Release 0.5.1.

README.md

@@ -7,8 +7,8 @@ Minimal, auditable JS implementation of elliptic curve cryptography.
 - [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)
-- 🔻 Tree-shaking-friendly: there is no entry point, which ensures small size of your app
 - 🔍 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:
 
@@ -84,11 +84,12 @@ 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/modular](#abstractmodular)
+- [abstract/utils](#abstractutils)
 
 ### Overview
 
@@ -324,20 +325,70 @@ 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/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

benchmark/index.js

@@ -96,6 +96,10 @@ 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 +128,10 @@ 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 +153,10 @@ 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 +180,12 @@ 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: () => {

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

@@ -1,6 +1,6 @@
 {
   "name": "@noble/curves",
-  "version": "0.5.0",
+  "version": "0.5.1",
   "description": "Minimal, auditable JS implementation of elliptic curve cryptography",
   "files": [
     "lib"

src/abstract/hash-to-curve.ts

@@ -17,10 +17,11 @@ 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;
 };
 
@@ -29,7 +30,8 @@ export function validateHTFOpts(opts: htfOpts) {
   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');
 }
@@ -101,13 +103,40 @@ 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 {
+  // 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: htfOpts): bigint[][] {
   // if options is provided but incomplete, fill any missing fields with the
   // value in hftDefaults (ie hash to G2).
@@ -116,8 +145,10 @@ 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++) {

src/abstract/modular.ts

@@ -1,10 +1,11 @@
 /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
+// TODO: remove circular imports
 import * as utils from './utils.js';
 // Utilities for modular arithmetics and finite fields
 // 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);
 
@@ -66,26 +67,68 @@ 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).
+// https://eprint.iacr.org/2012/685.pdf (page 12)
- * * (a | p) ≡ 1    if a is a square (mod p)
+export function tonelliShanks(P: bigint) {
- * * (a | p) ≡ -1   if a is not a square (mod p)
+  // Legendre constant: used to calculate Legendre symbol (a | p),
- * * (a | p) ≡ 0    if a ≡ 0 (mod p)
+  // which denotes the value of a^((p-1)/2) (mod p).
- */
+  // (a | p) ≡ 1    if a is a square (mod p)
-export function legendre(num: bigint, fieldPrime: bigint): bigint {
+  // (a | p) ≡ -1   if a is not a square (mod p)
-  return pow(num, (fieldPrime - _1n) / _2n, fieldPrime);
+  // (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 = q2s 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.equals(Fp.square(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) must be ≡ 1
+    if (Fp.pow(n, legendreC) !== Fp.ONE) throw new Error('Cannot find square root');
+    let s = S;
+
+    let c = pow(Z, Q, P);
+    let r = Fp.pow(n, Q1div2);
+    let t = Fp.pow(n, Q);
+
+    let t2 = Fp.ZERO;
+    while (!Fp.equals(Fp.sub(t, Fp.ONE), Fp.ZERO)) {
+      t2 = Fp.square(t);
+      let i;
+      for (i = 1; i < s; i++) {
+        // stop if t2-1 == 0
+        if (Fp.equals(Fp.sub(t2, Fp.ONE), Fp.ZERO)) break;
+        // t2 *= t2
+        t2 = Fp.square(t2);
+      }
+      let b = pow(c, BigInt(1 << (s - i - 1)), P);
+      r = Fp.mul(r, b);
+      c = mod(b * b, P);
+      t = Fp.mul(t, c);
+      s = i;
+    }
+    return r;
+  };
 }
 
-/**
+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 +137,54 @@ 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);
-    return root;
+      // Throw if root**2 != n
+      if (!Fp.equals(Fp.square(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.equals(Fp.square(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);
@@ -176,6 +225,7 @@ export interface Field<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;
   pow(lhs: T, power: bigint): T;
@@ -246,21 +296,31 @@ 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));
 }
 
+// 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.equals(p, f.ZERO) || f.equals(p, f.ONE);
+  };
+}
+
 // 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);
   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,
@@ -292,7 +352,7 @@ export function Fp(
     mulN: (lhs, rhs) => lhs * rhs,
 
     invert: (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
@@ -305,87 +365,18 @@ export function Fp(
         throw new Error(`Fp.fromBytes: expected ${BYTES}, got ${bytes.length}`);
       return isLE ? utils.bytesToNumberLE(bytes) : utils.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.negate(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.negate(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);
-  };
-  // Constant-time Tonelli-Shanks algorithm
-  let l = _0n;
-  for (let o = q - _1n; o % _2n === _0n; o /= _2n) l += _1n;
-  const c1 = l; // 1. c1, the largest integer such that 2^c1 divides q - 1.
-  const c2 = (q - _1n) / _2n ** c1; // 2. c2 = (q - 1) / (2^c1)        # Integer arithmetic
-  const c3 = (c2 - _1n) / _2n; // 3. c3 = (c2 - 1) / 2            # Integer arithmetic
-  //  4. c4, a non-square value in F
-  //  5. c5 = c4^c2 in F
-  let c4 = Fp.ONE;
-  while (isSquare(c4)) c4 = Fp.add(c4, Fp.ONE);
-  const c5 = Fp.pow(c4, c2);
-
-  let sqrt: (x: T) => T = (x) => {
-    let z = Fp.pow(x, c3); // 1.  z = x^c3
-    let t = Fp.square(z); // 2.  t = z * z
-    t = Fp.mul(t, x); // 3.  t = t * x
-    z = Fp.mul(z, x); // 4.  z = z * x
-    let b = t; // 5.  b = t
-    let c = c5; // 6.  c = c5
-    // 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/utils.ts

@@ -12,7 +12,7 @@ export type CHash = {
   (message: Uint8Array | string): Uint8Array;
   blockLen: number;
   outputLen: number;
-  create(): any;
+  create(opts?: { dkLen?: number }): any; // For shake
 };
 
 // NOTE: these are generic, even if curve is on some polynominal field (bls), it will still have P/n/h

src/bls12-381.ts

@@ -926,12 +926,12 @@ 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)

src/ed25519.ts

@@ -3,7 +3,7 @@ import { sha512 } from '@noble/hashes/sha512';
 import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';
 import { twistedEdwards, ExtendedPointType } 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,
@@ -91,7 +91,80 @@ export const ED25519_TORSION_SUBGROUP = [
   'c7176a703d4dd84fba3c0b760d10670f2a2053fa2c39ccc64ec7fd7792ac03fa',
 ];
 
-const Fp = Field(ED25519_P);
+const Fp = Field(ED25519_P, undefined, true);
+
+// Hash To Curve Elligator2 Map (NOTE: different from ristretto255 elligator)
+// NOTE: very important part is usage of FpSqrtEven for ELL2_C1_EDWARDS, since
+// SageMath returns different root first and everything falls apart
+
+const ELL2_C1 = (Fp.ORDER + BigInt(3)) / BigInt(8); // 1. c1 = (q + 3) / 8       # Integer arithmetic
+
+const ELL2_C2 = Fp.pow(_2n, ELL2_C1); // 2. c2 = 2^c1
+const ELL2_C3 = Fp.sqrt(Fp.negate(Fp.ONE)); // 3. c3 = sqrt(-1)
+const ELL2_C4 = (Fp.ORDER - BigInt(5)) / BigInt(8); // 4. c4 = (q - 5) / 8       # Integer arithmetic
+const ELL2_J = BigInt(486662);
+
+// prettier-ignore
+function map_to_curve_elligator2_curve25519(u: bigint) {
+  let tv1 = Fp.square(u);       //  1.  tv1 = u^2
+  tv1 = Fp.mul(tv1, _2n);       //  2.  tv1 = 2 * tv1
+  let xd = Fp.add(tv1, Fp.ONE); //  3.   xd = tv1 + 1         # Nonzero: -1 is square (mod p), tv1 is not
+  let x1n = Fp.negate(ELL2_J);  //  4.  x1n = -J              # x1 = x1n / xd = -J / (1 + 2 * u^2)
+  let tv2 = Fp.square(xd);      //  5.  tv2 = xd^2
+  let gxd = Fp.mul(tv2, xd);    //  6.  gxd = tv2 * xd        # gxd = xd^3
+  let gx1 = Fp.mul(tv1, ELL2_J); //  7.  gx1 = J * tv1         # x1n + J * xd
+  gx1 = Fp.mul(gx1, x1n);       //  8.  gx1 = gx1 * x1n       # x1n^2 + J * x1n * xd
+  gx1 = Fp.add(gx1, tv2);       //  9.  gx1 = gx1 + tv2       # x1n^2 + J * x1n * xd + xd^2
+  gx1 = Fp.mul(gx1, x1n);       //  10. gx1 = gx1 * x1n       # x1n^3 + J * x1n^2 * xd + x1n * xd^2
+  let tv3 = Fp.square(gxd);     //  11. tv3 = gxd^2
+  tv2 = Fp.square(tv3);         //  12. tv2 = tv3^2           # gxd^4
+  tv3 = Fp.mul(tv3, gxd);       //  13. tv3 = tv3 * gxd       # gxd^3
+  tv3 = Fp.mul(tv3, gx1);       //  14. tv3 = tv3 * gx1       # gx1 * gxd^3
+  tv2 = Fp.mul(tv2, tv3);       //  15. tv2 = tv2 * tv3       # gx1 * gxd^7
+  let y11 = Fp.pow(tv2, ELL2_C4); //  16. y11 = tv2^c4        # (gx1 * gxd^7)^((p - 5) / 8)
+  y11 = Fp.mul(y11, tv3);       //  17. y11 = y11 * tv3       # gx1*gxd^3*(gx1*gxd^7)^((p-5)/8)
+  let y12 = Fp.mul(y11, ELL2_C3); //  18. y12 = y11 * c3
+  tv2 = Fp.square(y11);         //  19. tv2 = y11^2
+  tv2 = Fp.mul(tv2, gxd);       //  20. tv2 = tv2 * gxd
+  let e1 = Fp.equals(tv2, gx1); //  21.  e1 = tv2 == gx1
+  let y1 = Fp.cmov(y12, y11, e1); //  22.  y1 = CMOV(y12, y11, e1)  # If g(x1) is square, this is its sqrt
+  let x2n = Fp.mul(x1n, tv1);   //  23. x2n = x1n * tv1       # x2 = x2n / xd = 2 * u^2 * x1n / xd
+  let y21 = Fp.mul(y11, u);     //  24. y21 = y11 * u
+  y21 = Fp.mul(y21, ELL2_C2);   //  25. y21 = y21 * c2
+  let y22 = Fp.mul(y21, ELL2_C3); //  26. y22 = y21 * c3
+  let gx2 = Fp.mul(gx1, tv1);   //  27. gx2 = gx1 * tv1       # g(x2) = gx2 / gxd = 2 * u^2 * g(x1)
+  tv2 = Fp.square(y21);         //  28. tv2 = y21^2
+  tv2 = Fp.mul(tv2, gxd);       //  29. tv2 = tv2 * gxd
+  let e2 = Fp.equals(tv2, gx2); //  30.  e2 = tv2 == gx2
+  let y2 = Fp.cmov(y22, y21, e2); //  31.  y2 = CMOV(y22, y21, e2)  # If g(x2) is square, this is its sqrt
+  tv2 = Fp.square(y1);          //  32. tv2 = y1^2
+  tv2 = Fp.mul(tv2, gxd);       //  33. tv2 = tv2 * gxd
+  let e3 = Fp.equals(tv2, gx1); //  34.  e3 = tv2 == gx1
+  let xn = Fp.cmov(x2n, x1n, e3); //  35.  xn = CMOV(x2n, x1n, e3)  # If e3, x = x1, else x = x2
+  let y = Fp.cmov(y2, y1, e3);  //  36.   y = CMOV(y2, y1, e3)    # If e3, y = y1, else y = y2
+  let e4 = Fp.isOdd(y);         //  37.  e4 = sgn0(y) == 1        # Fix sign of y
+  y = Fp.cmov(y, Fp.negate(y), e3 !== e4); //  38.   y = CMOV(y, -y, e3 XOR e4)
+  return { xMn: xn, xMd: xd, yMn: y, yMd: 1n }; //  39. return (xn, xd, y, 1)
+}
+
+const ELL2_C1_EDWARDS = FpSqrtEven(Fp, Fp.negate(BigInt(486664))); // sgn0(c1) MUST equal 0
+function map_to_curve_elligator2_edwards25519(u: bigint) {
+  const { xMn, xMd, yMn, yMd } = map_to_curve_elligator2_curve25519(u); //  1.  (xMn, xMd, yMn, yMd) = map_to_curve_elligator2_curve25519(u)
+  let xn = Fp.mul(xMn, yMd); //  2.  xn = xMn * yMd
+  xn = Fp.mul(xn, ELL2_C1_EDWARDS); //  3.  xn = xn * c1
+  let xd = Fp.mul(xMd, yMn); //  4.  xd = xMd * yMn    # xn / xd = c1 * xM / yM
+  let yn = Fp.sub(xMn, xMd); //  5.  yn = xMn - xMd
+  let yd = Fp.add(xMn, xMd); //  6.  yd = xMn + xMd    # (n / d - 1) / (n / d + 1) = (n - d) / (n + d)
+  let tv1 = Fp.mul(xd, yd); //  7. tv1 = xd * yd
+  let e = Fp.equals(tv1, Fp.ZERO); //  8.   e = tv1 == 0
+  xn = Fp.cmov(xn, Fp.ZERO, e); //  9.  xn = CMOV(xn, 0, e)
+  xd = Fp.cmov(xd, Fp.ONE, e); //  10. xd = CMOV(xd, 1, e)
+  yn = Fp.cmov(yn, Fp.ONE, e); //  11. yn = CMOV(yn, 1, e)
+  yd = Fp.cmov(yd, Fp.ONE, e); //  12. yd = CMOV(yd, 1, e)
+
+  const inv = Fp.invertBatch([xd, yd]); // batch division
+  return { x: Fp.mul(xn, inv[0]), y: Fp.mul(yn, inv[1]) }; //  13. return (xn, xd, yn, yd)
+}
 
 const ED25519_DEF = {
   // Param: a
@@ -121,14 +194,10 @@ const ED25519_DEF = {
     p: Fp.ORDER,
     m: 1,
     k: 128,
-    expand: true,
+    expand: 'xmd',
     hash: sha512,
   },
-  mapToCurve: (scalars: bigint[]): { x: bigint; y: bigint } => {
+  mapToCurve: (scalars: bigint[]) => map_to_curve_elligator2_edwards25519(scalars[0]),
-    throw new Error('Not supported yet');
-    // const { x, y } = calcElligatorRistrettoMap(scalars[0]).toAffine();
-    // return { x, y };
-  },
 } as const;
 
 export const ed25519 = twistedEdwards(ED25519_DEF);

src/ed448.ts

@@ -2,7 +2,7 @@
 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';
 
 /**
@@ -52,6 +52,83 @@ function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
   return bytes;
 }
 
+const Fp = Field(ed448P, 456, true);
+
+// Hash To Curve Elligator2 Map
+const ELL2_C1 = (Fp.ORDER - BigInt(3)) / BigInt(4); // 1. c1 = (q - 3) / 4         # Integer arithmetic
+const ELL2_J = BigInt(156326);
+function map_to_curve_elligator2_curve448(u: bigint) {
+  let tv1 = Fp.square(u); // 1.  tv1 = u^2
+  let e1 = Fp.equals(tv1, Fp.ONE); // 2.   e1 = tv1 == 1
+  tv1 = Fp.cmov(tv1, Fp.ZERO, e1); // 3.  tv1 = CMOV(tv1, 0, e1)  # If Z * u^2 == -1, set tv1 = 0
+  let xd = Fp.sub(Fp.ONE, tv1); // 4.   xd = 1 - tv1
+  let x1n = Fp.negate(ELL2_J); // 5.  x1n = -J
+  let tv2 = Fp.square(xd); // 6.  tv2 = xd^2
+  let gxd = Fp.mul(tv2, xd); // 7.  gxd = tv2 * xd          # gxd = xd^3
+  let gx1 = Fp.mul(tv1, Fp.negate(ELL2_J)); // 8.  gx1 = -J * tv1          # x1n + J * xd
+  gx1 = Fp.mul(gx1, x1n); // 9.  gx1 = gx1 * x1n         # x1n^2 + J * x1n * xd
+  gx1 = Fp.add(gx1, tv2); // 10. gx1 = gx1 + tv2         # x1n^2 + J * x1n * xd + xd^2
+  gx1 = Fp.mul(gx1, x1n); // 11. gx1 = gx1 * x1n         # x1n^3 + J * x1n^2 * xd + x1n * xd^2
+  let tv3 = Fp.square(gxd); // 12. tv3 = gxd^2
+  tv2 = Fp.mul(gx1, gxd); // 13. tv2 = gx1 * gxd         # gx1 * gxd
+  tv3 = Fp.mul(tv3, tv2); // 14. tv3 = tv3 * tv2         # gx1 * gxd^3
+  let y1 = Fp.pow(tv3, ELL2_C1); // 15.  y1 = tv3^c1            # (gx1 * gxd^3)^((p - 3) / 4)
+  y1 = Fp.mul(y1, tv2); // 16.  y1 = y1 * tv2          # gx1 * gxd * (gx1 * gxd^3)^((p - 3) / 4)
+  let x2n = Fp.mul(x1n, Fp.negate(tv1)); // 17. x2n = -tv1 * x1n        # x2 = x2n / xd = -1 * u^2 * x1n / xd
+  let y2 = Fp.mul(y1, u); // 18.  y2 = y1 * u
+  y2 = Fp.cmov(y2, Fp.ZERO, e1); // 19.  y2 = CMOV(y2, 0, e1)
+  tv2 = Fp.square(y1); // 20. tv2 = y1^2
+  tv2 = Fp.mul(tv2, gxd); // 21. tv2 = tv2 * gxd
+  let e2 = Fp.equals(tv2, gx1); // 22.  e2 = tv2 == gx1
+  let xn = Fp.cmov(x2n, x1n, e2); // 23.  xn = CMOV(x2n, x1n, e2)  # If e2, x = x1, else x = x2
+  let y = Fp.cmov(y2, y1, e2); // 24.   y = CMOV(y2, y1, e2)    # If e2, y = y1, else y = y2
+  let e3 = Fp.isOdd(y); // 25.  e3 = sgn0(y) == 1        # Fix sign of y
+  y = Fp.cmov(y, Fp.negate(y), e2 !== e3); // 26.   y = CMOV(y, -y, e2 XOR e3)
+  return { xn, xd, yn: y, yd: Fp.ONE }; // 27. return (xn, xd, y, 1)
+}
+function map_to_curve_elligator2_edwards448(u: bigint) {
+  let { xn, xd, yn, yd } = map_to_curve_elligator2_curve448(u); // 1. (xn, xd, yn, yd) = map_to_curve_elligator2_curve448(u)
+  let xn2 = Fp.square(xn); // 2.  xn2 = xn^2
+  let xd2 = Fp.square(xd); // 3.  xd2 = xd^2
+  let xd4 = Fp.square(xd2); // 4.  xd4 = xd2^2
+  let yn2 = Fp.square(yn); // 5.  yn2 = yn^2
+  let yd2 = Fp.square(yd); // 6.  yd2 = yd^2
+  let xEn = Fp.sub(xn2, xd2); // 7.  xEn = xn2 - xd2
+  let tv2 = Fp.sub(xEn, xd2); // 8.  tv2 = xEn - xd2
+  xEn = Fp.mul(xEn, xd2); // 9.  xEn = xEn * xd2
+  xEn = Fp.mul(xEn, yd); // 10. xEn = xEn * yd
+  xEn = Fp.mul(xEn, yn); // 11. xEn = xEn * yn
+  xEn = Fp.mul(xEn, 4n); // 12. xEn = xEn * 4
+  tv2 = Fp.mul(tv2, xn2); // 13. tv2 = tv2 * xn2
+  tv2 = Fp.mul(tv2, yd2); // 14. tv2 = tv2 * yd2
+  let tv3 = Fp.mul(yn2, 4n); // 15. tv3 = 4 * yn2
+  let tv1 = Fp.add(tv3, yd2); // 16. tv1 = tv3 + yd2
+  tv1 = Fp.mul(tv1, xd4); // 17. tv1 = tv1 * xd4
+  let xEd = Fp.add(tv1, tv2); // 18. xEd = tv1 + tv2
+  tv2 = Fp.mul(tv2, xn); // 19. tv2 = tv2 * xn
+  let tv4 = Fp.mul(xn, xd4); // 20. tv4 = xn * xd4
+  let yEn = Fp.sub(tv3, yd2); // 21. yEn = tv3 - yd2
+  yEn = Fp.mul(yEn, tv4); // 22. yEn = yEn * tv4
+  yEn = Fp.sub(yEn, tv2); // 23. yEn = yEn - tv2
+  tv1 = Fp.add(xn2, xd2); // 24. tv1 = xn2 + xd2
+  tv1 = Fp.mul(tv1, xd2); // 25. tv1 = tv1 * xd2
+  tv1 = Fp.mul(tv1, xd); // 26. tv1 = tv1 * xd
+  tv1 = Fp.mul(tv1, yn2); // 27. tv1 = tv1 * yn2
+  tv1 = Fp.mul(tv1, BigInt(-2)); // 28. tv1 = -2 * tv1
+  let yEd = Fp.add(tv2, tv1); // 29. yEd = tv2 + tv1
+  tv4 = Fp.mul(tv4, yd2); // 30. tv4 = tv4 * yd2
+  yEd = Fp.add(yEd, tv4); // 31. yEd = yEd + tv4
+  tv1 = Fp.mul(xEd, yEd); // 32. tv1 = xEd * yEd
+  let e = Fp.equals(tv1, Fp.ZERO); // 33.   e = tv1 == 0
+  xEn = Fp.cmov(xEn, Fp.ZERO, e); // 34. xEn = CMOV(xEn, 0, e)
+  xEd = Fp.cmov(xEd, Fp.ONE, e); // 35. xEd = CMOV(xEd, 1, e)
+  yEn = Fp.cmov(yEn, Fp.ONE, e); // 36. yEn = CMOV(yEn, 1, e)
+  yEd = Fp.cmov(yEd, Fp.ONE, e); // 37. yEd = CMOV(yEd, 1, e)
+
+  const inv = Fp.invertBatch([xEd, yEd]); // batch division
+  return { x: Fp.mul(xEn, inv[0]), y: Fp.mul(yEn, inv[1]) }; // 38. return (xEn, xEd, yEn, yEd)
+}
+
 const ED448_DEF = {
   // Param: a
   a: BigInt(1),
@@ -60,7 +137,7 @@ 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
   n: BigInt(
     '181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779'
@@ -111,6 +188,15 @@ const ED448_DEF = {
     // square root exists, and the decoding fails.
     return { isValid: mod(x2 * v, P) === u, value: x };
   },
+  htfDefaults: {
+    DST: 'edwards448_XOF:SHAKE256_ELL2_RO_',
+    p: Fp.ORDER,
+    m: 1,
+    k: 224,
+    expand: 'xof',
+    hash: shake256,
+  },
+  mapToCurve: (scalars: bigint[]) => map_to_curve_elligator2_edwards448(scalars[0]),
 } as const;
 
 export const ed448 = twistedEdwards(ED448_DEF);

src/p256.ts

@@ -37,7 +37,7 @@ export const P256 = createCurve(
       p: Fp.ORDER,
       m: 1,
       k: 128,
-      expand: true,
+      expand: 'xmd',
       hash: sha256,
     },
   } as const,

src/p384.ts

@@ -41,7 +41,7 @@ export const P384 = createCurve({
       p: Fp.ORDER,
       m: 1,
       k: 192,
-      expand: true,
+      expand: 'xmd',
       hash: sha384,
     },
   } as const,

src/p521.ts

@@ -54,7 +54,7 @@ export const P521 = createCurve({
     p: Fp.ORDER,
     m: 1,
     k: 256,
-    expand: true,
+      expand: 'xmd',
     hash: sha512,
   },
 } as const, sha512);

src/secp256k1.ts

@@ -56,7 +56,9 @@ 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.equals(Fp.square(root), y)) throw new Error('Cannot find square root');
+  return root;
 }
 
 const Fp = Field(secp256k1P, undefined, undefined, { sqrt: sqrtMod });
@@ -152,7 +154,7 @@ export const secp256k1 = createCurve(
       p: Fp.ORDER,
       m: 1,
       k: 128,
-      expand: true,
+      expand: 'xmd',
       hash: sha256,
     },
   },

src/stark.ts

@@ -97,7 +97,7 @@ 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);
 }
@@ -203,6 +203,8 @@ 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);

test/basic.test.js

@@ -15,7 +15,252 @@ 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);
+    should(`${name} equality`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (num) => {
+          const a = create(num);
+          const b = create(num);
+          deepStrictEqual(Fp.equals(a, b), true);
+          deepStrictEqual(Fp.equals(b, a), true);
+        })
+      );
+    });
+    should(`${name} non-equality`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
+          const a = create(num1);
+          const b = create(num2);
+          deepStrictEqual(Fp.equals(a, b), num1 === num2);
+          deepStrictEqual(Fp.equals(b, a), num1 === num2);
+        })
+      );
+    });
+    should(`${name} add/subtract/commutativity`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
+          const a = create(num1);
+          const b = create(num2);
+          deepStrictEqual(Fp.add(a, b), Fp.add(b, a));
+        })
+      );
+    });
+    should(`${name} 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(`${name} add/subtract/x+0=x`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (num) => {
+          const a = create(num);
+          deepStrictEqual(Fp.add(a, Fp.ZERO), a);
+        })
+      );
+    });
+    should(`${name} 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(`${name} add/subtract/negate equality`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (num1) => {
+          const a = create(num1);
+          const b = create(num1);
+          deepStrictEqual(Fp.sub(Fp.ZERO, a), Fp.negate(a));
+          deepStrictEqual(Fp.sub(a, b), Fp.add(a, Fp.negate(b)));
+          deepStrictEqual(Fp.sub(a, b), Fp.add(a, Fp.mul(b, Fp.create(-1n))));
+        })
+      );
+    });
+    should(`${name} add/subtract/negate`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (num) => {
+          const a = create(num);
+          deepStrictEqual(Fp.negate(a), Fp.sub(Fp.ZERO, a));
+          deepStrictEqual(Fp.negate(a), Fp.mul(a, Fp.create(-1n)));
+        })
+      );
+    });
+
+    should(`${name} multiply/commutativity`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
+          const a = create(num1);
+          const b = create(num2);
+          deepStrictEqual(Fp.mul(a, b), Fp.mul(b, a));
+        })
+      );
+    });
+    should(`${name} 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(`${name} multiply/distributivity`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
+          const a = create(num1);
+          const b = create(num2);
+          const c = create(num3);
+          deepStrictEqual(Fp.mul(a, Fp.add(b, c)), Fp.add(Fp.mul(b, a), Fp.mul(c, a)));
+        })
+      );
+    });
+    should(`${name} 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(`${name} multiply/square equality`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (num) => {
+          const a = create(num);
+          deepStrictEqual(Fp.square(a), Fp.mul(a, a));
+        })
+      );
+    });
+    should(`${name} 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));
+        })
+      );
+    });
+    const isSquare = mod.FpIsSquare(Fp);
+    should(`${name} multiply/sqrt`, () => {
+      if (Fp === bls12_381.CURVE.Fp12) return; // Not implemented
+      fc.assert(
+        fc.property(FC_BIGINT, (num) => {
+          const a = create(num);
+          let root;
+          try {
+            root = Fp.sqrt(a);
+          } catch (e) {
+            deepStrictEqual(isSquare(a), false);
+            return;
+          }
+          deepStrictEqual(isSquare(a), true);
+          deepStrictEqual(Fp.equals(Fp.square(root), a), true, 'sqrt(a)^2 == a');
+          deepStrictEqual(Fp.equals(Fp.square(Fp.negate(root)), a), true, '(-sqrt(a))^2 == a');
+        })
+      );
+    });
+
+    should(`${name} div/division by one equality`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (num) => {
+          const a = create(num);
+          if (Fp.equals(a, Fp.ZERO)) return; // No division by zero
+          deepStrictEqual(Fp.div(a, Fp.ONE), a);
+          deepStrictEqual(Fp.div(a, a), Fp.ONE);
+        })
+      );
+    });
+    should(`${name} zero division equality`, () => {
+      fc.assert(
+        fc.property(FC_BIGINT, (num) => {
+          const a = create(num);
+          deepStrictEqual(Fp.div(Fp.ZERO, a), Fp.ZERO);
+        })
+      );
+    });
+    should(`${name} 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(`${name} 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.invert(b)));
+        })
+      );
+    });
+  }
+}
+
+// Group tests
 // prettier-ignore
 const CURVES = {
   secp192r1, secp224r1, secp256r1, secp384r1, secp521r1,
@@ -29,6 +274,7 @@ const CURVES = {
 };
 
 const NUM_RUNS = 5;
+
 const getXY = (p) => ({ x: p.x, y: p.y });
 
 function equal(a, b, comment) {

test/bls12-381.test.js

@@ -41,145 +41,7 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
 {
   const Fp = bls.Fp;
   const FC_BIGINT = fc.bigInt(1n, Fp.ORDER - 1n);
-  should('bls12-381/Fp/equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.create(num);
-        const b = Fp.create(num);
-        deepStrictEqual(Fp.equals(a, b), true);
-        deepStrictEqual(Fp.equals(b, a), true);
-      })
-    );
-  });
-  should('bls12-381/Fp/non-equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        deepStrictEqual(Fp.equals(a, b), num1 === num2);
-        deepStrictEqual(Fp.equals(b, a), num1 === num2);
-      })
-    );
-  });
-  should('bls12-381/Fp/add/subtract/commutativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        deepStrictEqual(Fp.add(a, b), Fp.add(b, a));
-      })
-    );
-  });
-  should('bls12-381/Fp/add/subtract/associativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        const c = Fp.create(num3);
-        deepStrictEqual(Fp.add(a, Fp.add(b, c)), Fp.add(Fp.add(a, b), c));
-      })
-    );
-  });
-  should('bls12-381/Fp/add/subtract/x+0=x', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.create(num);
-        deepStrictEqual(Fp.add(a, Fp.ZERO), a);
-      })
-    );
-  });
-  should('bls12-381/Fp/add/subtract/x-0=x', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.create(num);
-        deepStrictEqual(Fp.sub(a, Fp.ZERO), a);
-        deepStrictEqual(Fp.sub(a, a), Fp.ZERO);
-      })
-    );
-  });
-  should('bls12-381/Fp/add/subtract/negate equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num1) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num1);
-        deepStrictEqual(Fp.sub(Fp.ZERO, a), Fp.negate(a));
-        deepStrictEqual(Fp.sub(a, b), Fp.add(a, Fp.negate(b)));
-        deepStrictEqual(Fp.sub(a, b), Fp.add(a, Fp.mul(b, Fp.create(-1n))));
-      })
-    );
-  });
-  should('bls12-381/Fp/add/subtract/negate', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.create(num);
-        deepStrictEqual(Fp.negate(a), Fp.sub(Fp.ZERO, a));
-        deepStrictEqual(Fp.negate(a), Fp.mul(a, Fp.create(-1n)));
-      })
-    );
-  });
 
-  should('bls12-381/Fp/multiply/commutativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        deepStrictEqual(Fp.mul(a, b), Fp.mul(b, a));
-      })
-    );
-  });
-  should('bls12-381/Fp/multiply/associativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        const c = Fp.create(num3);
-        deepStrictEqual(Fp.mul(a, Fp.mul(b, c)), Fp.mul(Fp.mul(a, b), c));
-      })
-    );
-  });
-  should('bls12-381/Fp/multiply/distributivity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        const c = Fp.create(num3);
-        deepStrictEqual(Fp.mul(a, Fp.add(b, c)), Fp.add(Fp.mul(b, a), Fp.mul(c, a)));
-      })
-    );
-  });
-  should('bls12-381/Fp/multiply/add equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.create(num);
-        deepStrictEqual(Fp.mul(a, Fp.create(0n)), Fp.ZERO);
-        deepStrictEqual(Fp.mul(a, Fp.ZERO), Fp.ZERO);
-        deepStrictEqual(Fp.mul(a, Fp.create(1n)), a);
-        deepStrictEqual(Fp.mul(a, Fp.ONE), a);
-        deepStrictEqual(Fp.mul(a, Fp.create(2n)), Fp.add(a, a));
-        deepStrictEqual(Fp.mul(a, Fp.create(3n)), Fp.add(Fp.add(a, a), a));
-        deepStrictEqual(Fp.mul(a, Fp.create(4n)), Fp.add(Fp.add(Fp.add(a, a), a), a));
-      })
-    );
-  });
-  should('bls12-381/Fp/multiply/square equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.create(num);
-        deepStrictEqual(Fp.square(a), Fp.mul(a, a));
-      })
-    );
-  });
-  should('bls12-381/Fp/multiply/pow equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.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('bls12-381/Fp/multiply/sqrt', () => {
     let sqr1 = Fp.sqrt(Fp.create(300855555557n));
     deepStrictEqual(
@@ -188,43 +50,6 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
     );
     throws(() => Fp.sqrt(Fp.create(72057594037927816n)));
   });
-
-  should('bls12-381/Fp/div/division by one equality', () => {
-    fc.assert(
-      fc.property(fc.bigInt(1n, Fp.ORDER - 1n), (num) => {
-        const a = Fp.create(num);
-        deepStrictEqual(Fp.div(a, Fp.ONE), a);
-        deepStrictEqual(Fp.div(a, a), Fp.ONE);
-      })
-    );
-  });
-  should('bls12-381/Fp/div/division by zero equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, (num) => {
-        const a = Fp.create(num);
-        deepStrictEqual(Fp.div(Fp.ZERO, a), Fp.ZERO);
-      })
-    );
-  });
-  should('bls12-381/Fp/div/division distributivity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, FC_BIGINT, (num1, num2, num3) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        const c = Fp.create(num3);
-        deepStrictEqual(Fp.div(Fp.add(a, b), c), Fp.add(Fp.div(a, c), Fp.div(b, c)));
-      })
-    );
-  });
-  should('bls12-381/Fp/div/division and multiplication equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT, FC_BIGINT, (num1, num2) => {
-        const a = Fp.create(num1);
-        const b = Fp.create(num2);
-        deepStrictEqual(Fp.div(a, b), Fp.mul(a, Fp.invert(b)));
-      })
-    );
-  });
 }
 
 // Fp2
@@ -234,16 +59,6 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
   const FC_BIGINT = fc.bigInt(1n, Fp.ORDER - 1n);
   const FC_BIGINT_2 = fc.array(FC_BIGINT, { minLength: 2, maxLength: 2 });
 
-  should('bls12-381 Fp2/equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        const b = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.equals(a, b), true);
-        deepStrictEqual(Fp2.equals(b, a), true);
-      })
-    );
-  });
   should('bls12-381 Fp2/non-equality', () => {
     fc.assert(
       fc.property(FC_BIGINT_2, FC_BIGINT_2, (num1, num2) => {
@@ -254,136 +69,7 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
       })
     );
   });
-  should('bls12-381 Fp2/add/subtract/commutativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, FC_BIGINT_2, (num1, num2) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num2[0], num2[1]]);
-        deepStrictEqual(Fp2.add(a, b), Fp2.add(b, a));
-      })
-    );
-  });
-  should('bls12-381 Fp2/add/subtract/associativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, FC_BIGINT_2, FC_BIGINT_2, (num1, num2, num3) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num2[0], num2[1]]);
-        const c = Fp2.fromBigTuple([num3[0], num3[1]]);
-        deepStrictEqual(Fp2.add(a, Fp2.add(b, c)), Fp2.add(Fp2.add(a, b), c));
-      })
-    );
-  });
-  should('bls12-381 Fp2/add/subtract/x+0=x', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.add(a, Fp2.ZERO), a);
-      })
-    );
-  });
-  should('bls12-381 Fp2/add/subtract/x-0=x', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.sub(a, Fp2.ZERO), a);
-        deepStrictEqual(Fp2.sub(a, a), Fp2.ZERO);
-      })
-    );
-  });
-  should('bls12-381 Fp2/add/subtract/negate equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num1) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num1[0], num1[1]]);
-        deepStrictEqual(Fp2.sub(Fp2.ZERO, a), Fp2.negate(a));
-        deepStrictEqual(Fp2.sub(a, b), Fp2.add(a, Fp2.negate(b)));
-        deepStrictEqual(Fp2.sub(a, b), Fp2.add(a, Fp2.mul(b, -1n)));
-      })
-    );
-  });
-  should('bls12-381 Fp2/add/subtract/negate', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.negate(a), Fp2.sub(Fp2.ZERO, a));
-        deepStrictEqual(Fp2.negate(a), Fp2.mul(a, -1n));
-      })
-    );
-  });
 
-  should('bls12-381 Fp2/multiply/commutativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, FC_BIGINT_2, (num1, num2) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num2[0], num2[1]]);
-        deepStrictEqual(Fp2.mul(a, b), Fp2.mul(b, a));
-      })
-    );
-  });
-  should('bls12-381 Fp2/multiply/associativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, FC_BIGINT_2, FC_BIGINT_2, (num1, num2, num3) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num2[0], num2[1]]);
-        const c = Fp2.fromBigTuple([num3[0], num3[1]]);
-        deepStrictEqual(Fp2.mul(a, Fp2.mul(b, c)), Fp2.mul(Fp2.mul(a, b), c));
-      })
-    );
-  });
-  should('bls12-381 Fp2/multiply/distributivity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, FC_BIGINT_2, FC_BIGINT_2, (num1, num2, num3) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num2[0], num2[1]]);
-        const c = Fp2.fromBigTuple([num3[0], num3[1]]);
-        deepStrictEqual(Fp2.mul(a, Fp2.add(b, c)), Fp2.add(Fp2.mul(b, a), Fp2.mul(c, a)));
-      })
-    );
-  });
-  should('bls12-381 Fp2/multiply/add equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.mul(a, 0n), Fp2.ZERO);
-        deepStrictEqual(Fp2.mul(a, Fp2.ZERO), Fp2.ZERO);
-        deepStrictEqual(Fp2.mul(a, 1n), a);
-        deepStrictEqual(Fp2.mul(a, Fp2.ONE), a);
-        deepStrictEqual(Fp2.mul(a, 2n), Fp2.add(a, a));
-        deepStrictEqual(Fp2.mul(a, 3n), Fp2.add(Fp2.add(a, a), a));
-        deepStrictEqual(Fp2.mul(a, 4n), Fp2.add(Fp2.add(Fp2.add(a, a), a), a));
-      })
-    );
-  });
-  should('bls12-381 Fp2/multiply/square equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.square(a), Fp2.mul(a, a));
-      })
-    );
-  });
-  should('bls12-381 Fp2/multiply/pow equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.pow(a, 0n), Fp2.ONE);
-        deepStrictEqual(Fp2.pow(a, 1n), a);
-        deepStrictEqual(Fp2.pow(a, 2n), Fp2.mul(a, a));
-        deepStrictEqual(Fp2.pow(a, 3n), Fp2.mul(Fp2.mul(a, a), a));
-      })
-    );
-  });
-
-  should('bls12-381 Fp2/div/distributivity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, FC_BIGINT_2, FC_BIGINT_2, (num1, num2, num3) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num2[0], num2[1]]);
-        const c = Fp2.fromBigTuple([num3[0], num3[1]]);
-        deepStrictEqual(Fp2.div(Fp2.add(a, b), c), Fp2.add(Fp2.div(a, c), Fp2.div(b, c)));
-      })
-    );
-  });
   should('bls12-381 Fp2/div/x/1=x', () => {
     fc.assert(
       fc.property(FC_BIGINT_2, (num) => {
@@ -394,23 +80,6 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
       })
     );
   });
-  should('bls12-381 Fp2/div/ x/0=0', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, (num) => {
-        const a = Fp2.fromBigTuple([num[0], num[1]]);
-        deepStrictEqual(Fp2.div(Fp2.ZERO, a), Fp2.ZERO);
-      })
-    );
-  });
-  should('bls12-381 Fp2/div/ multiply equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_2, FC_BIGINT_2, (num1, num2) => {
-        const a = Fp2.fromBigTuple([num1[0], num1[1]]);
-        const b = Fp2.fromBigTuple([num2[0], num2[1]]);
-        deepStrictEqual(Fp2.div(a, b), Fp2.mul(a, Fp2.invert(b)));
-      })
-    );
-  });
 
   should('bls12-381 Fp2/frobenius', () => {
     // expect(Fp2.FROBENIUS_COEFFICIENTS[0].equals(Fp.ONE)).toBe(true);
@@ -472,195 +141,6 @@ const getPubKey = (priv) => bls.getPublicKey(priv);
   });
 }
 
-// Fp12
-{
-  const Fp = bls.Fp;
-  const Fp12 = bls.Fp12;
-  const FC_BIGINT = fc.bigInt(1n, Fp.ORDER - 1n);
-  const FC_BIGINT_12 = fc.array(FC_BIGINT, {
-    minLength: 12,
-    maxLength: 12,
-  });
-
-  should('bls12-381 Fp12/equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        const b = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.equals(a, b), true);
-        deepStrictEqual(Fp12.equals(b, a), true);
-      })
-    );
-  });
-  should('bls12-381 Fp12/non-equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, (num1, num2) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        deepStrictEqual(Fp12.equals(a, b), num1[0] === num2[0] && num1[1] === num2[1]);
-        deepStrictEqual(Fp12.equals(b, a), num1[0] === num2[0] && num1[1] === num2[1]);
-      })
-    );
-  });
-  should('bls12-381 Fp12/add/subtract/commutativuty', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, (num1, num2) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        deepStrictEqual(Fp12.add(a, b), Fp12.add(b, a));
-      })
-    );
-  });
-  should('bls12-381 Fp12/add/subtract/associativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, FC_BIGINT_12, (num1, num2, num3) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        const c = Fp12.fromBigTwelve(num3);
-        deepStrictEqual(Fp12.add(a, Fp12.add(b, c)), Fp12.add(Fp12.add(a, b), c));
-      })
-    );
-  });
-  should('bls12-381 Fp12/add/subtract/x+0=x', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.add(a, Fp12.ZERO), a);
-      })
-    );
-  });
-  should('bls12-381 Fp12/add/subtract/x-0=x', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.sub(a, Fp12.ZERO), a);
-        deepStrictEqual(Fp12.sub(a, a), Fp12.ZERO);
-      })
-    );
-  });
-  should('bls12-381 Fp12/add/subtract/negate equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num1) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num1);
-        deepStrictEqual(Fp12.sub(Fp12.ZERO, a), Fp12.negate(a));
-        deepStrictEqual(Fp12.sub(a, b), Fp12.add(a, Fp12.negate(b)));
-        deepStrictEqual(Fp12.sub(a, b), Fp12.add(a, Fp12.mul(b, -1n)));
-      })
-    );
-  });
-  should('bls12-381 Fp12/add/subtract/negate', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.negate(a), Fp12.sub(Fp12.ZERO, a));
-        deepStrictEqual(Fp12.negate(a), Fp12.mul(a, -1n));
-      })
-    );
-  });
-
-  should('bls12-381 Fp12/multiply/commutativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, (num1, num2) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        deepStrictEqual(Fp12.mul(a, b), Fp12.mul(b, a));
-      })
-    );
-  });
-  should('bls12-381 Fp12/multiply/associativity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, FC_BIGINT_12, (num1, num2, num3) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        const c = Fp12.fromBigTwelve(num3);
-        deepStrictEqual(Fp12.mul(a, Fp12.mul(b, c)), Fp12.mul(Fp12.mul(a, b), c));
-      })
-    );
-  });
-  should('bls12-381 Fp12/multiply/distributivity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, FC_BIGINT_12, (num1, num2, num3) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        const c = Fp12.fromBigTwelve(num3);
-        deepStrictEqual(Fp12.mul(a, Fp12.add(b, c)), Fp12.add(Fp12.mul(b, a), Fp12.mul(c, a)));
-      })
-    );
-  });
-  should('bls12-381 Fp12/multiply/add equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.mul(a, 0n), Fp12.ZERO);
-        deepStrictEqual(Fp12.mul(a, Fp12.ZERO), Fp12.ZERO);
-        deepStrictEqual(Fp12.mul(a, 1n), a);
-        deepStrictEqual(Fp12.mul(a, Fp12.ONE), a);
-        deepStrictEqual(Fp12.mul(a, 2n), Fp12.add(a, a));
-        deepStrictEqual(Fp12.mul(a, 3n), Fp12.add(Fp12.add(a, a), a));
-        deepStrictEqual(Fp12.mul(a, 4n), Fp12.add(Fp12.add(Fp12.add(a, a), a), a));
-      })
-    );
-  });
-  should('bls12-381 Fp12/multiply/square equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.square(a), Fp12.mul(a, a));
-      })
-    );
-  });
-  should('bls12-381 Fp12/multiply/pow equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.pow(a, 0n), Fp12.ONE);
-        deepStrictEqual(Fp12.pow(a, 1n), a);
-        deepStrictEqual(Fp12.pow(a, 2n), Fp12.mul(a, a));
-        deepStrictEqual(Fp12.pow(a, 3n), Fp12.mul(Fp12.mul(a, a), a));
-      })
-    );
-  });
-
-  should('bls12-381 Fp12/div/x/1=x', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.div(a, 1n), a);
-        deepStrictEqual(Fp12.div(a, Fp12.ONE), a);
-        deepStrictEqual(Fp12.div(a, a), Fp12.ONE);
-      })
-    );
-  });
-  should('bls12-381 Fp12/div/x/0=0', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, (num) => {
-        const a = Fp12.fromBigTwelve(num);
-        deepStrictEqual(Fp12.div(Fp12.ZERO, a), Fp12.ZERO);
-      })
-    );
-  });
-  should('bls12-381 Fp12/div/distributivity', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, FC_BIGINT_12, (num1, num2, num3) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        const c = Fp12.fromBigTwelve(num3);
-        deepStrictEqual(Fp12.div(Fp12.add(a, b), c), Fp12.add(Fp12.div(a, c), Fp12.div(b, c)));
-      })
-    );
-  });
-  should('bls12-381 Fp12/div/multiply equality', () => {
-    fc.assert(
-      fc.property(FC_BIGINT_12, FC_BIGINT_12, (num1, num2) => {
-        const a = Fp12.fromBigTwelve(num1);
-        const b = Fp12.fromBigTwelve(num2);
-        deepStrictEqual(Fp12.div(a, b), Fp12.mul(a, Fp12.invert(b)));
-      })
-    );
-  });
-}
-
 // Point
 {
   const Fp = bls.Fp;

test/hash-to-curve.test.js

@@ -4,16 +4,27 @@ 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 { shake128, shake256 } from '@noble/hashes/sha3';
 import { secp256r1 } from '../lib/esm/p256.js';
 import { secp384r1 } from '../lib/esm/p384.js';
 import { secp521r1 } from '../lib/esm/p521.js';
+import { ed25519 } from '../lib/esm/ed25519.js';
+import { ed448 } from '../lib/esm/ed448.js';
 import { 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' };
@@ -58,6 +69,26 @@ testExpandXMD(sha256, xmd_sha256_38);
 testExpandXMD(sha256, xmd_sha256_256);
 testExpandXMD(sha512, xmd_sha512_38);
 
+function testExpandXOF(hash, vectors) {
+  for (let i = 0; i < vectors.tests.length; i++) {
+    const t = vectors.tests[i];
+    should(`expand_message_xof/${vectors.hash}/${vectors.DST.length}/${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);
+    });
+  }
+}
+
+testExpandXOF(shake128, xof_shake128_36);
+testExpandXOF(shake128, xof_shake128_256);
+testExpandXOF(shake256, xof_shake256_36);
+
 function stringToFp(s) {
   // bls-G2 support
   if (s.includes(',')) {
@@ -97,8 +128,8 @@ testCurve(secp521r1, p521_ro, p521_nu);
 testCurve(bls12_381.G1, g1_ro, g1_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';