Add BLS signatures. Fix stark/P521 privkeys.

curve-definitions/benchmark/index.js

@@ -1,5 +1,7 @@
 import * as bench from 'micro-bmark';
 const { run, mark } = bench; // or bench.mark
+import { readFileSync } from 'fs';
+
 // Curves
 import { secp256k1 } from '../lib/secp256k1.js';
 import { P256 } from '../lib/p256.js';
@@ -7,6 +9,7 @@ import { P384 } from '../lib/p384.js';
 import { P521 } from '../lib/p521.js';
 import { ed25519 } from '../lib/ed25519.js';
 import { ed448 } from '../lib/ed448.js';
+import { bls12_381 as bls } from '../lib/bls12-381.js';
 
 // Others
 import { hmac } from '@noble/hashes/hmac';
@@ -14,6 +17,7 @@ import { sha256 } from '@noble/hashes/sha256';
 import { sha512 } from '@noble/hashes/sha512';
 
 import * as old_secp from '@noble/secp256k1';
+import * as old_bls from '@noble/bls12-381';
 import { concatBytes, hexToBytes } from '@noble/hashes/utils';
 
 import * as starkwareCrypto from '@starkware-industries/starkware-crypto-utils';
@@ -32,6 +36,14 @@ old_secp.utils.hmacSha256Sync = (key, ...msgs) =>
 import * as noble_ed25519 from '@noble/ed25519';
 noble_ed25519.utils.sha512Sync = (...m) => sha512(concatBytes(...m));
 
+// BLS
+const G2_VECTORS = readFileSync('../test/bls12-381/bls12-381-g2-test-vectors.txt', 'utf-8')
+  .trim()
+  .split('\n')
+  .map((l) => l.split(':'));
+let p1, p2, oldp1, oldp2;
+// /BLS
+
 for (let item of [secp256k1, ed25519, ed448, P256, P384, P521, old_secp, noble_ed25519]) {
   item.utils.precompute(8);
 }
@@ -58,8 +70,8 @@ export const CURVES = {
     },
     getPublicKey255: {
       samples: 10000,
-      secp256k1_old: () => old_secp.getPublicKey(2n**255n-1n),
+      secp256k1_old: () => old_secp.getPublicKey(2n ** 255n - 1n),
-      secp256k1: () => secp256k1.getPublicKey(2n**255n-1n),
+      secp256k1: () => secp256k1.getPublicKey(2n ** 255n - 1n),
     },
     sign: {
       samples: 5000,
@@ -69,9 +81,9 @@ export const CURVES = {
     verify: {
       samples: 1000,
       secp256k1_old: ({ sig, msg, pub }) => {
-        return old_secp.verify((new old_secp.Signature(sig.r, sig.s)), msg, pub);
+        return old_secp.verify(new old_secp.Signature(sig.r, sig.s), msg, pub);
       },
-      secp256k1: ({ sig, msg, pub }) => secp256k1.verify(sig, msg, pub)
+      secp256k1: ({ sig, msg, pub }) => secp256k1.verify(sig, msg, pub),
     },
     getSharedSecret: {
       samples: 1000,
@@ -81,9 +93,9 @@ export const CURVES = {
     recoverPublicKey: {
       samples: 1000,
       secp256k1_old: ({ sig, msg }) =>
-        old_secp.recoverPublicKey(msg, (new old_secp.Signature(sig.r, sig.s)), sig.recovery),
+        old_secp.recoverPublicKey(msg, new old_secp.Signature(sig.r, sig.s), sig.recovery),
-      secp256k1: ({ sig, msg }) => sig.recoverPublicKey(msg)
+      secp256k1: ({ sig, msg }) => sig.recoverPublicKey(msg),
-    }
+    },
   },
   ed25519: {
     data: () => {
@@ -131,12 +143,12 @@ export const CURVES = {
     },
     verify: {
       samples: 500,
-      noble: ({ sig, msg, pub }) => ed448.verify(sig, msg, pub)
+      noble: ({ sig, msg, pub }) => ed448.verify(sig, msg, pub),
-    }
+    },
   },
   nist: {
     data: () => {
-      return { p256: generateData(P256), p384: generateData(P384), p521: generateData(P521) }
+      return { p256: generateData(P256), p384: generateData(P384), p521: generateData(P521) };
     },
     getPublicKey: {
       samples: 2500,
@@ -146,16 +158,16 @@ export const CURVES = {
     },
     sign: {
       samples: 1000,
-      P256: ({ p256: {msg, priv} }) => P256.sign(msg, priv),
+      P256: ({ p256: { msg, priv } }) => P256.sign(msg, priv),
-      P384: ({ p384: {msg, priv} }) => P384.sign(msg, priv),
+      P384: ({ p384: { msg, priv } }) => P384.sign(msg, priv),
-      P521: ({ p521: {msg, priv} }) => P521.sign(msg, priv),
+      P521: ({ p521: { msg, priv } }) => P521.sign(msg, priv),
     },
     verify: {
       samples: 250,
-      P256: ({ p256: {sig, msg, pub} }) => P256.verify(sig, msg, pub),
+      P256: ({ p256: { sig, msg, pub } }) => P256.verify(sig, msg, pub),
-      P384: ({ p384: {sig, msg, pub} }) => P384.verify(sig, msg, pub),
+      P384: ({ p384: { sig, msg, pub } }) => P384.verify(sig, msg, pub),
-      P521: ({ p521: {sig, msg, pub} }) => P521.verify(sig, msg, pub),
+      P521: ({ p521: { sig, msg, pub } }) => P521.verify(sig, msg, pub),
-    }
+    },
   },
   stark: {
     data: () => {
@@ -168,10 +180,11 @@ export const CURVES = {
       const msgHash = 'c465dd6b1bbffdb05442eb17f5ca38ad1aa78a6f56bf4415bdee219114a47';
       const keyPair = starkwareCrypto.default.ec.keyFromPrivate(privateKey, 'hex');
       const publicKeyStark = starkwareCrypto.default.ec.keyFromPublic(
-        keyPair.getPublic(true, 'hex'), 'hex'
+        keyPair.getPublic(true, 'hex'),
+        'hex'
       );
 
-      return { priv, sig, msg, pub, publicKeyStark, msgHash, keyPair }
+      return { priv, sig, msg, pub, publicKeyStark, msgHash, keyPair };
     },
     pedersen: {
       samples: 500,
@@ -179,14 +192,14 @@ export const CURVES = {
         return starkwareCrypto.default.pedersen([
           '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
           '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a',
-        ])
+        ]);
       },
       noble: () => {
         return stark.pedersen(
           '3d937c035c878245caf64531a5756109c53068da139362728feb561405371cb',
           '208a0a10250e382e1e4bbe2880906c2791bf6275695e02fbbc6aeff9cd8b31a'
-        )
+        );
-      }
+      },
     },
     verify: {
       samples: 500,
@@ -198,17 +211,170 @@ export const CURVES = {
         );
       },
       noble: ({ priv, msg, pub }) => {
-        return stark.verify(stark.sign(msg, priv), msg, pub)
+        return stark.verify(stark.sign(msg, priv), msg, pub);
-      }
+      },
-    }
+    },
-  }
+  },
+  'bls12-381': {
+    data: async () => {
+      const priv = '28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4c';
+      const pubs = G2_VECTORS.map((v) => bls.getPublicKey(v[0]));
+      const sigs = G2_VECTORS.map((v) => v[2]);
+      const pub = bls.getPublicKey(priv);
+      const pub512 = pubs.slice(0, 512); // .map(bls.PointG1.fromHex)
+      const pub32 = pub512.slice(0, 32);
+      const pub128 = pub512.slice(0, 128);
+      const pub2048 = pub512.concat(pub512, pub512, pub512);
+      const sig512 = sigs.slice(0, 512); // .map(bls.PointG2.fromSignature);
+      const sig32 = sig512.slice(0, 32);
+      const sig128 = sig512.slice(0, 128);
+      const sig2048 = sig512.concat(sig512, sig512, sig512);
+      return {
+        priv,
+        pubs,
+        sigs,
+        pub,
+        pub512,
+        pub32,
+        pub128,
+        pub2048,
+        sig32,
+        sig128,
+        sig512,
+        sig2048,
+      };
+    },
+    init: {
+      samples: 1,
+      old: () => {
+        oldp1 =
+          old_bls.PointG1.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
+          );
+        oldp2 =
+          old_bls.PointG2.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
+          );
+        old_bls.pairing(oldp1, oldp2);
+      },
+      noble: () => {
+        p1 =
+          bls.G1.Point.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn
+          );
+        p2 =
+          bls.G2.Point.BASE.multiply(
+            0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4dn
+          );
+        bls.pairing(p1, p2);
+      },
+    },
+    'getPublicKey (1-bit)': {
+      samples: 1000,
+      old: () => old_bls.getPublicKey('2'.padStart(64, '0')),
+      noble: () => bls.getPublicKey('2'.padStart(64, '0')),
+    },
+    getPublicKey: {
+      samples: 1000,
+      old: ({ priv }) => old_bls.getPublicKey(priv),
+      noble: ({ priv }) => bls.getPublicKey(priv),
+    },
+    sign: {
+      samples: 50,
+      old: ({ priv }) => old_bls.sign('09', priv),
+      noble: ({ priv }) => bls.sign('09', priv),
+    },
+    verify: {
+      samples: 50,
+      old: ({ pub }) =>
+        old_bls.verify(
+          '8647aa9680cd0cdf065b94e818ff2bb948cc97838bcee987b9bc1b76d0a0a6e0d85db4e9d75aaedfc79d4ea2733a21ae0579014de7636dd2943d45b87c82b1c66a289006b0b9767921bb8edd3f6c5c5dec0d54cd65f61513113c50cc977849e5',
+          '09',
+          pub
+        ),
+      noble: ({ pub }) =>
+        bls.verify(
+          '8647aa9680cd0cdf065b94e818ff2bb948cc97838bcee987b9bc1b76d0a0a6e0d85db4e9d75aaedfc79d4ea2733a21ae0579014de7636dd2943d45b87c82b1c66a289006b0b9767921bb8edd3f6c5c5dec0d54cd65f61513113c50cc977849e5',
+          '09',
+          pub
+        ),
+    },
+    pairing: {
+      samples: 100,
+      old: () => old_bls.pairing(oldp1, oldp2),
+      noble: () => bls.pairing(p1, p2),
+    },
+    // Requires points which we cannot init before (data fn same for all)
+    // await mark('sign/nc', 30, () => bls.sign(msgp, priv));
+    // await mark('verify/nc', 30, () => bls.verify(sigp, msgp, pubp));
+    'aggregatePublicKeys/8': {
+      samples: 100,
+      old: ({ pubs }) => old_bls.aggregatePublicKeys(pubs.slice(0, 8)),
+      noble: ({ pubs }) => bls.aggregatePublicKeys(pubs.slice(0, 8)),
+    },
+    'aggregatePublicKeys/32': {
+      samples: 50,
+      old: ({ pub32 }) => old_bls.aggregatePublicKeys(pub32.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub32 }) => bls.aggregatePublicKeys(pub32.map(bls.G1.Point.fromHex)),
+    },
+    'aggregatePublicKeys/128': {
+      samples: 20,
+      old: ({ pub128 }) => old_bls.aggregatePublicKeys(pub128.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub128 }) => bls.aggregatePublicKeys(pub128.map(bls.G1.Point.fromHex)),
+    },
+    'aggregatePublicKeys/512': {
+      samples: 10,
+      old: ({ pub512 }) => old_bls.aggregatePublicKeys(pub512.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub512 }) => bls.aggregatePublicKeys(pub512.map(bls.G1.Point.fromHex)),
+    },
+    'aggregatePublicKeys/2048': {
+      samples: 5,
+      old: ({ pub2048 }) => old_bls.aggregatePublicKeys(pub2048.map(old_bls.PointG1.fromHex)),
+      noble: ({ pub2048 }) => bls.aggregatePublicKeys(pub2048.map(bls.G1.Point.fromHex)),
+    },
+    'aggregateSignatures/8': {
+      samples: 50,
+      old: ({ sigs }) => old_bls.aggregateSignatures(sigs.slice(0, 8)),
+      noble: ({ sigs }) => bls.aggregateSignatures(sigs.slice(0, 8)),
+    },
+    'aggregateSignatures/32': {
+      samples: 10,
+      old: ({ sig32 }) => old_bls.aggregateSignatures(sig32.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig32 }) => bls.aggregateSignatures(sig32.map(bls.Signature.decode)),
+    },
+    'aggregateSignatures/128': {
+      samples: 5,
+      old: ({ sig128 }) => old_bls.aggregateSignatures(sig128.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig128 }) => bls.aggregateSignatures(sig128.map(bls.Signature.decode)),
+    },
+    'aggregateSignatures/512': {
+      samples: 3,
+      old: ({ sig512 }) => old_bls.aggregateSignatures(sig512.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig512 }) => bls.aggregateSignatures(sig512.map(bls.Signature.decode)),
+    },
+    'aggregateSignatures/2048': {
+      samples: 2,
+      old: ({ sig2048 }) => old_bls.aggregateSignatures(sig2048.map(old_bls.PointG2.fromSignature)),
+      noble: ({ sig2048 }) => bls.aggregateSignatures(sig2048.map(bls.Signature.decode)),
+    },
+    'hashToCurve/G1': {
+      samples: 500,
+      old: () => old_bls.PointG1.hashToCurve('abcd'),
+      noble: () => bls.G1.Point.hashToCurve('abcd'),
+    },
+    'hashToCurve/G2': {
+      samples: 200,
+      old: () => old_bls.PointG2.hashToCurve('abcd'),
+      noble: () => bls.G2.Point.hashToCurve('abcd'),
+    },
+  },
 };
 
 const main = () =>
   run(async () => {
     for (const [name, curve] of Object.entries(CURVES)) {
       console.log(`==== ${name} ====`);
-      const data = curve.data();
+      const data = await curve.data();
       for (const [fnName, libs] of Object.entries(curve)) {
         if (fnName === 'data') continue;
         const samples = libs.samples;

curve-definitions/benchmark/package.json

@@ -15,6 +15,7 @@
         "micro-bmark": "0.2.0"
     },
     "dependencies": {
+        "@noble/bls12-381": "^1.4.0",
         "@noble/ed25519": "^1.7.1",
         "@noble/secp256k1": "^1.7.0",
         "@starkware-industries/starkware-crypto-utils": "^0.0.2"

curve-definitions/package.json

@@ -9,7 +9,7 @@
   "module": "lib/index.js",
   "types": "lib/index.d.ts",
   "dependencies": {
-    "@noble/curves": "0.2.1",
+    "@noble/curves": "file:../",
     "@noble/hashes": "1.1.5"
   },
   "devDependencies": {

curve-definitions/src/_shortw_utils.ts

@@ -1,6 +1,7 @@
 import { hmac } from '@noble/hashes/hmac';
 import { concatBytes, randomBytes } from '@noble/hashes/utils';
-import { weierstrass, CurveType, CHash } from '@noble/curves/weierstrass';
+import { weierstrass, CurveType } from '@noble/curves/weierstrass';
+import { CHash } from '@noble/curves/utils';
 
 export function getHash(hash: CHash) {
   return {

curve-definitions/src/bn.ts

@@ -2,7 +2,7 @@
 import { weierstrass } from '@noble/curves/weierstrass';
 import { sha256 } from '@noble/hashes/sha256';
 import { getHash } from './_shortw_utils.js';
-
+import { Fp } from '@noble/curves/modular';
 /**
  * bn254 pairing-friendly curve.
  * Previously known as alt_bn_128, when it had 128-bit security.
@@ -12,7 +12,7 @@ import { getHash } from './_shortw_utils.js';
 export const bn254 = weierstrass({
   a: BigInt(0),
   b: BigInt(3),
-  P: BigInt('0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47'),
+  Fp: Fp(BigInt('0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47')),
   n: BigInt('0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001'),
   Gx: BigInt(1),
   Gy: BigInt(2),

curve-definitions/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 '@noble/curves/edwards';
 import { montgomery } from '@noble/curves/montgomery';
-import { mod, pow2, isNegativeLE } from '@noble/curves/modular';
+import { mod, pow2, isNegativeLE, Fp as FpFn } from '@noble/curves/modular';
 import {
   ensureBytes,
   equalBytes,
@@ -49,18 +49,14 @@ function ed25519_pow_2_252_3(x: bigint) {
   // ^ To pow to (p+3)/8, multiply it by x.
   return { pow_p_5_8, b2 };
 }
-
-/**
- * For X25519, in order to decode 32 random bytes as an integer scalar,
- * set the
- * three least significant bits of the first byte 0b1111_1000,
- * and the most significant bit of the last to zero 0b0111_1111,
- * set the second most significant bit of the last byte to 1 0b0100_0000
- */
 function adjustScalarBytes(bytes: Uint8Array): Uint8Array {
-  bytes[0] &= 248;
+  // Section 5: For X25519, in order to decode 32 random bytes as an integer scalar,
-  bytes[31] &= 127;
+  // set the three least significant bits of the first byte
-  bytes[31] |= 64;
+  bytes[0] &= 248; // 0b1111_1000
+  // and the most significant bit of the last to zero,
+  bytes[31] &= 127; // 0b0111_1111
+  // set the second most significant bit of the last byte to 1
+  bytes[31] |= 64; // 0b0100_0000
   return bytes;
 }
 // sqrt(u/v)
@@ -102,7 +98,7 @@ const ED25519_DEF = {
   // Negative number is P - number, and division is invert(number, P)
   d: BigInt('37095705934669439343138083508754565189542113879843219016388785533085940283555'),
   // Finite field 𝔽p over which we'll do calculations; 2n ** 255n - 19n
-  P: ED25519_P,
+  Fp: FpFn(ED25519_P),
   // Subgroup order: how many points ed25519 has
   // 2n ** 252n + 27742317777372353535851937790883648493n;
   n: BigInt('7237005577332262213973186563042994240857116359379907606001950938285454250989'),
@@ -202,7 +198,8 @@ export class RistrettoPoint {
   // Computes Elligator map for Ristretto
   // https://ristretto.group/formulas/elligator.html
   private static calcElligatorRistrettoMap(r0: bigint): ExtendedPoint {
-    const { d, P } = ed25519.CURVE;
+    const { d } = ed25519.CURVE;
+    const P = ed25519.CURVE.Fp.ORDER;
     const { mod } = ed25519.utils;
     const r = mod(SQRT_M1 * r0 * r0); // 1
     const Ns = mod((r + _1n) * ONE_MINUS_D_SQ); // 2
@@ -245,7 +242,8 @@ export class RistrettoPoint {
    */
   static fromHex(hex: Hex): RistrettoPoint {
     hex = ensureBytes(hex, 32);
-    const { a, d, P } = ed25519.CURVE;
+    const { a, d } = ed25519.CURVE;
+    const P = ed25519.CURVE.Fp.ORDER;
     const { mod } = ed25519.utils;
     const emsg = 'RistrettoPoint.fromHex: the hex is not valid encoding of RistrettoPoint';
     const s = bytes255ToNumberLE(hex);
@@ -275,7 +273,7 @@ export class RistrettoPoint {
    */
   toRawBytes(): Uint8Array {
     let { x, y, z, t } = this.ep;
-    const { P } = ed25519.CURVE;
+    const P = ed25519.CURVE.Fp.ORDER;
     const { mod } = ed25519.utils;
     const u1 = mod(mod(z + y) * mod(z - y)); // 1
     const u2 = mod(x * y); // 2

curve-definitions/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 '@noble/curves/edwards';
-import { mod, pow2 } from '@noble/curves/modular';
+import { mod, pow2, Fp } from '@noble/curves/modular';
 import { montgomery } from '../../lib/montgomery.js';
 
 /**
@@ -59,7 +59,7 @@ const ED448_DEF = {
     '726838724295606890549323807888004534353641360687318060281490199180612328166730772686396383698676545930088884461843637361053498018326358'
   ),
   // Finite field 𝔽p over which we'll do calculations; 2n ** 448n - 2n ** 224n - 1n
-  P: ed448P,
+  Fp: Fp(ed448P, 456),
   // Subgroup order: how many points ed448 has; 2n**446n - 13818066809895115352007386748515426880336692474882178609894547503885n
   n: BigInt(
     '181709681073901722637330951972001133588410340171829515070372549795146003961539585716195755291692375963310293709091662304773755859649779'

curve-definitions/src/jubjub.ts

@@ -3,6 +3,7 @@ import { sha256 } from '@noble/hashes/sha256';
 import { concatBytes, randomBytes, utf8ToBytes } from '@noble/hashes/utils';
 import { twistedEdwards } from '@noble/curves/edwards';
 import { blake2s } from '@noble/hashes/blake2s';
+import { Fp } from '@noble/curves/modular';
 
 /**
  * jubjub Twisted Edwards curve.
@@ -14,7 +15,7 @@ export const jubjub = twistedEdwards({
   a: BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000'),
   d: BigInt('0x2a9318e74bfa2b48f5fd9207e6bd7fd4292d7f6d37579d2601065fd6d6343eb1'),
   // Finite field 𝔽p over which we'll do calculations
-  P: BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001'),
+  Fp: Fp(BigInt('0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001')),
   // Subgroup order: how many points ed25519 has
   // 2n ** 252n + 27742317777372353535851937790883648493n;
   n: BigInt('0xe7db4ea6533afa906673b0101343b00a6682093ccc81082d0970e5ed6f72cb7'),

curve-definitions/src/p192.ts

@@ -1,6 +1,7 @@
 /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { createCurve } from './_shortw_utils.js';
 import { sha256 } from '@noble/hashes/sha256';
+import { Fp } from '@noble/curves/modular';
 
 // NIST secp192r1 aka P192
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/secg/secp192r1
@@ -10,7 +11,7 @@ export const P192 = createCurve(
     a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffc'),
     b: BigInt('0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1'),
     // Field over which we'll do calculations; 2n ** 192n - 2n ** 64n - 1n
-    P: BigInt('0xfffffffffffffffffffffffffffffffeffffffffffffffff'),
+    Fp: Fp(BigInt('0xfffffffffffffffffffffffffffffffeffffffffffffffff')),
     // Curve order, total count of valid points in the field.
     n: BigInt('0xffffffffffffffffffffffff99def836146bc9b1b4d22831'),
     // Base point (x, y) aka generator point

curve-definitions/src/p224.ts

@@ -1,6 +1,7 @@
 /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { createCurve } from './_shortw_utils.js';
 import { sha256 } from '@noble/hashes/sha256';
+import { Fp } from '@noble/curves/modular';
 
 // NIST secp224r1 aka P224
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-224
@@ -10,7 +11,7 @@ export const P224 = createCurve(
     a: BigInt('0xfffffffffffffffffffffffffffffffefffffffffffffffffffffffe'),
     b: BigInt('0xb4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4'),
     // Field over which we'll do calculations; 2n**224n - 2n**96n + 1n
-    P: BigInt('0xffffffffffffffffffffffffffffffff000000000000000000000001'),
+    Fp: Fp(BigInt('0xffffffffffffffffffffffffffffffff000000000000000000000001')),
     // Curve order, total count of valid points in the field
     n: BigInt('0xffffffffffffffffffffffffffff16a2e0b8f03e13dd29455c5c2a3d'),
     // Base point (x, y) aka generator point

curve-definitions/src/p256.ts

@@ -1,6 +1,7 @@
 /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { createCurve } from './_shortw_utils.js';
 import { sha256 } from '@noble/hashes/sha256';
+import { Fp } from '@noble/curves/modular';
 
 // NIST secp256r1 aka P256
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-256
@@ -10,7 +11,7 @@ export const P256 = createCurve(
     a: BigInt('0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc'),
     b: BigInt('0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b'),
     // Field over which we'll do calculations; 2n**224n * (2n**32n-1n) + 2n**192n + 2n**96n-1n
-    P: BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff'),
+    Fp: Fp(BigInt('0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff')),
     // Curve order, total count of valid points in the field
     n: BigInt('0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551'),
     // Base point (x, y) aka generator point

curve-definitions/src/p384.ts

@@ -1,6 +1,7 @@
 /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { createCurve } from './_shortw_utils.js';
 import { sha384 } from '@noble/hashes/sha512';
+import { Fp } from '@noble/curves/modular';
 
 // NIST secp384r1 aka P384
 // https://www.secg.org/sec2-v2.pdf, https://neuromancer.sk/std/nist/P-384
@@ -10,7 +11,7 @@ export const P384 = createCurve({
   a: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffc'),
   b: BigInt('0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef'),
   // Field over which we'll do calculations. 2n**384n - 2n**128n - 2n**96n + 2n**32n - 1n
-  P: BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff'),
+  Fp: Fp(BigInt('0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffff')),
   // Curve order, total count of valid points in the field.
   n: BigInt('0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973'),
   // Base point (x, y) aka generator point

curve-definitions/src/p521.ts

@@ -1,6 +1,8 @@
 /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { createCurve } from './_shortw_utils.js';
+import { Fp } from '@noble/curves/modular';
 import { sha512 } from '@noble/hashes/sha512';
+import { bytesToHex, PrivKey } from '@noble/curves/utils';
 
 // NIST secp521r1 aka P521
 // Note that it's 521, which differs from 512 of its hash function.
@@ -11,7 +13,7 @@ export const P521 = createCurve({
   a: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffc'),
   b: BigInt('0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00'),
   // Field over which we'll do calculations; 2n**521n - 1n
-  P: BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff'),
+  Fp: Fp(BigInt('0x1ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff')),
   // Curve order, total count of valid points in the field
   n: BigInt('0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409'),
   // Base point (x, y) aka generator point
@@ -19,5 +21,13 @@ export const P521 = createCurve({
   Gy: BigInt('0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650'),
   h: BigInt(1),
   lowS: false,
+  normalizePrivateKey(key: PrivKey) {
+    if (typeof key === 'bigint') return key;
+    if (key instanceof Uint8Array) key = bytesToHex(key);
+    if (typeof key !== 'string' || !([130, 131, 132].includes(key.length))) {
+      throw new Error('Invalid key');
+    }
+    return key.padStart(66 * 2, '0');
+  }
 } as const, sha512);
 export const secp521r1 = P521;

curve-definitions/src/pasta.ts

@@ -11,7 +11,7 @@ const q = BigInt('0x40000000000000000000000000000000224698fc0994a8dd8c46eb210000
 export const pallas = weierstrass({
   a: BigInt(0),
   b: BigInt(5),
-  P: p,
+  Fp: mod.Fp(p),
   n: q,
   Gx: mod.mod(BigInt(-1), p),
   Gy: BigInt(2),
@@ -22,7 +22,7 @@ export const pallas = weierstrass({
 export const vesta = weierstrass({
   a: BigInt(0),
   b: BigInt(5),
-  P: q,
+  Fp: mod.Fp(q),
   n: p,
   Gx: mod.mod(BigInt(-1), q),
   Gy: BigInt(2),

curve-definitions/src/secp256k1.ts

@@ -1,6 +1,6 @@
 /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
 import { sha256 } from '@noble/hashes/sha256';
-import { mod, pow2 } from '@noble/curves/modular';
+import { Fp as FpFn, mod, pow2 } from '@noble/curves/modular';
 import { createCurve } from './_shortw_utils.js';
 import { PointType } from '@noble/curves/weierstrass';
 import {
@@ -57,6 +57,8 @@ function sqrtMod(y: bigint): bigint {
   return pow2(t2, _2n, P);
 }
 
+const Fp = FpFn(secp256k1P, undefined, undefined, { sqrt: sqrtMod });
+
 export const secp256k1 = createCurve(
   {
     // Params: a, b
@@ -65,7 +67,7 @@ export const secp256k1 = createCurve(
     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
-    P: secp256k1P,
+    Fp,
     // Curve order, total count of valid points in the field
     n: secp256k1N,
     // Base point (x, y) aka generator point
@@ -74,7 +76,6 @@ export const secp256k1 = createCurve(
     h: BigInt(1),
     // Alllow only low-S signatures by default in sign() and verify()
     lowS: true,
-    sqrtMod,
     endo: {
       // Params taken from https://gist.github.com/paulmillr/eb670806793e84df628a7c434a873066
       beta: BigInt('0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee'),
@@ -111,7 +112,7 @@ const numTo32bStr = secp256k1.utils._bigintToString;
 const normalizePrivateKey = secp256k1.utils._normalizePrivateKey;
 
 // TODO: export?
-function normalizePublicKey(publicKey: Hex | PointType): PointType {
+function normalizePublicKey(publicKey: Hex | PointType<bigint>): PointType<bigint> {
   if (publicKey instanceof secp256k1.Point) {
     publicKey.assertValidity();
     return publicKey;
@@ -125,7 +126,7 @@ function normalizePublicKey(publicKey: Hex | PointType): PointType {
       let y = sqrtMod(y2); // y = y² ^ (p+1)/4
       const isYOdd = (y & _1n) === _1n;
       // Schnorr
-      if (isYOdd) y = mod(-y, secp256k1.CURVE.P);
+      if (isYOdd) y = secp256k1.CURVE.Fp.negate(y);
       const point = new secp256k1.Point(x, y);
       point.assertValidity();
       return point;
@@ -156,7 +157,7 @@ export function taggedHash(tag: string, ...messages: Uint8Array[]): Uint8Array {
   return sha256(concatBytes(tagP, ...messages));
 }
 
-const toRawX = (point: PointType) => point.toRawBytes(true).slice(1);
+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.

curve-definitions/src/stark.ts

@@ -3,20 +3,14 @@ import { keccak_256 } from '@noble/hashes/sha3';
 import { sha256 } from '@noble/hashes/sha256';
 import { hmac } from '@noble/hashes/hmac';
 import { concatBytes, randomBytes } from '@noble/hashes/utils';
-import { weierstrass, CHash, JacobianPointType } from '@noble/curves/weierstrass';
+import { weierstrass, JacobianPointType } from '@noble/curves/weierstrass';
 import * as cutils from '@noble/curves/utils';
+import { Fp } from '@noble/curves/modular';
+import { getHash } from './_shortw_utils.js';
 
+type JacobianPoint = JacobianPointType<bigint>;
 // Stark-friendly elliptic curve
 // https://docs.starkware.co/starkex/stark-curve.html
-// TODO: clarify exports; it is exporting both starkCurve and sign() now, can be confusing
-
-function getHash(hash: CHash) {
-  return {
-    hash,
-    hmac: (key: Uint8Array, ...msgs: Uint8Array[]) => hmac(hash, key, concatBytes(...msgs)),
-    randomBytes,
-  };
-}
 
 const CURVE_N = BigInt(
   '3618502788666131213697322783095070105526743751716087489154079457884512865583'
@@ -28,7 +22,7 @@ export const starkCurve = weierstrass({
   b: BigInt('3141592653589793238462643383279502884197169399375105820974944592307816406665'),
   // Field over which we'll do calculations; 2n**251n + 17n * 2n**192n + 1n
   // There is no efficient sqrt for field (P%4==1)
-  P: BigInt('0x800000000000011000000000000000000000000000000000000000000000001'),
+  Fp: Fp(BigInt('0x800000000000011000000000000000000000000000000000000000000000001')),
   // Curve order, total count of valid points in the field.
   n: CURVE_N,
   nBitLength: nBitLength, // len(bin(N).replace('0b',''))
@@ -95,23 +89,34 @@ function ensureBytes0x(hex: Hex): Uint8Array {
   return hex instanceof Uint8Array ? Uint8Array.from(hex) : hexToBytes0x(hex);
 }
 
+function normalizePrivateKey(privKey: Hex) {
+  return cutils.bytesToHex(ensureBytes0x(privKey)).padStart(32 * 2, '0');
+}
+function getPublicKey0x(privKey: Hex, isCompressed?: boolean) {
+  return starkCurve.getPublicKey(normalizePrivateKey(privKey), isCompressed);
+}
+function getSharedSecret0x(privKeyA: Hex, pubKeyB: Hex) {
+  return starkCurve.getSharedSecret(normalizePrivateKey(privKeyA), pubKeyB);
+}
+
 function sign0x(msgHash: Hex, privKey: Hex, opts: any) {
-  return starkCurve.sign(ensureBytes0x(msgHash), ensureBytes0x(privKey), opts);
+  if (typeof privKey === 'string') privKey = strip0x(privKey).padStart(64, '0');
+  return starkCurve.sign(ensureBytes0x(msgHash), normalizePrivateKey(privKey), opts);
 }
 function verify0x(signature: Hex, msgHash: Hex, pubKey: Hex) {
   const sig = signature instanceof Signature ? signature : ensureBytes0x(signature);
   return starkCurve.verify(sig, ensureBytes0x(msgHash), ensureBytes0x(pubKey));
 }
 
-const { CURVE, Point, JacobianPoint, Signature, getPublicKey, getSharedSecret } = starkCurve;
+const { CURVE, Point, JacobianPoint, Signature } = starkCurve;
 export const utils = starkCurve.utils;
 export {
   CURVE,
   Point,
   Signature,
   JacobianPoint,
-  getPublicKey,
+  getPublicKey0x as getPublicKey,
-  getSharedSecret,
+  getSharedSecret0x as getSharedSecret,
   sign0x as sign,
   verify0x as verify,
 };
@@ -144,8 +149,7 @@ export function grindKey(seed: Hex) {
 }
 
 export function getStarkKey(privateKey: Hex) {
-  const priv = typeof privateKey === 'string' ? strip0x(privateKey) : privateKey;
+  return bytesToHexEth(getPublicKey0x(privateKey, true).slice(1));
-  return bytesToHexEth(Point.fromPrivateKey(priv).toRawBytes(true).slice(1));
 }
 
 export function ethSigToPrivate(signature: string) {
@@ -194,8 +198,8 @@ const PEDERSEN_POINTS = [
 // for (const p of PEDERSEN_POINTS) p._setWindowSize(8);
 const PEDERSEN_POINTS_JACOBIAN = PEDERSEN_POINTS.map(JacobianPoint.fromAffine);
 
-function pedersenPrecompute(p1: JacobianPointType, p2: JacobianPointType): JacobianPointType[] {
+function pedersenPrecompute(p1: JacobianPoint, p2: JacobianPoint): JacobianPoint[] {
-  const out: JacobianPointType[] = [];
+  const out: JacobianPoint[] = [];
   let p = p1;
   for (let i = 0; i < 248; i++) {
     out.push(p);
@@ -226,16 +230,12 @@ function pedersenArg(arg: PedersenArg): bigint {
     value = BigInt(arg);
   } else value = bytesToNumber0x(ensureBytes0x(arg));
   // [0..Fp)
-  if (!(0n <= value && value < starkCurve.CURVE.P))
+  if (!(0n <= value && value < starkCurve.CURVE.Fp.ORDER))
     throw new Error(`PedersenArg should be 0 <= value < CURVE.P: ${value}`);
   return value;
 }
 
-function pedersenSingle(
+function pedersenSingle(point: JacobianPoint, value: PedersenArg, constants: JacobianPoint[]) {
-  point: JacobianPointType,
-  value: PedersenArg,
-  constants: JacobianPointType[]
-) {
   let x = pedersenArg(value);
   for (let j = 0; j < 252; j++) {
     const pt = constants[j];
@@ -248,7 +248,7 @@ function pedersenSingle(
 
 // shift_point + x_low * P_0 + x_high * P1 + y_low * P2  + y_high * P3
 export function pedersen(x: PedersenArg, y: PedersenArg) {
-  let point: JacobianPointType = PEDERSEN_POINTS_JACOBIAN[0];
+  let point: JacobianPoint = PEDERSEN_POINTS_JACOBIAN[0];
   point = pedersenSingle(point, x, PEDERSEN_POINTS1);
   point = pedersenSingle(point, y, PEDERSEN_POINTS2);
   return bytesToHexEth(point.toAffine().toRawBytes(true).slice(1));

curve-definitions/test/bls12-381/bls12-381-g2-test-vectors.txt

@@ -0,0 +1,559 @@
+db29a6e1db5d6dcb485f26c174d11dd0ab1ecc54125e31dde2949b03e925ef23::8e49a02dc374bb1702ec4c8aa514c6d72e0884d3611334ae749462eb545a4d0a6086ef0a6b1bbc5db2934d297bf766c60dbe665dfc33d3aa765d071712075b4102a71f518e16376fc58c982d30a6196fdd8319090bcb2728c9bbbd8045fc7863
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+177c50ec35b1da25f68b9f7bad8f1c443a01fa2b20de37be0caec8b62db5c902:d2:8166ef48e7c1de5f8256a670511aad114f956382eed36f3bb45a7a1bf473e982f0e399924b4dc92795d043d9475402aa0d065e10f05a2026a0961882b6c2e6c6ae429edd17c7a43586a814121044e41c5c1d3397452b2fc61fdc523cc943ef68
+e99d0f7a4f8a9e3f74a6bd9677b3fd5be32f7cea4e5b898ed3dea735fa647632:0d98:a70b42352845ca47713a20a243ec2aeb63bab7c4126d9cbd390b6f59372de383b93698c66f7e75452cbc569147b1f9f70be3b03539a4d110c65082f7918942b962543494469a5271208cdec9c234689bcae9c88c7cdc3ef9eefdf11a522794c6
+2c864f383cd664839ce6d7d049f8083870b628d7bb8a4539cc84a35bbd723736:4a35:88c76ed5872fb011f4fc0fc8ff2751513dd6f22a9b7cb125ed39bdfffdd996ba1b5d9ea6332e8b4c34e591cb9dcf4efe112a096754db0d723269bb1a758f986d5e0cfbdcc22f8678f72f1804459c98be59ee7632c666206255dcaa816188cf2b
+cd8ccf5c229e37a4a4b5490c84882af890cdc4c70170ad5f0ee2f3a86ffa3080:05caf3:83b4087858c3585a2f978fe1c79b94d9eb927500066e6c793392f1d5be2eff1ebfdd893555f6a89934f4e27ec810489a07f0740124c065fb82246a6d6f924f70069edfaf04fc4d1021f3314b9d09dfadc344fd2dcafaeb09586b194b3ea73374
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+ac47cf8395c7858c34896e1501c77b1028bb00f15721d92b4208a13cad2fbdac:3c65e5bd83d0464de9:9414a283286bb2eebde7e00e5510e406e96750a3595a104b0a003fa181ca8022eb688d6ed5363711b59d86f3f0cc696d08ee7c6939b9d7ec44a8d597880e15700d6cdff0fdd76ff814797b7b928f123a8dc22425333064821992559baf7f4b4c

curve-definitions/test/bls12-381/bls12-381-scalar-test-vectors.txt

@@ -0,0 +1,3 @@
+:0000000000000000000000000000000000000000000000000000000000000000
+aaaaaabbbbbbccccccddddddeeeeeeffffffgggggghhhhhh:2228450bf55d8fe62395161bd3677ff6fc28e45b89bc87e02a818eda11a8c5da
+111111222222333333444444555555666666777777888888:4aa543cbd2f0c8f37f8a375ce2e383eb343e7e3405f61e438b0a15fb8899d1ae

curve-definitions/test/bls12-381/go_pairing_vectors/go.mod

@@ -0,0 +1,8 @@
+module blstests
+
+go 1.19
+
+require (
+	github.com/kilic/bls12-381 v0.1.0 // indirect
+	golang.org/x/sys v0.0.0-20201101102859-da207088b7d1 // indirect
+)

curve-definitions/test/bls12-381/go_pairing_vectors/go.sum

@@ -0,0 +1,4 @@
+github.com/kilic/bls12-381 v0.1.0 h1:encrdjqKMEvabVQ7qYOKu1OvhqpK4s47wDYtNiPtlp4=
+github.com/kilic/bls12-381 v0.1.0/go.mod h1:vDTTHJONJ6G+P2R74EhnyotQDTliQDnFEwhdmfzw1ig=
+golang.org/x/sys v0.0.0-20201101102859-da207088b7d1 h1:a/mKvvZr9Jcc8oKfcmgzyp7OwF73JPWsQLvH1z2Kxck=
+golang.org/x/sys v0.0.0-20201101102859-da207088b7d1/go.mod h1:h1NjWce9XRLGQEsW7wpKNCjG9DtNlClVuFLEZdDNbEs=

curve-definitions/test/bls12-381/go_pairing_vectors/t.go

@@ -0,0 +1,29 @@
+package main
+
+import (
+	"encoding/hex"
+	"encoding/json"
+	"fmt"
+
+	kilic "github.com/kilic/bls12-381"
+)
+
+func main() {
+	g1 := kilic.NewG1()
+	g2 := kilic.NewG2()
+	gt := kilic.NewGT()
+	p1 := g1.One()
+	p2 := g2.One()
+	bls := kilic.NewEngine()
+	out := []string{}
+	for i := 0; i < 1000; i++ {
+		res := bls.AddPair(p1, p2).Result()
+		out = append(out, hex.EncodeToString(gt.ToBytes(res)))
+		g1.Add(p1, p1, g1.One())
+		g2.Add(p2, p2, g2.One())
+
+	}
+	bytes, _ := json.Marshal(out)
+	fmt.Println(string(bytes))
+
+}

curve-definitions/test/bls12-381/zkcrypto/convert.js

@@ -0,0 +1,25 @@
+// This can be done inside of tests, but ESM is broken, jest doesn't want to work with it,
+// and ESM itself contaminates everything it touches
+
+(async () => {
+  const P = await import('micro-packed');
+  const { readFileSync } = require('fs');
+
+  const CompresedG1 = P.array(null, P.hex(48));
+  const UncompresedG1 = P.array(null, P.hex(2 * 48));
+  const CompresedG2 = P.array(null, P.hex(2 * 48));
+  const UncompresedG2 = P.array(null, P.hex(4 * 48));
+
+  const out = {
+    G1_Compressed: CompresedG1.decode(readFileSync('./g1_compressed_valid_test_vectors.dat')),
+    G1_Uncompressed: UncompresedG1.decode(readFileSync('./g1_uncompressed_valid_test_vectors.dat')),
+    G2_Compressed: CompresedG2.decode(readFileSync('./g2_compressed_valid_test_vectors.dat')),
+    G2_Uncompressed: UncompresedG2.decode(readFileSync('./g2_uncompressed_valid_test_vectors.dat')),
+  };
+  // Should be 1000
+  // console.log(
+  //   'T',
+  //   Object.values(out).map((i) => i.length)
+  // );
+  console.log(JSON.stringify(out));
+})();

curve-definitions/test/index.test.js

@@ -8,5 +8,6 @@ import './ed25519.test.js';
 import './secp256k1.test.js';
 import './stark/stark.test.js';
 import './jubjub.test.js';
+import './bls12-381.test.js';
 
 should.run();

curve-definitions/test/nist.test.js

@@ -34,7 +34,7 @@ should('Curve Fields', () => {
     secp521r1:
       0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffn,
   };
-  for (const n in vectors) deepStrictEqual(NIST[n].CURVE.P, vectors[n]);
+  for (const n in vectors) deepStrictEqual(NIST[n].CURVE.Fp.ORDER, vectors[n]);
 });
 
 should('wychenproof ECDSA vectors', () => {
@@ -330,7 +330,6 @@ function runWycheproof(name, CURVE, group, index) {
       } else {
         deepStrictEqual(verified, true, `${index}: valid`);
       }
-
     } else if (test.result === 'invalid') {
       let failed = false;
       try {

curve-definitions/test/secp256k1.test.js

@@ -16,6 +16,7 @@ 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];
 

package.json

@@ -52,6 +52,21 @@
       "import": "./lib/esm/weierstrass.js",
       "default": "./lib/weierstrass.js"
     },
+    "./bls": {
+      "types": "./lib/bls.d.ts",
+      "import": "./lib/esm/bls.js",
+      "default": "./lib/bls.js"
+    },
+    "./hashToCurve": {
+      "types": "./lib/hashToCurve.d.ts",
+      "import": "./lib/esm/hashToCurve.js",
+      "default": "./lib/hashToCurve.js"
+    },
+    "./group": {
+      "types": "./lib/group.d.ts",
+      "import": "./lib/esm/group.js",
+      "default": "./lib/group.js"
+    },
     "./utils": {
       "types": "./lib/utils.d.ts",
       "import": "./lib/esm/utils.js",
@@ -63,12 +78,6 @@
     "curve",
     "cryptography",
     "hyperelliptic",
-    "weierstrass",
-    "edwards",
-    "montgomery",
-    "secp256k1",
-    "ed25519",
-    "ed448",
     "p256",
     "p384",
     "p521",

src/bls.ts

@@ -0,0 +1,418 @@
+// Barreto-Lynn-Scott Curves. A family of pairing friendly curves, with embedding degree = 12 or 24
+// NOTE: only 12 supported for now
+// Constructed from pair of weierstrass curves, based pairing logic
+import * as mod from './modular.js';
+import { ensureBytes, numberToBytesBE, bytesToNumberBE, bitLen, bitGet } from './utils.js';
+import * as utils from './utils.js';
+// Types
+import { hexToBytes, bytesToHex, Hex, PrivKey } from './utils.js';
+import { htfOpts, stringToBytes, hash_to_field, expand_message_xmd } from './hashToCurve.js';
+import { CurvePointsType, PointType, CurvePointsRes, weierstrassPoints } from './weierstrass.js';
+
+type Fp = bigint; // Can be different field?
+
+export type SignatureCoder<Fp2> = {
+  decode(hex: Hex): PointType<Fp2>;
+  encode(point: PointType<Fp2>): Uint8Array;
+};
+
+export type CurveType<Fp, Fp2, Fp6, Fp12> = {
+  r: bigint;
+  G1: Omit<CurvePointsType<Fp>, 'n'>;
+  G2: Omit<CurvePointsType<Fp2>, 'n'> & {
+    Signature: SignatureCoder<Fp2>;
+  };
+  x: bigint;
+  Fp: mod.Field<Fp>;
+  Fr: mod.Field<bigint>;
+  Fp2: mod.Field<Fp2> & {
+    reim: (num: Fp2) => { re: bigint; im: bigint };
+    multiplyByB: (num: Fp2) => Fp2;
+    frobeniusMap(num: Fp2, power: number): Fp2;
+  };
+  Fp6: mod.Field<Fp6>;
+  Fp12: mod.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;
+  hash: utils.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>;
+  Fp: mod.Field<Fp>;
+  Fp2: mod.Field<Fp2>;
+  Fp6: mod.Field<Fp6>;
+  Fp12: mod.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][];
+  pairing: (P: PointType<Fp>, Q: PointType<Fp2>, withFinalExponent?: boolean) => Fp12;
+  getPublicKey: (privateKey: PrivKey) => Uint8Array;
+  sign: {
+    (message: Hex, privateKey: PrivKey): Uint8Array;
+    (message: PointType<Fp2>, privateKey: PrivKey): PointType<Fp2>;
+  };
+  verify: (
+    signature: Hex | PointType<Fp2>,
+    message: Hex | PointType<Fp2>,
+    publicKey: Hex | PointType<Fp>
+  ) => boolean;
+  aggregatePublicKeys: {
+    (publicKeys: Hex[]): Uint8Array;
+    (publicKeys: PointType<Fp>[]): PointType<Fp>;
+  };
+  aggregateSignatures: {
+    (signatures: Hex[]): Uint8Array;
+    (signatures: PointType<Fp2>[]): PointType<Fp2>;
+  };
+  verifyBatch: (
+    signature: Hex | PointType<Fp2>,
+    messages: (Hex | PointType<Fp2>)[],
+    publicKeys: (Hex | PointType<Fp>)[]
+  ) => boolean;
+  utils: {
+    bytesToHex: typeof utils.bytesToHex;
+    hexToBytes: typeof utils.hexToBytes;
+    stringToBytes: typeof stringToBytes;
+    hashToField: typeof hash_to_field;
+    expandMessageXMD: typeof expand_message_xmd;
+    mod: typeof mod.mod;
+    getDSTLabel: () => string;
+    setDSTLabel(newLabel: string): void;
+  };
+};
+
+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 Fr = CURVE.Fr;
+  const Fp2 = CURVE.Fp2;
+  const Fp6 = CURVE.Fp6;
+  const Fp12 = CURVE.Fp12;
+  const BLS_X_LEN = bitLen(CURVE.x);
+
+  // Pre-compute coefficients for sparse multiplication
+  // Point addition and point double calculations is reused for coefficients
+  function calcPairingPrecomputes(x: Fp2, y: Fp2) {
+    // prettier-ignore
+    const Qx = x, Qy = y, Qz = Fp2.ONE;
+    // prettier-ignore
+    let Rx = Qx, Ry = Qy, Rz = Qz;
+    let ell_coeff: [Fp2, Fp2, Fp2][] = [];
+    for (let i = BLS_X_LEN - 2; i >= 0; i--) {
+      // Double
+      let t0 = Fp2.square(Ry); // Ry²
+      let t1 = Fp2.square(Rz); // Rz²
+      let t2 = Fp2.multiplyByB(Fp2.multiply(t1, 3n)); // 3 * T1 * B
+      let t3 = Fp2.multiply(t2, 3n); // 3 * T2
+      let t4 = Fp2.subtract(Fp2.subtract(Fp2.square(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0
+      ell_coeff.push([
+        Fp2.subtract(t2, t0), // T2 - T0
+        Fp2.multiply(Fp2.square(Rx), 3n), // 3 * Rx²
+        Fp2.negate(t4), // -T4
+      ]);
+      Rx = Fp2.div(Fp2.multiply(Fp2.multiply(Fp2.subtract(t0, t3), Rx), Ry), 2n); // ((T0 - T3) * Rx * Ry) / 2
+      Ry = Fp2.subtract(Fp2.square(Fp2.div(Fp2.add(t0, t3), 2n)), Fp2.multiply(Fp2.square(t2), 3n)); // ((T0 + T3) / 2)² - 3 * T2²
+      Rz = Fp2.multiply(t0, t4); // T0 * T4
+      if (bitGet(CURVE.x, i)) {
+        // Addition
+        let t0 = Fp2.subtract(Ry, Fp2.multiply(Qy, Rz)); // Ry - Qy * Rz
+        let t1 = Fp2.subtract(Rx, Fp2.multiply(Qx, Rz)); // Rx - Qx * Rz
+        ell_coeff.push([
+          Fp2.subtract(Fp2.multiply(t0, Qx), Fp2.multiply(t1, Qy)), // T0 * Qx - T1 * Qy
+          Fp2.negate(t0), // -T0
+          t1, // T1
+        ]);
+        let t2 = Fp2.square(t1); // T1²
+        let t3 = Fp2.multiply(t2, t1); // T2 * T1
+        let t4 = Fp2.multiply(t2, Rx); // T2 * Rx
+        let t5 = Fp2.add(Fp2.subtract(t3, Fp2.multiply(t4, 2n)), Fp2.multiply(Fp2.square(t0), Rz)); // T3 - 2 * T4 + T0² * Rz
+        Rx = Fp2.multiply(t1, t5); // T1 * T5
+        Ry = Fp2.subtract(Fp2.multiply(Fp2.subtract(t4, t5), t0), Fp2.multiply(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry
+        Rz = Fp2.multiply(Rz, t3); // Rz * T3
+      }
+    }
+    return ell_coeff;
+  }
+
+  function millerLoop(ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]): Fp12 {
+    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.multiply(E[1], Px), Fp2.multiply(E[2], Py));
+      if (bitGet(CURVE.x, i)) {
+        j += 1;
+        const F = ell[j];
+        f12 = Fp12.multiplyBy014(f12, F[0], Fp2.multiply(F[1], Px), Fp2.multiply(F[2], Py));
+      }
+      if (i !== 0) f12 = Fp12.square(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,
+    // TODO: do we need to export it here?
+    hashToField: (msg: Uint8Array, count: number, options: Partial<typeof htfDefaults> = {}) =>
+      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),
+
+    /**
+     * Can take 40 or more bytes of uniform input e.g. from CSPRNG or KDF
+     * 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,
+  });
+
+  // Sparse multiplication against precomputed coefficients
+  // TODO: replace with weakmap?
+  type withPairingPrecomputes = { _PPRECOMPUTES: [Fp2, Fp2, Fp2][] | undefined };
+  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);
+    return p._PPRECOMPUTES;
+  }
+
+  function clearPairingPrecomputes(point: G2) {
+    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 { Signature } = CURVE.G2;
+
+  // Calculates bilinear pairing
+  function pairing(P: G1, Q: G2, withFinalExponent: boolean = true): Fp12 {
+    if (P.equals(G1.Point.ZERO) || Q.equals(G2.Point.ZERO))
+      throw new Error('No pairings at point of Infinity');
+    P.assertValidity();
+    Q.assertValidity();
+    // Performance: 9ms for millerLoop and ~14ms for exp.
+    const looped = millerLoopG1(P, Q);
+    return withFinalExponent ? Fp12.finalExponentiate(looped) : looped;
+  }
+  type G1 = typeof G1.Point.BASE;
+  type G2 = typeof G2.Point.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);
+  }
+  function normP2(point: G2Hex): G2 {
+    return point instanceof G2.Point ? point : Signature.decode(point);
+  }
+  function normP2Hash(point: G2Hex): G2 {
+    return point instanceof G2.Point ? point : G2.Point.hashToCurve(point);
+  }
+
+  // Multiplies generator by private key.
+  // P = pk x G
+  function getPublicKey(privateKey: PrivKey): Uint8Array {
+    return G1.Point.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: G2, privateKey: PrivKey): G2;
+  function sign(message: G2Hex, privateKey: PrivKey): Uint8Array | G2 {
+    const msgPoint = normP2Hash(message);
+    msgPoint.assertValidity();
+    const sigPoint = msgPoint.multiply(normalizePrivKey(privateKey));
+    if (message instanceof G2.Point) 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 {
+    const P = normP1(publicKey);
+    const Hm = normP2Hash(message);
+    const G = G1.Point.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.multiply(eGS, ePHm));
+    return Fp12.equals(exp, Fp12.ONE);
+  }
+
+  // Adds a bunch of public key points together.
+  // pk1 + pk2 + pk3 = pkA
+  function aggregatePublicKeys(publicKeys: Hex[]): Uint8Array;
+  function aggregatePublicKeys(publicKeys: G1[]): G1;
+  function aggregatePublicKeys(publicKeys: G1Hex[]): Uint8Array | G1 {
+    if (!publicKeys.length) throw new Error('Expected non-empty array');
+    const agg = publicKeys
+      .map(normP1)
+      .reduce((sum, p) => sum.add(G1.JacobianPoint.fromAffine(p)), G1.JacobianPoint.ZERO);
+    const aggAffine = agg.toAffine();
+    if (publicKeys[0] instanceof G1.Point) {
+      aggAffine.assertValidity();
+      return aggAffine;
+    }
+    // toRawBytes ensures point validity
+    return aggAffine.toRawBytes(true);
+  }
+
+  // Adds a bunch of signature points together.
+  function aggregateSignatures(signatures: Hex[]): Uint8Array;
+  function aggregateSignatures(signatures: G2[]): G2;
+  function aggregateSignatures(signatures: G2Hex[]): Uint8Array | G2 {
+    if (!signatures.length) throw new Error('Expected non-empty array');
+    const agg = signatures
+      .map(normP2)
+      .reduce((sum, s) => sum.add(G2.JacobianPoint.fromAffine(s)), G2.JacobianPoint.ZERO);
+    const aggAffine = agg.toAffine();
+    if (signatures[0] instanceof G2.Point) {
+      aggAffine.assertValidity();
+      return aggAffine;
+    }
+    return Signature.encode(aggAffine);
+  }
+
+  // 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 {
+    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 nPublicKeys = publicKeys.map(normP1);
+    try {
+      const paired = [];
+      for (const message of new Set(nMessages)) {
+        const groupPublicKey = nMessages.reduce(
+          (groupPublicKey, subMessage, i) =>
+            subMessage === message ? groupPublicKey.add(nPublicKeys[i]) : groupPublicKey,
+          G1.Point.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));
+      const product = paired.reduce((a, b) => Fp12.multiply(a, b), Fp12.ONE);
+      const exp = Fp12.finalExponentiate(product);
+      return Fp12.equals(exp, Fp12.ONE);
+    } catch {
+      return false;
+    }
+  }
+
+  // Pre-compute points. Refer to README.
+  G1.Point.BASE._setWindowSize(4);
+  return {
+    CURVE,
+    Fr,
+    Fp,
+    Fp2,
+    Fp6,
+    Fp12,
+    G1,
+    G2,
+    Signature,
+    millerLoop,
+    calcPairingPrecomputes,
+    pairing,
+    getPublicKey,
+    sign,
+    verify,
+    aggregatePublicKeys,
+    aggregateSignatures,
+    verifyBatch,
+    utils,
+  };
+}

src/edwards.ts

@@ -37,7 +37,7 @@ export type CHash = {
   create(): any;
 };
 
-export type CurveType = BasicCurve & {
+export type CurveType = BasicCurve<bigint> & {
   // Params: a, d
   a: bigint;
   d: bigint;
@@ -132,8 +132,8 @@ export type CurveFn = {
   ExtendedPoint: ExtendedPointConstructor;
   Signature: SignatureConstructor;
   utils: {
-    mod: (a: bigint, b?: bigint) => bigint;
+    mod: (a: bigint) => bigint;
-    invert: (number: bigint, modulo?: bigint) => bigint;
+    invert: (number: bigint) => bigint;
     randomPrivateKey: () => Uint8Array;
     getExtendedPublicKey: (key: PrivKey) => {
       head: Uint8Array;
@@ -148,21 +148,22 @@ export type CurveFn = {
 // NOTE: 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 CURVE_ORDER = CURVE.n;
-  const fieldLen = CURVE.nByteLength; // 32 (length of one field element)
+  const fieldLen = Fp.BYTES; // 32 (length of one field element)
   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 { P, randomBytes } = CURVE;
+  const { randomBytes } = CURVE;
-  const modP = (a: bigint) => mod.mod(a, P);
+  const modP = Fp.create;
 
   // sqrt(u/v)
   function _uvRatio(u: bigint, v: bigint) {
     try {
-      const value = mod.sqrt(u * mod.invert(v, P), P);
+      const value = Fp.sqrt(u * Fp.invert(v));
       return { isValid: true, value };
     } catch (e) {
       return { isValid: false, value: _0n };
@@ -199,10 +200,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     // invert on all of them. invert is very slow operation,
     // so this improves performance massively.
     static toAffineBatch(points: ExtendedPoint[]): Point[] {
-      const toInv = mod.invertBatch(
+      const toInv = Fp.invertBatch(points.map((p) => p.z));
-        points.map((p) => p.z),
-        P
-      );
       return points.map((p, i) => p.toAffine(toInv[i]));
     }
 
@@ -349,7 +347,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     toAffine(invZ?: bigint): Point {
       const { x, y, z } = this;
       const is0 = this.equals(ExtendedPoint.ZERO);
-      if (invZ == null) invZ = is0 ? _8n : mod.invert(z, P); // 8 was chosen arbitrarily
+      if (invZ == null) invZ = is0 ? _8n : (Fp.invert(z) as bigint); // 8 was chosen arbitrarily
       const ax = modP(x * invZ);
       const ay = modP(y * invZ);
       const zz = modP(z * invZ);
@@ -392,7 +390,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
     // Converts hash string or Uint8Array to Point.
     // Uses algo from RFC8032 5.1.3.
     static fromHex(hex: Hex, strict = true) {
-      const { d, P, a } = CURVE;
+      const { d, a } = CURVE;
       hex = ensureBytes(hex, fieldLen);
       // 1.  First, interpret the string as an integer in little-endian
       // representation. Bit 255 of this number is the least significant
@@ -404,7 +402,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
       normed[fieldLen - 1] = lastByte & ~0x80;
       const y = bytesToNumberLE(normed);
 
-      if (strict && y >= P) throw new Error('Expected 0 < hex < P');
+      if (strict && y >= Fp.ORDER) throw new Error('Expected 0 < hex < P');
       if (!strict && y >= maxGroupElement) throw new Error('Expected 0 < hex < 2**256');
 
       // 2.  To recover the x-coordinate, the curve equation implies
@@ -644,7 +642,7 @@ export function twistedEdwards(curveDef: CurveType): CurveFn {
   const utils = {
     getExtendedPublicKey,
     mod: modP,
-    invert: (a: bigint, m = CURVE.P) => mod.invert(a, m),
+    invert: Fp.invert,
 
     /**
      * Not needed for ed25519 private keys. Needed if you use scalars directly (rare).

src/group.ts

@@ -23,7 +23,6 @@ export function wNAF<T extends Group<T>>(c: GroupConstructor<T>, bits: number) {
     return condition ? neg : item;
   };
   const opts = (W: number) => {
-    if (256 % W) throw new Error('Invalid precomputation window, must be power of 2');
     const windows = Math.ceil(bits / W) + 1; // +1, because
     const windowSize = 2 ** (W - 1); // -1 because we skip zero
     return { windows, windowSize };
@@ -73,6 +72,8 @@ export function wNAF<T extends Group<T>>(c: GroupConstructor<T>, bits: number) {
      * @returns real and fake (for const-time) points
      */
     wNAF(W: number, precomputes: T[], n: bigint): { p: T; f: T } {
+      // TODO: maybe check that scalar is less than group order? wNAF will fail otherwise
+      // But need to carefully remove other checks before wNAF. ORDER == bits here
       const { windows, windowSize } = opts(W);
 
       let p = c.ZERO;

src/hashToCurve.ts

@@ -0,0 +1,131 @@
+import { CHash, concatBytes } from './utils.js';
+import * as mod from './modular.js';
+
+export 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: boolean;
+  // 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: CHash;
+};
+
+export function validateHTFOpts(opts: htfOpts) {
+  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 (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen))
+    throw new Error('Invalid htf/hash function');
+}
+
+// UTF8 to ui8a
+export function stringToBytes(str: string) {
+  const bytes = new Uint8Array(str.length);
+  for (let i = 0; i < str.length; i++) bytes[i] = str.charCodeAt(i);
+  return bytes;
+}
+
+// Octet Stream to Integer (bytesToNumberBE)
+function os2ip(bytes: Uint8Array): bigint {
+  let result = 0n;
+  for (let i = 0; i < bytes.length; i++) {
+    result <<= 8n;
+    result += BigInt(bytes[i]);
+  }
+  return result;
+}
+
+// Integer to Octet Stream
+function i2osp(value: number, length: number): Uint8Array {
+  if (value < 0 || value >= 1 << (8 * length)) {
+    throw new Error(`bad I2OSP call: value=${value} length=${length}`);
+  }
+  const res = Array.from({ length }).fill(0) as number[];
+  for (let i = length - 1; i >= 0; i--) {
+    res[i] = value & 0xff;
+    value >>>= 8;
+  }
+  return new Uint8Array(res);
+}
+
+function strxor(a: Uint8Array, b: Uint8Array): Uint8Array {
+  const arr = new Uint8Array(a.length);
+  for (let i = 0; i < a.length; i++) {
+    arr[i] = a[i] ^ b[i];
+  }
+  return arr;
+}
+
+// Produces a uniformly random byte string using a cryptographic hash function H that outputs b bits
+// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-5.4.1
+export function expand_message_xmd(
+  msg: Uint8Array,
+  DST: Uint8Array,
+  lenInBytes: number,
+  H: CHash
+): Uint8Array {
+  // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-5.3.3
+  if (DST.length > 255) DST = H(concatBytes(stringToBytes('H2C-OVERSIZE-DST-'), DST));
+  const b_in_bytes = H.outputLen;
+  const r_in_bytes = b_in_bytes * 2;
+  const ell = Math.ceil(lenInBytes / b_in_bytes);
+  if (ell > 255) throw new Error('Invalid xmd length');
+  const DST_prime = concatBytes(DST, i2osp(DST.length, 1));
+  const Z_pad = i2osp(0, r_in_bytes);
+  const l_i_b_str = i2osp(lenInBytes, 2);
+  const b = new Array<Uint8Array>(ell);
+  const b_0 = H(concatBytes(Z_pad, msg, l_i_b_str, i2osp(0, 1), DST_prime));
+  b[0] = H(concatBytes(b_0, i2osp(1, 1), DST_prime));
+  for (let i = 1; i <= ell; i++) {
+    const args = [strxor(b_0, b[i - 1]), i2osp(i + 1, 1), DST_prime];
+    b[i] = H(concatBytes(...args));
+  }
+  const pseudo_random_bytes = concatBytes(...b);
+  return pseudo_random_bytes.slice(0, lenInBytes);
+}
+
+// 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
+// Inputs:
+// msg - a byte string containing the message to hash.
+// count - the number of elements of F to output.
+// Outputs:
+// [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).
+  const log2p = options.p.toString(2).length;
+  const L = Math.ceil((log2p + options.k) / 8); // section 5.1 of ietf draft link above
+  const len_in_bytes = count * options.m * L;
+  const DST = stringToBytes(options.DST);
+  let pseudo_random_bytes = msg;
+  if (options.expand) {
+    pseudo_random_bytes = expand_message_xmd(msg, DST, len_in_bytes, options.hash);
+  }
+  const u = new Array(count);
+  for (let i = 0; i < count; i++) {
+    const e = new Array(options.m);
+    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);
+    }
+    u[i] = e;
+  }
+  return u;
+}

src/modular.ts

@@ -1,13 +1,9 @@
 /*! @noble/curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
-
+import * as utils from './utils.js';
 // Utilities for modular arithmetics
 const _0n = BigInt(0);
 const _1n = BigInt(1);
 const _2n = BigInt(2);
-const _3n = BigInt(3);
-const _4n = BigInt(4);
-const _5n = BigInt(5);
-const _8n = BigInt(8);
 
 // Calculates a modulo b
 export function mod(a: bigint, b: bigint): bigint {
@@ -16,9 +12,11 @@ export function mod(a: bigint, b: bigint): bigint {
 }
 /**
  * Efficiently exponentiate num to power and do modular division.
+ * Unsafe in some contexts: uses ladder, so can expose bigint bits.
  * @example
  * powMod(2n, 6n, 11n) // 64n % 11n == 9n
  */
+// TODO: use field version && remove
 export function pow(num: bigint, power: bigint, modulo: bigint): bigint {
   if (modulo <= _0n || power < _0n) throw new Error('Expected power/modulo > 0');
   if (modulo === _1n) return _0n;
@@ -32,6 +30,7 @@ export function pow(num: bigint, power: bigint, modulo: bigint): bigint {
 }
 
 // Does x ^ (2 ^ power) mod p. pow2(30, 4) == 30 ^ (2 ^ 4)
+// TODO: Fp version?
 export function pow2(x: bigint, power: bigint, modulo: bigint): bigint {
   let res = x;
   while (power-- > _0n) {
@@ -65,44 +64,11 @@ export function invert(number: bigint, modulo: bigint): bigint {
 }
 
 /**
- * Division over finite field.
+ * Calculates Legendre symbol (a | p), which denotes the value of a^((p-1)/2) (mod p).
- * `a/b mod p == a * invert(b) mod p`
+ * * (a | p) ≡ 1    if a is a square (mod p)
+ * * (a | p) ≡ -1   if a is not a square (mod p)
+ * * (a | p) ≡ 0    if a ≡ 0 (mod p)
  */
-export function div(numerator: bigint, denominator: bigint, modulo: bigint): bigint {
-  const num = mod(numerator, modulo);
-  const iden = invert(denominator, modulo);
-  return mod(num * iden, modulo);
-}
-
-/**
- * Takes a list of numbers, efficiently inverts all of them.
- * @param nums list of bigints
- * @param p modulo
- * @returns list of inverted bigints
- * @example
- * invertBatch([1n, 2n, 4n], 21n);
- * // => [1n, 11n, 16n]
- */
-export function invertBatch(nums: bigint[], modulo: bigint): bigint[] {
-  const scratch = new Array(nums.length);
-  // Walk from first to last, multiply them by each other MOD p
-  const lastMultiplied = nums.reduce((acc, num, i) => {
-    if (num === _0n) return acc;
-    scratch[i] = acc;
-    return mod(acc * num, modulo);
-  }, _1n);
-  // Invert last element
-  const inverted = invert(lastMultiplied, modulo);
-  // Walk from last to first, multiply them by inverted each other MOD p
-  nums.reduceRight((acc, num, i) => {
-    if (num === _0n) return acc;
-    scratch[i] = mod(acc * scratch[i], modulo);
-    return mod(acc * num, modulo);
-  }, inverted);
-  return scratch;
-}
-
-// Calculates Legendre symbol: num^((P-1)/2)
 export function legendre(num: bigint, fieldPrime: bigint): bigint {
   return pow(num, (fieldPrime - _1n) / _2n, fieldPrime);
 }
@@ -110,16 +76,28 @@ export function legendre(num: bigint, fieldPrime: bigint): bigint {
 /**
  * Calculates square root of a number in a finite field.
  */
+// TODO: rewrite as generic Fp function && remove bls versions
 export function sqrt(number: bigint, modulo: bigint): bigint {
+  // prettier-ignore
+  const _3n = BigInt(3), _4n = BigInt(4), _5n = BigInt(5), _8n = BigInt(8);
   const n = number;
   const P = modulo;
   const p1div4 = (P + _1n) / _4n;
 
-  // P = 3 (mod 4)
+  // P ≡ 3 (mod 4)
   // sqrt n = n^((P+1)/4)
-  if (P % _4n === _3n) return pow(n, p1div4, P);
+  if (P % _4n === _3n) {
+    // Not all roots possible!
+    // const ORDER =
+    //   0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn;
+    // const NUM = 72057594037927816n;
+    // TODO: fix sqrtMod in secp256k1
+    const root = pow(n, p1div4, P);
+    if (mod(root * root, modulo) !== number) throw new Error('Cannot find square root');
+    return root;
+  }
 
-  // P = 5 (mod 8)
+  // P ≡ 5 (mod 8)
   if (P % _8n === _5n) {
     const n2 = mod(n * _2n, P);
     const v = pow(n2, (P - _5n) / _8n, P);
@@ -160,10 +138,164 @@ export function sqrt(number: bigint, modulo: bigint): bigint {
 // Little-endian check for first LE bit (last BE bit);
 export const isNegativeLE = (num: bigint, modulo: bigint) => (mod(num, modulo) & _1n) === _1n;
 
-// An idea on modular arithmetic for bls12-381:
+// Currently completly inconsistent naming:
-// const FIELD = {add, pow, sqrt, mul};
+// - readable: add, mul, sqr, sqrt, inv, div, pow, eq, sub
-// Functions will take field elements, no need for an additional class
+// - unreadable mess: addition, multiply, square, squareRoot, inversion, divide, power, equals, subtract
-// Could be faster. 1 bigint field will just do operations and mod later:
+
-// instead of 'r = mod(r * b, P)' we will write r = mul(r, b);
+export interface Field<T> {
-// Could be insecure without shape check, so it needs to be done.
+  ORDER: bigint;
-// Functions could be inlined by JIT.
+  BYTES: number;
+  BITS: number;
+  MASK: bigint;
+  ZERO: T;
+  ONE: T;
+  // 1-arg
+  create: (num: T) => T;
+  isValid: (num: T) => boolean;
+  isZero: (num: T) => boolean;
+  negate(num: T): T;
+  invert(num: T): T;
+  sqrt(num: T): T;
+  square(num: T): T;
+  // 2-args
+  equals(lhs: T, rhs: T): boolean;
+  add(lhs: T, rhs: T): T;
+  subtract(lhs: T, rhs: T): T;
+  multiply(lhs: T, rhs: T | bigint): T;
+  pow(lhs: T, power: bigint): T;
+  div(lhs: T, rhs: T | bigint): T;
+  // N for NonNormalized (for now)
+  addN(lhs: T, rhs: T): T;
+  subtractN(lhs: T, rhs: T): T;
+  multiplyN(lhs: T, rhs: T | bigint): T;
+  squareN(num: T): T;
+
+  // Optional
+  isOdd?(num: T): boolean; // Odd instead of even since we have it for Fp2
+  legendre?(num: T): T;
+  pow(lhs: T, power: bigint): T;
+  invertBatch: (lst: T[]) => T[];
+  toBytes(num: T): Uint8Array;
+  fromBytes(bytes: Uint8Array): T;
+}
+// prettier-ignore
+const FIELD_FIELDS = [
+  'create', 'isValid', 'isZero', 'negate', 'invert', 'sqrt', 'square',
+  'equals', 'add', 'subtract', 'multiply', 'pow', 'div',
+  'addN', 'subtractN', 'multiplyN', 'squareN'
+] as const;
+export function validateField<T>(field: Field<T>) {
+  for (const i of ['ORDER', 'MASK'] as const) {
+    if (typeof field[i] !== 'bigint')
+      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  }
+  for (const i of ['BYTES', 'BITS'] as const) {
+    if (typeof field[i] !== 'number')
+      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  }
+  for (const i of FIELD_FIELDS) {
+    if (typeof field[i] !== 'function')
+      throw new Error(`Invalid field param ${i}=${field[i]} (${typeof field[i]})`);
+  }
+}
+
+// Generic field functions
+export function FpPow<T>(f: Field<T>, num: T, power: bigint): T {
+  // Should have same speed as pow for bigints
+  // TODO: benchmark!
+  if (power < _0n) throw new Error('Expected power > 0');
+  if (power === _0n) return f.ONE;
+  if (power === _1n) return num;
+  let p = f.ONE;
+  let d = num;
+  while (power > _0n) {
+    if (power & _1n) p = f.multiply(p, d);
+    d = f.square(d);
+    power >>= 1n;
+  }
+  return p;
+}
+
+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;
+    tmp[i] = acc;
+    return f.multiply(acc, num);
+  }, f.ONE);
+  // Invert last element
+  const inverted = f.invert(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;
+    tmp[i] = f.multiply(acc, tmp[i]);
+    return f.multiply(acc, num);
+  }, inverted);
+  return tmp;
+}
+
+export function FpDiv<T>(f: Field<T>, lhs: T, rhs: T | bigint): T {
+  return f.multiply(lhs, typeof rhs === 'bigint' ? invert(rhs, f.ORDER) : f.invert(rhs));
+}
+
+// NOTE: very fragile, always bench. Major performance points:
+// - NonNormalized ops
+// - Object.freeze
+// - same shape of object (don't add/remove keys)
+export function Fp(
+  ORDER: bigint,
+  bitLen?: number,
+  isLE = false,
+  redef: Partial<Field<bigint>> = {}
+): Readonly<Field<bigint>> {
+  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 f: Field<bigint> = Object.freeze({
+    ORDER,
+    BITS,
+    BYTES,
+    MASK: utils.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;
+    },
+    isZero: (num) => num === _0n,
+    isOdd: (num) => (num & _1n) === _1n,
+    negate: (num) => mod(-num, ORDER),
+    equals: (lhs, rhs) => lhs === rhs,
+
+    square: (num) => mod(num * num, ORDER),
+    add: (lhs, rhs) => mod(lhs + rhs, ORDER),
+    subtract: (lhs, rhs) => mod(lhs - rhs, ORDER),
+    multiply: (lhs, rhs) => mod(lhs * rhs, ORDER),
+    pow: (num, power) => FpPow(f, num, power),
+    div: (lhs, rhs) => mod(lhs * invert(rhs, ORDER), ORDER),
+
+    // Same as above, but doesn't normalize
+    squareN: (num) => num * num,
+    addN: (lhs, rhs) => lhs + rhs,
+    subtractN: (lhs, rhs) => lhs - rhs,
+    multiplyN: (lhs, rhs) => lhs * rhs,
+
+    invert: (num) => invert(num, ORDER),
+    sqrt: redef.sqrt || sqrtP,
+    invertBatch: (lst) => FpInvertBatch(f, lst),
+
+    toBytes: (num) =>
+      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);
+    },
+  } as Field<bigint>);
+  return Object.freeze(f);
+}

src/utils.ts

@@ -1,15 +1,25 @@
 /*! @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);
 
 // 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 CHash = {
+  (message: Uint8Array | string): Uint8Array;
+  blockLen: number;
+  outputLen: number;
+  create(): any;
+};
 
 // 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 = {
+export type BasicCurve<T> = {
   // Field over which we'll do calculations (Fp)
-  P: bigint;
+  Fp: mod.Field<T>;
   // Curve order, total count of valid points in the field
   n: bigint;
   // Bit/byte length of curve order
@@ -19,16 +29,26 @@ export type BasicCurve = {
   // 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: bigint;
+  Gx: T;
-  Gy: bigint;
+  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<T extends BasicCurve>(curve: T) {
+export function validateOpts<FP, T>(curve: BasicCurve<FP> & T) {
-  for (const i of ['P', 'n', 'h', 'Gx', 'Gy'] as const) {
+  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]))
@@ -38,8 +58,6 @@ export function validateOpts<T extends BasicCurve>(curve: T) {
   return Object.freeze({ ...nLength(curve.n, curve.nBitLength), ...curve } as const);
 }
 
-import * as mod from './modular.js';
-
 const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0'));
 export function bytesToHex(uint8a: Uint8Array): string {
   if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array');
@@ -133,7 +151,6 @@ export function nLength(n: bigint, nBitLength?: number) {
  * @param hash hash output from sha512, or a similar function
  * @returns valid private scalar
  */
-const _1n = BigInt(1);
 export function hashToPrivateScalar(hash: Hex, CURVE_ORDER: bigint, isLE = false): bigint {
   hash = ensureBytes(hash);
   const orderLen = nLength(CURVE_ORDER).nByteLength;
@@ -150,3 +167,21 @@ export function equalBytes(b1: Uint8Array, b2: Uint8Array) {
   for (let i = 0; i < b1.length; i++) if (b1[i] !== b2[i]) return false;
   return true;
 }
+
+// Bit operations
+
+// Amount of bits inside bigint (Same as n.toString(2).length)
+export function bitLen(n: bigint) {
+  let len;
+  for (len = 0; n > 0n; n >>= _1n, len += 1);
+  return len;
+}
+// Gets single bit at position. NOTE: first bit position is 0 (same as arrays)
+// Same as !!+Array.from(n.toString(2)).reverse()[pos]
+export const bitGet = (n: bigint, pos: number) => (n >> BigInt(pos)) & 1n;
+// Sets single bit at position
+export const bitSet = (n: bigint, pos: number, value: boolean) =>
+  n | ((value ? _1n : _0n) << BigInt(pos));
+// Return mask for N bits (Same as BigInt(`0b${Array(i).fill('1').join('')}`))
+// Not using ** operator with bigints for old engines.
+export const bitMask = (n: number) => (_2n << BigInt(n - 1)) - _1n;