInt(2n, ristretto25519.PRIME_ORDER),
-// //     async (message, privateKey) => {
+  // //     async (message, privateKey) => {
-// //       const publicKey = await ristretto25519.getPublicKey(privateKey);
+  // //       const publicKey = await ristretto25519.getPublicKey(privateKey);
-// //       const signature = await ristretto25519.sign(message, privateKey);
+  // //       const signature = await ristretto25519.sign(message, privateKey);
-// //       expect(publicKey.length).toBe(32);
+  // //       expect(publicKey.length).toBe(32);
-// //       expect(signature.length).toBe(64);
+  // //       expect(signature.length).toBe(64);
-// //       expect(await ristretto25519.verify(signature, message, publicKey)).toBe(true);
+  // //       expect(await ristretto25519.verify(signature, message, publicKey)).toBe(true);
-// //     }),
+  // //     }),
-// //    { numRuns: 1 }
+  // //    { numRuns: 1 }
-// //   );
+  // //   );
-// // });
+  // // });
-// // it("should not verify sign with wrong message", async () => {
+  // // it("should not verify sign with wrong message", async () => {
-// //   await fc.assert(fc.asyncProperty(
+  // //   await fc.assert(fc.asyncProperty(
-// //     fc.array(fc.integer(0x00, 0xff)),
+  // //     fc.array(fc.integer(0x00, 0xff)),
-// //     fc.array(fc.integer(0x00, 0xff)),
+  // //     fc.array(fc.integer(0x00, 0xff)),
-// //     fc.bigInt(2n, ristretto25519.PRIME_ORDER),
+  // //     fc.bigInt(2n, ristretto25519.PRIME_ORDER),
-// //     async (bytes, wrongBytes, privateKey) => {
+  // //     async (bytes, wrongBytes, privateKey) => {
-// //       const message = new Uint8Array(bytes);
+  // //       const message = new Uint8Array(bytes);
-// //       const wrongMessage = new Uint8Array(wrongBytes);
+  // //       const wrongMessage = new Uint8Array(wrongBytes);
-// //       const publicKey = await ristretto25519.getPublicKey(privateKey);
+  // //       const publicKey = await ristretto25519.getPublicKey(privateKey);
-// //       const signature = await ristretto25519.sign(message, privateKey);
+  // //       const signature = await ristretto25519.sign(message, privateKey);
-// //       expect(await ristretto25519.verify(signature, wrongMessage, publicKey)).toBe(
+  // //       expect(await ristretto25519.verify(signature, wrongMessage, publicKey)).toBe(
-// //         bytes.toString() === wrongBytes.toString()
+  // //         bytes.toString() === wrongBytes.toString()
-// //       );
+  // //       );
-// //     }),
+  // //     }),
-// //    { numRuns: 1 }
+  // //    { numRuns: 1 }
-// //   );
+  // //   );
-// // });
+  // // });
-// // it("should sign and verify", async () => {
+  // // it("should sign and verify", async () => {
-// //   const publicKey = await ristretto25519.getPublicKey(PRIVATE_KEY);
+  // //   const publicKey = await ristretto25519.getPublicKey(PRIVATE_KEY);
-// //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
+  // //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
-// //   expect(await ristretto25519.verify(signature, MESSAGE, publicKey)).toBe(true);
+  // //   expect(await ristretto25519.verify(signature, MESSAGE, publicKey)).toBe(true);
-// // });
+  // // });
-// // it("should not verify signature with wrong public key", async () => {
+  // // it("should not verify signature with wrong public key", async () => {
-// //   const publicKey = await ristretto25519.getPublicKey(12);
+  // //   const publicKey = await ristretto25519.getPublicKey(12);
-// //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
+  // //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
-// //   expect(await ristretto25519.verify(signature, MESSAGE, publicKey)).toBe(false);
+  // //   expect(await ristretto25519.verify(signature, MESSAGE, publicKey)).toBe(false);
-// // });
+  // // });
-// // it("should not verify signature with wrong hash", async () => {
+  // // it("should not verify signature with wrong hash", async () => {
-// //   const publicKey = await ristretto25519.getPublicKey(PRIVATE_KEY);
+  // //   const publicKey = await ristretto25519.getPublicKey(PRIVATE_KEY);
-// //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
+  // //   const signature = await ristretto25519.sign(MESSAGE, PRIVATE_KEY);
-// //   expect(await ristretto25519.verify(signature, WRONG_MESSAGE, publicKey)).toBe(false);
+  // //   expect(await ristretto25519.verify(signature, WRONG_MESSAGE, publicKey)).toBe(false);
-// // });
+  // // });
-should('ristretto255/should follow the byte encodings of small multiples', () => {
+  should('ristretto255/should follow the byte encodings of small multiples', () => {
     const encodingsOfSmallMultiples = [
       // This is the identity point
       '0000000000000000000000000000000000000000000000000000000000000000',
@@ -329,8 +321,8 @@ should('ristretto255/should follow the byte encodings of small multiples', () =>
       deepStrictEqual(RistrettoPoint.fromHex(encoded).toHex(), encoded);
       P = P.add(B);
     }
-});
+  });
-should('ristretto255/should not convert bad bytes encoding', () => {
+  should('ristretto255/should not convert bad bytes encoding', () => {
     const badEncodings = [
       // These are all bad because they're non-canonical field encodings.
       '00ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff',
@@ -371,8 +363,8 @@ should('ristretto255/should not convert bad bytes encoding', () => {
       const b = hexToBytes(badBytes);
       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',
@@ -397,9 +389,9 @@ should('ristretto255/should create right points from uniform hash', async () =>
       const point = RistrettoPoint.hashToCurve(hash);
       deepStrictEqual(point.toHex(), encodedHashToPoints[i]);
     }
-});
+  });
 
-should('input immutability: sign/verify are immutable', () => {
+  should('input immutability: sign/verify are immutable', () => {
     const privateKey = ed.utils.randomPrivateKey();
     const publicKey = ed.getPublicKey(privateKey);
 
@@ -417,11 +409,11 @@ should('input immutability: sign/verify are immutable', () => {
       if (!ed.verify(signatureCopy, payload, publicKey))
         throw new Error('Copied signature verification failed');
     }
-});
+  });
 
-// https://zips.z.cash/zip-0215
+  // https://zips.z.cash/zip-0215
-// Vectors from https://gist.github.com/hdevalence/93ed42d17ecab8e42138b213812c8cc7
+  // Vectors from https://gist.github.com/hdevalence/93ed42d17ecab8e42138b213812c8cc7
-should('ZIP-215 compliance tests/should pass all of them', () => {
+  should('ZIP-215 compliance tests/should pass all of them', () => {
     const str = utf8ToBytes('Zcash');
     for (let v of zip215) {
       let noble = false;
@@ -430,16 +422,17 @@ should('ZIP-215 compliance tests/should pass all of them', () => {
       } 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', () => {
+  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 = [
+  const rfc7748Mul = [
     {
       scalar: 'a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4',
       u: 'e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c',
@@ -450,29 +443,29 @@ const rfc7748Mul = [
       u: 'e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a493',
       outputU: '95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957',
     },
-];
+  ];
-for (let i = 0; i < rfc7748Mul.length; i++) {
+  for (let i = 0; i < rfc7748Mul.length; i++) {
     const v = rfc7748Mul[i];
     should(`RFC7748: scalarMult (${i})`, () => {
       deepStrictEqual(hex(x25519.scalarMult(v.scalar, v.u)), v.outputU);
     });
-}
+  }
 
-const rfc7748Iter = [
+  const rfc7748Iter = [
     { scalar: '422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079', iters: 1 },
     { scalar: '684cf59ba83309552800ef566f2f4d3c1c3887c49360e3875f2eb94d99532c51', iters: 1000 },
     // { scalar: '7c3911e0ab2586fd864497297e575e6f3bc601c0883c30df5f4dd2d24f665424', iters: 1000000 },
-];
+  ];
-for (let i = 0; i < rfc7748Iter.length; i++) {
+  for (let i = 0; i < rfc7748Iter.length; i++) {
     const { scalar, iters } = rfc7748Iter[i];
     should(`RFC7748: scalarMult iteration (${i})`, () => {
       let k = x25519.Gu;
       for (let i = 0, u = k; i < iters; i++) [k, u] = [x25519.scalarMult(k, u), k];
       deepStrictEqual(hex(k), scalar);
     });
-}
+  }
 
-should('RFC7748 getSharedKey', () => {
+  should('RFC7748 getSharedKey', () => {
     const alicePrivate = '77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a';
     const alicePublic = '8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a';
     const bobPrivate = '5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb';
@@ -482,31 +475,31 @@ should('RFC7748 getSharedKey', () => {
     deepStrictEqual(bobPublic, hex(x25519.getPublicKey(bobPrivate)));
     deepStrictEqual(hex(x25519.scalarMult(alicePrivate, bobPublic)), shared);
     deepStrictEqual(hex(x25519.scalarMult(bobPrivate, alicePublic)), shared);
-});
+  });
 
-// should('X25519/getSharedSecret() should be commutative', () => {
+  // should('X25519/getSharedSecret() should be commutative', () => {
-//   for (let i = 0; i < 512; i++) {
+  //   for (let i = 0; i < 512; i++) {
-//     const asec = ed.utils.randomPrivateKey();
+  //     const asec = ed.utils.randomPrivateKey();
-//     const apub = ed.getPublicKey(asec);
+  //     const apub = ed.getPublicKey(asec);
-//     const bsec = ed.utils.randomPrivateKey();
+  //     const bsec = ed.utils.randomPrivateKey();
-//     const bpub = ed.getPublicKey(bsec);
+  //     const bpub = ed.getPublicKey(bsec);
-//     try {
+  //     try {
-//       deepStrictEqual(ed.getSharedSecret(asec, bpub), ed.getSharedSecret(bsec, apub));
+  //       deepStrictEqual(ed.getSharedSecret(asec, bpub), ed.getSharedSecret(bsec, apub));
-//     } catch (error) {
+  //     } catch (error) {
-//       console.error('not commutative', { asec, apub, bsec, bpub });
+  //       console.error('not commutative', { asec, apub, bsec, bpub });
-//       throw error;
+  //       throw error;
-//     }
+  //     }
-//   }
+  //   }
-// });
+  // });
 
-// should('X25519: should convert base point to montgomery using fromPoint', () => {
+  // should('X25519: should convert base point to montgomery using fromPoint', () => {
-//   deepStrictEqual(
+  //   deepStrictEqual(
-//     hex(ed.montgomeryCurve.UfromPoint(ed.Point.BASE)),
+  //     hex(ed.montgomeryCurve.UfromPoint(Point.BASE)),
-//     ed.montgomeryCurve.BASE_POINT_U
+  //     ed.montgomeryCurve.BASE_POINT_U
-//   );
+  //   );
-// });
+  // });
 
-{
+  {
     const group = x25519vectors.testGroups[0];
     should(`Wycheproof/X25519`, () => {
       for (let i = 0; i < group.tests.length; i++) {
@@ -533,9 +526,9 @@ should('RFC7748 getSharedKey', () => {
         } else throw new Error('unknown test result');
       }
     });
-}
+  }
 
-should(`Wycheproof/ED25519`, () => {
+  should(`Wycheproof/ED25519`, () => {
     for (let g = 0; g < ed25519vectors.testGroups.length; g++) {
       const group = ed25519vectors.testGroups[g];
       const key = group.key;
@@ -557,16 +550,16 @@ should(`Wycheproof/ED25519`, () => {
         } else throw new Error('unknown test result');
       }
     }
-});
+  });
 
-should('Property test issue #1', () => {
+  should('Property test issue #1', () => {
     const message = new Uint8Array([12, 12, 12]);
     const signature = ed.sign(message, to32Bytes(1n));
     const publicKey = ed.getPublicKey(to32Bytes(1n)); // <- was 1n
     deepStrictEqual(ed.verify(signature, message, publicKey), true);
-});
+  });
 
-const VECTORS_RFC8032_CTX = [
+  const VECTORS_RFC8032_CTX = [
     {
       secretKey: '0305334e381af78f141cb666f6199f57bc3495335a256a95bd2a55bf546663f6',
       publicKey: 'dfc9425e4f968f7f0c29f0259cf5f9aed6851c2bb4ad8bfb860cfee0ab248292',
@@ -611,18 +604,18 @@ const VECTORS_RFC8032_CTX = [
         'e9b86a7b6005ea868337ff2d20a7f5fb' +
         'd4cd10b0be49a68da2b2e0dc0ad8960f',
     },
-];
+  ];
 
-for (let i = 0; i < VECTORS_RFC8032_CTX.length; i++) {
+  for (let i = 0; i < VECTORS_RFC8032_CTX.length; i++) {
     const v = VECTORS_RFC8032_CTX[i];
     should(`RFC8032ctx/${i}`, () => {
       deepStrictEqual(hex(ed25519ctx.getPublicKey(v.secretKey)), v.publicKey);
       deepStrictEqual(hex(ed25519ctx.sign(v.message, v.secretKey, v.context)), v.signature);
       deepStrictEqual(ed25519ctx.verify(v.signature, v.message, v.publicKey, v.context), true);
     });
-}
+  }
 
-const VECTORS_RFC8032_PH = [
+  const VECTORS_RFC8032_PH = [
     {
       secretKey: '833fe62409237b9d62ec77587520911e9a759cec1d19755b7da901b96dca3d42',
       publicKey: 'ec172b93ad5e563bf4932c70e1245034c35467ef2efd4d64ebf819683467e2bf',
@@ -633,21 +626,34 @@ const VECTORS_RFC8032_PH = [
         '31f85042463c2a355a2003d062adf5aa' +
         'a10b8c61e636062aaad11c2a26083406',
     },
-];
+  ];
 
-for (let i = 0; i < VECTORS_RFC8032_PH.length; i++) {
+  for (let i = 0; i < VECTORS_RFC8032_PH.length; i++) {
     const v = VECTORS_RFC8032_PH[i];
     should(`RFC8032ph/${i}`, () => {
       deepStrictEqual(hex(ed25519ph.getPublicKey(v.secretKey)), v.publicKey);
       deepStrictEqual(hex(ed25519ph.sign(v.message, v.secretKey)), v.signature);
       deepStrictEqual(ed25519ph.verify(v.signature, v.message, v.publicKey), true);
     });
-}
+  }
 
-should('X25519 base point', () => {
+  should('X25519 base point', () => {
-  const { y } = ed25519.Point.BASE;
+    const { y } = ed25519.ExtendedPoint.BASE;
-  const u = ed25519.utils.mod((y + 1n) * ed25519.utils.invert(1n - y, ed25519.CURVE.P));
+    const { Fp } = ed25519.CURVE;
+    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(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}`);
+      strictEqual(cleared.isTorsionFree(), true, `cleared must be torsionFree: ${hex}`);
+    }
+  });
 });
 
 // ESM is broken.

test/ed448.test.js

@@ -1,5 +1,5 @@
 import { deepStrictEqual, throws } from 'assert';
-import { should } from 'micro-should';
+import { describe, should } from 'micro-should';
 import * as fc from 'fast-check';
 import { ed448, ed448ph, x448 } from '../lib/esm/ed448.js';
 import { hexToBytes, bytesToHex, randomBytes } from '@noble/hashes/utils';
@@ -7,12 +7,14 @@ import { numberToBytesLE } from '../lib/esm/abstract/utils.js';
 import { default as ed448vectors } from './wycheproof/ed448_test.json' assert { type: 'json' };
 import { default as x448vectors } from './wycheproof/x448_test.json' assert { type: 'json' };
 
-const ed = ed448;
+describe('ed448', () => {
-const hex = bytesToHex;
+  const ed = ed448;
-ed.utils.precompute(4);
+  const hex = bytesToHex;
+  ed.utils.precompute(4);
+  const Point = ed.ExtendedPoint;
 
-should(`Basic`, () => {
+  should(`Basic`, () => {
-  const G1 = ed.Point.BASE;
+    const G1 = Point.BASE.toAffine();
     deepStrictEqual(
       G1.x,
       224580040295924300187604334099896036246789641632564134246125461686950415467406032909029192869357953282578032075146446173674602635247710n
@@ -21,7 +23,7 @@ should(`Basic`, () => {
       G1.y,
       298819210078481492676017930443930673437544040154080242095928241372331506189835876003536878655418784733982303233503462500531545062832660n
     );
-  const G2 = ed.Point.BASE.multiply(2n);
+    const G2 = Point.BASE.multiply(2n).toAffine();
     deepStrictEqual(
       G2.x,
       484559149530404593699549205258669689569094240458212040187660132787056912146709081364401144455726350866276831544947397859048262938744149n
@@ -30,7 +32,7 @@ should(`Basic`, () => {
       G2.y,
       494088759867433727674302672526735089350544552303727723746126484473087719117037293890093462157703888342865036477787453078312060500281069n
     );
-  const G3 = ed.Point.BASE.multiply(3n);
+    const G3 = Point.BASE.multiply(3n).toAffine();
     deepStrictEqual(
       G3.x,
       23839778817283171003887799738662344287085130522697782688245073320169861206004018274567429238677677920280078599146891901463786155880335n
@@ -39,18 +41,18 @@ should(`Basic`, () => {
       G3.y,
       636046652612779686502873775776967954190574036985351036782021535703553242737829645273154208057988851307101009474686328623630835377952508n
     );
-});
+  });
 
-should('Basic/decompress', () => {
+  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 = [
+  const VECTORS_RFC8032 = [
     {
       secretKey:
         '6c82a562cb808d10d632be89c8513ebf' +
@@ -312,29 +314,31 @@ const VECTORS_RFC8032 = [
         '3603ce30d8bb761785dc30dbc320869e' +
         '1a00',
     },
-];
+  ];
 
-for (let i = 0; i < VECTORS_RFC8032.length; i++) {
+  describe('RFC8032', () => {
+    for (let i = 0; i < VECTORS_RFC8032.length; i++) {
       const v = VECTORS_RFC8032[i];
-  should(`RFC8032/${i}`, () => {
+      should(`${i}`, () => {
         deepStrictEqual(hex(ed.getPublicKey(v.secretKey)), v.publicKey);
         deepStrictEqual(hex(ed.sign(v.message, v.secretKey)), v.signature);
         deepStrictEqual(ed.verify(v.signature, v.message, v.publicKey), true);
       });
-}
+    }
+  });
 
-should('ed448/should not accept >57byte private keys', async () => {
+  should('not accept >57byte private keys', () => {
     const invalidPriv =
       100000000000000000000000000000000000009000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000090000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000800073278156000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000n;
     throws(() => ed.getPublicKey(invalidPriv));
-});
+  });
 
-function to57Bytes(numOrStr) {
+  function to57Bytes(numOrStr) {
     let hex = typeof numOrStr === 'string' ? numOrStr : numOrStr.toString(16);
     return hexToBytes(hex.padStart(114, '0'));
-}
+  }
 
-should('ed448/should verify recent signature', () => {
+  should('verify recent signature', () => {
     fc.assert(
       fc.property(
         fc.hexaString({ minLength: 2, maxLength: 57 }),
@@ -349,8 +353,8 @@ should('ed448/should verify recent signature', () => {
       ),
       { numRuns: 5 }
     );
-});
+  });
-should('ed448/should not verify signature with wrong message', () => {
+  should('not verify signature with wrong message', () => {
     fc.assert(
       fc.property(
         fc.array(fc.integer({ min: 0x00, max: 0xff })),
@@ -370,49 +374,52 @@ should('ed448/should not verify signature with wrong message', () => {
       ),
       { numRuns: 5 }
     );
-});
+  });
-const privKey = to57Bytes('a665a45920422f9d417e4867ef');
+  const privKey = to57Bytes('a665a45920422f9d417e4867ef');
-const msg = hexToBytes('874f9960c5d2b7a9b5fad383e1ba44719ebb743a');
+  const msg = hexToBytes('874f9960c5d2b7a9b5fad383e1ba44719ebb743a');
-const wrongMsg = hexToBytes('589d8c7f1da0a24bc07b7381ad48b1cfc211af1c');
+  const wrongMsg = hexToBytes('589d8c7f1da0a24bc07b7381ad48b1cfc211af1c');
-should('ed25519/basic methods/should sign and verify', () => {
+  describe('basic methods', () => {
+    should('sign and verify', () => {
       const publicKey = ed.getPublicKey(privKey);
       const signature = ed.sign(msg, privKey);
       deepStrictEqual(ed.verify(signature, msg, publicKey), true);
-});
+    });
-should('ed25519/basic methods/should not verify signature with wrong public key', () => {
+    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('ed25519/basic methods/should not verify signature with wrong hash', () => {
+    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);
-});
+    });
-
+  });
-should('ed25519/sync methods/should sign and verify', () => {
+  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('ed25519/sync methods/should not verify signature with wrong public key', async () => {
+    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('ed25519/sync methods/should not verify signature with wrong hash', async () => {
+    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);
-});
+    });
+  });
 
-should('ed25519/BASE_POINT.multiply()/should throw Point#multiply on TEST 5', () => {
+  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));
     }
-});
+  });
 
-should('input immutability: sign/verify are immutable', () => {
+  should('input immutability: sign/verify are immutable', () => {
     const privateKey = ed.utils.randomPrivateKey();
     const publicKey = ed.getPublicKey(privateKey);
 
@@ -430,16 +437,16 @@ should('input immutability: sign/verify are immutable', () => {
       if (!ed.verify(signatureCopy, payload, publicKey))
         throw new Error('Copied signature verification failed');
     }
-});
+  });
 
-{
+  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}`;
@@ -458,10 +465,10 @@ should('input immutability: sign/verify are immutable', () => {
         }
       });
     }
-}
+  });
 
-// ECDH
+  // ECDH
-const rfc7748Mul = [
+  const rfc7748Mul = [
     {
       scalar:
         '3d262fddf9ec8e88495266fea19a34d28882acef045104d0d1aae121700a779c984c24f8cdd78fbff44943eba368f54b29259a4f1c600ad3',
@@ -476,15 +483,17 @@ const rfc7748Mul = [
       outputU:
         '884a02576239ff7a2f2f63b2db6a9ff37047ac13568e1e30fe63c4a7ad1b3ee3a5700df34321d62077e63633c575c1c954514e99da7c179d',
     },
-];
+  ];
-for (let i = 0; i < rfc7748Mul.length; i++) {
+  describe('RFC7748', () => {
+    for (let i = 0; i < rfc7748Mul.length; i++) {
       const v = rfc7748Mul[i];
-  should(`RFC7748: scalarMult (${i})`, () => {
+      should(`scalarMult (${i})`, () => {
         deepStrictEqual(hex(x448.scalarMult(v.scalar, v.u)), v.outputU);
       });
-}
+    }
+  });
 
-const rfc7748Iter = [
+  const rfc7748Iter = [
     {
       scalar:
         '3f482c8a9f19b01e6c46ee9711d9dc14fd4bf67af30765c2ae2b846a4d23a8cd0db897086239492caf350b51f833868b9bc2b3bca9cf4113',
@@ -496,17 +505,17 @@ const rfc7748Iter = [
       iters: 1000,
     },
     // { scalar: '077f453681caca3693198420bbe515cae0002472519b3e67661a7e89cab94695c8f4bcd66e61b9b9c946da8d524de3d69bd9d9d66b997e37', iters: 1000000 },
-];
+  ];
-for (let i = 0; i < rfc7748Iter.length; i++) {
+  for (let i = 0; i < rfc7748Iter.length; i++) {
     const { scalar, iters } = rfc7748Iter[i];
     should(`RFC7748: scalarMult iteration (${i})`, () => {
       let k = x448.Gu;
       for (let i = 0, u = k; i < iters; i++) [k, u] = [x448.scalarMult(k, u), k];
       deepStrictEqual(hex(k), scalar);
     });
-}
+  }
 
-should('RFC7748 getSharedKey', () => {
+  should('RFC7748 getSharedKey', () => {
     const alicePrivate =
       '9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28dd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b';
     const alicePublic =
@@ -521,11 +530,11 @@ should('RFC7748 getSharedKey', () => {
     deepStrictEqual(bobPublic, hex(x448.getPublicKey(bobPrivate)));
     deepStrictEqual(hex(x448.scalarMult(alicePrivate, bobPublic)), shared);
     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}`;
@@ -551,31 +560,31 @@ should('RFC7748 getSharedKey', () => {
         } else throw new Error('unknown test result');
       }
     });
-}
+  });
 
-// should('X448: should convert base point to montgomery using fromPoint', () => {
+  // should('X448: should convert base point to montgomery using fromPoint', () => {
-//   deepStrictEqual(
+  //   deepStrictEqual(
-//     hex(ed.montgomeryCurve.UfromPoint(ed.Point.BASE)),
+  //     hex(ed.montgomeryCurve.UfromPoint(Point.BASE)),
-//     ed.montgomeryCurve.BASE_POINT_U
+  //     ed.montgomeryCurve.BASE_POINT_U
-//   );
+  //   );
-// });
+  // });
 
-// should('X448/getSharedSecret() should be commutative', async () => {
+  // should('X448/getSharedSecret() should be commutative', async () => {
-//   for (let i = 0; i < 512; i++) {
+  //   for (let i = 0; i < 512; i++) {
-//     const asec = ed.utils.randomPrivateKey();
+  //     const asec = ed.utils.randomPrivateKey();
-//     const apub = ed.getPublicKey(asec);
+  //     const apub = ed.getPublicKey(asec);
-//     const bsec = ed.utils.randomPrivateKey();
+  //     const bsec = ed.utils.randomPrivateKey();
-//     const bpub = ed.getPublicKey(bsec);
+  //     const bpub = ed.getPublicKey(bsec);
-//     try {
+  //     try {
-//       deepStrictEqual(ed.getSharedSecret(asec, bpub), ed.getSharedSecret(bsec, apub));
+  //       deepStrictEqual(ed.getSharedSecret(asec, bpub), ed.getSharedSecret(bsec, apub));
-//     } catch (error) {
+  //     } catch (error) {
-//       console.error('not commutative', { asec, apub, bsec, bpub });
+  //       console.error('not commutative', { asec, apub, bsec, bpub });
-//       throw error;
+  //       throw error;
-//     }
+  //     }
-//   }
+  //   }
-// });
+  // });
 
-const VECTORS_RFC8032_CTX = [
+  const VECTORS_RFC8032_CTX = [
     {
       secretKey:
         'c4eab05d357007c632f3dbb48489924d552b08fe0c353a0d4a1f00acda2c463afbea67c5e8d2877c5e3bc397a659949ef8021e954e0a12274e',
@@ -593,18 +602,18 @@ const VECTORS_RFC8032_CTX = [
         '5428407e85dcbc98a49155c13764e66c' +
         '3c00',
     },
-];
+  ];
 
-for (let i = 0; i < VECTORS_RFC8032_CTX.length; i++) {
+  for (let i = 0; i < VECTORS_RFC8032_CTX.length; i++) {
     const v = VECTORS_RFC8032_CTX[i];
     should(`RFC8032ctx/${i}`, () => {
       deepStrictEqual(hex(ed.getPublicKey(v.secretKey)), v.publicKey);
       deepStrictEqual(hex(ed.sign(v.message, v.secretKey, v.context)), v.signature);
       deepStrictEqual(ed.verify(v.signature, v.message, v.publicKey, v.context), true);
     });
-}
+  }
 
-const VECTORS_RFC8032_PH = [
+  const VECTORS_RFC8032_PH = [
     {
       secretKey:
         '833fe62409237b9d62ec77587520911e9a759cec1d19755b7da901b96dca3d42ef7822e0d5104127dc05d6dbefde69e3ab2cec7c867c6e2c49',
@@ -638,23 +647,25 @@ const VECTORS_RFC8032_PH = [
         '4f8d0704a608c54a6b62d97beb511d13' +
         '2100',
     },
-];
+  ];
 
-for (let i = 0; i < VECTORS_RFC8032_PH.length; i++) {
+  for (let i = 0; i < VECTORS_RFC8032_PH.length; i++) {
     const v = VECTORS_RFC8032_PH[i];
     should(`RFC8032ph/${i}`, () => {
       deepStrictEqual(hex(ed448ph.getPublicKey(v.secretKey)), v.publicKey);
       deepStrictEqual(hex(ed448ph.sign(v.message, v.secretKey, v.context)), v.signature);
       deepStrictEqual(ed448ph.verify(v.signature, v.message, v.publicKey, v.context), true);
     });
-}
+  }
 
-should('X448 base point', () => {
+  should('X448 base point', () => {
-  const { x, y } = ed448.Point.BASE;
+    const { x, y } = Point.BASE;
-  const { P } = ed448.CURVE;
+    const { Fp } = ed448.CURVE;
-  const invX = ed448.utils.invert(x * x, P); // x²
+    // const invX = Fp.invert(x * x); // x²
-  const u = ed448.utils.mod(y * y * invX, P); // (y²/x²)
+    const u = Fp.div(Fp.create(y * y), Fp.create(x * x)); // (y²/x²)
+    // const u = Fp.create(y * y * invX);
     deepStrictEqual(hex(numberToBytesLE(u, 56)), x448.Gu);
+  });
 });
 
 // ESM is broken.

test/hash-to-curve.test.js

@@ -1,19 +1,30 @@
 import { deepStrictEqual } from 'assert';
-import { should } from 'micro-should';
+import { describe, should } from 'micro-should';
 import { bytesToHex } from '@noble/hashes/utils';
 // Generic tests for all curves in package
 import { sha256 } from '@noble/hashes/sha256';
 import { sha512 } from '@noble/hashes/sha512';
-import { secp256r1 } from '../lib/esm/p256.js';
+import { shake128, shake256 } from '@noble/hashes/sha3';
-import { secp384r1 } from '../lib/esm/p384.js';
+import * as secp256r1 from '../lib/esm/p256.js';
-import { secp521r1 } from '../lib/esm/p521.js';
+import * as secp384r1 from '../lib/esm/p384.js';
-import { secp256k1 } from '../lib/esm/secp256k1.js';
+import * as secp521r1 from '../lib/esm/p521.js';
+import * as ed25519 from '../lib/esm/ed25519.js';
+import * as ed448 from '../lib/esm/ed448.js';
+import * as secp256k1 from '../lib/esm/secp256k1.js';
 import { bls12_381 } from '../lib/esm/bls12-381.js';
-import { stringToBytes, expand_message_xmd } from '../lib/esm/abstract/hash-to-curve.js';
+import {
-
+  stringToBytes,
+  expand_message_xmd,
+  expand_message_xof,
+} from '../lib/esm/abstract/hash-to-curve.js';
+// XMD
 import { default as xmd_sha256_38 } from './hash-to-curve/expand_message_xmd_SHA256_38.json' assert { type: 'json' };
 import { default as xmd_sha256_256 } from './hash-to-curve/expand_message_xmd_SHA256_256.json' assert { type: 'json' };
 import { default as xmd_sha512_38 } from './hash-to-curve/expand_message_xmd_SHA512_38.json' assert { type: 'json' };
+// XOF
+import { default as xof_shake128_36 } from './hash-to-curve/expand_message_xof_SHAKE128_36.json' assert { type: 'json' };
+import { default as xof_shake128_256 } from './hash-to-curve/expand_message_xof_SHAKE128_256.json' assert { type: 'json' };
+import { default as xof_shake256_36 } from './hash-to-curve/expand_message_xof_SHAKE256_36.json' assert { type: 'json' };
 // P256
 import { default as p256_ro } from './hash-to-curve/P256_XMD:SHA-256_SSWU_RO_.json' assert { type: 'json' };
 import { default as p256_nu } from './hash-to-curve/P256_XMD:SHA-256_SSWU_NU_.json' assert { type: 'json' };
@@ -40,9 +51,10 @@ import { default as ed448_ro } from './hash-to-curve/edwards448_XOF:SHAKE256_ELL
 import { default as ed448_nu } from './hash-to-curve/edwards448_XOF:SHAKE256_ELL2_NU_.json' assert { type: 'json' };
 
 function testExpandXMD(hash, vectors) {
+  describe(`${vectors.hash}/${vectors.DST.length}`, () => {
     for (let i = 0; i < vectors.tests.length; i++) {
       const t = vectors.tests[i];
-    should(`expand_message_xmd/${vectors.hash}/${vectors.DST.length}/${i}`, () => {
+      should(`${vectors.hash}/${vectors.DST.length}/${i}`, () => {
         const p = expand_message_xmd(
           stringToBytes(t.msg),
           stringToBytes(vectors.DST),
@@ -52,11 +64,38 @@ function testExpandXMD(hash, vectors) {
         deepStrictEqual(bytesToHex(p), t.uniform_bytes);
       });
     }
+  });
 }
 
-testExpandXMD(sha256, xmd_sha256_38);
+describe('expand_message_xmd', () => {
-testExpandXMD(sha256, xmd_sha256_256);
+  testExpandXMD(sha256, xmd_sha256_38);
-testExpandXMD(sha512, xmd_sha512_38);
+  testExpandXMD(sha256, xmd_sha256_256);
+  testExpandXMD(sha512, xmd_sha512_38);
+});
+
+function testExpandXOF(hash, vectors) {
+  describe(`${vectors.hash}/${vectors.DST.length}`, () => {
+    for (let i = 0; i < vectors.tests.length; i++) {
+      const t = vectors.tests[i];
+      should(`${i}`, () => {
+        const p = expand_message_xof(
+          stringToBytes(t.msg),
+          stringToBytes(vectors.DST),
+          +t.len_in_bytes,
+          vectors.k,
+          hash
+        );
+        deepStrictEqual(bytesToHex(p), t.uniform_bytes);
+      });
+    }
+  });
+}
+
+describe('expand_message_xof', () => {
+  testExpandXOF(shake128, xof_shake128_36);
+  testExpandXOF(shake128, xof_shake128_256);
+  testExpandXOF(shake256, xof_shake256_36);
+});
 
 function stringToFp(s) {
   // bls-G2 support
@@ -68,37 +107,44 @@ function stringToFp(s) {
 }
 
 function testCurve(curve, ro, nu) {
+  describe(`${ro.curve}/${ro.ciphersuite}`, () => {
     for (let i = 0; i < ro.vectors.length; i++) {
       const t = ro.vectors[i];
-    should(`${ro.curve}/${ro.ciphersuite}(${i})`, () => {
+      should(`(${i})`, () => {
-      const p = curve.Point.hashToCurve(stringToBytes(t.msg), {
+        const p = curve
+          .hashToCurve(stringToBytes(t.msg), {
             DST: ro.dst,
-      });
+          })
+          .toAffine();
         deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
         deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
       });
     }
+  });
+  describe(`${nu.curve}/${nu.ciphersuite}`, () => {
     for (let i = 0; i < nu.vectors.length; i++) {
       const t = nu.vectors[i];
-    should(`${nu.curve}/${nu.ciphersuite}(${i})`, () => {
+      should(`(${i})`, () => {
-      const p = curve.Point.encodeToCurve(stringToBytes(t.msg), {
+        const p = curve
+          .encodeToCurve(stringToBytes(t.msg), {
             DST: nu.dst,
-      });
+          })
+          .toAffine();
         deepStrictEqual(p.x, stringToFp(t.P.x), 'Px');
         deepStrictEqual(p.y, stringToFp(t.P.y), 'Py');
       });
     }
+  });
 }
 
 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(ed25519, ed25519_ro, ed25519_nu);
-//testCurve(ed448, ed448_ro, ed448_nu);
+testCurve(ed448, ed448_ro, ed448_nu);
 
 // ESM is broken.
 import url from 'url';

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 { should } from 'micro-should';
+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,
@@ -18,10 +18,11 @@ const G_PROOF = new jubjub.ExtendedPoint(
 
 const getXY = (p) => ({ x: p.x, y: p.y });
 
-should('toHex/fromHex', () => {
+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,
@@ -30,14 +31,14 @@ should('toHex/fromHex', () => {
     );
     // 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,
+          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, 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,
@@ -46,25 +47,32 @@ should('toHex/fromHex', () => {
     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));
     deepStrictEqual(getXY(G_PROOF.double().toAffine()), getXY(P2_exp));
-});
+  });
 
-should('Find generators', () => {
+  should('Find generators', () => {
-  const spend = findGroupHash(new Uint8Array(), new Uint8Array([90, 99, 97, 115, 104, 95, 71, 95]));
+    const spend = findGroupHash(
-  const proof = findGroupHash(new Uint8Array(), new Uint8Array([90, 99, 97, 115, 104, 95, 72, 95]));
+      new Uint8Array(),
+      new Uint8Array([90, 99, 97, 115, 104, 95, 71, 95])
+    );
+    const proof = findGroupHash(
+      new Uint8Array(),
+      new Uint8Array([90, 99, 97, 115, 104, 95, 72, 95])
+    );
     deepStrictEqual(getXY(spend.toAffine()), getXY(G_SPEND.toAffine()));
     deepStrictEqual(getXY(proof.toAffine()), getXY(G_PROOF.toAffine()));
+  });
 });
 
 // ESM is broken.

test/nist.test.js

@@ -1,5 +1,5 @@
 import { deepStrictEqual, throws } from 'assert';
-import { should } from 'micro-should';
+import { describe, should } from 'micro-should';
 import { secp192r1, P192 } from '../lib/esm/p192.js';
 import { secp224r1, P224 } from '../lib/esm/p224.js';
 import { secp256r1, P256 } from '../lib/esm/p256.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 +46,121 @@ 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) {
+            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');
+      }
+    });
+  }
+
+  // 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) {
+                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');
+          }
+        });
+      }
+    }
+  }
+});
+
 const WYCHEPROOF_ECDSA = {
   P224: {
     curve: P224,
@@ -309,31 +271,33 @@ 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;
       }
@@ -342,12 +306,53 @@ function runWycheproof(name, CURVE, group, index) {
   }
 }
 
-for (const name in WYCHEPROOF_ECDSA) {
+describe('wycheproof ECDSA', () => {
+  should('generic', () => {
+    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.ProjectivePoint.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.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(`Wycheproof/WYCHEPROOF_ECDSA ${name}/${hName}`, () => {
+        should(`${name}/${hName}`, () => {
           for (let i = 0; i < tests.length; i++) {
             const groups = tests[i].testGroups;
             for (let j = 0; j < groups.length; j++) {
@@ -357,15 +362,18 @@ for (const name in WYCHEPROOF_ECDSA) {
           }
         });
       }
-}
+    });
+  }
+});
 
 const hexToBigint = (hex) => BigInt(`0x${hex}`);
-should('RFC6979', () => {
+describe('RFC6979', () => {
   for (const v of rfc6979) {
+    should(v.curve, () => {
       const curve = NIST[v.curve];
       deepStrictEqual(curve.CURVE.n, hexToBigint(v.q));
       const pubKey = curve.getPublicKey(v.private);
-    const pubPoint = curve.Point.fromHex(pubKey);
+      const pubPoint = curve.ProjectivePoint.fromHex(pubKey);
       deepStrictEqual(pubPoint.x, hexToBigint(v.Ux));
       deepStrictEqual(pubPoint.y, hexToBigint(v.Uy));
       for (const c of v.cases) {
@@ -376,6 +384,7 @@ should('RFC6979', () => {
         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

@@ -1,22 +1,24 @@
 import * as fc from 'fast-check';
 import { secp256k1, schnorr } from '../lib/esm/secp256k1.js';
+import { Fp } from '../lib/esm/abstract/modular.js';
+import { bytesToNumberBE, 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' };
 import { default as privates } from './vectors/privates.json' assert { type: 'json' };
 import { default as points } from './vectors/points.json' assert { type: 'json' };
 import { default as wp } from './vectors/wychenproof.json' assert { type: 'json' };
-import { should } from 'micro-should';
+import { should, describe } from 'micro-should';
 import { deepStrictEqual, throws } from 'assert';
 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');
 
 const FC_BIGINT = fc.bigInt(1n + 1n, secp.CURVE.n - 1n);
-const P = secp.CURVE.Fp.ORDER;
 // prettier-ignore
 const INVALID_ITEMS = ['deadbeef', Math.pow(2, 53), [1], 'xyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxyxyzxyzxy', secp.CURVE.n + 2n];
 
@@ -24,108 +26,110 @@ 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}`);
 }
 
-should('secp256k1.getPublicKey()', () => {
+describe('secp256k1', () => {
+  should('getPublicKey()', () => {
     const data = privatesTxt
       .split('\n')
       .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('secp256k1.getPublicKey() rejects invalid keys', () => {
+  should('getPublicKey() rejects invalid keys', () => {
-  // for (const item of INVALID_ITEMS) {
+    for (const item of INVALID_ITEMS) {
-  //   throws(() => secp.getPublicKey(item));
+      throws(() => secp.getPublicKey(item));
-  // }
+    }
-});
+  });
-should('secp256k1.precompute', () => {
+  should('precompute', () => {
     secp.utils.precompute(4);
     const data = privatesTxt
       .split('\n')
       .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('secp256k1.Point.isValidPoint()', () => {
+  describe('Point', () => {
+    should('fromHex() assertValidity', () => {
       for (const vector of points.valid.isPoint) {
         const { P, expected } = vector;
         if (expected) {
-      secp.Point.fromHex(P);
+          Point.fromHex(P);
         } else {
-      throws(() => secp.Point.fromHex(P));
+          throws(() => Point.fromHex(P));
         }
       }
-});
+    });
 
-should('secp256k1.Point.fromPrivateKey()', () => {
+    should('.fromPrivateKey()', () => {
       for (const vector of points.valid.pointFromScalar) {
         const { d, expected } = vector;
-    let p = secp.Point.fromPrivateKey(d);
+        let p = Point.fromPrivateKey(d);
         deepStrictEqual(p.toHex(true), expected);
       }
-});
+    });
 
-should('secp256k1.Point#toHex(compressed)', () => {
+    should('#toHex(compressed)', () => {
       for (const vector of points.valid.pointCompress) {
         const { P, compress, expected } = vector;
-    let p = secp.Point.fromHex(P);
+        let p = Point.fromHex(P);
         deepStrictEqual(p.toHex(compress), expected);
       }
-});
+    });
 
-should('secp256k1.Point#toHex() roundtrip (failed case)', () => {
+    should('#toHex() roundtrip (failed case)', () => {
       const point1 =
-    secp.Point.fromPrivateKey(
+        Point.fromPrivateKey(
           88572218780422190464634044548753414301110513745532121983949500266768436236425n
         );
       // const hex = point1.toHex(true);
-  // deepStrictEqual(secp.Point.fromHex(hex).toHex(true), hex);
+      // deepStrictEqual(Point.fromHex(hex).toHex(true), hex);
-});
+    });
 
-should('secp256k1.Point#toHex() roundtrip', () => {
+    should('#toHex() roundtrip', () => {
       fc.assert(
         fc.property(FC_BIGINT, (x) => {
-      const point1 = secp.Point.fromPrivateKey(x);
+          const point1 = Point.fromPrivateKey(x);
           const hex = point1.toHex(true);
-      deepStrictEqual(secp.Point.fromHex(hex).toHex(true), hex);
+          deepStrictEqual(Point.fromHex(hex).toHex(true), hex);
         })
       );
-});
+    });
 
-should('secp256k1.Point#add(other)', () => {
+    should('#add(other)', () => {
       for (const vector of points.valid.pointAdd) {
         const { P, Q, expected } = vector;
-    let p = secp.Point.fromHex(P);
+        let p = Point.fromHex(P);
-    let q = secp.Point.fromHex(Q);
+        let q = Point.fromHex(Q);
         if (expected) {
           deepStrictEqual(p.add(q).toHex(true), expected);
         } else {
@@ -134,14 +138,14 @@ should('secp256k1.Point#add(other)', () => {
           }
         }
       }
-});
+    });
 
-should('secp256k1.Point#multiply(privateKey)', () => {
+    should('#multiply(privateKey)', () => {
       for (const vector of points.valid.pointMultiply) {
         const { P, d, expected } = vector;
-    const p = secp.Point.fromHex(P);
+        const p = Point.fromHex(P);
         if (expected) {
-      deepStrictEqual(p.multiply(hexToNumber(d)).toHex(true), expected);
+          deepStrictEqual(p.multiply(hexToNumber(d)).toHex(true), expected, P);
         } else {
           throws(() => {
             p.multiply(hexToNumber(d)).toHex(true);
@@ -153,47 +157,50 @@ should('secp256k1.Point#multiply(privateKey)', () => {
         const { P, d } = vector;
         if (hexToNumber(d) < secp.CURVE.n) {
           throws(() => {
-        const p = secp.Point.fromHex(P);
+            const p = Point.fromHex(P);
             p.multiply(hexToNumber(d)).toHex(true);
           });
         }
       }
       for (const num of [0n, 0, -1n, -1, 1.1]) {
-    throws(() => secp.Point.BASE.multiply(num));
+        throws(() => Point.BASE.multiply(num));
       }
-});
+    });
+  });
 
-// multiply() should equal multiplyUnsafe()
+  // multiply() should equal multiplyUnsafe()
-// should('ProjectivePoint#multiplyUnsafe', () => {
+  // should('ProjectivePoint#multiplyUnsafe', () => {
-//   const p0 = new secp.ProjectivePoint(
+  //   const p0 = new secp.ProjectivePoint(
-//     55066263022277343669578718895168534326250603453777594175500187360389116729240n,
+  //     55066263022277343669578718895168534326250603453777594175500187360389116729240n,
-//     32670510020758816978083085130507043184471273380659243275938904335757337482424n,
+  //     32670510020758816978083085130507043184471273380659243275938904335757337482424n,
-//     1n
+  //     1n
-//   );
+  //   );
-//   const z = 106011723082030650010038151861333186846790370053628296836951575624442507889495n;
+  //   const z = 106011723082030650010038151861333186846790370053628296836951575624442507889495n;
-//   console.log(p0.multiply(z));
+  //   console.log(p0.multiply(z));
-//   console.log(secp.ProjectivePoint.normalizeZ([p0.multiplyUnsafe(z)])[0])
+  //   console.log(secp.ProjectivePoint.normalizeZ([p0.multiplyUnsafe(z)])[0])
-// });
+  // });
-
+  describe('Signature', () => {
-should('secp256k1.Signature.fromCompactHex() roundtrip', () => {
+    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('secp256k1.Signature.fromDERHex() roundtrip', () => {
+    should('.fromDERHex() roundtrip', () => {
       fc.assert(
         fc.property(FC_BIGINT, FC_BIGINT, (r, s) => {
           const sig = new secp.Signature(r, s);
           deepStrictEqual(secp.Signature.fromDER(sig.toDERHex()), sig);
         })
       );
-});
+    });
+  });
 
-should('secp256k1.sign()/should create deterministic signatures with RFC 6979', () => {
+  describe('sign()', () => {
+    should('create deterministic signatures with RFC 6979', () => {
       for (const vector of ecdsa.valid) {
         let usig = secp.sign(vector.m, vector.d);
         let sig = usig.toCompactHex();
@@ -201,20 +208,20 @@ should('secp256k1.sign()/should create deterministic signatures with RFC 6979',
         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', () => {
+    should('not create invalid deterministic signatures with RFC 6979', () => {
       for (const vector of ecdsa.invalid.sign) {
         throws(() => secp.sign(vector.m, vector.d));
       }
-});
+    });
 
-should('secp256k1.sign()/edge cases', () => {
+    should('edge cases', () => {
       throws(() => secp.sign());
       throws(() => secp.sign(''));
-});
+    });
 
-should('secp256k1.sign()/should create correct DER encoding against libsecp256k1', () => {
+    should('create correct DER encoding against libsecp256k1', () => {
       const CASES = [
         [
           'd1a9dc8ed4e46a6a3e5e594615ca351d7d7ef44df1e4c94c1802f3592183794b',
@@ -229,15 +236,17 @@ should('secp256k1.sign()/should create correct DER encoding against libsecp256k1
           '3045022100d18990bba7832bb283e3ecf8700b67beb39acc73f4200ed1c331247c46edccc602202e5c8bbfe47ae159512c583b30a3fa86575cddc62527a03de7756517ae4c6c73',
         ],
       ];
-  const privKey = hexToBytes('0101010101010101010101010101010101010101010101010101010101010101');
+      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('secp256k1.sign()/sign ecdsa extraData', () => {
+    should('handle {extraData} option', () => {
       const ent1 = '0000000000000000000000000000000000000000000000000000000000000000';
       const ent2 = '0000000000000000000000000000000000000000000000000000000000000001';
       const ent3 = '6e723d3fd94ed5d2b6bdd4f123364b0f3ca52af829988a63f8afe91d29db1c33';
@@ -256,35 +265,37 @@ should('secp256k1.sign()/sign ecdsa extraData', () => {
         deepStrictEqual(sign(ent4), e.extraEntropyN);
         deepStrictEqual(sign(ent5), e.extraEntropyMax);
       }
-});
+    });
+  });
 
-should('secp256k1.verify()/should verify signature', () => {
+  describe('verify()', () => {
+    should('verify signature', () => {
       const MSG = '01'.repeat(32);
       const PRIV_KEY = 0x2n;
       const signature = secp.sign(MSG, PRIV_KEY);
       const publicKey = secp.getPublicKey(PRIV_KEY);
-  deepStrictEqual(publicKey.length, 65);
+      deepStrictEqual(publicKey.length, 33);
       deepStrictEqual(secp.verify(signature, MSG, publicKey), true);
-});
+    });
-should('secp256k1.verify()/should not verify signature with wrong public key', () => {
+    should(' not verify signature with wrong public key', () => {
       const MSG = '01'.repeat(32);
-  const PRIV_KEY = 0x2n;
+      const PRIV_KEY = '01'.repeat(32);
-  const WRONG_PRIV_KEY = 0x22n;
+      const WRONG_PRIV_KEY = '02'.repeat(32);
       const signature = secp.sign(MSG, PRIV_KEY);
-  const publicKey = secp.Point.fromPrivateKey(WRONG_PRIV_KEY).toHex();
+      const publicKey = Point.fromPrivateKey(WRONG_PRIV_KEY).toHex();
-  deepStrictEqual(publicKey.length, 130);
+      deepStrictEqual(publicKey.length, 66);
       deepStrictEqual(secp.verify(signature, MSG, publicKey), false);
-});
+    });
-should('secp256k1.verify()/should not verify signature with wrong hash', () => {
+    should('not verify signature with wrong hash', () => {
       const MSG = '01'.repeat(32);
       const PRIV_KEY = 0x2n;
       const WRONG_MSG = '11'.repeat(32);
       const signature = secp.sign(MSG, PRIV_KEY);
       const publicKey = secp.getPublicKey(PRIV_KEY);
-  deepStrictEqual(publicKey.length, 65);
+      deepStrictEqual(publicKey.length, 33);
       deepStrictEqual(secp.verify(signature, WRONG_MSG, publicKey), false);
-});
+    });
-should('secp256k1.verify()/should verify random signatures', () =>
+    should('verify random signatures', () =>
       fc.assert(
         fc.property(FC_BIGINT, fc.hexaString({ minLength: 64, maxLength: 64 }), (privKey, msg) => {
           const pub = secp.getPublicKey(privKey);
@@ -292,18 +303,19 @@ should('secp256k1.verify()/should verify random signatures', () =>
           deepStrictEqual(secp.verify(sig, msg, pub), true);
         })
       )
-);
+    );
-should('secp256k1.verify()/should not verify signature with invalid r/s', () => {
+    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,
+        0xbb, 0x5a, 0x52, 0xf4, 0x2f, 0x9c, 0x92, 0x61, 0xed, 0x43, 0x61, 0xf5, 0x94, 0x22, 0xa1,
-    0x00, 0x36, 0xe7, 0xc3, 0x2b, 0x27, 0x0c, 0x88, 0x07, 0xa4, 0x19, 0xfe, 0xca, 0x60, 0x50, 0x23,
+        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 pub = new Point(x, y, 1n).toRawBytes();
       const signature = new secp.Signature(2n, 2n);
       signature.r = r;
       signature.s = s;
@@ -311,45 +323,44 @@ should('secp256k1.verify()/should not verify signature with invalid r/s', () =>
       const verified = secp.verify(signature, msg, pub);
       // Verifies, but it shouldn't, because signature S > curve order
       deepStrictEqual(verified, false);
-});
+    });
-should('secp256k1.verify()/should not verify msg = curve order', () => {
+    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 pub = new Point(x, y, 1n).toRawBytes();
       const sig = new secp.Signature(r, s);
       deepStrictEqual(secp.verify(sig, msg, pub), false);
-});
+    });
-should('secp256k1.verify()/should verify non-strict msg bb5a...', () => {
+    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 pub = new Point(x, y, 1n).toRawBytes();
       const sig = new secp.Signature(r, s);
       deepStrictEqual(secp.verify(sig, msg, pub, { strict: false }), true);
-});
+    });
-should(
+    should('not verify invalid deterministic signatures with RFC 6979', () => {
-  '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
+    const vectors = schCsv
       .split('\n')
       .map((line) => line.split(','))
       .slice(1, -1);
-for (let vec of vectors) {
+    for (let vec of vectors) {
       const [index, sec, pub, rnd, msg, expSig, passes, comment] = vec;
-  should(`sign with Schnorr scheme vector ${index}`, () => {
+      should(`${comment || 'vector ' + index}`, () => {
         if (sec) {
           deepStrictEqual(hex(schnorr.getPublicKey(sec)), pub.toLowerCase());
           const sig = schnorr.sign(msg, sec, rnd);
@@ -360,35 +371,37 @@ for (let vec of vectors) {
           deepStrictEqual(passed, passes === 'TRUE');
         }
       });
-}
+    }
+  });
 
-should('secp256k1.recoverPublicKey()/should recover public key from recovery bit', () => {
+  describe('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 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(), publicKey);
+      deepStrictEqual(recoveredPubkey.toHex(false), publicKey);
       deepStrictEqual(secp.verify(sig, message, publicKey), true);
-});
+    });
-should('secp256k1.recoverPublicKey()/should not recover zero points', () => {
+    should('not recover zero points', () => {
       const msgHash = '6b8d2c81b11b2d699528dde488dbdf2f94293d0d33c32e347f255fa4a6c1f0a9';
       const sig =
         '79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f817986b8d2c81b11b2d699528dde488dbdf2f94293d0d33c32e347f255fa4a6c1f0a9';
       const recovery = 0;
       throws(() => secp.recoverPublicKey(msgHash, sig, recovery));
-});
+    });
-should('secp256k1.recoverPublicKey()/should handle all-zeros msghash', () => {
+    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 sig = secp.sign(zeros, privKey);
       const recoveredKey = sig.recoverPublicKey(zeros);
       deepStrictEqual(recoveredKey.toRawBytes(), pub);
-});
+    });
-should('secp256k1.recoverPublicKey()/should handle RFC 6979 vectors', () => {
+    should('handle RFC 6979 vectors', () => {
       for (const vector of ecdsa.valid) {
         let usig = secp.sign(vector.m, vector.d);
         let sig = usig.toDERHex();
@@ -396,13 +409,15 @@ should('secp256k1.recoverPublicKey()/should handle RFC 6979 vectors', () => {
         const recovered = usig.recoverPublicKey(vector.m);
         deepStrictEqual(recovered.toHex(), hex(vpub));
       }
-});
+    });
+  });
 
-// TODO: Real implementation.
+  describe('getSharedSecret()', () => {
-function derToPub(der) {
+    // TODO: Real implementation.
+    function derToPub(der) {
       return der.slice(46);
-}
+    }
-should('secp256k1.getSharedSecret()/should produce correct results', () => {
+    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) {
@@ -414,8 +429,8 @@ should('secp256k1.getSharedSecret()/should produce correct results', () => {
           deepStrictEqual(hex(res.slice(1)), `${vector.shared}`);
         }
       }
-});
+    });
-should('secp256k1.getSharedSecret()/priv/pub order matters', () => {
+    should('priv/pub order matters', () => {
       for (const vector of ecdh.testGroups[0].tests.slice(0, 100)) {
         if (vector.result === 'valid') {
           let priv = vector.private;
@@ -423,87 +438,99 @@ should('secp256k1.getSharedSecret()/priv/pub order matters', () => {
           throws(() => secp.getSharedSecret(derToPub(vector.public), priv, true));
         }
       }
-});
+    });
-should('secp256k1.getSharedSecret()/rejects invalid keys', () => {
+    should('reject invalid keys', () => {
       throws(() => secp.getSharedSecret('01', '02'));
-});
+    });
+  });
 
-should('secp256k1.utils.isValidPrivateKey()', () => {
+  should('utils.isValidPrivateKey()', () => {
     for (const vector of privates.valid.isPrivate) {
       const { d, expected } = vector;
       deepStrictEqual(secp.utils.isValidPrivateKey(d), expected);
     }
-});
+  });
-const normal = secp.utils._normalizePrivateKey;
+  should('have proper curve equation in assertValidity()', () => {
-const tweakUtils = {
+    throws(() => {
+      const { Fp } = secp.CURVE;
+      let point = new Point(Fp.create(-2n), Fp.create(-1n), Fp.create(1n));
+      point.assertValidity();
+    });
+  });
+
+  describe('tweak utilities (legacy)', () => {
+    const Fn = Fp(secp.CURVE.n);
+    const normal = secp.utils._normalizePrivateKey;
+    const tweakUtils = {
       privateAdd: (privateKey, tweak) => {
         const p = normal(privateKey);
         const t = normal(tweak);
-    return secp.utils._bigintToBytes(secp.utils.mod(p + t, secp.CURVE.n));
+        return numberToBytesBE(Fn.create(p + t), 32);
       },
 
       privateNegate: (privateKey) => {
-    const p = normal(privateKey);
+        return numberToBytesBE(Fn.neg(normal(privateKey)), 32);
-    return secp.utils._bigintToBytes(secp.CURVE.n - p);
       },
 
       pointAddScalar: (p, tweak, isCompressed) => {
-    const P = secp.Point.fromHex(p);
+        const P = Point.fromHex(p);
         const t = normal(tweak);
-    const Q = secp.Point.BASE.multiplyAndAddUnsafe(P, t, 1n);
+        const Q = Point.BASE.multiplyAndAddUnsafe(P, t, 1n);
         if (!Q) throw new Error('Tweaked point at infinity');
         return Q.toRawBytes(isCompressed);
       },
 
       pointMultiply: (p, tweak, isCompressed) => {
-    const P = secp.Point.fromHex(p);
+        const P = Point.fromHex(p);
         const h = typeof tweak === 'string' ? tweak : bytesToHex(tweak);
         const t = BigInt(`0x${h}`);
         return P.multiply(t).toRawBytes(isCompressed);
       },
-};
+    };
 
-should('secp256k1.privateAdd()', () => {
+    should('privateAdd()', () => {
       for (const vector of privates.valid.add) {
         const { a, b, expected } = vector;
         deepStrictEqual(bytesToHex(tweakUtils.privateAdd(a, b)), expected);
       }
-});
+    });
-should('secp256k1.privateNegate()', () => {
+    should('privateNegate()', () => {
       for (const vector of privates.valid.negate) {
         const { a, expected } = vector;
         deepStrictEqual(bytesToHex(tweakUtils.privateNegate(a)), expected);
       }
-});
+    });
-should('secp256k1.pointAddScalar()', () => {
+    should('pointAddScalar()', () => {
       for (const vector of points.valid.pointAddScalar) {
         const { description, P, d, expected } = vector;
         const compressed = !!expected && expected.length === 66; // compressed === 33 bytes
         deepStrictEqual(bytesToHex(tweakUtils.pointAddScalar(P, d, compressed)), expected);
       }
-});
+    });
-should('secp256k1.pointAddScalar() invalid', () => {
+    should('pointAddScalar() invalid', () => {
       for (const vector of points.invalid.pointAddScalar) {
         const { P, d, exception } = vector;
         throws(() => tweakUtils.pointAddScalar(P, d));
       }
-});
+    });
-should('secp256k1.pointMultiply()', () => {
+    should('pointMultiply()', () => {
       for (const vector of points.valid.pointMultiply) {
         const { P, d, expected } = vector;
         deepStrictEqual(bytesToHex(tweakUtils.pointMultiply(P, d, true)), expected);
       }
-});
+    });
-should('secp256k1.pointMultiply() invalid', () => {
+    should('pointMultiply() invalid', () => {
       for (const vector of points.invalid.pointMultiply) {
         const { P, d, exception } = vector;
         throws(() => tweakUtils.pointMultiply(P, d));
       }
-});
+    });
+  });
 
-should('secp256k1.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') {
@@ -527,6 +554,7 @@ should('secp256k1.wychenproof vectors', () => {
         }
       }
     }
+  });
 });
 
 // ESM is broken.

test/stark/basic.test.js

@@ -1,57 +1,60 @@
 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' };
+import * as bip32 from '@scure/bip32';
+import * as bip39 from '@scure/bip39';
 
-should('Basic elliptic sanity check', () => {
+describe('starknet basic', () => {
-  const g1 = starknet.Point.BASE;
+  should('Basic elliptic sanity check', () => {
+    const g1 = starknet.ProjectivePoint.BASE;
     deepStrictEqual(
-    g1.x.toString(16),
+      g1.toAffine().x.toString(16),
       '1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca'
     );
     deepStrictEqual(
-    g1.y.toString(16),
+      g1.toAffine().y.toString(16),
       '5668060aa49730b7be4801df46ec62de53ecd11abe43a32873000c36e8dc1f'
     );
     const g2 = g1.double();
     deepStrictEqual(
-    g2.x.toString(16),
+      g2.toAffine().x.toString(16),
       '759ca09377679ecd535a81e83039658bf40959283187c654c5416f439403cf5'
     );
     deepStrictEqual(
-    g2.y.toString(16),
+      g2.toAffine().y.toString(16),
       '6f524a3400e7708d5c01a28598ad272e7455aa88778b19f93b562d7a9646c41'
     );
     const g3 = g2.add(g1);
     deepStrictEqual(
-    g3.x.toString(16),
+      g3.toAffine().x.toString(16),
       '411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20'
     );
     deepStrictEqual(
-    g3.y.toString(16),
+      g3.toAffine().y.toString(16),
       '7e1b3ebac08924d2c26f409549191fcf94f3bf6f301ed3553e22dfb802f0686'
     );
-  const g32 = g1.multiply(3);
+    const g32 = g1.multiply(3n);
     deepStrictEqual(
-    g32.x.toString(16),
+      g32.toAffine().x.toString(16),
       '411494b501a98abd8262b0da1351e17899a0c4ef23dd2f96fec5ba847310b20'
     );
     deepStrictEqual(
-    g32.y.toString(16),
+      g32.toAffine().y.toString(16),
       '7e1b3ebac08924d2c26f409549191fcf94f3bf6f301ed3553e22dfb802f0686'
     );
     const minus1 = g1.multiply(starknet.CURVE.n - 1n);
     deepStrictEqual(
-    minus1.x.toString(16),
+      minus1.toAffine().x.toString(16),
       '1ef15c18599971b7beced415a40f0c7deacfd9b0d1819e03d723d8bc943cfca'
     );
     deepStrictEqual(
-    minus1.y.toString(16),
+      minus1.toAffine().y.toString(16),
       '7a997f9f55b68e04841b7fe20b9139d21ac132ee541bc5cd78cfff3c91723e2'
     );
-});
+  });
 
-should('Pedersen', () => {
+  should('Pedersen', () => {
     deepStrictEqual(
       starknet.pedersen(2, 3),
       '0x5774fa77b3d843ae9167abd61cf80365a9b2b02218fc2f628494b5bdc9b33b8'
@@ -64,16 +67,16 @@ should('Pedersen', () => {
       starknet.pedersen(3, 4),
       '0x262697b88544f733e5c6907c3e1763131e9f14c51ee7951258abbfb29415fbf'
     );
-});
+  });
 
-should('Hash chain', () => {
+  should('Hash chain', () => {
     deepStrictEqual(
       starknet.hashChain([1, 2, 3]),
       '0x5d9d62d4040b977c3f8d2389d494e4e89a96a8b45c44b1368f1cc6ec5418915'
     );
-});
+  });
 
-should('Pedersen hash edgecases', () => {
+  should('Pedersen hash edgecases', () => {
     // >>> pedersen_hash(0,0)
     const zero = '0x49ee3eba8c1600700ee1b87eb599f16716b0b1022947733551fde4050ca6804';
     deepStrictEqual(starknet.pedersen(0, 0), zero);
@@ -100,9 +103,9 @@ should('Pedersen hash edgecases', () => {
     throws(() => starknet.pedersen(false, false), 'false');
     throws(() => starknet.pedersen(true, true), 'true');
     throws(() => starknet.pedersen(10.1, 10.1), 'float');
-});
+  });
 
-should('hashChain edgecases', () => {
+  should('hashChain edgecases', () => {
     deepStrictEqual(starknet.hashChain([32312321312321312312312321n]), '0x1aba6672c014b4838cc201');
     deepStrictEqual(
       starknet.hashChain([1n, 2n]),
@@ -118,9 +121,9 @@ should('hashChain edgecases', () => {
       starknet.hashChain([1, 2]),
       '0x5bb9440e27889a364bcb678b1f679ecd1347acdedcbf36e83494f857cc58026'
     );
-});
+  });
 
-should('Pedersen hash, issue #2', () => {
+  should('Pedersen hash, issue #2', () => {
     // Verified with starnet.js
     deepStrictEqual(
       starknet.computeHashOnElements(issue2),
@@ -134,12 +137,10 @@ should('Pedersen hash, issue #2', () => {
       starknet.computeHashOnElements([1]),
       '0x78d74f61aeaa8286418fd34b3a12a610445eba11d00ecc82ecac2542d55f7a4'
     );
-});
+  });
 
-import * as bip32 from '@scure/bip32';
-import * as bip39 from '@scure/bip39';
 
-should('Seed derivation (example)', () => {
+  should('Seed derivation (example)', () => {
     const layer = 'starkex';
     const application = 'starkdeployement';
     const mnemonic =
@@ -153,18 +154,18 @@ should('Seed derivation (example)', () => {
       starknet.grindKey(hdKey.privateKey),
       '6cf0a8bf113352eb863157a45c5e5567abb34f8d32cddafd2c22aa803f4892c'
     );
-});
+  });
 
-should('Compressed keys', () => {
+  should('Compressed keys', () => {
-  const G = starknet.Point.BASE;
+    const G = starknet.ProjectivePoint.BASE;
     const half = starknet.CURVE.n / 2n;
     const last = starknet.CURVE.n;
     const vectors = [
-    1,
+      1n,
-    2,
+      2n,
-    3,
+      3n,
-    4,
+      4n,
-    5,
+      5n,
       half - 5n,
       half - 4n,
       half - 3n,
@@ -182,17 +183,17 @@ should('Compressed keys', () => {
       last - 2n,
       last - 1n,
     ].map((i) => G.multiply(i));
-  const fixPoint = (pt) => ({ ...pt, _WINDOW_SIZE: undefined });
+    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.Point.fromHex(uncompressed)), exp);
+      deepStrictEqual(fixPoint(starknet.ProjectivePoint.fromHex(uncompressed)), exp);
-    deepStrictEqual(fixPoint(starknet.Point.fromHex(compressed)), exp);
+      deepStrictEqual(fixPoint(starknet.ProjectivePoint.fromHex(compressed)), exp);
-    deepStrictEqual(starknet.Point.fromHex(compressed).toHex(), uncompressed);
+      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
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
+      and conversions to other media types.
+
+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
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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 = [
+    [
+        2950795762459345168613727575620414179244544320470208355568817838579231751791,
+        1587446564224215276866294500450702039420286416111469274423465069420553242820,
+        1645965921169490687904413452218868659025437693527479459426157555728339600137,
+    ],
+    [
+        2782373324549879794752287702905278018819686065818504085638398966973694145741,
+        3409172630025222641379726933524480516420204828329395644967085131392375707302,
+        2379053116496905638239090788901387719228422033660130943198035907032739387135,
+    ],
+    [
+        2570819397480941104144008784293466051718826502582588529995520356691856497111,
+        3546220846133880637977653625763703334841539452343273304410918449202580719746,
+        2720682389492889709700489490056111332164748138023159726590726667539759963454,
+    ],
+    [
+        1899653471897224903834726250400246354200311275092866725547887381599836519005,
+        2369443697923857319844855392163763375394720104106200469525915896159690979559,
+        2354174693689535854311272135513626412848402744119855553970180659094265527996,
+    ],
+    [
+        2404084503073127963385083467393598147276436640877011103379112521338973185443,
+        950320777137731763811524327595514151340412860090489448295239456547370725376,
+        2121140748740143694053732746913428481442990369183417228688865837805149503386,
+    ],
+    [
+        2372065044800422557577242066480215868569521938346032514014152523102053709709,
+        2618497439310693947058545060953893433487994458443568169824149550389484489896,
+        3518297267402065742048564133910509847197496119850246255805075095266319996916,
+    ],
+    [
+        340529752683340505065238931581518232901634742162506851191464448040657139775,
+        1954876811294863748406056845662382214841467408616109501720437541211031966538,
+        813813157354633930267029888722341725864333883175521358739311868164460385261,
+    ],
+    [
+        71901595776070443337150458310956362034911936706490730914901986556638720031,
+        2789761472166115462625363403490399263810962093264318361008954888847594113421,
+        2628791615374802560074754031104384456692791616314774034906110098358135152410,
+    ],
+    [
+        3617032588734559635167557152518265808024917503198278888820567553943986939719,
+        2624012360209966117322788103333497793082705816015202046036057821340914061980,
+        149101987103211771991327927827692640556911620408176100290586418839323044234,
+    ],
+    [
+        1039927963829140138166373450440320262590862908847727961488297105916489431045,
+        2213946951050724449162431068646025833746639391992751674082854766704900195669,
+        2792724903541814965769131737117981991997031078369482697195201969174353468597,
+    ],
+    [
+        3212031629728871219804596347439383805499808476303618848198208101593976279441,
+        3343514080098703935339621028041191631325798327656683100151836206557453199613,
+        614054702436541219556958850933730254992710988573177298270089989048553060199,
+    ],
+    [
+        148148081026449726283933484730968827750202042869875329032965774667206931170,
+        1158283532103191908366672518396366136968613180867652172211392033571980848414,
+        1032400527342371389481069504520755916075559110755235773196747439146396688513,
+    ],
+    [
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+        462498083559902778091095573017508352472262817904991134671058825705968404510,
+        1003580119810278869589347418043095667699674425582646347949349245557449452503,
+    ],
+    [
+        619074932220101074089137133998298830285661916867732916607601635248249357793,
+        2635090520059500019661864086615522409798872905401305311748231832709078452746,
+        978252636251682252755279071140187792306115352460774007308726210405257135181,
+    ],
+    [
+        1766912167973123409669091967764158892111310474906691336473559256218048677083,
+        1663265127259512472182980890707014969235283233442916350121860684522654120381,
+        3532407621206959585000336211742670185380751515636605428496206887841428074250,
+    ],
+    [
+        2507023127157093845256722098502856938353143387711652912931112668310034975446,
+        3321152907858462102434883844787153373036767230808678981306827073335525034593,
+        3039253036806065280643845548147711477270022154459620569428286684179698125661,
+    ],
+    [
+        103480338868480851881924519768416587261556021758163719199282794248762465380,
+        2394049781357087698434751577708655768465803975478348134669006211289636928495,
+        2660531560345476340796109810821127229446538730404600368347902087220064379579,
+    ],
+    [
+        3603166934034556203649050570865466556260359798872408576857928196141785055563,
+        1553799760191949768532188139643704561532896296986025007089826672890485412324,
+        2744284717053657689091306578463476341218866418732695211367062598446038965164,
+    ],
+    [
+        320745764922149897598257794663594419839885234101078803811049904310835548856,
+        979382242100682161589753881721708883681034024104145498709287731138044566302,
+        1860426855810549882740147175136418997351054138609396651615467358416651354991,
+    ],
+    [
+        336173081054369235994909356892506146234495707857220254489443629387613956145,
+        1632470326779699229772327605759783482411227247311431865655466227711078175883,
+        921958250077481394074960433988881176409497663777043304881055317463712938502,
+    ],
+    [
+        3034358982193370602048539901033542101022185309652879937418114324899281842797,
+        25626282149517463867572353922222474817434101087272320606729439087234878607,
+        3002662261401575565838149305485737102400501329139562227180277188790091853682,
+    ],
+    [
+        2939684373453383817196521641512509179310654199629514917426341354023324109367,
+        1076484609897998179434851570277297233169621096172424141759873688902355505136,
+        2575095284833160494841112025725243274091830284746697961080467506739203605049,
+    ],
+    [
+        3565075264617591783581665711620369529657840830498005563542124551465195621851,
+        2197016502533303822395077038351174326125210255869204501838837289716363437993,
+        331415322883530754594261416546036195982886300052707474899691116664327869405,
+    ],
+    [
+        1935011233711290003793244296594669823169522055520303479680359990463281661839,
+        3495901467168087413996941216661589517270845976538454329511167073314577412322,
+        954195417117133246453562983448451025087661597543338750600301835944144520375,
+    ],
+    [
+        1271840477709992894995746871435810599280944810893784031132923384456797925777,
+        2565310762274337662754531859505158700827688964841878141121196528015826671847,
+        3365022288251637014588279139038152521653896670895105540140002607272936852513,
+    ],
+    [
+        1660592021628965529963974299647026602622092163312666588591285654477111176051,
+        970104372286014048279296575474974982288801187216974504035759997141059513421,
+        2617024574317953753849168721871770134225690844968986289121504184985993971227,
+    ],
+    [
+        999899815343607746071464113462778273556695659506865124478430189024755832262,
+        2228536129413411161615629030408828764980855956560026807518714080003644769896,
+        2701953891198001564547196795777701119629537795442025393867364730330476403227,
+    ],
+    [
+        837078355588159388741598313782044128527494922918203556465116291436461597853,
+        2121749601840466143704862369657561429793951309962582099604848281796392359214,
+        771812260179247428733132708063116523892339056677915387749121983038690154755,
+    ],
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+        3317336423132806446086732225036532603224267214833263122557471741829060578219,
+        481570067997721834712647566896657604857788523050900222145547508314620762046,
+        242195042559343964206291740270858862066153636168162642380846129622127460192,
+    ],
+    [
+        2855462178889999218204481481614105202770810647859867354506557827319138379686,
+        3525521107148375040131784770413887305850308357895464453970651672160034885202,
+        1320839531502392535964065058804908871811967681250362364246430459003920305799,
+    ],
+    [
+        2514191518588387125173345107242226637171897291221681115249521904869763202419,
+        2798335750958827619666318316247381695117827718387653874070218127140615157902,
+        2808467767967035643407948058486565877867906577474361783201337540214875566395,
+    ],
+    [
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+        761519904537984520554247997444508040636526566551719396202550009393012691157,
+    ],
+    [
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+        199541098009731541347317515995192175813554789571447733944970283654592727138,
+        192100490643078165121235261796864975568292640203635147901612231594408079071,
+    ],
+    [
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+        2831653363992091308880573627558515686245403755586311978724025292003353336665,
+    ],
+    [
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+        3538757242013734574731807289786598937548399719866320954894004830207085723125,
+    ],
+    [
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+        2345013122330545298606028187653996682275206910242635100920038943391319595180,
+        3528369671971445493932880023233332035122954362711876290904323783426765912206,
+    ],
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+        378514724418106317738164464176041649567501099164061863402473942795977719726,
+    ],
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test/stark/poseidon/poseidon4.txt

@@ -0,0 +1,559 @@
+Rate = 3
+Capacity = 1
+FullRounds = 8
+PartialRounds = 84
+MDS = [[2, 1, 1, 1], [1, 1, 1, 1], [1, 1, 0, 1], [1, 1, 1, -1]]
+RoundKeys = [
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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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+        2888553035909938253628892138500390690221493345071933642853222968481016605919,
+        3386241569867597612447901482685846444743718781330869478721963580925825915450,
+        1205126220630896984850042596877918177217334376800874965105642874206963597698,
+        3590072615491710252422997155203204584659171612188004116415640739580250394190,
+        692469013329617220154003334549812915100479873898898958632988703738125356983,
+    ],
+    [
+        1623178235190707102808841905143937367808788834203621005714003335195182126335,
+        1972826180775011489122426045504602288576507493792470102803637471568052321297,
+        3415141329098504418158191749675997877417539760075593313736376750580696083073,
+        587811537889727046473915684463981273175495137461951211739526104349163747811,
+        2523982964351069134084525951849317400231659428055762640605248929856135518199,
+    ],
+    [
+        2686176526711834950207666047281383173339057216783586039351834948812568447629,
+        983144446441739425577690449774542566745526459152966545642451764143532586964,
+        171558252019175695567663688494555626159399786667979998273792882504784080805,
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+        1264669683963885571544813806669118319675288608634733888843804451222546848295,
+    ],
+    [
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+        11387399609384288947733630450855186629703576293221897150193655994854764608,
+        2541728569046079092074077754414781968906176513081761690404588216304985421091,
+        47685947554980329431290582269851186106577733250761848107645535357326439312,
+        472176388418187405374813530639596064799362505024895746833751173199773896628,
+    ],
+    [
+        2764298116617383397920343358525617195195060562266243809245480210157942112738,
+        486863835068754002670800862273365477867695879270721744227071001883208334054,
+        2973492686137102577527656941792991264994301121122130295965761350095846874635,
+        178385615141132702906181473263873416748818415607305319148067639744074654009,
+        533624640096756667052211553746016402543259206286603356120804827761339634127,
+    ],
+    [
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+        531851793767260921861217458033110066464894334064526987603936107947006031387,
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+        838191718603413598040249006803464503100808192944407407147899973659013630611,
+        1574561296941310904780257598780779812250055948216417844567262310524022037406,
+    ],
+    [
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+        445076790942318675726839050057337819004979443030540904213920669247413907302,
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+        2240507606126946994415203252302826782042951346966859379502140796364876543253,
+    ],
+    [
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+        671929312763821646360589403212798993954209530574443543917757335777610372144,
+    ],
+    [
+        2513909805455654095962542944994577107405216428214873444765576238504714067396,
+        870121102846043786263357605823753628974859886859187558617096145653709171231,
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+        2855046250836680633532995284655778407402587437073106249445470889390454667586,
+        2063679741125384345396981490971605710211281905716315529671473143278849561151,
+    ],
+    [
+        1433753212258929925682201698758056443128516570551146995210728194816988328337,
+        3334984763425011856632257855270507440816274246647423607159847074739331865077,
+        337911293622078184850923533628334646725451591671907148383867096651211846605,
+        559587005295238702015018022040357402231957131094636365177008701077975941644,
+        885963059604819264377490633589388189646118257469490919900554134369512794660,
+    ],
+    [
+        1957748763518471091057032383332840331641373304981058387824598000170709016333,
+        3175295982155056798972302481564899381103533409383494814704562889625572018450,
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+        947374835104260364630171441676101001841507588423166778786886198914150312958,
+        906933977754491302438795274167251538820934378773708095543613756654712689280,
+    ],
+    [
+        2170116291766863179909957030577284618726490893598499117272497866180009722894,
+        1801335399574515889082584621772588704763181408217893911806726119813067220453,
+        1942500232535842474530840356353427989892065499159260166135596750084681859966,
+        62936080219825306823124060587235998278756755377419521154040408253893795176,
+        3091993939935137795359769774909373279950941171574748645375255810204590357753,
+    ],
+    [
+        1283528386884634267663661033944552098742115012555712906773586466375284501324,
+        1581820717639229420476069802992937438655873471854930764425841549067913106065,
+        2301986095388751633126546121528329200085681648876910655269533407603441046514,
+        2850003828037698751961753862613545302539465803982364898225617297398939302949,
+        48024691078494936445046366770271288984930221238071705874025261821606393528,
+    ],
+    [
+        1482336297033144958942154923925185950152551534403871620222916667536030875354,
+        3081177564717719643771186007689458633949181485535169123213511264603782950049,
+        3315701127039521853279746297714590495201061397709680410650043502532250578075,
+        3514407611000441301995070394422463400067690470546731164089622325748803106020,
+        368970178199930154322724953487299516224498421233447528815195701420122548537,
+    ],
+    [
+        584353160413525267849669053228533951552602295860601556035386665117717227391,
+        752038702160385294706011538400822066722189014251268673051846350397729870418,
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+        1367902435756906062215608264424138718742854099315395230911274560900857414183,
+        1828549068951502746189364466794037234789986878381694857475972053743463890779,
+    ],
+    [
+        488172495141237210878388657234137733008417573114482400652274985829148564248,
+        962906242461930394022372340919543491337923491322497419797555620396501785566,
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+        1966395064658902622886154686288219600816893261614483533899715888994623208964,
+        3496095878293416917311185659829821476802828534554531050412634978086916288609,
+    ],
+    [
+        3368478822390537245916137403277928093536087427951052230723275731232142463388,
+        3397410259276620127103231993277518800970669191016277541098821699302368873803,
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+        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

@@ -1,48 +1,50 @@
 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', () => {
+  should('Point#toHex() roundtrip', () => {
     fc.assert(
       fc.property(FC_BIGINT, (x) => {
-      const point1 = starknet.Point.fromPrivateKey(x);
+        const point1 = starknet.ProjectivePoint.fromPrivateKey(x);
         const hex = point1.toHex(true);
-      deepStrictEqual(starknet.Point.fromHex(hex).toHex(true), hex);
+        deepStrictEqual(starknet.ProjectivePoint.fromHex(hex).toHex(true), hex);
       })
     );
-});
+  });
 
-should('Signature.fromCompactHex() roundtrip', () => {
+  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', () => {
+  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', () =>
+  should('verify()/should verify random signatures', () =>
     fc.assert(
-    fc.asyncProperty(FC_BIGINT, fc.hexaString({ minLength: 64, maxLength: 64 }), (privNum, msg) => {
+      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);
       })
     )
-);
+  );
+});
 
 // ESM is broken.
 import url from 'url';

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';
@@ -7,22 +7,23 @@ 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', () => {
+  should('custom keccak', () => {
     const value = starknet.keccak(utf8.decode('hello'));
     deepStrictEqual(value, 0x8aff950685c2ed4bc3174f3472287b56d9517b9c948127319a09a7a36deac8n);
     deepStrictEqual(value < 2n ** 250n, true);
-});
+  });
 
-should('RFC6979', () => {
+  should('RFC6979', () => {
     for (const msg of sigVec.messages) {
       const { r, s } = starknet.sign(msg.hash, sigVec.private_key);
       // const { r, s } = starknet.Signature.fromDER(sig);
       deepStrictEqual(r.toString(10), msg.r);
       deepStrictEqual(s.toString(10), msg.s);
     }
-});
+  });
 
-should('Signatures', () => {
+  should('Signatures', () => {
     const vectors = [
       {
         // Message hash of length 61.
@@ -59,9 +60,9 @@ should('Signatures', () => {
       deepStrictEqual(s.toString(16), v.s, 's equality');
       deepStrictEqual(starknet.verify(sig, v.msg, publicKey), true, 'verify');
     }
-});
+  });
 
-should('Invalid signatures', () => {
+  should('Invalid signatures', () => {
     /*
 
     it('should not verify invalid signature inputs lengths', () => {
@@ -155,11 +156,11 @@ should('Invalid signatures', () => {
         starkwareCrypto.verify(keyPairPub, msgHash.toString(16), msgSignature)
       ).to.be.false;
     });
-});
+  });
     */
-});
+  });
 
-should('Pedersen', () => {
+  should('Pedersen', () => {
     deepStrictEqual(
       starknet.pedersen(
         '0x3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
@@ -174,13 +175,13 @@ should('Pedersen', () => {
       ),
       '0x68cc0b76cddd1dd4ed2301ada9b7c872b23875d5ff837b3a87993e0d9996b87'
     );
-});
+  });
 
-should('Hash chain', () => {
+  should('Hash chain', () => {
     deepStrictEqual(starknet.hashChain([1, 2, 3]), starknet.pedersen(1, starknet.pedersen(2, 3)));
-});
+  });
 
-should('Key grinding', () => {
+  should('Key grinding', () => {
     deepStrictEqual(
       starknet.grindKey('86F3E7293141F20A8BAFF320E8EE4ACCB9D4A4BF2B4D295E8CEE784DB46E0519'),
       '5c8c8683596c732541a59e03007b2d30dbbbb873556fe65b5fb63c16688f941'
@@ -190,9 +191,9 @@ should('Key grinding', () => {
       starknet.grindKey('94F3E7293141F20A8BAFF320E8EE4ACCB9D4A4BF2B4D295E8CEE784DB46E0595'),
       '33880b9aba464c1c01c9f8f5b4fc1134698f9b0a8d18505cab6cdd34d93dc02'
     );
-});
+  });
 
-should('Private to stark key', () => {
+  should('Private to stark key', () => {
     deepStrictEqual(
       starknet.getStarkKey('0x178047D3869489C055D7EA54C014FFB834A069C9595186ABE04EA4D1223A03F'),
       '0x1895a6a77ae14e7987b9cb51329a5adfb17bd8e7c638f92d6892d76e51cebcf'
@@ -200,9 +201,9 @@ should('Private to stark key', () => {
     for (const [privKey, expectedPubKey] of Object.entries(precomputedKeys)) {
       deepStrictEqual(starknet.getStarkKey(privKey), expectedPubKey);
     }
-});
+  });
 
-should('Private stark key from eth signature', () => {
+  should('Private stark key from eth signature', () => {
     const ethSignature =
       '0x21fbf0696d5e0aa2ef41a2b4ffb623bcaf070461d61cf7251c74161f82fec3a43' +
       '70854bc0a34b3ab487c1bc021cd318c734c51ae29374f2beb0e6f2dd49b4bf41c';
@@ -210,9 +211,9 @@ should('Private stark key from eth signature', () => {
       starknet.ethSigToPrivate(ethSignature),
       '766f11e90cd7c7b43085b56da35c781f8c067ac0d578eabdceebc4886435bda'
     );
-});
+  });
 
-should('Key derivation', () => {
+  should('Key derivation', () => {
     const layer = 'starkex';
     const application = 'starkdeployement';
     const mnemonic =
@@ -242,10 +243,10 @@ should('Key derivation', () => {
       deepStrictEqual(realPath, path);
       deepStrictEqual(starknet.grindKey(hd.derive(realPath).privateKey), privateKey);
     }
-});
+  });
 
-// Verified against starknet.js
+  // Verified against starknet.js
-should('Starknet.js cross-tests', () => {
+  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
@@ -255,7 +256,7 @@ should('Starknet.js cross-tests', () => {
     );
     const msgHash = '0x6d1706bd3d1ba7c517be2a2a335996f63d4738e2f182144d078a1dd9997062e';
     const sig = starknet.sign(msgHash, privateKey);
-  const { r, s } = (sig);
+    const { r, s } = sig;
 
     deepStrictEqual(
       r.toString(),
@@ -277,6 +278,7 @@ should('Starknet.js cross-tests', () => {
       2440689354481625417078677634625227600823892606910345662891037256374285369343n
     );
     deepStrictEqual(starknet.verify(sig2.toDERHex(), hashMsg2, pubKey), true);
+  });
 });
 
 // ESM is broken.