diff --git a/curve-definitions/benchmark/index.js b/curve-definitions/benchmark/index.js index b9dbe48..8b44e4d 100644 --- a/curve-definitions/benchmark/index.js +++ b/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: () => secp256k1.getPublicKey(2n**255n-1n), + secp256k1_old: () => old_secp.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), - secp256k1: ({ sig, msg }) => sig.recoverPublicKey(msg) - } + old_secp.recoverPublicKey(msg, new old_secp.Signature(sig.r, sig.s), sig.recovery), + 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), - P384: ({ p384: {msg, priv} }) => P384.sign(msg, priv), - P521: ({ p521: {msg, priv} }) => P521.sign(msg, priv), + P256: ({ p256: { msg, priv } }) => P256.sign(msg, priv), + P384: ({ p384: { msg, priv } }) => P384.sign(msg, priv), + P521: ({ p521: { msg, priv } }) => P521.sign(msg, priv), }, verify: { samples: 250, - P256: ({ p256: {sig, msg, pub} }) => P256.verify(sig, msg, pub), - P384: ({ p384: {sig, msg, pub} }) => P384.verify(sig, msg, pub), - P521: ({ p521: {sig, msg, pub} }) => P521.verify(sig, msg, pub), - } + P256: ({ p256: { sig, msg, pub } }) => P256.verify(sig, msg, pub), + P384: ({ p384: { sig, msg, pub } }) => P384.verify(sig, msg, pub), + P521: ({ p521: { sig, msg, pub } }) => P521.verify(sig, msg, pub), + }, }, 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; diff --git a/curve-definitions/benchmark/package.json b/curve-definitions/benchmark/package.json index e9873aa..07b4b6b 100644 --- a/curve-definitions/benchmark/package.json +++ b/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" diff --git a/curve-definitions/package.json b/curve-definitions/package.json index f251bdb..17994fe 100644 --- a/curve-definitions/package.json +++ b/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": { @@ -55,4 +55,4 @@ "url": "https://paulmillr.com/funding/" } ] -} \ No newline at end of file +} diff --git a/curve-definitions/src/_shortw_utils.ts b/curve-definitions/src/_shortw_utils.ts index b4968af..1084572 100644 --- a/curve-definitions/src/_shortw_utils.ts +++ b/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 { diff --git a/curve-definitions/src/bls12-381.ts b/curve-definitions/src/bls12-381.ts new file mode 100644 index 0000000..601b38c --- /dev/null +++ b/curve-definitions/src/bls12-381.ts @@ -0,0 +1,1370 @@ +import { sha256 } from '@noble/hashes/sha256'; +import { randomBytes } from '@noble/hashes/utils'; +import { bls, CurveFn } from '@noble/curves/bls'; +import * as mod from '@noble/curves/modular'; +import { + concatBytes, + ensureBytes, + numberToBytesBE, + bytesToNumberBE, + bitLen, + bitSet, + bitGet, + Hex, + bitMask, +} from '@noble/curves/utils'; +// Types +import { PointType, JacobianPointType, JacobianConstructor } from '@noble/curves/weierstrass'; + +// Differences from bls12-381: +// - PointG1 -> G1.Point +// - PointG2 -> G2.Point +// - PointG2.fromSignature -> Signature.decode +// - PointG2.toSignature -> Signature.encode +// Points now have only two coordinates + +// CURVE FIELDS +// Finite field over p. +const Fp = + mod.Fp( + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn + ); +type Fp = bigint; +// Finite field over r. +// This particular field is not used anywhere in bls12-381, but it is still useful. +const Fr = mod.Fp(0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n); + +// Fp₂ over complex plane +type BigintTuple = [bigint, bigint]; +type Fp2 = { c0: bigint; c1: bigint }; +const Fp2Add = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({ + c0: Fp.add(c0, r0), + c1: Fp.add(c1, r1), +}); +const Fp2Subtract = ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => ({ + c0: Fp.subtract(c0, r0), + c1: Fp.subtract(c1, r1), +}); +const Fp2Multiply = ({ c0, c1 }: Fp2, rhs: Fp2) => { + if (typeof rhs === 'bigint') return { c0: Fp.multiply(c0, rhs), c1: Fp.multiply(c1, rhs) }; + // (a+bi)(c+di) = (ac−bd) + (ad+bc)i + const { c0: r0, c1: r1 } = rhs; + let t1 = Fp.multiply(c0, r0); // c0 * o0 + let t2 = Fp.multiply(c1, r1); // c1 * o1 + // (T1 - T2) + ((c0 + c1) * (r0 + r1) - (T1 + T2))*i + const o0 = Fp.subtract(t1, t2); + const o1 = Fp.subtract(Fp.multiply(Fp.add(c0, c1), Fp.add(r0, r1)), Fp.add(t1, t2)); + return { c0: o0, c1: o1 }; +}; +const Fp2Square = ({ c0, c1 }: Fp2) => { + const a = Fp.add(c0, c1); + const b = Fp.subtract(c0, c1); + const c = Fp.add(c0, c0); + return { c0: Fp.multiply(a, b), c1: Fp.multiply(c, c1) }; +}; +type Fp2Utils = { + fromBigTuple: (tuple: BigintTuple | bigint[]) => Fp2; + reim: (num: Fp2) => { re: bigint; im: bigint }; + mulByNonresidue: (num: Fp2) => Fp2; + multiplyByB: (num: Fp2) => Fp2; + frobeniusMap(num: Fp2, power: number): Fp2; +}; +// G2 is the order-q subgroup of E2(Fp²) : y² = x³+4(1+√−1), +// where Fp2 is Fp[√−1]/(x2+1). #E2(Fp2 ) = h2q, where +// G² - 1 +// h2q +const FP2_ORDER = + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaabn ** + 2n - + 1n; + +const Fp2: mod.Field & Fp2Utils = { + ORDER: FP2_ORDER, + BITS: bitLen(FP2_ORDER), + BYTES: Math.ceil(bitLen(FP2_ORDER) / 8), + MASK: bitMask(bitLen(FP2_ORDER)), + ZERO: { c0: Fp.ZERO, c1: Fp.ZERO }, + ONE: { c0: Fp.ONE, c1: Fp.ZERO }, + create: (num) => num, + isValid: ({ c0, c1 }) => typeof c0 === 'bigint' && typeof c1 === 'bigint', + isZero: ({ c0, c1 }) => Fp.isZero(c0) && Fp.isZero(c1), + equals: ({ c0, c1 }: Fp2, { c0: r0, c1: r1 }: Fp2) => Fp.equals(c0, r0) && Fp.equals(c1, r1), + negate: ({ c0, c1 }) => ({ c0: Fp.negate(c0), c1: Fp.negate(c1) }), + pow: (num, power) => mod.FpPow(Fp2, num, power), + invertBatch: (nums) => mod.FpInvertBatch(Fp2, nums), + // Normalized + add: Fp2Add, + subtract: Fp2Subtract, + multiply: Fp2Multiply, + square: Fp2Square, + // NonNormalized stuff + addN: Fp2Add, + subtractN: Fp2Subtract, + multiplyN: Fp2Multiply, + squareN: Fp2Square, + // Why inversion for bigint inside Fp instead of Fp2? it is even used in that context? + div: (lhs, rhs) => + Fp2.multiply(lhs, typeof rhs === 'bigint' ? Fp.invert(Fp.create(rhs)) : Fp2.invert(rhs)), + invert: ({ c0: a, c1: b }) => { + // We wish to find the multiplicative inverse of a nonzero + // element a + bu in Fp2. We leverage an identity + // + // (a + bu)(a - bu) = a² + b² + // + // which holds because u² = -1. This can be rewritten as + // + // (a + bu)(a - bu)/(a² + b²) = 1 + // + // because a² + b² = 0 has no nonzero solutions for (a, b). + // This gives that (a - bu)/(a² + b²) is the inverse + // of (a + bu). Importantly, this can be computing using + // only a single inversion in Fp. + const factor = Fp.invert(Fp.create(a * a + b * b)); + return { c0: Fp.multiply(factor, Fp.create(a)), c1: Fp.multiply(factor, Fp.create(-b)) }; + }, + sqrt: (num) => { + // TODO: Optimize this line. It's extremely slow. + // Speeding this up would boost aggregateSignatures. + // https://eprint.iacr.org/2012/685.pdf applicable? + // https://github.com/zkcrypto/bls12_381/blob/080eaa74ec0e394377caa1ba302c8c121df08b07/src/fp2.rs#L250 + // https://github.com/supranational/blst/blob/aae0c7d70b799ac269ff5edf29d8191dbd357876/src/exp2.c#L1 + // Inspired by https://github.com/dalek-cryptography/curve25519-dalek/blob/17698df9d4c834204f83a3574143abacb4fc81a5/src/field.rs#L99 + const candidateSqrt = Fp2.pow(num, (Fp2.ORDER + 8n) / 16n); + const check = Fp2.div(Fp2.square(candidateSqrt), num); // candidateSqrt.square().div(this); + const R = FP2_ROOTS_OF_UNITY; + const divisor = [R[0], R[2], R[4], R[6]].find((r) => Fp2.equals(r, check)); + if (!divisor) throw new Error('No root'); + const index = R.indexOf(divisor); + const root = R[index / 2]; + if (!root) throw new Error('Invalid root'); + const x1 = Fp2.div(candidateSqrt, root); + const x2 = Fp2.negate(x1); + const { re: re1, im: im1 } = Fp2.reim(x1); + const { re: re2, im: im2 } = Fp2.reim(x2); + if (im1 > im2 || (im1 === im2 && re1 > re2)) return x1; + return x2; + }, + // Bytes util + fromBytes(b: Uint8Array): Fp2 { + if (b.length !== Fp2.BYTES) throw new Error(`fromBytes wrong length=${b.length}`); + return { c0: Fp.fromBytes(b.subarray(0, Fp.BYTES)), c1: Fp.fromBytes(b.subarray(Fp.BYTES)) }; + }, + toBytes: ({ c0, c1 }) => concatBytes(Fp.toBytes(c0), Fp.toBytes(c1)), + // Specific utils + // toString() { + // return `Fp2(${this.c0} + ${this.c1}×i)`; + // } + reim: ({ c0, c1 }) => ({ re: c0, im: c1 }), + // multiply by u + 1 + mulByNonresidue: ({ c0, c1 }) => ({ c0: Fp.subtract(c0, c1), c1: Fp.add(c0, c1) }), + multiplyByB: ({ c0, c1 }) => { + let t0 = Fp.multiply(c0, 4n); // 4 * c0 + let t1 = Fp.multiply(c1, 4n); // 4 * c1 + // (T0-T1) + (T0+T1)*i + return { c0: Fp.subtract(t0, t1), c1: Fp.add(t0, t1) }; + }, + fromBigTuple: (tuple: BigintTuple | bigint[]) => { + if (tuple.length !== 2) throw new Error('Invalid tuple'); + const fps = tuple.map((n) => Fp.create(n)) as [Fp, Fp]; + return { c0: fps[0], c1: fps[1] }; + }, + frobeniusMap: ({ c0, c1 }, power: number): Fp2 => ({ + c0, + c1: Fp.multiply(c1, FP2_FROBENIUS_COEFFICIENTS[power % 2]), + }), +}; +// Finite extension field over irreducible polynominal. +// Fp(u) / (u² - β) where β = -1 +const FP2_FROBENIUS_COEFFICIENTS = [ + 0x1n, + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaan, +].map((item) => Fp.create(item)); + +// For Fp2 roots of unity. +const rv1 = + 0x6af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09n; +const ev1 = + 0x699be3b8c6870965e5bf892ad5d2cc7b0e85a117402dfd83b7f4a947e02d978498255a2aaec0ac627b5afbdf1bf1c90n; +const ev2 = + 0x8157cd83046453f5dd0972b6e3949e4288020b5b8a9cc99ca07e27089a2ce2436d965026adad3ef7baba37f2183e9b5n; +const ev3 = + 0xab1c2ffdd6c253ca155231eb3e71ba044fd562f6f72bc5bad5ec46a0b7a3b0247cf08ce6c6317f40edbc653a72dee17n; +const ev4 = + 0xaa404866706722864480885d68ad0ccac1967c7544b447873cc37e0181271e006df72162a3d3e0287bf597fbf7f8fc1n; + +// Eighth roots of unity, used for computing square roots in Fp2. +// To verify or re-calculate: +// Array(8).fill(new Fp2([1n, 1n])).map((fp2, k) => fp2.pow(Fp2.ORDER * BigInt(k) / 8n)) +const FP2_ROOTS_OF_UNITY = [ + [1n, 0n], + [rv1, -rv1], + [0n, 1n], + [rv1, rv1], + [-1n, 0n], + [-rv1, rv1], + [0n, -1n], + [-rv1, -rv1], +].map((pair) => Fp2.fromBigTuple(pair)); +// eta values, used for computing sqrt(g(X1(t))) +const FP2_ETAs = [ + [ev1, ev2], + [-ev2, ev1], + [ev3, ev4], + [-ev4, ev3], +].map((pair) => Fp2.fromBigTuple(pair)); + +// Finite extension field over irreducible polynominal. +// Fp2(v) / (v³ - ξ) where ξ = u + 1 +type BigintSix = [bigint, bigint, bigint, bigint, bigint, bigint]; +type Fp6 = { c0: Fp2; c1: Fp2; c2: Fp2 }; +const Fp6Add = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({ + c0: Fp2.add(c0, r0), + c1: Fp2.add(c1, r1), + c2: Fp2.add(c2, r2), +}); +const Fp6Subtract = ({ c0, c1, c2 }: Fp6, { c0: r0, c1: r1, c2: r2 }: Fp6) => ({ + c0: Fp2.subtract(c0, r0), + c1: Fp2.subtract(c1, r1), + c2: Fp2.subtract(c2, r2), +}); +const Fp6Multiply = ({ c0, c1, c2 }: Fp6, rhs: Fp6 | bigint) => { + if (typeof rhs === 'bigint') { + return { + c0: Fp2.multiply(c0, rhs), + c1: Fp2.multiply(c1, rhs), + c2: Fp2.multiply(c2, rhs), + }; + } + const { c0: r0, c1: r1, c2: r2 } = rhs; + const t0 = Fp2.multiply(c0, r0); // c0 * o0 + const t1 = Fp2.multiply(c1, r1); // c1 * o1 + const t2 = Fp2.multiply(c2, r2); // c2 * o2 + return { + // t0 + (c1 + c2) * (r1 * r2) - (T1 + T2) * (u + 1) + c0: Fp2.add( + t0, + Fp2.mulByNonresidue( + Fp2.subtract(Fp2.multiply(Fp2.add(c1, c2), Fp2.add(r1, r2)), Fp2.add(t1, t2)) + ) + ), + // (c0 + c1) * (r0 + r1) - (T0 + T1) + T2 * (u + 1) + c1: Fp2.add( + Fp2.subtract(Fp2.multiply(Fp2.add(c0, c1), Fp2.add(r0, r1)), Fp2.add(t0, t1)), + Fp2.mulByNonresidue(t2) + ), + // T1 + (c0 + c2) * (r0 + r2) - T0 + T2 + c2: Fp2.subtract(Fp2.add(t1, Fp2.multiply(Fp2.add(c0, c2), Fp2.add(r0, r2))), Fp2.add(t0, t2)), + }; +}; +const Fp6Square = ({ c0, c1, c2 }: Fp6) => { + let t0 = Fp2.square(c0); // c0² + let t1 = Fp2.multiply(Fp2.multiply(c0, c1), 2n); // 2 * c0 * c1 + let t3 = Fp2.multiply(Fp2.multiply(c1, c2), 2n); // 2 * c1 * c2 + let t4 = Fp2.square(c2); // c2² + return { + c0: Fp2.add(Fp2.mulByNonresidue(t3), t0), // T3 * (u + 1) + T0 + c1: Fp2.add(Fp2.mulByNonresidue(t4), t1), // T4 * (u + 1) + T1 + // T1 + (c0 - c1 + c2)² + T3 - T0 - T4 + c2: Fp2.subtract( + Fp2.subtract(Fp2.add(Fp2.add(t1, Fp2.square(Fp2.add(Fp2.subtract(c0, c1), c2))), t3), t0), + t4 + ), + }; +}; +type Fp6Utils = { + fromBigSix: (tuple: BigintSix) => Fp6; + mulByNonresidue: (num: Fp6) => Fp6; + frobeniusMap(num: Fp6, power: number): Fp6; + multiplyBy1(num: Fp6, b1: Fp2): Fp6; + multiplyBy01(num: Fp6, b0: Fp2, b1: Fp2): Fp6; + multiplyByFp2(lhs: Fp6, rhs: Fp2): Fp6; +}; + +const Fp6: mod.Field & Fp6Utils = { + ORDER: Fp2.ORDER, // TODO: unused, but need to verify + BITS: 3 * Fp2.BITS, + BYTES: 3 * Fp2.BYTES, + MASK: bitMask(3 * Fp2.BITS), + ZERO: { c0: Fp2.ZERO, c1: Fp2.ZERO, c2: Fp2.ZERO }, + ONE: { c0: Fp2.ONE, c1: Fp2.ZERO, c2: Fp2.ZERO }, + create: (num) => num, + isValid: ({ c0, c1, c2 }) => Fp2.isValid(c0) && Fp2.isValid(c1) && Fp2.isValid(c2), + isZero: ({ c0, c1, c2 }) => Fp2.isZero(c0) && Fp2.isZero(c1) && Fp2.isZero(c2), + negate: ({ c0, c1, c2 }) => ({ c0: Fp2.negate(c0), c1: Fp2.negate(c1), c2: Fp2.negate(c2) }), + equals: ({ c0, c1, c2 }, { c0: r0, c1: r1, c2: r2 }) => + Fp2.equals(c0, r0) && Fp2.equals(c1, r1) && Fp2.equals(c2, r2), + sqrt: () => { + throw new Error('Not implemented'); + }, + // Do we need division by bigint at all? Should be done via order: + div: (lhs, rhs) => + Fp6.multiply(lhs, typeof rhs === 'bigint' ? Fp.invert(Fp.create(rhs)) : Fp6.invert(rhs)), + pow: (num, power) => mod.FpPow(Fp6, num, power), + invertBatch: (nums) => mod.FpInvertBatch(Fp6, nums), + // Normalized + add: Fp6Add, + subtract: Fp6Subtract, + multiply: Fp6Multiply, + square: Fp6Square, + // NonNormalized stuff + addN: Fp6Add, + subtractN: Fp6Subtract, + multiplyN: Fp6Multiply, + squareN: Fp6Square, + + invert: ({ c0, c1, c2 }) => { + let t0 = Fp2.subtract(Fp2.square(c0), Fp2.mulByNonresidue(Fp2.multiply(c2, c1))); // c0² - c2 * c1 * (u + 1) + let t1 = Fp2.subtract(Fp2.mulByNonresidue(Fp2.square(c2)), Fp2.multiply(c0, c1)); // c2² * (u + 1) - c0 * c1 + let t2 = Fp2.subtract(Fp2.square(c1), Fp2.multiply(c0, c2)); // c1² - c0 * c2 + // 1/(((c2 * T1 + c1 * T2) * v) + c0 * T0) + let t4 = Fp2.invert( + Fp2.add( + Fp2.mulByNonresidue(Fp2.add(Fp2.multiply(c2, t1), Fp2.multiply(c1, t2))), + Fp2.multiply(c0, t0) + ) + ); + return { c0: Fp2.multiply(t4, t0), c1: Fp2.multiply(t4, t1), c2: Fp2.multiply(t4, t2) }; + }, + // Bytes utils + fromBytes: (b: Uint8Array): Fp6 => { + if (b.length !== Fp6.BYTES) throw new Error(`fromBytes wrong length=${b.length}`); + return { + c0: Fp2.fromBytes(b.subarray(0, Fp2.BYTES)), + c1: Fp2.fromBytes(b.subarray(Fp2.BYTES, 2 * Fp2.BYTES)), + c2: Fp2.fromBytes(b.subarray(2 * Fp2.BYTES)), + }; + }, + toBytes: ({ c0, c1, c2 }): Uint8Array => + concatBytes(Fp2.toBytes(c0), Fp2.toBytes(c1), Fp2.toBytes(c2)), + + // Utils + // fromTriple(triple: [Fp2, Fp2, Fp2]) { + // return new Fp6(...triple); + // } + // toString() { + // return `Fp6(${this.c0} + ${this.c1} * v, ${this.c2} * v^2)`; + // } + fromBigSix: (t: BigintSix): Fp6 => { + if (!Array.isArray(t) || t.length !== 6) throw new Error('Invalid Fp6 usage'); + return { + c0: Fp2.fromBigTuple(t.slice(0, 2)), + c1: Fp2.fromBigTuple(t.slice(2, 4)), + c2: Fp2.fromBigTuple(t.slice(4, 6)), + }; + }, + frobeniusMap: ({ c0, c1, c2 }, power: number) => ({ + c0: Fp2.frobeniusMap(c0, power), + c1: Fp2.multiply(Fp2.frobeniusMap(c1, power), FP6_FROBENIUS_COEFFICIENTS_1[power % 6]), + c2: Fp2.multiply(Fp2.frobeniusMap(c2, power), FP6_FROBENIUS_COEFFICIENTS_2[power % 6]), + }), + mulByNonresidue: ({ c0, c1, c2 }) => ({ c0: Fp2.mulByNonresidue(c2), c1: c0, c2: c1 }), + + // Sparse multiplication + multiplyBy1: ({ c0, c1, c2 }, b1: Fp2): Fp6 => ({ + c0: Fp2.mulByNonresidue(Fp2.multiply(c2, b1)), + c1: Fp2.multiply(c0, b1), + c2: Fp2.multiply(c1, b1), + }), + // Sparse multiplication + multiplyBy01({ c0, c1, c2 }, b0: Fp2, b1: Fp2): Fp6 { + let t0 = Fp2.multiply(c0, b0); // c0 * b0 + let t1 = Fp2.multiply(c1, b1); // c1 * b1 + return { + // ((c1 + c2) * b1 - T1) * (u + 1) + T0 + c0: Fp2.add(Fp2.mulByNonresidue(Fp2.subtract(Fp2.multiply(Fp2.add(c1, c2), b1), t1)), t0), + // (b0 + b1) * (c0 + c1) - T0 - T1 + c1: Fp2.subtract(Fp2.subtract(Fp2.multiply(Fp2.add(b0, b1), Fp2.add(c0, c1)), t0), t1), + // (c0 + c2) * b0 - T0 + T1 + c2: Fp2.add(Fp2.subtract(Fp2.multiply(Fp2.add(c0, c2), b0), t0), t1), + }; + }, + + multiplyByFp2: ({ c0, c1, c2 }, rhs: Fp2): Fp6 => ({ + c0: Fp2.multiply(c0, rhs), + c1: Fp2.multiply(c1, rhs), + c2: Fp2.multiply(c2, rhs), + }), +}; + +const FP6_FROBENIUS_COEFFICIENTS_1 = [ + [0x1n, 0x0n], + [ + 0x0n, + 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaacn, + ], + [ + 0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffen, + 0x0n, + ], + [0x0n, 0x1n], + [ + 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaacn, + 0x0n, + ], + [ + 0x0n, + 0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffen, + ], +].map((pair) => Fp2.fromBigTuple(pair)); +const FP6_FROBENIUS_COEFFICIENTS_2 = [ + [0x1n, 0x0n], + [ + 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaadn, + 0x0n, + ], + [ + 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaacn, + 0x0n, + ], + [ + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaan, + 0x0n, + ], + [ + 0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffen, + 0x0n, + ], + [ + 0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffffn, + 0x0n, + ], +].map((pair) => Fp2.fromBigTuple(pair)); + +// Finite extension field over irreducible polynominal. +// Fp₁₂ = Fp₆² => Fp₂³ +// Fp₆(w) / (w² - γ) where γ = v +type Fp12 = { c0: Fp6; c1: Fp6 }; +// The BLS parameter x for BLS12-381 +const BLS_X = 0xd201000000010000n; +const BLS_X_LEN = bitLen(BLS_X); + +// prettier-ignore +type BigintTwelve = [ + bigint, bigint, bigint, bigint, bigint, bigint, + bigint, bigint, bigint, bigint, bigint, bigint + ]; +const Fp12Add = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({ + c0: Fp6.add(c0, r0), + c1: Fp6.add(c1, r1), +}); +const Fp12Subtract = ({ c0, c1 }: Fp12, { c0: r0, c1: r1 }: Fp12) => ({ + c0: Fp6.subtract(c0, r0), + c1: Fp6.subtract(c1, r1), +}); +const Fp12Multiply = ({ c0, c1 }: Fp12, rhs: Fp12 | bigint) => { + if (typeof rhs === 'bigint') return { c0: Fp6.multiply(c0, rhs), c1: Fp6.multiply(c1, rhs) }; + let { c0: r0, c1: r1 } = rhs; + let t1 = Fp6.multiply(c0, r0); // c0 * r0 + let t2 = Fp6.multiply(c1, r1); // c1 * r1 + return { + c0: Fp6.add(t1, Fp6.mulByNonresidue(t2)), // T1 + T2 * v + // (c0 + c1) * (r0 + r1) - (T1 + T2) + c1: Fp6.subtract(Fp6.multiply(Fp6.add(c0, c1), Fp6.add(r0, r1)), Fp6.add(t1, t2)), + }; +}; +const Fp12Square = ({ c0, c1 }: Fp12) => { + let ab = Fp6.multiply(c0, c1); // c0 * c1 + return { + // (c1 * v + c0) * (c0 + c1) - AB - AB * v + c0: Fp6.subtract( + Fp6.subtract(Fp6.multiply(Fp6.add(Fp6.mulByNonresidue(c1), c0), Fp6.add(c0, c1)), ab), + Fp6.mulByNonresidue(ab) + ), + c1: Fp6.add(ab, ab), + }; // AB + AB +}; +function Fp4Square(a: Fp2, b: Fp2): { first: Fp2; second: Fp2 } { + const a2 = Fp2.square(a); + const b2 = Fp2.square(b); + return { + first: Fp2.add(Fp2.mulByNonresidue(b2), a2), // b² * Nonresidue + a² + second: Fp2.subtract(Fp2.subtract(Fp2.square(Fp2.add(a, b)), a2), b2), // (a + b)² - a² - b² + }; +} +type Fp12Utils = { + fromBigTwelve: (t: BigintTwelve) => Fp12; + frobeniusMap(num: Fp12, power: number): Fp12; + multiplyBy014(num: Fp12, o0: Fp2, o1: Fp2, o4: Fp2): Fp12; + multiplyByFp2(lhs: Fp12, rhs: Fp2): Fp12; + conjugate(num: Fp12): Fp12; + finalExponentiate(num: Fp12): Fp12; + _cyclotomicSquare(num: Fp12): Fp12; + _cyclotomicExp(num: Fp12, n: bigint): Fp12; +}; + +const Fp12: mod.Field & Fp12Utils = { + ORDER: Fp2.ORDER, // TODO: unused, but need to verify + BITS: 2 * Fp2.BITS, + BYTES: 2 * Fp2.BYTES, + MASK: bitMask(2 * Fp2.BITS), + ZERO: { c0: Fp6.ZERO, c1: Fp6.ZERO }, + ONE: { c0: Fp6.ONE, c1: Fp6.ZERO }, + create: (num) => num, + isValid: ({ c0, c1 }) => Fp6.isValid(c0) && Fp6.isValid(c1), + isZero: ({ c0, c1 }) => Fp6.isZero(c0) && Fp6.isZero(c1), + negate: ({ c0, c1 }) => ({ c0: Fp6.negate(c0), c1: Fp6.negate(c1) }), + equals: ({ c0, c1 }, { c0: r0, c1: r1 }) => Fp6.equals(c0, r0) && Fp6.equals(c1, r1), + sqrt: () => { + throw new Error('Not implemented'); + }, + invert: ({ c0, c1 }) => { + let t = Fp6.invert(Fp6.subtract(Fp6.square(c0), Fp6.mulByNonresidue(Fp6.square(c1)))); // 1 / (c0² - c1² * v) + return { c0: Fp6.multiply(c0, t), c1: Fp6.negate(Fp6.multiply(c1, t)) }; // ((C0 * T) * T) + (-C1 * T) * w + }, + div: (lhs, rhs) => + Fp12.multiply(lhs, typeof rhs === 'bigint' ? Fp.invert(Fp.create(rhs)) : Fp12.invert(rhs)), + pow: (num, power) => mod.FpPow(Fp12, num, power), + invertBatch: (nums) => mod.FpInvertBatch(Fp12, nums), + // Normalized + add: Fp12Add, + subtract: Fp12Subtract, + multiply: Fp12Multiply, + square: Fp12Square, + // NonNormalized stuff + addN: Fp12Add, + subtractN: Fp12Subtract, + multiplyN: Fp12Multiply, + squareN: Fp12Square, + + // Bytes utils + fromBytes: (b: Uint8Array): Fp12 => { + if (b.length !== Fp12.BYTES) throw new Error(`fromBytes wrong length=${b.length}`); + return { + c0: Fp6.fromBytes(b.subarray(0, Fp6.BYTES)), + c1: Fp6.fromBytes(b.subarray(Fp6.BYTES)), + }; + }, + toBytes: ({ c0, c1 }): Uint8Array => concatBytes(Fp6.toBytes(c0), Fp6.toBytes(c1)), + + // Utils + // toString() { + // return `Fp12(${this.c0} + ${this.c1} * w)`; + // }, + // fromTuple(c: [Fp6, Fp6]) { + // return new Fp12(...c); + // } + fromBigTwelve: (t: BigintTwelve): Fp12 => ({ + c0: Fp6.fromBigSix(t.slice(0, 6) as BigintSix), + c1: Fp6.fromBigSix(t.slice(6, 12) as BigintSix), + }), + // Raises to q**i -th power + frobeniusMap(lhs, power: number) { + const r0 = Fp6.frobeniusMap(lhs.c0, power); + const { c0, c1, c2 } = Fp6.frobeniusMap(lhs.c1, power); + const coeff = FP12_FROBENIUS_COEFFICIENTS[power % 12]; + return { + c0: r0, + c1: Fp6.create({ + c0: Fp2.multiply(c0, coeff), + c1: Fp2.multiply(c1, coeff), + c2: Fp2.multiply(c2, coeff), + }), + }; + }, + // Sparse multiplication + multiplyBy014: ({ c0, c1 }, o0: Fp2, o1: Fp2, o4: Fp2) => { + let t0 = Fp6.multiplyBy01(c0, o0, o1); + let t1 = Fp6.multiplyBy1(c1, o4); + return { + c0: Fp6.add(Fp6.mulByNonresidue(t1), t0), // T1 * v + T0 + // (c1 + c0) * [o0, o1+o4] - T0 - T1 + c1: Fp6.subtract( + Fp6.subtract(Fp6.multiplyBy01(Fp6.add(c1, c0), o0, Fp2.add(o1, o4)), t0), + t1 + ), + }; + }, + multiplyByFp2: ({ c0, c1 }, rhs: Fp2): Fp12 => ({ + c0: Fp6.multiplyByFp2(c0, rhs), + c1: Fp6.multiplyByFp2(c1, rhs), + }), + conjugate: ({ c0, c1 }): Fp12 => ({ c0, c1: Fp6.negate(c1) }), + + // A cyclotomic group is a subgroup of Fp^n defined by + // GΦₙ(p) = {α ∈ Fpⁿ : α^Φₙ(p) = 1} + // The result of any pairing is in a cyclotomic subgroup + // https://eprint.iacr.org/2009/565.pdf + _cyclotomicSquare: ({ c0, c1 }): Fp12 => { + const { c0: c0c0, c1: c0c1, c2: c0c2 } = c0; + const { c0: c1c0, c1: c1c1, c2: c1c2 } = c1; + const { first: t3, second: t4 } = Fp4Square(c0c0, c1c1); + const { first: t5, second: t6 } = Fp4Square(c1c0, c0c2); + const { first: t7, second: t8 } = Fp4Square(c0c1, c1c2); + let t9 = Fp2.mulByNonresidue(t8); // T8 * (u + 1) + return { + c0: Fp6.create({ + c0: Fp2.add(Fp2.multiply(Fp2.subtract(t3, c0c0), 2n), t3), // 2 * (T3 - c0c0) + T3 + c1: Fp2.add(Fp2.multiply(Fp2.subtract(t5, c0c1), 2n), t5), // 2 * (T5 - c0c1) + T5 + c2: Fp2.add(Fp2.multiply(Fp2.subtract(t7, c0c2), 2n), t7), + }), // 2 * (T7 - c0c2) + T7 + c1: Fp6.create({ + c0: Fp2.add(Fp2.multiply(Fp2.add(t9, c1c0), 2n), t9), // 2 * (T9 + c1c0) + T9 + c1: Fp2.add(Fp2.multiply(Fp2.add(t4, c1c1), 2n), t4), // 2 * (T4 + c1c1) + T4 + c2: Fp2.add(Fp2.multiply(Fp2.add(t6, c1c2), 2n), t6), + }), + }; // 2 * (T6 + c1c2) + T6 + }, + _cyclotomicExp(num, n) { + let z = Fp12.ONE; + for (let i = BLS_X_LEN - 1; i >= 0; i--) { + z = Fp12._cyclotomicSquare(z); + if (bitGet(n, i)) z = Fp12.multiply(z, num); + } + return z; + }, + // https://eprint.iacr.org/2010/354.pdf + // https://eprint.iacr.org/2009/565.pdf + finalExponentiate: (num) => { + const x = BLS_X; + // this^(q⁶) / this + const t0 = Fp12.div(Fp12.frobeniusMap(num, 6), num); + // t0^(q²) * t0 + const t1 = Fp12.multiply(Fp12.frobeniusMap(t0, 2), t0); + const t2 = Fp12.conjugate(Fp12._cyclotomicExp(t1, x)); + const t3 = Fp12.multiply(Fp12.conjugate(Fp12._cyclotomicSquare(t1)), t2); + const t4 = Fp12.conjugate(Fp12._cyclotomicExp(t3, x)); + const t5 = Fp12.conjugate(Fp12._cyclotomicExp(t4, x)); + const t6 = Fp12.multiply( + Fp12.conjugate(Fp12._cyclotomicExp(t5, x)), + Fp12._cyclotomicSquare(t2) + ); + const t7 = Fp12.conjugate(Fp12._cyclotomicExp(t6, x)); + const t2_t5_pow_q2 = Fp12.frobeniusMap(Fp12.multiply(t2, t5), 2); + const t4_t1_pow_q3 = Fp12.frobeniusMap(Fp12.multiply(t4, t1), 3); + const t6_t1c_pow_q1 = Fp12.frobeniusMap(Fp12.multiply(t6, Fp12.conjugate(t1)), 1); + const t7_t3c_t1 = Fp12.multiply(Fp12.multiply(t7, Fp12.conjugate(t3)), t1); + // (t2 * t5)^(q²) * (t4 * t1)^(q³) * (t6 * t1.conj)^(q^1) * t7 * t3.conj * t1 + return Fp12.multiply( + Fp12.multiply(Fp12.multiply(t2_t5_pow_q2, t4_t1_pow_q3), t6_t1c_pow_q1), + t7_t3c_t1 + ); + }, +}; +const FP12_FROBENIUS_COEFFICIENTS = [ + [0x1n, 0x0n], + [ + 0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8n, + 0x00fc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3n, + ], + [ + 0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffeffffn, + 0x0n, + ], + [ + 0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2n, + 0x06af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09n, + ], + [ + 0x00000000000000005f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffen, + 0x0n, + ], + [ + 0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995n, + 0x05b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116n, + ], + [ + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaan, + 0x0n, + ], + [ + 0x00fc3e2b36c4e03288e9e902231f9fb854a14787b6c7b36fec0c8ec971f63c5f282d5ac14d6c7ec22cf78a126ddc4af3n, + 0x1904d3bf02bb0667c231beb4202c0d1f0fd603fd3cbd5f4f7b2443d784bab9c4f67ea53d63e7813d8d0775ed92235fb8n, + ], + [ + 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaacn, + 0x0n, + ], + [ + 0x06af0e0437ff400b6831e36d6bd17ffe48395dabc2d3435e77f76e17009241c5ee67992f72ec05f4c81084fbede3cc09n, + 0x135203e60180a68ee2e9c448d77a2cd91c3dedd930b1cf60ef396489f61eb45e304466cf3e67fa0af1ee7b04121bdea2n, + ], + [ + 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaadn, + 0x0n, + ], + [ + 0x05b2cfd9013a5fd8df47fa6b48b1e045f39816240c0b8fee8beadf4d8e9c0566c63a3e6e257f87329b18fae980078116n, + 0x144e4211384586c16bd3ad4afa99cc9170df3560e77982d0db45f3536814f0bd5871c1908bd478cd1ee605167ff82995n, + ], +].map((n) => Fp2.fromBigTuple(n)); +// END OF CURVE FIELDS + +// HashToCurve +// TODO: try to move-out generic version + +// Utilities for 3-isogeny map from E' to E. +const ISOGENY_COEFFICIENTS_G2: [Fp2[], Fp2[], Fp2[], Fp2[]] = [ + // xNum + [ + [ + 0x171d6541fa38ccfaed6dea691f5fb614cb14b4e7f4e810aa22d6108f142b85757098e38d0f671c7188e2aaaaaaaa5ed1n, + 0x0n, + ], + [ + 0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71en, + 0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38dn, + ], + [ + 0x0n, + 0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71an, + ], + [ + 0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6n, + 0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97d6n, + ], + ], + // xDen + [ + [0x0n, 0x0n], + [0x1n, 0x0n], + [ + 0xcn, + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa9fn, + ], + [ + 0x0n, + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa63n, + ], + ], + // yNum + [ + [ + 0x124c9ad43b6cf79bfbf7043de3811ad0761b0f37a1e26286b0e977c69aa274524e79097a56dc4bd9e1b371c71c718b10n, + 0x0n, + ], + [ + 0x11560bf17baa99bc32126fced787c88f984f87adf7ae0c7f9a208c6b4f20a4181472aaa9cb8d555526a9ffffffffc71cn, + 0x8ab05f8bdd54cde190937e76bc3e447cc27c3d6fbd7063fcd104635a790520c0a395554e5c6aaaa9354ffffffffe38fn, + ], + [ + 0x0n, + 0x5c759507e8e333ebb5b7a9a47d7ed8532c52d39fd3a042a88b58423c50ae15d5c2638e343d9c71c6238aaaaaaaa97ben, + ], + [ + 0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706n, + 0x1530477c7ab4113b59a4c18b076d11930f7da5d4a07f649bf54439d87d27e500fc8c25ebf8c92f6812cfc71c71c6d706n, + ], + ], + // yDen + [ + [0x1n, 0x0n], + [ + 0x12n, + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaa99n, + ], + [ + 0x0n, + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa9d3n, + ], + [ + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fbn, + 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffa8fbn, + ], + ], +].map((i) => i.map((pair) => Fp2.fromBigTuple(pair))) as [Fp2[], Fp2[], Fp2[], Fp2[]]; + +const ISOGENY_COEFFICIENTS_G1: [Fp[], Fp[], Fp[], Fp[]] = [ + // xNum + [ + 0x06e08c248e260e70bd1e962381edee3d31d79d7e22c837bc23c0bf1bc24c6b68c24b1b80b64d391fa9c8ba2e8ba2d229n, + 0x10321da079ce07e272d8ec09d2565b0dfa7dccdde6787f96d50af36003b14866f69b771f8c285decca67df3f1605fb7bn, + 0x169b1f8e1bcfa7c42e0c37515d138f22dd2ecb803a0c5c99676314baf4bb1b7fa3190b2edc0327797f241067be390c9en, + 0x080d3cf1f9a78fc47b90b33563be990dc43b756ce79f5574a2c596c928c5d1de4fa295f296b74e956d71986a8497e317n, + 0x17b81e7701abdbe2e8743884d1117e53356de5ab275b4db1a682c62ef0f2753339b7c8f8c8f475af9ccb5618e3f0c88en, + 0x0d6ed6553fe44d296a3726c38ae652bfb11586264f0f8ce19008e218f9c86b2a8da25128c1052ecaddd7f225a139ed84n, + 0x1630c3250d7313ff01d1201bf7a74ab5db3cb17dd952799b9ed3ab9097e68f90a0870d2dcae73d19cd13c1c66f652983n, + 0x0e99726a3199f4436642b4b3e4118e5499db995a1257fb3f086eeb65982fac18985a286f301e77c451154ce9ac8895d9n, + 0x1778e7166fcc6db74e0609d307e55412d7f5e4656a8dbf25f1b33289f1b330835336e25ce3107193c5b388641d9b6861n, + 0x0d54005db97678ec1d1048c5d10a9a1bce032473295983e56878e501ec68e25c958c3e3d2a09729fe0179f9dac9edcb0n, + 0x17294ed3e943ab2f0588bab22147a81c7c17e75b2f6a8417f565e33c70d1e86b4838f2a6f318c356e834eef1b3cb83bbn, + 0x11a05f2b1e833340b809101dd99815856b303e88a2d7005ff2627b56cdb4e2c85610c2d5f2e62d6eaeac1662734649b7n, + ], + // xDen + [ + 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001n, + 0x095fc13ab9e92ad4476d6e3eb3a56680f682b4ee96f7d03776df533978f31c1593174e4b4b7865002d6384d168ecdd0an, + 0x0a10ecf6ada54f825e920b3dafc7a3cce07f8d1d7161366b74100da67f39883503826692abba43704776ec3a79a1d641n, + 0x14a7ac2a9d64a8b230b3f5b074cf01996e7f63c21bca68a81996e1cdf9822c580fa5b9489d11e2d311f7d99bbdcc5a5en, + 0x0772caacf16936190f3e0c63e0596721570f5799af53a1894e2e073062aede9cea73b3538f0de06cec2574496ee84a3an, + 0x0e7355f8e4e667b955390f7f0506c6e9395735e9ce9cad4d0a43bcef24b8982f7400d24bc4228f11c02df9a29f6304a5n, + 0x13a8e162022914a80a6f1d5f43e7a07dffdfc759a12062bb8d6b44e833b306da9bd29ba81f35781d539d395b3532a21en, + 0x03425581a58ae2fec83aafef7c40eb545b08243f16b1655154cca8abc28d6fd04976d5243eecf5c4130de8938dc62cd8n, + 0x0b2962fe57a3225e8137e629bff2991f6f89416f5a718cd1fca64e00b11aceacd6a3d0967c94fedcfcc239ba5cb83e19n, + 0x12561a5deb559c4348b4711298e536367041e8ca0cf0800c0126c2588c48bf5713daa8846cb026e9e5c8276ec82b3bffn, + 0x08ca8d548cff19ae18b2e62f4bd3fa6f01d5ef4ba35b48ba9c9588617fc8ac62b558d681be343df8993cf9fa40d21b1cn, + ], + // yNum + [ + 0x15e6be4e990f03ce4ea50b3b42df2eb5cb181d8f84965a3957add4fa95af01b2b665027efec01c7704b456be69c8b604n, + 0x05c129645e44cf1102a159f748c4a3fc5e673d81d7e86568d9ab0f5d396a7ce46ba1049b6579afb7866b1e715475224bn, + 0x0245a394ad1eca9b72fc00ae7be315dc757b3b080d4c158013e6632d3c40659cc6cf90ad1c232a6442d9d3f5db980133n, + 0x0b182cac101b9399d155096004f53f447aa7b12a3426b08ec02710e807b4633f06c851c1919211f20d4c04f00b971ef8n, + 0x18b46a908f36f6deb918c143fed2edcc523559b8aaf0c2462e6bfe7f911f643249d9cdf41b44d606ce07c8a4d0074d8en, + 0x19713e47937cd1be0dfd0b8f1d43fb93cd2fcbcb6caf493fd1183e416389e61031bf3a5cce3fbafce813711ad011c132n, + 0x0e1bba7a1186bdb5223abde7ada14a23c42a0ca7915af6fe06985e7ed1e4d43b9b3f7055dd4eba6f2bafaaebca731c30n, + 0x09fc4018bd96684be88c9e221e4da1bb8f3abd16679dc26c1e8b6e6a1f20cabe69d65201c78607a360370e577bdba587n, + 0x0987c8d5333ab86fde9926bd2ca6c674170a05bfe3bdd81ffd038da6c26c842642f64550fedfe935a15e4ca31870fb29n, + 0x04ab0b9bcfac1bbcb2c977d027796b3ce75bb8ca2be184cb5231413c4d634f3747a87ac2460f415ec961f8855fe9d6f2n, + 0x16603fca40634b6a2211e11db8f0a6a074a7d0d4afadb7bd76505c3d3ad5544e203f6326c95a807299b23ab13633a5f0n, + 0x08cc03fdefe0ff135caf4fe2a21529c4195536fbe3ce50b879833fd221351adc2ee7f8dc099040a841b6daecf2e8fedbn, + 0x01f86376e8981c217898751ad8746757d42aa7b90eeb791c09e4a3ec03251cf9de405aba9ec61deca6355c77b0e5f4cbn, + 0x00cc786baa966e66f4a384c86a3b49942552e2d658a31ce2c344be4b91400da7d26d521628b00523b8dfe240c72de1f6n, + 0x134996a104ee5811d51036d776fb46831223e96c254f383d0f906343eb67ad34d6c56711962fa8bfe097e75a2e41c696n, + 0x090d97c81ba24ee0259d1f094980dcfa11ad138e48a869522b52af6c956543d3cd0c7aee9b3ba3c2be9845719707bb33n, + ], + // yDen + [ + 0x000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001n, + 0x0e0fa1d816ddc03e6b24255e0d7819c171c40f65e273b853324efcd6356caa205ca2f570f13497804415473a1d634b8fn, + 0x02660400eb2e4f3b628bdd0d53cd76f2bf565b94e72927c1cb748df27942480e420517bd8714cc80d1fadc1326ed06f7n, + 0x0ad6b9514c767fe3c3613144b45f1496543346d98adf02267d5ceef9a00d9b8693000763e3b90ac11e99b138573345ccn, + 0x0accbb67481d033ff5852c1e48c50c477f94ff8aefce42d28c0f9a88cea7913516f968986f7ebbea9684b529e2561092n, + 0x04d2f259eea405bd48f010a01ad2911d9c6dd039bb61a6290e591b36e636a5c871a5c29f4f83060400f8b49cba8f6aa8n, + 0x167a55cda70a6e1cea820597d94a84903216f763e13d87bb5308592e7ea7d4fbc7385ea3d529b35e346ef48bb8913f55n, + 0x1866c8ed336c61231a1be54fd1d74cc4f9fb0ce4c6af5920abc5750c4bf39b4852cfe2f7bb9248836b233d9d55535d4an, + 0x16a3ef08be3ea7ea03bcddfabba6ff6ee5a4375efa1f4fd7feb34fd206357132b920f5b00801dee460ee415a15812ed9n, + 0x166007c08a99db2fc3ba8734ace9824b5eecfdfa8d0cf8ef5dd365bc400a0051d5fa9c01a58b1fb93d1a1399126a775cn, + 0x08d9e5297186db2d9fb266eaac783182b70152c65550d881c5ecd87b6f0f5a6449f38db9dfa9cce202c6477faaf9b7acn, + 0x0be0e079545f43e4b00cc912f8228ddcc6d19c9f0f69bbb0542eda0fc9dec916a20b15dc0fd2ededda39142311a5001dn, + 0x16b7d288798e5395f20d23bf89edb4d1d115c5dbddbcd30e123da489e726af41727364f2c28297ada8d26d98445f5416n, + 0x058df3306640da276faaae7d6e8eb15778c4855551ae7f310c35a5dd279cd2eca6757cd636f96f891e2538b53dbf67f2n, + 0x1962d75c2381201e1a0cbd6c43c348b885c84ff731c4d59ca4a10356f453e01f78a4260763529e3532f6102c2e49a03dn, + 0x16112c4c3a9c98b252181140fad0eae9601a6de578980be6eec3232b5be72e7a07f3688ef60c206d01479253b03663c1n, + ], +]; + +// Looks like is_y_even for fp + fp2? +// For Fp2: if (sgn0_fp2(t) !== sgn0_fp2(y)) y = Fp2.negate(y); +// For Fp: const y = sgn0_m_eq_1(u) == sgn0_m_eq_1(yPos) ? yPos : yNeg; + +function sgn0_fp2(x: Fp2) { + const { re: x0, im: x1 } = Fp2.reim(x); + const sign_0 = x0 % 2n; + const zero_0 = x0 === 0n; + const sign_1 = x1 % 2n; + return BigInt(sign_0 || (zero_0 && sign_1)); +} + +function sgn0_m_eq_1(x: Fp) { + return Boolean(x % 2n); +} + +const P_MINUS_9_DIV_16 = (Fp.ORDER ** 2n - 9n) / 16n; +// Does not return a square root. +// Returns uv⁷ * (uv¹⁵)^((p² - 9) / 16) * root of unity +// if valid square root is found +function sqrt_div_fp2(u: Fp2, v: Fp2) { + const v7 = Fp2.pow(v, 7n); + const uv7 = Fp2.multiply(u, v7); + const uv15 = Fp2.multiply(uv7, Fp2.multiply(v7, v)); + // gamma = uv⁷ * (uv¹⁵)^((p² - 9) / 16) + const gamma = Fp2.multiply(Fp2.pow(uv15, P_MINUS_9_DIV_16), uv7); + let success = false; + let result = gamma; + // Constant-time routine, so we do not early-return. + const positiveRootsOfUnity = FP2_ROOTS_OF_UNITY.slice(0, 4); + positiveRootsOfUnity.forEach((root) => { + // Valid if (root * gamma)² * v - u == 0 + const candidate = Fp2.multiply(root, gamma); + if (Fp2.isZero(Fp2.subtract(Fp2.multiply(Fp2.pow(candidate, 2n), v), u)) && !success) { + success = true; + result = candidate; + } + }); + return { success, sqrtCandidateOrGamma: result }; +} + +// Optimized SWU Map - Fp2 to G2': y² = x³ + 240i * x + 1012 + 1012i +// Found in Section 4 of https://eprint.iacr.org/2019/403 +// Note: it's constant-time +// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-G.2.3 +function map_to_curve_simple_swu_9mod16(t: bigint[] | Fp2): [Fp2, Fp2] { + const iso_3_a = Fp2.create({ c0: Fp.create(0n), c1: Fp.create(240n) }); + const iso_3_b = Fp2.create({ c0: Fp.create(1012n), c1: Fp.create(1012n) }); + const iso_3_z = Fp2.create({ c0: Fp.create(-2n), c1: Fp.create(-1n) }); + if (Array.isArray(t)) t = Fp2.fromBigTuple(t); + + const t2 = Fp2.pow(t, 2n); + const iso_3_z_t2 = Fp2.multiply(iso_3_z, t2); + const ztzt = Fp2.add(iso_3_z_t2, Fp2.pow(iso_3_z_t2, 2n)); // (Z * t² + Z² * t⁴) + let denominator = Fp2.negate(Fp2.multiply(iso_3_a, ztzt)); // -a(Z * t² + Z² * t⁴) + let numerator = Fp2.multiply(iso_3_b, Fp2.add(ztzt, Fp2.ONE)); // b(Z * t² + Z² * t⁴ + 1) + + // Exceptional case + if (Fp2.isZero(denominator)) denominator = Fp2.multiply(iso_3_z, iso_3_a); + + // v = D³ + let v = Fp2.pow(denominator, 3n); + // u = N³ + a * N * D² + b * D³ + let u = Fp2.add( + Fp2.add( + Fp2.pow(numerator, 3n), + Fp2.multiply(Fp2.multiply(iso_3_a, numerator), Fp2.pow(denominator, 2n)) + ), + Fp2.multiply(iso_3_b, v) + ); + // Attempt y = sqrt(u / v) + const { success, sqrtCandidateOrGamma } = sqrt_div_fp2(u, v); + let y; + if (success) y = sqrtCandidateOrGamma; + // Handle case where (u / v) is not square + // sqrt_candidate(x1) = sqrt_candidate(x0) * t³ + const sqrtCandidateX1 = Fp2.multiply(sqrtCandidateOrGamma, Fp2.pow(t, 3n)); + + // u(x1) = Z³ * t⁶ * u(x0) + u = Fp2.multiply(Fp2.pow(iso_3_z_t2, 3n), u); + let success2 = false; + FP2_ETAs.forEach((eta) => { + // Valid solution if (eta * sqrt_candidate(x1))² * v - u == 0 + const etaSqrtCandidate = Fp2.multiply(eta, sqrtCandidateX1); + const temp = Fp2.subtract(Fp2.multiply(Fp2.pow(etaSqrtCandidate, 2n), v), u); + if (Fp2.isZero(temp) && !success && !success2) { + y = etaSqrtCandidate; + success2 = true; + } + }); + if (!success && !success2) throw new Error('Hash to Curve - Optimized SWU failure'); + if (success2) numerator = Fp2.multiply(numerator, iso_3_z_t2); + y = y as Fp2; + if (sgn0_fp2(t) !== sgn0_fp2(y)) y = Fp2.negate(y); + return [Fp2.div(numerator, denominator), y]; +} +// Optimized SWU Map - Fp to G1 +// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-G.2.1 +function map_to_curve_simple_swu_3mod4(u: Fp): [Fp, Fp] { + const A = + Fp.create( + 0x144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1dn + ); + const B = + Fp.create( + 0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0n + ); + const Z = Fp.create(11n); + const c1 = (Fp.ORDER - 3n) / 4n; // (q - 3) / 4 + // Static value so we can know that is there always root + const c2 = Fp.sqrt(Fp.pow(Fp.negate(Z), 3n)); // sqrt((-Z) ^ 3) + const tv1 = Fp.square(u); // u ** 2n; + const tv3 = Fp.multiply(Z, tv1); // + let xDen = Fp.add(Fp.square(tv3), tv3); + // X + const xNum1 = Fp.multiply(Fp.add(xDen, Fp.ONE), B); // (xd + 1) * B + const xNum2 = Fp.multiply(tv3, xNum1); // x2 = x2n / xd = Z * u^2 * x1n / xd + xDen = Fp.multiply(Fp.negate(A), xDen); // -A * xDen + if (Fp.isZero(xDen)) xDen = Fp.multiply(A, Z); + let tv2 = Fp.square(xDen); // xDen ^ 2 + const gxd = Fp.multiply(tv2, xDen); // xDen ^ 3 + tv2 = Fp.multiply(A, tv2); // A * tv2 + let gx1 = Fp.multiply(Fp.add(Fp.square(xNum1), tv2), xNum1); // x1n^3 + A * x1n * xd^2 + tv2 = Fp.multiply(B, gxd); // B * gxd + gx1 = Fp.add(gx1, tv2); // x1n^3 + A * x1n * xd^2 + B * xd^3 + tv2 = Fp.multiply(gx1, gxd); // gx1 * gxd + const tv4 = Fp.multiply(Fp.square(gxd), tv2); // gx1 * gxd^3 + // Y + const y1 = Fp.multiply(Fp.pow(tv4, c1), tv2); // gx1 * gxd * (gx1 * gxd^3)^((q - 3) / 4) + const y2 = Fp.multiply(Fp.multiply(Fp.multiply(y1, c2), tv1), u); // y1 * c2 * tv1 * u + let xNum, yPos; + // y1^2 * gxd == gx1 + if (Fp.equals(Fp.multiply(Fp.square(y1), gxd), gx1)) { + xNum = xNum1; + yPos = y1; + } else { + xNum = xNum2; + yPos = y2; + } + const yNeg = Fp.negate(yPos); + const y = sgn0_m_eq_1(u) == sgn0_m_eq_1(yPos) ? yPos : yNeg; + // NOTE: we can batch inversion for hashToCurve, but it doesn't impact performance + return [Fp.div(xNum, xDen), y]; +} + +function isogenyMap>( + field: F, + COEFF: [T[], T[], T[], T[]], + x: T, + y: T +): [T, T] { + const [xNum, xDen, yNum, yDen] = COEFF.map((val) => + val.reduce((acc, i) => field.add(field.multiply(acc, x), i)) + ); + x = field.div(xNum, xDen); // xNum / xDen + y = field.multiply(y, field.div(yNum, yDen)); // y * (yNum / yDev) + return [x, y]; +} +// 3-isogeny map from E' to E +// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#appendix-E.3 +const isogenyMapG2 = (x: Fp2, y: Fp2) => isogenyMap(Fp2, ISOGENY_COEFFICIENTS_G2, x, y); +// 11-isogeny map from E' to E +const isogenyMapG1 = (x: Fp, y: Fp) => isogenyMap(Fp, ISOGENY_COEFFICIENTS_G1, x, y); + +// Endomorphisms (for fast cofactor clearing) +// Ψ(P) endomorphism +const ut_root = Fp6.create({ c0: Fp2.ZERO, c1: Fp2.ONE, c2: Fp2.ZERO }); +const wsq = Fp12.create({ c0: ut_root, c1: Fp6.ZERO }); +const wcu = Fp12.create({ c0: Fp6.ZERO, c1: ut_root }); +const [wsq_inv, wcu_inv] = Fp12.invertBatch([wsq, wcu]); +function psi(x: Fp2, y: Fp2): [Fp2, Fp2] { + // Untwist Fp2->Fp12 && frobenius(1) && twist back + const x2 = Fp12.multiply(Fp12.frobeniusMap(Fp12.multiplyByFp2(wsq_inv, x), 1), wsq).c0.c0; + const y2 = Fp12.multiply(Fp12.frobeniusMap(Fp12.multiplyByFp2(wcu_inv, y), 1), wcu).c0.c0; + return [x2, y2]; +} +// Ψ endomorphism +function G2psi(c: JacobianConstructor, P: JacobianPointType) { + const affine = P.toAffine(); + const p = psi(affine.x, affine.y); + return new c(p[0], p[1], Fp2.ONE); +} +// Ψ²(P) endomorphism +// 1 / F2(2)^((p-1)/3) in GF(p²) +const PSI2_C1 = + 0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaacn; + +function psi2(x: Fp2, y: Fp2): [Fp2, Fp2] { + return [Fp2.multiply(x, PSI2_C1), Fp2.negate(y)]; +} +function G2psi2(c: JacobianConstructor, P: JacobianPointType) { + const affine = P.toAffine(); + const p = psi2(affine.x, affine.y); + return new c(p[0], p[1], Fp2.ONE); +} + +// Default hash_to_field options are for hash to G2. +// +// Parameter definitions are in section 5.3 of the spec unless otherwise noted. +// Parameter values come from section 8.8.2 of the spec. +// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-8.8.2 +// +// Base field F is GF(p^m) +// p = 0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab +// m = 2 (or 1 for G1 see section 8.8.1) +// k = 128 +const htfDefaults = { + // DST: a domain separation tag + // defined in section 2.2.5 + // Use utils.getDSTLabel(), utils.setDSTLabel(value) + DST: 'BLS_SIG_BLS12381G2_XMD:SHA-256_SSWU_RO_NUL_', + // p: the characteristic of F + // where F is a finite field of characteristic p and order q = p^m + p: Fp.ORDER, + // m: the extension degree of F, m >= 1 + // where F is a finite field of characteristic p and order q = p^m + m: 2, + // k: the target security level for the suite in bits + // defined in section 5.1 + k: 128, + // option to use a message that has already been processed by + // expand_message_xmd + expand: true, + // 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, +}; + +// Encoding utils +// Point on G1 curve: (x, y) +const C_BIT_POS = Fp.BITS; // C_bit, compression bit for serialization flag +const I_BIT_POS = Fp.BITS + 1; // I_bit, point-at-infinity bit for serialization flag +const S_BIT_POS = Fp.BITS + 2; // S_bit, sign bit for serialization flag +// Compressed point of infinity +const COMPRESSED_ZERO = Fp.toBytes(bitSet(bitSet(0n, I_BIT_POS, true), S_BIT_POS, true)); // set compressed & point-at-infinity bits + +// To verify curve parameters, see pairing-friendly-curves spec: +// https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-pairing-friendly-curves-09 +// Basic math is done over finite fields over p. +// More complicated math is done over polynominal extension fields. +// To simplify calculations in Fp12, we construct extension tower: +// Fp₁₂ = Fp₆² => Fp₂³ +// Fp(u) / (u² - β) where β = -1 +// Fp₂(v) / (v³ - ξ) where ξ = u + 1 +// Fp₆(w) / (w² - γ) where γ = v +// Here goes constants && point encoding format +export const bls12_381: CurveFn = bls({ + // Fields + Fr, + Fp, + Fp2, + Fp6, + Fp12, + // order; z⁴ − z² + 1 + r: Fr.ORDER, // Same as N in other curves + // G1 is the order-q subgroup of E1(Fp) : y² = x³ + 4, #E1(Fp) = h1q, where + // characteristic; z + (z⁴ - z² + 1)(z - 1)²/3 + G1: { + Fp, + // cofactor; (z - 1)²/3 + h: 0x396c8c005555e1568c00aaab0000aaabn, + // generator's coordinates + // x = 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507 + // y = 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569 + Gx: 0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bbn, + Gy: 0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1n, + a: Fp.ZERO, + b: 4n, + htfDefaults: { ...htfDefaults, m: 1 }, + wrapPrivateKey: true, + allowInfinityPoint: true, + // Checks is the point resides in prime-order subgroup. + // point.isTorsionFree() should return true for valid points + // It returns false for shitty points. + // https://eprint.iacr.org/2021/1130.pdf + isTorsionFree: (c, point): boolean => { + // φ endomorphism + const cubicRootOfUnityModP = + 0x5f19672fdf76ce51ba69c6076a0f77eaddb3a93be6f89688de17d813620a00022e01fffffffefffen; + const phi = new c(Fp.multiply(point.x, cubicRootOfUnityModP), point.y, point.z); + + // todo: unroll + const xP = point.multiplyUnsafe(bls12_381.CURVE.x).negate(); // [x]P + const u2P = xP.multiplyUnsafe(bls12_381.CURVE.x); // [u2]P + return u2P.equals(phi); + + // https://eprint.iacr.org/2019/814.pdf + // (z² − 1)/3 + // const c1 = 0x396c8c005555e1560000000055555555n; + // const P = this; + // const S = P.sigma(); + // const Q = S.double(); + // const S2 = S.sigma(); + // // [(z² − 1)/3](2σ(P) − P − σ²(P)) − σ²(P) = O + // const left = Q.subtract(P).subtract(S2).multiplyUnsafe(c1); + // const C = left.subtract(S2); + // return C.isZero(); + }, + // Clear cofactor of G1 + // https://eprint.iacr.org/2019/403 + clearCofactor: (c, point) => { + // return this.multiplyUnsafe(CURVE.h); + return point.multiplyUnsafe(bls12_381.CURVE.x).add(point); // x*P + P + }, + mapToCurve: (scalars: bigint[]) => { + const [x0, y0] = map_to_curve_simple_swu_3mod4(Fp.create(scalars[0])); + const [x, y] = isogenyMapG1(x0, y0); + return { x, y }; + }, + fromBytes: (bytes: Uint8Array): { x: Fp; y: Fp } => { + if (bytes.length === 48) { + const P = Fp.ORDER; + const compressedValue = bytesToNumberBE(bytes); + const bflag = bitGet(compressedValue, I_BIT_POS); + // Zero + if (bflag === 1n) return { x: 0n, y: 0n }; + const x = Fp.create(compressedValue & Fp.MASK); + const right = Fp.add(Fp.pow(x, 3n), Fp.create(bls12_381.CURVE.G1.b)); // y² = x³ + b + let y = Fp.sqrt(right); + if (!y) throw new Error('Invalid compressed G1 point'); + const aflag = bitGet(compressedValue, C_BIT_POS); + if ((y * 2n) / P !== aflag) y = Fp.negate(y); + return { x: Fp.create(x), y: Fp.create(y) }; + } else if (bytes.length === 96) { + // Check if the infinity flag is set + if ((bytes[0] & (1 << 6)) !== 0) return bls12_381.G1.Point.ZERO; + const x = bytesToNumberBE(bytes.slice(0, Fp.BYTES)); + const y = bytesToNumberBE(bytes.slice(Fp.BYTES)); + return { x: Fp.create(x), y: Fp.create(y) }; + } else { + throw new Error('Invalid point G1, expected 48/96 bytes'); + } + }, + toBytes: (c, point, isCompressed) => { + const isZero = point.equals(c.ZERO); + const { x, y } = point; + if (isCompressed) { + if (isZero) return COMPRESSED_ZERO.slice(); + const P = Fp.ORDER; + let num; + num = bitSet(x, C_BIT_POS, Boolean((y * 2n) / P)); // set aflag + num = bitSet(num, S_BIT_POS, true); + return numberToBytesBE(num, Fp.BYTES); + } else { + if (isZero) { + // 2x PUBLIC_KEY_LENGTH + const x = concatBytes(new Uint8Array([0x40]), new Uint8Array(2 * Fp.BYTES - 1)); + return x; + } else { + return concatBytes(numberToBytesBE(x, Fp.BYTES), numberToBytesBE(y, Fp.BYTES)); + } + } + }, + }, + // G2 is the order-q subgroup of E2(Fp²) : y² = x³+4(1+√−1), + // where Fp2 is Fp[√−1]/(x2+1). #E2(Fp2 ) = h2q, where + // G² - 1 + // h2q + G2: { + Fp: Fp2, + // cofactor + h: 0x5d543a95414e7f1091d50792876a202cd91de4547085abaa68a205b2e5a7ddfa628f1cb4d9e82ef21537e293a6691ae1616ec6e786f0c70cf1c38e31c7238e5n, + Gx: Fp2.fromBigTuple([ + 0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8n, + 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7en, + ]), + // y = + // 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582, + // 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905 + Gy: Fp2.fromBigTuple([ + 0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801n, + 0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79ben, + ]), + a: Fp2.ZERO, + b: Fp2.fromBigTuple([4n, 4n]), + hEff: 0xbc69f08f2ee75b3584c6a0ea91b352888e2a8e9145ad7689986ff031508ffe1329c2f178731db956d82bf015d1212b02ec0ec69d7477c1ae954cbc06689f6a359894c0adebbf6b4e8020005aaa95551n, + htfDefaults: { ...htfDefaults }, + wrapPrivateKey: true, + allowInfinityPoint: true, + mapToCurve: (scalars: bigint[]) => { + const [x0, y0] = map_to_curve_simple_swu_9mod16(Fp2.fromBigTuple(scalars)); + const [x, y] = isogenyMapG2(x0, y0); + return { x, y }; + }, + // Checks is the point resides in prime-order subgroup. + // point.isTorsionFree() should return true for valid points + // It returns false for shitty points. + // https://eprint.iacr.org/2021/1130.pdf + // prettier-ignore + isTorsionFree: (c, P): boolean => { + return P.multiplyUnsafe(bls12_381.CURVE.x).negate().equals(G2psi(c, P)); // ψ(P) == [u](P) + // https://eprint.iacr.org/2019/814.pdf + // const psi2 = P.psi2(); // Ψ²(P) + // const psi3 = psi2.psi(); // Ψ³(P) + // const zPsi3 = psi3.mulNegX(); // [z]Ψ³(P) where z = -x + // return zPsi3.subtract(psi2).add(P).isZero(); // [z]Ψ³(P) - Ψ²(P) + P == O + }, + // Maps the point into the prime-order subgroup G2. + // clear_cofactor_bls12381_g2 from cfrg-hash-to-curve-11 + // https://eprint.iacr.org/2017/419.pdf + // prettier-ignore + clearCofactor: (c, P) => { + // prettier-ignore + let t1 = P.multiplyUnsafe(bls12_381.CURVE.x).negate(); // [-x]P + let t2 = G2psi(c, P); // Ψ(P) + let t3 = P.double(); // 2P + t3 = G2psi2(c, t3); // Ψ²(2P) + t3 = t3.subtract(t2); // Ψ²(2P) - Ψ(P) + t2 = t1.add(t2); // [-x]P + Ψ(P) + t2 = t2.multiplyUnsafe(bls12_381.CURVE.x).negate(); // [x²]P - [x]Ψ(P) + t3 = t3.add(t2); // Ψ²(2P) - Ψ(P) + [x²]P - [x]Ψ(P) + t3 = t3.subtract(t1); // Ψ²(2P) - Ψ(P) + [x²]P - [x]Ψ(P) + [x]P + const Q = t3.subtract(P); // Ψ²(2P) - Ψ(P) + [x²]P - [x]Ψ(P) + [x]P - 1P => + return Q; // [x²-x-1]P + [x-1]Ψ(P) + Ψ²(2P) + }, + fromBytes: (bytes: Uint8Array): { x: Fp2; y: Fp2 } => { + const m_byte = bytes[0] & 0xe0; + if (m_byte === 0x20 || m_byte === 0x60 || m_byte === 0xe0) { + throw new Error('Invalid encoding flag: ' + m_byte); + } + const bitC = m_byte & 0x80; // compression bit + const bitI = m_byte & 0x40; // point at infinity bit + const bitS = m_byte & 0x20; // sign bit + if (bytes.length === 96 && bitC) { + const { b } = bls12_381.CURVE.G2; + const P = Fp.ORDER; + + bytes[0] = bytes[0] & 0x1f; // clear flags + if (bitI) { + // check that all bytes are 0 + if (bytes.reduce((p, c) => (p !== 0 ? c + 1 : c), 0) > 0) { + throw new Error('Invalid compressed G2 point'); + } + return { x: Fp2.ZERO, y: Fp2.ZERO }; + } + const x_1 = bytesToNumberBE(bytes.slice(0, Fp.BYTES)); + const x_0 = bytesToNumberBE(bytes.slice(Fp.BYTES)); + const x = Fp2.create({ c0: Fp.create(x_0), c1: Fp.create(x_1) }); + const right = Fp2.add(Fp2.pow(x, 3n), b); // y² = x³ + 4 * (u+1) = x³ + b + let y = Fp2.sqrt(right); + const Y_bit = y.c1 === 0n ? (y.c0 * 2n) / P : (y.c1 * 2n) / P ? 1n : 0n; + y = bitS > 0 && Y_bit > 0 ? y : Fp2.negate(y); + return { x, y }; + } else if (bytes.length === 192 && !bitC) { + // Check if the infinity flag is set + if ((bytes[0] & (1 << 6)) !== 0) { + return { x: Fp2.ZERO, y: Fp2.ZERO }; + } + const x1 = bytesToNumberBE(bytes.slice(0, Fp.BYTES)); + const x0 = bytesToNumberBE(bytes.slice(Fp.BYTES, 2 * Fp.BYTES)); + const y1 = bytesToNumberBE(bytes.slice(2 * Fp.BYTES, 3 * Fp.BYTES)); + const y0 = bytesToNumberBE(bytes.slice(3 * Fp.BYTES)); + return { x: Fp2.fromBigTuple([x0, x1]), y: Fp2.fromBigTuple([y0, y1]) }; + } else { + throw new Error('Invalid point G2, expected 96/192 bytes'); + } + }, + toBytes: (c, point, isCompressed) => { + const isZero = point.equals(c.ZERO); + const { x, y } = point; + if (isCompressed) { + const P = Fp.ORDER; + if (isZero) return concatBytes(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES)); + const flag = Boolean(y.c1 === 0n ? (y.c0 * 2n) / P : (y.c1 * 2n) / P); + // set compressed & sign bits (looks like different offsets than for G1/Fp?) + let x_1 = bitSet(x.c1, C_BIT_POS, flag); + x_1 = bitSet(x_1, S_BIT_POS, true); + return concatBytes(numberToBytesBE(x_1, Fp.BYTES), numberToBytesBE(x.c0, Fp.BYTES)); + } else { + if (isZero) return concatBytes(new Uint8Array([0x40]), new Uint8Array(4 * Fp.BYTES - 1)); // bytes[0] |= 1 << 6; + const { re: x0, im: x1 } = Fp2.reim(x); + const { re: y0, im: y1 } = Fp2.reim(y); + return concatBytes( + numberToBytesBE(x1, Fp.BYTES), + numberToBytesBE(x0, Fp.BYTES), + numberToBytesBE(y1, Fp.BYTES), + numberToBytesBE(y0, Fp.BYTES) + ); + } + }, + Signature: { + // TODO: Optimize, it's very slow because of sqrt. + decode(hex: Hex): PointType { + hex = ensureBytes(hex); + const P = Fp.ORDER; + const half = hex.length / 2; + if (half !== 48 && half !== 96) + throw new Error('Invalid compressed signature length, must be 96 or 192'); + const z1 = bytesToNumberBE(hex.slice(0, half)); + const z2 = bytesToNumberBE(hex.slice(half)); + // Indicates the infinity point + const bflag1 = bitGet(z1, I_BIT_POS); + if (bflag1 === 1n) return bls12_381.G2.Point.ZERO; + + const x1 = Fp.create(z1 & Fp.MASK); + const x2 = Fp.create(z2); + const x = Fp2.create({ c0: x2, c1: x1 }); + const y2 = Fp2.add(Fp2.pow(x, 3n), bls12_381.CURVE.G2.b); // y² = x³ + 4 + // The slow part + let y = Fp2.sqrt(y2); + if (!y) throw new Error('Failed to find a square root'); + + // Choose the y whose leftmost bit of the imaginary part is equal to the a_flag1 + // If y1 happens to be zero, then use the bit of y0 + const { re: y0, im: y1 } = Fp2.reim(y); + const aflag1 = bitGet(z1, 381); + const isGreater = y1 > 0n && (y1 * 2n) / P !== aflag1; + const isZero = y1 === 0n && (y0 * 2n) / P !== aflag1; + if (isGreater || isZero) y = Fp2.negate(y); + const point = new bls12_381.G2.Point(x, y); + point.assertValidity(); + return point; + }, + encode(point: PointType) { + // NOTE: by some reasons it was missed in bls12-381, looks like bug + point.assertValidity(); + if (point.equals(bls12_381.G2.Point.ZERO)) + return concatBytes(COMPRESSED_ZERO, numberToBytesBE(0n, Fp.BYTES)); + const { re: x0, im: x1 } = Fp2.reim(point.x); + const { re: y0, im: y1 } = Fp2.reim(point.y); + const tmp = y1 > 0n ? y1 * 2n : y0 * 2n; + const aflag1 = Boolean((tmp / Fp.ORDER) & 1n); + const z1 = bitSet(bitSet(x1, 381, aflag1), S_BIT_POS, true); + const z2 = x0; + return concatBytes(numberToBytesBE(z1, Fp.BYTES), numberToBytesBE(z2, Fp.BYTES)); + }, + }, + }, + // The BLS parameter x for BLS12-381 + x: BLS_X, + htfDefaults, + hash: sha256, + randomBytes, +}); diff --git a/curve-definitions/src/bn.ts b/curve-definitions/src/bn.ts index 1e74529..d8eda2a 100644 --- a/curve-definitions/src/bn.ts +++ b/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), diff --git a/curve-definitions/src/ed25519.ts b/curve-definitions/src/ed25519.ts index 5639245..260518b 100644 --- a/curve-definitions/src/ed25519.ts +++ b/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; - bytes[31] &= 127; - bytes[31] |= 64; + // Section 5: For X25519, in order to decode 32 random bytes as an integer scalar, + // set the three least significant bits of the first byte + 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 diff --git a/curve-definitions/src/ed448.ts b/curve-definitions/src/ed448.ts index 971fba1..da810f3 100644 --- a/curve-definitions/src/ed448.ts +++ b/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' diff --git a/curve-definitions/src/jubjub.ts b/curve-definitions/src/jubjub.ts index 209cd25..e6e48e3 100644 --- a/curve-definitions/src/jubjub.ts +++ b/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'), diff --git a/curve-definitions/src/p192.ts b/curve-definitions/src/p192.ts index 6d548a4..68238e8 100644 --- a/curve-definitions/src/p192.ts +++ b/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 diff --git a/curve-definitions/src/p224.ts b/curve-definitions/src/p224.ts index 2b8325f..072ec38 100644 --- a/curve-definitions/src/p224.ts +++ b/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 diff --git a/curve-definitions/src/p256.ts b/curve-definitions/src/p256.ts index 5e92774..a6fb43e 100644 --- a/curve-definitions/src/p256.ts +++ b/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 diff --git a/curve-definitions/src/p384.ts b/curve-definitions/src/p384.ts index 4e6a497..6f16588 100644 --- a/curve-definitions/src/p384.ts +++ b/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 diff --git a/curve-definitions/src/p521.ts b/curve-definitions/src/p521.ts index 5edf981..5cae339 100644 --- a/curve-definitions/src/p521.ts +++ b/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; diff --git a/curve-definitions/src/pasta.ts b/curve-definitions/src/pasta.ts index 427e297..1990ec9 100644 --- a/curve-definitions/src/pasta.ts +++ b/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), diff --git a/curve-definitions/src/secp256k1.ts b/curve-definitions/src/secp256k1.ts index 807868c..7733f50 100644 --- a/curve-definitions/src/secp256k1.ts +++ b/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): PointType { 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) => point.toRawBytes(true).slice(1); // Schnorr signatures are superior to ECDSA from above. // Below is Schnorr-specific code as per BIP0340. diff --git a/curve-definitions/src/stark.ts b/curve-definitions/src/stark.ts index 2c822c0..31c71e7 100644 --- a/curve-definitions/src/stark.ts +++ b/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; // 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, - getSharedSecret, + getPublicKey0x as getPublicKey, + 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(Point.fromPrivateKey(priv).toRawBytes(true).slice(1)); + return bytesToHexEth(getPublicKey0x(privateKey, 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[] { - const out: JacobianPointType[] = []; +function pedersenPrecompute(p1: JacobianPoint, p2: JacobianPoint): JacobianPoint[] { + 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( - point: JacobianPointType, - value: PedersenArg, - constants: JacobianPointType[] -) { +function pedersenSingle(point: JacobianPoint, value: PedersenArg, constants: JacobianPoint[]) { 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)); diff --git a/curve-definitions/test/bls12-381.test.js b/curve-definitions/test/bls12-381.test.js new file mode 100644 index 0000000..00cbf19 --- /dev/null +++ b/curve-definitions/test/bls12-381.test.js @@ -0,0 +1,2474 @@ +import { bls12_381 } from '../lib/bls12-381.js'; +import { should } from 'micro-should'; +import { deepStrictEqual, notDeepStrictEqual, throws } from 'assert'; +import { sha512 } from '@noble/hashes/sha512'; +import * as fc from 'fast-check'; +import { readFileSync } from 'fs'; +import zkVectors from './bls12-381/zkcrypto/converted.json' assert { type: 'json' }; +import pairingVectors from './bls12-381/go_pairing_vectors/pairing.json' assert { type: 'json' }; +import { wNAF } from '@noble/curves/group'; +const bls = bls12_381; +const { Fp2 } = bls; + +const G2_VECTORS = readFileSync('./test/bls12-381/bls12-381-g2-test-vectors.txt', 'utf-8') + .trim() + .split('\n') + .map((l) => l.split(':')); +// Vectors come from +// https://github.com/zkcrypto/bls12-381/blob/e501265cd36849a4981fe55e10dc87c38ee2213d/src/hash_to_curve/map_scalar.rs#L20 +const SCALAR_VECTORS = readFileSync('./test/bls12-381/bls12-381-scalar-test-vectors.txt', 'utf-8') + .trim() + .split('\n') + .map((l) => l.split(':')); + +// @ts-ignore +const NUM_RUNS = Number(process.env.RUNS_COUNT || 10); // reduce to 1 to shorten test time +fc.configureGlobal({ numRuns: NUM_RUNS }); + +// @ts-ignore +const CURVE_ORDER = bls.CURVE.r; + +const FC_MSG = fc.hexaString({ minLength: 64, maxLength: 64 }); +const FC_MSG_5 = fc.array(FC_MSG, { minLength: 5, maxLength: 5 }); +const FC_BIGINT = fc.bigInt(1n, CURVE_ORDER - 1n); +const FC_BIGINT_5 = fc.array(FC_BIGINT, { minLength: 5, maxLength: 5 }); +const B_192_40 = '40'.padEnd(192, '0'); +const B_384_40 = '40'.padEnd(384, '0'); // [0x40, 0, 0...] + +const getPubKey = (priv) => bls.getPublicKey(priv); + +// Fp +{ + 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.subtract(a, Fp.ZERO), a); + deepStrictEqual(Fp.subtract(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.subtract(Fp.ZERO, a), Fp.negate(a)); + deepStrictEqual(Fp.subtract(a, b), Fp.add(a, Fp.negate(b))); + deepStrictEqual(Fp.subtract(a, b), Fp.add(a, Fp.multiply(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.subtract(Fp.ZERO, a)); + deepStrictEqual(Fp.negate(a), Fp.multiply(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.multiply(a, b), Fp.multiply(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.multiply(a, Fp.multiply(b, c)), Fp.multiply(Fp.multiply(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.multiply(a, Fp.add(b, c)), Fp.add(Fp.multiply(b, a), Fp.multiply(c, a))); + }) + ); + }); + should('bls12-381/Fp/multiply/add equality', () => { + fc.assert( + fc.property(FC_BIGINT, (num) => { + const a = Fp.create(num); + deepStrictEqual(Fp.multiply(a, Fp.create(0n)), Fp.ZERO); + deepStrictEqual(Fp.multiply(a, Fp.ZERO), Fp.ZERO); + deepStrictEqual(Fp.multiply(a, Fp.create(1n)), a); + deepStrictEqual(Fp.multiply(a, Fp.ONE), a); + deepStrictEqual(Fp.multiply(a, Fp.create(2n)), Fp.add(a, a)); + deepStrictEqual(Fp.multiply(a, Fp.create(3n)), Fp.add(Fp.add(a, a), a)); + deepStrictEqual(Fp.multiply(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.multiply(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.multiply(a, a)); + deepStrictEqual(Fp.pow(a, 3n), Fp.multiply(Fp.multiply(a, a), a)); + }) + ); + }); + should('bls12-381/Fp/multiply/sqrt', () => { + let sqr1 = Fp.sqrt(Fp.create(300855555557n)); + deepStrictEqual( + sqr1 && sqr1.toString(), + '364533921369419647282142659217537440628656909375169620464770009670699095647614890229414882377952296797827799113624' + ); + 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.multiply(a, Fp.invert(b))); + }) + ); + }); +} + +// Fp2 +{ + const Fp = bls.Fp; + const Fp2 = bls.Fp2; + 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) => { + const a = Fp2.fromBigTuple([num1[0], num1[1]]); + const b = Fp2.fromBigTuple([num2[0], num2[1]]); + deepStrictEqual(Fp2.equals(a, b), num1[0] === num2[0] && num1[1] === num2[1]); + deepStrictEqual(Fp2.equals(b, a), num1[0] === num2[0] && num1[1] === num2[1]); + }) + ); + }); + 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.subtract(a, Fp2.ZERO), a); + deepStrictEqual(Fp2.subtract(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.subtract(Fp2.ZERO, a), Fp2.negate(a)); + deepStrictEqual(Fp2.subtract(a, b), Fp2.add(a, Fp2.negate(b))); + deepStrictEqual(Fp2.subtract(a, b), Fp2.add(a, Fp2.multiply(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.subtract(Fp2.ZERO, a)); + deepStrictEqual(Fp2.negate(a), Fp2.multiply(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.multiply(a, b), Fp2.multiply(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.multiply(a, Fp2.multiply(b, c)), Fp2.multiply(Fp2.multiply(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.multiply(a, Fp2.add(b, c)), + Fp2.add(Fp2.multiply(b, a), Fp2.multiply(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.multiply(a, 0n), Fp2.ZERO); + deepStrictEqual(Fp2.multiply(a, Fp2.ZERO), Fp2.ZERO); + deepStrictEqual(Fp2.multiply(a, 1n), a); + deepStrictEqual(Fp2.multiply(a, Fp2.ONE), a); + deepStrictEqual(Fp2.multiply(a, 2n), Fp2.add(a, a)); + deepStrictEqual(Fp2.multiply(a, 3n), Fp2.add(Fp2.add(a, a), a)); + deepStrictEqual(Fp2.multiply(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.multiply(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.multiply(a, a)); + deepStrictEqual(Fp2.pow(a, 3n), Fp2.multiply(Fp2.multiply(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) => { + const a = Fp2.fromBigTuple([num[0], num[1]]); + deepStrictEqual(Fp2.div(a, Fp2.fromBigTuple([1n, 0n])), a); + deepStrictEqual(Fp2.div(a, Fp2.ONE), a); + deepStrictEqual(Fp2.div(a, a), Fp2.ONE); + }) + ); + }); + 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.multiply(a, Fp2.invert(b))); + }) + ); + }); + + should('bls12-381 Fp2/frobenius', () => { + // expect(Fp2.FROBENIUS_COEFFICIENTS[0].equals(Fp.ONE)).toBe(true); + // expect( + // Fp2.FROBENIUS_COEFFICIENTS[1].equals( + // Fp.ONE.negate().pow( + // 0x0f81ae6945026025546c75a2a5240311d8ab75fac730cbcacd117de46c663f3fdebb76c445078281bf953ed363fa069bn + // ) + // ) + // ).toBe(true); + let a = Fp2.fromBigTuple([ + 0x00f8d295b2ded9dcccc649c4b9532bf3b966ce3bc2108b138b1a52e0a90f59ed11e59ea221a3b6d22d0078036923ffc7n, + 0x012d1137b8a6a8374e464dea5bcfd41eb3f8afc0ee248cadbe203411c66fb3a5946ae52d684fa7ed977df6efcdaee0dbn, + ]); + a = Fp2.frobeniusMap(a, 0); + deepStrictEqual( + Fp2.equals( + a, + Fp2.fromBigTuple([ + 0x00f8d295b2ded9dcccc649c4b9532bf3b966ce3bc2108b138b1a52e0a90f59ed11e59ea221a3b6d22d0078036923ffc7n, + 0x012d1137b8a6a8374e464dea5bcfd41eb3f8afc0ee248cadbe203411c66fb3a5946ae52d684fa7ed977df6efcdaee0dbn, + ]) + ), + true + ); + a = Fp2.frobeniusMap(a, 1); + deepStrictEqual( + Fp2.equals( + a, + Fp2.fromBigTuple([ + 0x00f8d295b2ded9dcccc649c4b9532bf3b966ce3bc2108b138b1a52e0a90f59ed11e59ea221a3b6d22d0078036923ffc7n, + 0x18d400b280d93e62fcd559cbe77bd8b8b07e9bc405608611a9109e8f3041427e8a411ad149045812228109103250c9d0n, + ]) + ), + true + ); + a = Fp2.frobeniusMap(a, 1); + deepStrictEqual( + Fp2.equals( + a, + Fp2.fromBigTuple([ + 0x00f8d295b2ded9dcccc649c4b9532bf3b966ce3bc2108b138b1a52e0a90f59ed11e59ea221a3b6d22d0078036923ffc7n, + 0x012d1137b8a6a8374e464dea5bcfd41eb3f8afc0ee248cadbe203411c66fb3a5946ae52d684fa7ed977df6efcdaee0dbn, + ]) + ), + true + ); + a = Fp2.frobeniusMap(a, 2); + deepStrictEqual( + Fp2.equals( + a, + Fp2.fromBigTuple([ + 0x00f8d295b2ded9dcccc649c4b9532bf3b966ce3bc2108b138b1a52e0a90f59ed11e59ea221a3b6d22d0078036923ffc7n, + 0x012d1137b8a6a8374e464dea5bcfd41eb3f8afc0ee248cadbe203411c66fb3a5946ae52d684fa7ed977df6efcdaee0dbn, + ]) + ), + true + ); + }); +} + +// 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.subtract(a, Fp12.ZERO), a); + deepStrictEqual(Fp12.subtract(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.subtract(Fp12.ZERO, a), Fp12.negate(a)); + deepStrictEqual(Fp12.subtract(a, b), Fp12.add(a, Fp12.negate(b))); + deepStrictEqual(Fp12.subtract(a, b), Fp12.add(a, Fp12.multiply(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.subtract(Fp12.ZERO, a)); + deepStrictEqual(Fp12.negate(a), Fp12.multiply(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.multiply(a, b), Fp12.multiply(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.multiply(a, Fp12.multiply(b, c)), + Fp12.multiply(Fp12.multiply(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.multiply(a, Fp12.add(b, c)), + Fp12.add(Fp12.multiply(b, a), Fp12.multiply(c, a)) + ); + }) + ); + }); + should('bls12-381 Fp12/multiply/add equality', () => { + fc.assert( + fc.property(FC_BIGINT_12, (num) => { + const a = Fp12.fromBigTwelve(num); + deepStrictEqual(Fp12.multiply(a, 0n), Fp12.ZERO); + deepStrictEqual(Fp12.multiply(a, Fp12.ZERO), Fp12.ZERO); + deepStrictEqual(Fp12.multiply(a, 1n), a); + deepStrictEqual(Fp12.multiply(a, Fp12.ONE), a); + deepStrictEqual(Fp12.multiply(a, 2n), Fp12.add(a, a)); + deepStrictEqual(Fp12.multiply(a, 3n), Fp12.add(Fp12.add(a, a), a)); + deepStrictEqual(Fp12.multiply(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.multiply(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.multiply(a, a)); + deepStrictEqual(Fp12.pow(a, 3n), Fp12.multiply(Fp12.multiply(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.multiply(a, Fp12.invert(b))); + }) + ); + }); +} + +// Point +{ + const Fp = bls.Fp; + const FC_BIGINT = fc.bigInt(1n, Fp.ORDER - 1n); + const PointG1 = bls.G1.Point; + const PointG2 = bls.G2.Point; + + should('bls12-381 Point/Point with Fp coordinates/Point equality', () => { + fc.assert( + fc.property( + fc.array(FC_BIGINT, { minLength: 3, maxLength: 3 }), + fc.array(FC_BIGINT, { minLength: 3, maxLength: 3 }), + ([x1, y1, z1], [x2, y2, z2]) => { + const p1 = new PointG1(Fp.create(x1), Fp.create(y1), Fp.create(z1)); + const p2 = new PointG1(Fp.create(x2), Fp.create(y2), Fp.create(z2)); + deepStrictEqual(p1.equals(p1), true); + deepStrictEqual(p2.equals(p2), true); + deepStrictEqual(p1.equals(p2), false); + deepStrictEqual(p2.equals(p1), false); + } + ) + ); + }); + should('bls12-381 Point/Point with Fp coordinates/should be placed on curve vector 1', () => { + const a = new PointG1(Fp.create(0n), Fp.create(0n)); + a.assertValidity(); + }); + should('bls12-381 Point/Point with Fp coordinates/should not be placed on curve vector 1', () => { + const a = new PointG1(Fp.create(0n), Fp.create(1n)); + throws(() => a.assertValidity()); + }); + + should('bls12-381 Point/Point with Fp coordinates/should be placed on curve vector 2', () => { + const a = new PointG1( + Fp.create( + 0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bbn + ), + Fp.create( + 0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1n + ) + ); + a.assertValidity(); + }); + should('bls12-381 Point/Point with Fp coordinates/should be placed on curve vector 3', () => { + const a = new PointG1( + Fp.create( + 3971675556538908004130084773503021351583407620890695272226385332452194486153316625183061567093226342405194446632851n + ), + Fp.create( + 1120750640227410374130508113691552487207139112596221955734902008063040284119210871734388578113045163251615428544022n + ) + ); + + a.assertValidity(); + }); + should('bls12-381 Point/Point with Fp coordinates/should not be placed on curve vector 3', () => { + const a = new PointG1( + Fp.create( + 622186380008502900120948444810967255157373993223369845903602988014033704418470621816206856882891545628885272576827n + ), + Fp.create( + 1031339409279989180383920781105371089925712739630078633497696569127911841893478548110664124341123041182605140418539n + ) + ); + throws(() => a.assertValidity()); + }); + should('bls12-381 Point/Point with Fp coordinates/should not be placed on curve vector 2', () => { + const a = new PointG1( + Fp.create( + 0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6ban + ), + Fp.create( + 0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1n + ) + ); + throws(() => a.assertValidity()); + }); + + should( + 'bls12-381 Point/Point with Fp coordinates/should be doubled and placed on curve vector 1', + () => { + const a = new PointG1( + Fp.create( + 0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bbn + ), + Fp.create( + 0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1n + ) + ); + const double = a.double(); + double.assertValidity(); + deepStrictEqual( + double, + new PointG1( + Fp.create( + 838589206289216005799424730305866328161735431124665289961769162861615689790485775997575391185127590486775437397838n + ), + Fp.create( + 3450209970729243429733164009999191867485184320918914219895632678707687208996709678363578245114137957452475385814312n + ) + ) + ); + deepStrictEqual(double, a.multiply(2n)); + deepStrictEqual(double, a.add(a)); + } + ); + should( + 'bls12-381 Point/Point with Fp coordinates/should be pdoubled and placed on curve vector 2', + () => { + const a = new PointG1( + Fp.create( + 3971675556538908004130084773503021351583407620890695272226385332452194486153316625183061567093226342405194446632851n + ), + Fp.create( + 1120750640227410374130508113691552487207139112596221955734902008063040284119210871734388578113045163251615428544022n + ) + ); + const double = a.double(); + double.assertValidity(); + deepStrictEqual( + double, + new PointG1( + Fp.create( + 2820140907397376715097155275119328764341377106900140435029293933353987248389870417008333350832041425944924730501850n + ), + Fp.create( + 405067456352079478955518177787903714844851702189644746974501225918909272447622208969148740834643073317421487969112n + ) + ) + ); + deepStrictEqual(double, a.multiply(2n)); + deepStrictEqual(double, a.add(a)); + } + ); + should('bls12-381 Point/Point with Fp coordinates/should not validate incorrect point', () => { + const x = + 499001545268060011619089734015590154568173930614466321429631711131511181286230338880376679848890024401335766847607n; + const y = + 3934582309586258715640230772291917282844636728991757779640464479794033391537662970190753981664259511166946374555673n; + + const p = new PointG1(Fp.create(x), Fp.create(y)); + throws(() => p.assertValidity()); + }); + + should('bls12-381 Point/Point with Fp2 coordinates/Point equality', () => { + fc.assert( + fc.property( + fc.array(fc.array(FC_BIGINT, { minLength: 2, maxLength: 2 }), { + minLength: 3, + maxLength: 3, + }), + fc.array(fc.array(FC_BIGINT, { minLength: 2, maxLength: 2 }), { + minLength: 3, + maxLength: 3, + }), + ([x1, y1, z1], [x2, y2, z2]) => { + const p1 = new PointG2(Fp2.fromBigTuple(x1), Fp2.fromBigTuple(y1), Fp2.fromBigTuple(z1)); + const p2 = new PointG2(Fp2.fromBigTuple(x2), Fp2.fromBigTuple(y2), Fp2.fromBigTuple(z2)); + deepStrictEqual(p1.equals(p1), true); + deepStrictEqual(p2.equals(p2), true); + deepStrictEqual(p1.equals(p2), false); + deepStrictEqual(p2.equals(p1), false); + } + ) + ); + }); + // should('bls12-381 Point/Point with Fp2 coordinates/should be placed on curve vector 1', () => { + // const a = new PointG2(Fp2.fromBigTuple([0n, 0n]), Fp2.fromBigTuple([0n, 0n])); + // a.assertValidity(); + // }); + should('bls12-381 Point/Point with Fp2 coordinates/should be placed on curve vector 2', () => { + const a = new PointG2( + Fp2.fromBigTuple([ + 0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8n, + 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7en, + ]), + Fp2.fromBigTuple([ + 0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801n, + 0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79ben, + ]), + Fp2.fromBigTuple([1n, 0n]) + ); + a.assertValidity(); + }); + should('bls12-381 Point/Point with Fp2 coordinates/should be placed on curve vector 3', () => { + const a = new PointG2( + Fp2.fromBigTuple([ + 233289878585407360737561818812172281900488265436962145913969074168503452745466655442125797664134009339799716079103n, + 1890785404699189181161569277356497622423785178845737858235714310995835974899880469355250933575450045792782146044819n, + ]), + Fp2.fromBigTuple([ + 1215754321684097939278683023199690844646077558342794977283698289191570128272085945598449054373022460634252133664610n, + 2751025411942897795042193940345989612527395984463172615380574492034129474560903255212585680112858672276592527763585n, + ]) + ); + a.assertValidity(); + }); + should( + 'bls12-381 Point/Point with Fp2 coordinates/should not be placed on curve vector 1', + () => { + const a = new PointG2( + Fp2.fromBigTuple([0n, 0n]), + Fp2.fromBigTuple([1n, 0n]), + Fp2.fromBigTuple([1n, 0n]) + ); + throws(() => a.assertValidity()); + } + ); + should( + 'bls12-381 Point/Point with Fp2 coordinates/should not be placed on curve vector 2', + () => { + const a = new PointG2( + Fp2.fromBigTuple([ + 0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4410b647ae3d1770bac0326a805bbefd48056c8c121bdb8n, + 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7en, + ]), + Fp2.fromBigTuple([ + 0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d229a695160d12c923ac9cc3baca289e193548608b82801n, + 0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79ben, + ]), + Fp2.fromBigTuple([1n, 0n]) + ); + throws(() => a.assertValidity()); + } + ); + should( + 'bls12-381 Point/Point with Fp2 coordinates/should not be placed on curve vector 3', + () => { + const a = new PointG2( + Fp2.fromBigTuple([ + 0x877d52dd65245f8908a03288adcd396f489ef87ae23fe110c5aa48bc208fbd1a0ed403df5b1ac137922b915f1f38ec37n, + 0x0cf8158b9e689553d58194f79863fe02902c5f169f0d4ddf46e23f15bb4f24304a8e26f1e5febc57b750d1c3dc4261d8n, + ]), + Fp2.fromBigTuple([ + 0x065ae9215806e8a55fd2d9ec4af9d2d448599cdb85d9080b2c9b4766434c33d103730c92c30a69d0602a8804c2a7c65fn, + 0x0e9c342d8a6d4b3a1cbd02c7bdc0e0aa304de41a04569ae33184419e66bbc0271c361c973962955ba6405f0e51beb98bn, + ]), + Fp2.fromBigTuple([ + 0x19cbaa4ee4fadc2319939b8db45c6a355bfb3755197ba74eda8534d2a2c1a2592475939877594513c326a90c11705002n, + 0x0c0d89405d4e69986559a56057851733967c50fd0b4ec75e4ce92556ae5d33567e6e1a4eb9d83b4355520ebfe0bef37cn, + ]) + ); + throws(() => a.assertValidity()); + } + ); + + should('bls12-381 Point/should be doubled and placed on curve vector 1', () => { + const a = new PointG2( + Fp2.fromBigTuple([ + 0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8n, + 0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7en, + ]), + Fp2.fromBigTuple([ + 0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801n, + 0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79ben, + ]), + Fp2.fromBigTuple([1n, 0n]) + ); + const double = a.double(); + double.assertValidity(); + deepStrictEqual( + double, + new PointG2( + Fp2.fromBigTuple([ + 3419974069068927546093595533691935972093267703063689549934039433172037728172434967174817854768758291501458544631891n, + 1586560233067062236092888871453626466803933380746149805590083683748120990227823365075019078675272292060187343402359n, + ]), + Fp2.fromBigTuple([ + 678774053046495337979740195232911687527971909891867263302465188023833943429943242788645503130663197220262587963545n, + 2374407843478705782611042739236452317510200146460567463070514850492917978226342495167066333366894448569891658583283n, + ]) + ) + ); + deepStrictEqual(double, a.multiply(2n)); + deepStrictEqual(double, a.add(a)); + }); + should('bls12-381 Point/should be doubled and placed on curve vector 2', () => { + const a = new PointG2( + Fp2.fromBigTuple([ + 233289878585407360737561818812172281900488265436962145913969074168503452745466655442125797664134009339799716079103n, + 1890785404699189181161569277356497622423785178845737858235714310995835974899880469355250933575450045792782146044819n, + ]), + Fp2.fromBigTuple([ + 1215754321684097939278683023199690844646077558342794977283698289191570128272085945598449054373022460634252133664610n, + 2751025411942897795042193940345989612527395984463172615380574492034129474560903255212585680112858672276592527763585n, + ]) + ); + const double = a.double(); + double.assertValidity(); + deepStrictEqual( + double, + new PointG2( + Fp2.fromBigTuple([ + 725284069620738622060750301926991261102335618423691881774095602348039360646278290301007111649920759181128494302803n, + 919264895242212954093039181597172832206919609583188170141409360396089107784684267919047943917330182442049667967832n, + ]), + Fp2.fromBigTuple([ + 671406920027112857569775418033910829294759327652470956866749681326509356602892160214948716653598897872184523683037n, + 3055998868118150255613397668970777574660658983679486410738349400795670735303668556065367873243198246660959891663772n, + ]) + ) + ); + deepStrictEqual(double, a.multiply(2n)); + deepStrictEqual(double, a.add(a)); + }); + const wNAF_VECTORS = [ + 0x28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4cn, + 0x13eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n, + 0x23eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n, + 0x33eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n, + 0x43eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n, + 0x53eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001n, + 0x63eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000000n, + ]; + should('bls12-381 Point/wNAF multiplication same as unsafe (G1, W=1)', () => { + let G = PointG1.BASE.negate().negate(); // create new point + G._setWindowSize(1); + for (let k of wNAF_VECTORS) { + deepStrictEqual(G.multiply(k).equals(G.multiplyUnsafe(k)), true); + } + }); + should('bls12-381 Point/wNAF multiplication same as unsafe (G1, W=4)', () => { + let G = PointG1.BASE.negate().negate(); + G._setWindowSize(4); + for (let k of wNAF_VECTORS) { + deepStrictEqual(G.multiply(k).equals(G.multiplyUnsafe(k)), true); + } + }); + should('bls12-381 Point/wNAF multiplication same as unsafe (G1, W=5)', () => { + let G = PointG1.BASE.negate().negate(); + G._setWindowSize(5); + for (let k of wNAF_VECTORS) { + deepStrictEqual(G.multiply(k).equals(G.multiplyUnsafe(k)), true); + } + }); + should('bls12-381 Point/wNAF multiplication same as unsafe (G2, W=1)', () => { + let G = PointG2.BASE.negate().negate(); + G._setWindowSize(1); + for (let k of wNAF_VECTORS) { + deepStrictEqual(G.multiply(k).equals(G.multiplyUnsafe(k)), true); + } + }); + should('bls12-381 Point/wNAF multiplication same as unsafe (G2, W=4)', () => { + let G = PointG2.BASE.negate().negate(); + G._setWindowSize(4); + for (let k of wNAF_VECTORS) { + deepStrictEqual(G.multiply(k).equals(G.multiplyUnsafe(k)), true); + } + }); + should('bls12-381 Point/wNAF multiplication same as unsafe (G2, W=5)', () => { + let G = PointG2.BASE.negate().negate(); + G._setWindowSize(5); + for (let k of wNAF_VECTORS) { + deepStrictEqual(G.multiply(k).equals(G.multiplyUnsafe(k)), true); + } + }); + should('bls12-381 Point/PSI cofactor cleaning same as multiplication', () => { + const points = [ + new PointG2( + Fp2.fromBigTuple([ + 3241532514922300496112840946857937535679746598786089852337901560508502000671236210655544891931896207857529462155216n, + 1895396002326546958606807865184627576810563909325590769826854838265038910148901969770093629785689196200738594051207n, + ]), + Fp2.fromBigTuple([ + 3837310786345067009730271578787473898123345117675361644389016087559904243233782782806882170766697501716660726009081n, + 1677898256818258755710370015632820289344925154952470675147754839082216730170149764842062980567113751550792217387778n, + ]) + ), + new PointG2( + Fp2.fromBigTuple([ + 3953605227375649587553282126565793338489478933421008011676219910137022551750442290689597974472294891051907650111197n, + 2357556650209231585002654467241659159063900268360871707630297623496109598089657193704186795702074478622917895656384n, + ]), + Fp2.fromBigTuple([ + 2495601009524620857707705364800595215702994859258454180584354350679476916692161325761009870302795857111988758374874n, + 2636356076845621042340998927146453389877292467744110912831694031602037452225656755036030562878672313329396684758868n, + ]) + ), + new PointG2( + Fp2.fromBigTuple([ + 3194353741003351193683364524319044762011830478765020903432624057794333426495229091698895944358182869251271971124925n, + 3653808358303084112668893108836368862445971143336505524596401519323087809653188999580874561318367165116767192535630n, + ]), + Fp2.fromBigTuple([ + 1293147983982604948417085455043456439133874729834486879326988078136905862300347946661594156148773025247657033069058n, + 304385694250536139727810974742746004825746444239830780412067821920180289379490776439208435270467062610041367314353n, + ]) + ), + new PointG2( + Fp2.fromBigTuple([ + 3913848356631365121633829648186849525632038637523196801515536004438620269011326037518995697522336713513734205291154n, + 2892036022910655232784554063257167431129586441456677365843329976181438736451469367386635015809932785607079312857252n, + ]), + Fp2.fromBigTuple([ + 2946839687749075245408468852956330519059225766361204396943480879518352257697157665323514637184706466306723801095265n, + 1858741481287683941330484703798096212920693492850150667744795312336588840954530505769251621475693006537257913664280n, + ]) + ), + new PointG2( + Fp2.fromBigTuple([ + 3241532514922300496112840946857937535679746598786089852337901560508502000671236210655544891931896207857529462155216n, + 1895396002326546958606807865184627576810563909325590769826854838265038910148901969770093629785689196200738594051207n, + ]), + Fp2.fromBigTuple([ + 3837310786345067009730271578787473898123345117675361644389016087559904243233782782806882170766697501716660726009081n, + 1677898256818258755710370015632820289344925154952470675147754839082216730170149764842062980567113751550792217387778n, + ]) + ), + ]; + // Use wNAF allow scalars higher than CURVE.r + const w = wNAF(bls.G2.Point, 1); + for (let p of points) { + const ours = p.clearCofactor(); + const shouldBe = w.unsafeLadder(p, bls.CURVE.G2.hEff); + deepStrictEqual(ours.equals(shouldBe), true, 'clearLast'); + } + }); +} + +// index.ts + +// bls.PointG1.BASE.clearMultiplyPrecomputes(); +// bls.PointG1.BASE.calcMultiplyPrecomputes(4); + +should('bls12-381/basic/should construct point G1 from its uncompressed form (Raw Bytes)', () => { + // Test Zero + const g1 = bls.G1.Point.fromHex(B_192_40); + deepStrictEqual(g1.x, bls.G1.Point.ZERO.x); + deepStrictEqual(g1.y, bls.G1.Point.ZERO.y); + // Test Non-Zero + const x = bls.Fp.create( + BigInt( + '0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb' + ) + ); + const y = bls.Fp.create( + BigInt( + '0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ) + ); + + const g1_ = bls.G1.Point.fromHex( + '17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ); + + deepStrictEqual(g1_.x, x); + deepStrictEqual(g1_.y, y); +}); + +should('bls12-381/basic/should construct point G1 from its uncompressed form (Hex)', () => { + // Test Zero + const g1 = bls.G1.Point.fromHex(B_192_40); + + deepStrictEqual(g1.x, bls.G1.Point.ZERO.x); + deepStrictEqual(g1.y, bls.G1.Point.ZERO.y); + // Test Non-Zero + const x = bls.Fp.create( + BigInt( + '0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb' + ) + ); + const y = bls.Fp.create( + BigInt( + '0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ) + ); + + const g1_ = bls.G1.Point.fromHex( + '17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ); + + deepStrictEqual(g1_.x, x); + deepStrictEqual(g1_.y, y); +}); + +should('bls12-381/basic/should construct point G2 from its uncompressed form (Raw Bytes)', () => { + // Test Zero + const g2 = bls.G2.Point.fromHex(B_384_40); + deepStrictEqual(g2.x, bls.G2.Point.ZERO.x, 'zero(x)'); + deepStrictEqual(g2.y, bls.G2.Point.ZERO.y, 'zero(y)'); + // Test Non-Zero + const x = Fp2.fromBigTuple([ + BigInt( + '0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8' + ), + BigInt( + '0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e' + ), + ]); + const y = Fp2.fromBigTuple([ + BigInt( + '0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ), + BigInt( + '0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be' + ), + ]); + + const g2_ = bls.G2.Point.fromHex( + '13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ); + + deepStrictEqual(g2_.x, x); + deepStrictEqual(g2_.y, y); +}); + +should('bls12-381/basic/should construct point G2 from its uncompressed form (Hex)', () => { + // Test Zero + const g2 = bls.G2.Point.fromHex(B_384_40); + + deepStrictEqual(g2.x, bls.G2.Point.ZERO.x); + deepStrictEqual(g2.y, bls.G2.Point.ZERO.y); + // Test Non-Zero + const x = Fp2.fromBigTuple([ + BigInt( + '0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8' + ), + BigInt( + '0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e' + ), + ]); + const y = Fp2.fromBigTuple([ + BigInt( + '0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ), + BigInt( + '0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be' + ), + ]); + + const g2_ = bls.G2.Point.fromHex( + '13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ); + + deepStrictEqual(g2_.x, x); + deepStrictEqual(g2_.y, y); +}); + +should('bls12-381/basic/should get uncompressed form of point G1 (Raw Bytes)', () => { + // Test Zero + deepStrictEqual(bls.G1.Point.ZERO.toHex(false), B_192_40); + // Test Non-Zero + const x = bls.Fp.create( + BigInt( + '0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb' + ) + ); + const y = bls.Fp.create( + BigInt( + '0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ) + ); + const g1 = new bls.G1.Point(x, y); + deepStrictEqual( + g1.toHex(false), + '17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ); +}); + +should('bls12-381/basic/should get uncompressed form of point G1 (Hex)', () => { + // Test Zero + deepStrictEqual(bls.G1.Point.ZERO.toHex(false), B_192_40); + // Test Non-Zero + const x = bls.Fp.create( + BigInt( + '0x17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb' + ) + ); + const y = bls.Fp.create( + BigInt( + '0x08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ) + ); + const g1 = new bls.G1.Point(x, y); + deepStrictEqual( + g1.toHex(false), + '17f1d3a73197d7942695638c4fa9ac0fc3688c4f9774b905a14e3a3f171bac586c55e83ff97a1aeffb3af00adb22c6bb08b3f481e3aaa0f1a09e30ed741d8ae4fcf5e095d5d00af600db18cb2c04b3edd03cc744a2888ae40caa232946c5e7e1' + ); +}); + +should('bls12-381/basic/should get uncompressed form of point G2 (Raw Bytes)', () => { + // Test Zero + deepStrictEqual(bls.G2.Point.ZERO.toHex(false), B_384_40); + // Test Non-Zero + const x = Fp2.fromBigTuple([ + BigInt( + '0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8' + ), + BigInt( + '0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e' + ), + ]); + const y = Fp2.fromBigTuple([ + BigInt( + '0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ), + BigInt( + '0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be' + ), + ]); + const g2 = new bls.G2.Point(x, y); + deepStrictEqual( + g2.toHex(false), + '13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ); +}); + +should('bls12-381/basic/should get uncompressed form of point G2 (Hex)', () => { + // Test Zero + deepStrictEqual(bls.G2.Point.ZERO.toHex(false), B_384_40); + + // Test Non-Zero + const x = Fp2.fromBigTuple([ + BigInt( + '0x024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb8' + ), + BigInt( + '0x13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e' + ), + ]); + const y = Fp2.fromBigTuple([ + BigInt( + '0x0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ), + BigInt( + '0x0606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be' + ), + ]); + const g2 = new bls.G2.Point(x, y); + deepStrictEqual( + g2.toHex(false), + '13e02b6052719f607dacd3a088274f65596bd0d09920b61ab5da61bbdc7f5049334cf11213945d57e5ac7d055d042b7e024aa2b2f08f0a91260805272dc51051c6e47ad4fa403b02b4510b647ae3d1770bac0326a805bbefd48056c8c121bdb80606c4a02ea734cc32acd2b02bc28b99cb3e287e85a763af267492ab572e99ab3f370d275cec1da1aaa9075ff05f79be0ce5d527727d6e118cc9cdc6da2e351aadfd9baa8cbdd3a76d429a695160d12c923ac9cc3baca289e193548608b82801' + ); +}); + +should('bls12-381/basic/should compress and decompress G1 points', async () => { + const priv = bls.G1.Point.fromPrivateKey(42n); + const publicKey = priv.toHex(true); + const decomp = bls.G1.Point.fromHex(publicKey); + deepStrictEqual(publicKey, decomp.toHex(true)); +}); +should('bls12-381/basic/should not compress and decompress zero G1 point', () => { + throws(() => bls.G1.Point.fromPrivateKey(0n)); +}); +should('bls12-381/basic/should compress and decompress G2 points', () => { + const priv = bls.G2.Point.fromPrivateKey(42n); + const publicKey = priv.toHex(true); + const decomp = bls.G2.Point.fromHex(publicKey); + deepStrictEqual(publicKey, decomp.toHex(true)); +}); +should('bls12-381/basic/should not compress and decompress zero G2 point', () => { + throws(() => bls.G2.Point.fromPrivateKey(0n)); +}); +const VALID_G1 = new bls.G1.Point( + bls.Fp.create( + 3609742242174788176010452839163620388872641749536604986743596621604118973777515189035770461528205168143692110933639n + ), + bls.Fp.create( + 1619277690257184054444116778047375363103842303863153349133480657158810226683757397206929105479676799650932070320089n + ) +); +const VALID_G1_2 = new bls.G1.Point( + bls.Fp.create( + 1206972466279728255044019580914616126536509750250979180256809997983196363639429409634110400978470384566664128085207n + ), + bls.Fp.create( + 2991142246317096160788653339959532007292638191110818490939476869616372888657136539642598243964263069435065725313423n + ) +); + +const INVALID_G1 = new bls.G1.Point( + bls.Fp.create( + 499001545268060011619089734015590154568173930614466321429631711131511181286230338880376679848890024401335766847607n + ), + bls.Fp.create( + 3934582309586258715640230772291917282844636728991757779640464479794033391537662970190753981664259511166946374555673n + ) +); + +should('bls12-381/basic/should aggregate pubkeys', () => { + const agg = bls.aggregatePublicKeys([VALID_G1, VALID_G1_2]); + deepStrictEqual( + agg.x, + 2636337749883017793009944726560363863546595464242083394883491066895536780554574413337005575305023872925406746684807n + ); + deepStrictEqual( + agg.y, + 2200256264293372104833346444532839112556752874984721583125881868863625579979779052307146195064914375388929781136724n + ); +}); + +should('bls12-381/basic/should not aggregate invalid pubkeys', () => { + throws(() => bls.aggregatePublicKeys([VALID_G1, INVALID_G1])); +}); +// should aggregate signatures + +should(`should produce correct signatures (${G2_VECTORS.length} vectors)`, async () => { + for (let vector of G2_VECTORS) { + const [priv, msg, expected] = vector; + const sig = await bls.sign(msg, priv); + deepStrictEqual(bls.utils.bytesToHex(sig), expected); + } +}); +should(`should produce correct scalars (${SCALAR_VECTORS.length} vectors)`, async () => { + const options = { + p: bls.CURVE.r, + m: 1, + expand: false, + }; + for (let vector of SCALAR_VECTORS) { + const [okmAscii, expectedHex] = vector; + const expected = BigInt('0x' + expectedHex); + const okm = new Uint8Array(okmAscii.split('').map((c) => c.charCodeAt(0))); + const scalars = await bls.utils.hashToField(okm, 1, options); + deepStrictEqual(scalars[0][0], expected); + } +}); +should('bls12-381/basic/should verify signed message', async () => { + for (let i = 0; i < NUM_RUNS; i++) { + const [priv, msg] = G2_VECTORS[i]; + const sig = await bls.sign(msg, priv); + const pub = bls.getPublicKey(priv); + const res = await bls.verify(sig, msg, pub); + deepStrictEqual(res, true); + } +}); +should('bls12-381/basic/should not verify signature with wrong message', async () => { + for (let i = 0; i < NUM_RUNS; i++) { + const [priv, msg] = G2_VECTORS[i]; + const invMsg = G2_VECTORS[i + 1][1]; + const sig = await bls.sign(msg, priv); + const pub = bls.getPublicKey(priv); + const res = await bls.verify(sig, invMsg, pub); + deepStrictEqual(res, false); + } +}); +should('bls12-381/basic/should not verify signature with wrong key', async () => { + for (let i = 0; i < NUM_RUNS; i++) { + const [priv, msg] = G2_VECTORS[i]; + const sig = await bls.sign(msg, priv); + const invPriv = G2_VECTORS[i + 1][1].padStart(64, '0'); + const invPub = bls.getPublicKey(invPriv); + const res = await bls.verify(sig, msg, invPub); + deepStrictEqual(res, false); + } +}); +should('bls12-381/basic/should verify multi-signature', async () => { + await fc.assert( + fc.asyncProperty(FC_MSG_5, FC_BIGINT_5, async (messages, privateKeys) => { + privateKeys = privateKeys.slice(0, messages.length); + messages = messages.slice(0, privateKeys.length); + const publicKey = privateKeys.map(getPubKey); + const signatures = await Promise.all( + messages.map((message, i) => bls.sign(message, privateKeys[i])) + ); + const aggregatedSignature = await bls.aggregateSignatures(signatures); + deepStrictEqual(await bls.verifyBatch(aggregatedSignature, messages, publicKey), true); + }) + ); +}); +should('bls12-381/basic/should batch verify multi-signatures', async () => { + await fc.assert( + fc.asyncProperty( + FC_MSG_5, + FC_MSG_5, + FC_BIGINT_5, + async (messages, wrongMessages, privateKeys) => { + privateKeys = privateKeys.slice(0, messages.length); + messages = messages.slice(0, privateKeys.length); + wrongMessages = messages.map((a, i) => + typeof wrongMessages[i] === 'undefined' ? a : wrongMessages[i] + ); + const publicKey = await Promise.all(privateKeys.map(getPubKey)); + const signatures = await Promise.all( + messages.map((message, i) => bls.sign(message, privateKeys[i])) + ); + const aggregatedSignature = await bls.aggregateSignatures(signatures); + deepStrictEqual( + await bls.verifyBatch(aggregatedSignature, wrongMessages, publicKey), + messages.every((m, i) => m === wrongMessages[i]) + ); + } + ) + ); +}); +should('bls12-381/basic/should not verify multi-signature with wrong public keys', async () => { + await fc.assert( + fc.asyncProperty( + FC_MSG_5, + FC_BIGINT_5, + FC_BIGINT_5, + async (messages, privateKeys, wrongPrivateKeys) => { + privateKeys = privateKeys.slice(0, messages.length); + wrongPrivateKeys = privateKeys.map((a, i) => + wrongPrivateKeys[i] !== undefined ? wrongPrivateKeys[i] : a + ); + messages = messages.slice(0, privateKeys.length); + const wrongPublicKeys = await Promise.all(wrongPrivateKeys.map(getPubKey)); + const signatures = await Promise.all( + messages.map((message, i) => bls.sign(message, privateKeys[i])) + ); + const aggregatedSignature = await bls.aggregateSignatures(signatures); + deepStrictEqual( + await bls.verifyBatch(aggregatedSignature, messages, wrongPublicKeys), + wrongPrivateKeys.every((p, i) => p === privateKeys[i]) + ); + } + ) + ); +}); +should('bls12-381/basic/should verify multi-signature as simple signature', async () => { + await fc.assert( + fc.asyncProperty(FC_MSG, FC_BIGINT_5, async (message, privateKeys) => { + const publicKey = await Promise.all(privateKeys.map(getPubKey)); + const signatures = await Promise.all( + privateKeys.map((privateKey) => bls.sign(message, privateKey)) + ); + const aggregatedSignature = await bls.aggregateSignatures(signatures); + const aggregatedPublicKey = await bls.aggregatePublicKeys(publicKey); + deepStrictEqual(await bls.verify(aggregatedSignature, message, aggregatedPublicKey), true); + }) + ); +}); +should('bls12-381/basic/should not verify wrong multi-signature as simple signature', async () => { + await fc.assert( + fc.asyncProperty(FC_MSG, FC_MSG, FC_BIGINT_5, async (message, wrongMessage, privateKeys) => { + const publicKey = await Promise.all(privateKeys.map(getPubKey)); + const signatures = await Promise.all( + privateKeys.map((privateKey) => bls.sign(message, privateKey)) + ); + const aggregatedSignature = await bls.aggregateSignatures(signatures); + const aggregatedPublicKey = await bls.aggregatePublicKeys(publicKey); + deepStrictEqual( + await bls.verify(aggregatedSignature, wrongMessage, aggregatedPublicKey), + message === wrongMessage + ); + }) + ); +}); + +// Pairing +{ + const { pairing, Fp12 } = bls; + const G1 = bls.G1.Point.BASE; + const G2 = bls.G2.Point.BASE; + + should('pairing/creates negative G1 pairing', () => { + const p1 = pairing(G1, G2); + const p2 = pairing(G1.negate(), G2); + deepStrictEqual(Fp12.multiply(p1, p2), Fp12.ONE); + }); + should('pairing/creates negative G2 pairing', () => { + const p2 = pairing(G1.negate(), G2); + const p3 = pairing(G1, G2.negate()); + deepStrictEqual(p2, p3); + }); + should('pairing/creates proper pairing output order', () => { + const p1 = pairing(G1, G2); + const p2 = Fp12.pow(p1, CURVE_ORDER); + deepStrictEqual(p2, Fp12.ONE); + }); + should('pairing/G1 billinearity', () => { + const p1 = pairing(G1, G2); + const p2 = pairing(G1.multiply(2n), G2); + deepStrictEqual(Fp12.multiply(p1, p1), p2); + }); + should('pairing/should not degenerate', () => { + const p1 = pairing(G1, G2); + const p2 = pairing(G1.multiply(2n), G2); + const p3 = pairing(G1, G2.negate()); + notDeepStrictEqual(p1, p2); + notDeepStrictEqual(p1, p3); + notDeepStrictEqual(p2, p3); + }); + should('pairing/G2 billinearity', () => { + const p1 = pairing(G1, G2); + const p2 = pairing(G1, G2.multiply(2n)); + deepStrictEqual(Fp12.multiply(p1, p1), p2); + }); + should('pairing/proper pairing composite check', () => { + const p1 = pairing(G1.multiply(37n), G2.multiply(27n)); + const p2 = pairing(G1.multiply(999n), G2); + deepStrictEqual(p1, p2); + }); + should('pairing/vectors from https://github.com/zkcrypto/pairing', () => { + const p1 = pairing(G1, G2); + deepStrictEqual( + p1, + Fp12.fromBigTwelve([ + 0x1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6n, + 0x089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170fn, + 0x1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87n, + 0x193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934fn, + 0x01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5n, + 0x018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6n, + 0x19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89dn, + 0x06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1an, + 0x11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57n, + 0x03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2n, + 0x04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3efn, + 0x0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631n, + ]) + ); + }); + should('pairing/finalExponentiate is correct', () => { + const p1 = Fp12.fromBigTwelve([ + 690392658038414015999440694435086329841032295415825549843130960252222448232974816207293269712691075396080336239827n, + 1673244384695948045466836192250093912021245353707563547917201356526057153141766171738038843400145227470982267854187n, + 2521701268183363687370344286906817113258663667920912959304741393298699171323721428784215127759799558353547063603791n, + 3390741958986800271255412688995304356725465880212612704138250878957654428361390902500149993094444529404319700338173n, + 2937610222696584007500949263676832694169290902527467459057239718838706247113927802450975619528632522479509319939064n, + 1041774303946777132837448067285334026888352159489566377408630813368450973018459091749907377030858960140758778772908n, + 3864799331679524425952286895114884847547051478975342624231897335512502423735668201254948484826445296416036052803892n, + 3824221261758382083252395717303526902028176893529557070611185581959805652254106523709848773658607700988378551642979n, + 3323164764111867304984970151558732202678135525250230081908783488276670159769559857016787572497867551292231024927968n, + 1011304421692205285006791165988839444878224012950060115964565336021949568250312574884591704110914940911299353851697n, + 2263326825947267463771741379953930448565128050766360539694662323032637428903113943692772437175107441778689006777591n, + 2975309739982292949472410540684863862532494446476557866806093059134361887381947558323102825622690771432446161524562n, + ]); + deepStrictEqual( + Fp12.finalExponentiate(p1), + Fp12.fromBigTwelve([ + 0x09d72c189ba2fd4b09b63da857f321b791b45f8ec589858bc6d41c8f4eb05244ad7a22aea1119a958d890a19f6cacedan, + 0x153f579b44547ee81c5d1603571b4776a065e86b4e3da0bba32afedafcca10f0a40005e63c9408785761da689b4b7338n, + 0x00bb1efcca23009c3638ae9ec0ee5153fa94b4edca88c3438029bcd5909e838da44483f0bfb5877609dace3bfa7d4ff3n, + 0x0c0e22bf2d593bc5b7ce484f3ff81a23a0c36725909225c1cf2f277482144951ea3fe425d2a56a91b681e11abc56c7fan, + 0x12c99e5152ab314ca6baec31cddbeff18acdac3a91c0e62de63e029bee76d775e0940408447b0fddad84b8dde9b86deen, + 0x0fe6a726b7d4947bb7bcb22a06dd4a283ce7113e956bcbb0294883046944312a72536fff08166adcfa08dfd65e4c157fn, + 0x176bfe03f017f18f7a2af0f178b5f018434ef3623da77e40d7fc78fca08299f81f6879c69026f4a7ba639463893e0708n, + 0x0282d90ee23efd9a2e0d51af8a2048bbda4517a90a24318a75d0dd6addc29b068d17e7c89a04da84b142996aa29b1516n, + 0x0c2cdf5de0889c4b55752cf839e61a81feaebf97a812c7581c8f66395868b582cbea067c9d435dabb5722913da709bffn, + 0x0741ece37d164288d7a590b3d31d9e6f26ce0797f1b99a77cd0b5eba24eae26afcb8b69f39af06e701ceaabf94c3db5en, + 0x00c9dea49cc3e1c8be938f707bbb0239e8f960fa46617877f90b3212fc3f5890999082b9c2262c8543a278136f34b5dbn, + 0x08f574e635870b8f4ad8c18d162055ab6136db296ad5f25151244e3b1ce0d81389b9d1752a46af018e8fb1ac01b683e1n, + ]) + ); + }); +} +// hashToCurve +{ + const DST = 'QUUX-V01-CS02-with-expander-SHA256-128'; + const VECTORS = [ + { + msg: '', + len: 0x20, + expected: '68a985b87eb6b46952128911f2a4412bbc302a9d759667f87f7a21d803f07235', + }, + { + msg: 'abc', + len: 0x20, + expected: 'd8ccab23b5985ccea865c6c97b6e5b8350e794e603b4b97902f53a8a0d605615', + }, + { + msg: 'abcdef0123456789', + len: 0x20, + expected: 'eff31487c770a893cfb36f912fbfcbff40d5661771ca4b2cb4eafe524333f5c1', + }, + { + msg: + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', + len: 0x20, + expected: 'b23a1d2b4d97b2ef7785562a7e8bac7eed54ed6e97e29aa51bfe3f12ddad1ff9', + }, + { + msg: + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', + len: 0x20, + expected: '4623227bcc01293b8c130bf771da8c298dede7383243dc0993d2d94823958c4c', + }, + { + msg: '', + len: 0x80, + expected: + 'af84c27ccfd45d41914fdff5df25293e221afc53d8ad2ac0' + + '6d5e3e29485dadbee0d121587713a3e0dd4d5e69e93eb7cd4f5df4' + + 'cd103e188cf60cb02edc3edf18eda8576c412b18ffb658e3dd6ec8' + + '49469b979d444cf7b26911a08e63cf31f9dcc541708d3491184472' + + 'c2c29bb749d4286b004ceb5ee6b9a7fa5b646c993f0ced', + }, + { + msg: 'abc', + len: 0x80, + expected: + 'abba86a6129e366fc877aab32fc4ffc70120d8996c88aee2' + + 'fe4b32d6c7b6437a647e6c3163d40b76a73cf6a5674ef1d890f95b' + + '664ee0afa5359a5c4e07985635bbecbac65d747d3d2da7ec2b8221' + + 'b17b0ca9dc8a1ac1c07ea6a1e60583e2cb00058e77b7b72a298425' + + 'cd1b941ad4ec65e8afc50303a22c0f99b0509b4c895f40', + }, + { + msg: 'abcdef0123456789', + len: 0x80, + expected: + 'ef904a29bffc4cf9ee82832451c946ac3c8f8058ae97d8d6' + + '29831a74c6572bd9ebd0df635cd1f208e2038e760c4994984ce73f' + + '0d55ea9f22af83ba4734569d4bc95e18350f740c07eef653cbb9f8' + + '7910d833751825f0ebefa1abe5420bb52be14cf489b37fe1a72f7d' + + 'e2d10be453b2c9d9eb20c7e3f6edc5a60629178d9478df', + }, + { + msg: + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', + len: 0x80, + expected: + '80be107d0884f0d881bb460322f0443d38bd222db8bd0b0a' + + '5312a6fedb49c1bbd88fd75d8b9a09486c60123dfa1d73c1cc3169' + + '761b17476d3c6b7cbbd727acd0e2c942f4dd96ae3da5de368d26b3' + + '2286e32de7e5a8cb2949f866a0b80c58116b29fa7fabb3ea7d520e' + + 'e603e0c25bcaf0b9a5e92ec6a1fe4e0391d1cdbce8c68a', + }, + { + msg: + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', + len: 0x80, + expected: + '546aff5444b5b79aa6148bd81728704c32decb73a3ba76e9' + + 'e75885cad9def1d06d6792f8a7d12794e90efed817d96920d72889' + + '6a4510864370c207f99bd4a608ea121700ef01ed879745ee3e4cee' + + 'f777eda6d9e5e38b90c86ea6fb0b36504ba4a45d22e86f6db5dd43' + + 'd98a294bebb9125d5b794e9d2a81181066eb954966a487', + }, + ]; + for (let i = 0; i < VECTORS.length; i++) { + const t = VECTORS[i]; + should(`hash_to_field/expand_message_xmd(SHA-256) (${i})`, async () => { + const p = await bls.utils.expandMessageXMD( + bls.utils.stringToBytes(t.msg), + bls.utils.stringToBytes(DST), + t.len + ); + deepStrictEqual(bls.utils.bytesToHex(p), t.expected); + }); + } + const LONG_DST = + 'QUUX-V01-CS02-with-expander-SHA256-128-long-DST-111111' + + '111111111111111111111111111111111111111111111111111111' + + '111111111111111111111111111111111111111111111111111111' + + '111111111111111111111111111111111111111111111111111111' + + '1111111111111111111111111111111111111111'; + const VECTORS_BIG = [ + { + msg: '', + len: 0x20, + expected: 'e8dc0c8b686b7ef2074086fbdd2f30e3f8bfbd3bdf177f73f04b97ce618a3ed3', + }, + { + msg: 'abc', + len: 0x20, + expected: '52dbf4f36cf560fca57dedec2ad924ee9c266341d8f3d6afe5171733b16bbb12', + }, + { + msg: 'abcdef0123456789', + len: 0x20, + expected: '35387dcf22618f3728e6c686490f8b431f76550b0b2c61cbc1ce7001536f4521', + }, + { + msg: + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', + len: 0x20, + expected: '01b637612bb18e840028be900a833a74414140dde0c4754c198532c3a0ba42bc', + }, + { + msg: + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', + len: 0x20, + expected: '20cce7033cabc5460743180be6fa8aac5a103f56d481cf369a8accc0c374431b', + }, + { + msg: '', + len: 0x80, + expected: + '14604d85432c68b757e485c8894db3117992fc57e0e136f7' + + '1ad987f789a0abc287c47876978e2388a02af86b1e8d1342e5ce4f' + + '7aaa07a87321e691f6fba7e0072eecc1218aebb89fb14a0662322d' + + '5edbd873f0eb35260145cd4e64f748c5dfe60567e126604bcab1a3' + + 'ee2dc0778102ae8a5cfd1429ebc0fa6bf1a53c36f55dfc', + }, + { + msg: 'abc', + len: 0x80, + expected: + '1a30a5e36fbdb87077552b9d18b9f0aee16e80181d5b951d' + + '0471d55b66684914aef87dbb3626eaabf5ded8cd0686567e503853' + + 'e5c84c259ba0efc37f71c839da2129fe81afdaec7fbdc0ccd4c794' + + '727a17c0d20ff0ea55e1389d6982d1241cb8d165762dbc39fb0cee' + + '4474d2cbbd468a835ae5b2f20e4f959f56ab24cd6fe267', + }, + { + msg: 'abcdef0123456789', + len: 0x80, + expected: + 'd2ecef3635d2397f34a9f86438d772db19ffe9924e28a1ca' + + 'f6f1c8f15603d4028f40891044e5c7e39ebb9b31339979ff33a424' + + '9206f67d4a1e7c765410bcd249ad78d407e303675918f20f26ce6d' + + '7027ed3774512ef5b00d816e51bfcc96c3539601fa48ef1c07e494' + + 'bdc37054ba96ecb9dbd666417e3de289d4f424f502a982', + }, + { + msg: + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', + len: 0x80, + expected: + 'ed6e8c036df90111410431431a232d41a32c86e296c05d42' + + '6e5f44e75b9a50d335b2412bc6c91e0a6dc131de09c43110d9180d' + + '0a70f0d6289cb4e43b05f7ee5e9b3f42a1fad0f31bac6a625b3b5c' + + '50e3a83316783b649e5ecc9d3b1d9471cb5024b7ccf40d41d1751a' + + '04ca0356548bc6e703fca02ab521b505e8e45600508d32', + }, + { + msg: + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', + len: 0x80, + expected: + '78b53f2413f3c688f07732c10e5ced29a17c6a16f717179f' + + 'fbe38d92d6c9ec296502eb9889af83a1928cd162e845b0d3c5424e' + + '83280fed3d10cffb2f8431f14e7a23f4c68819d40617589e4c4116' + + '9d0b56e0e3535be1fd71fbb08bb70c5b5ffed953d6c14bf7618b35' + + 'fc1f4c4b30538236b4b08c9fbf90462447a8ada60be495', + }, + ]; + for (let i = 0; i < VECTORS_BIG.length; i++) { + const t = VECTORS_BIG[i]; + should(`hash_to_field/expand_message_xmd(SHA-256) (long DST) (${i})`, async () => { + const p = await bls.utils.expandMessageXMD( + bls.utils.stringToBytes(t.msg), + bls.utils.stringToBytes(LONG_DST), + t.len + ); + deepStrictEqual(bls.utils.bytesToHex(p), t.expected); + }); + } + const DST_512 = 'QUUX-V01-CS02-with-expander-SHA512-256'; + const VECTORS_SHA512 = [ + { + msg: '', + len: 0x20, + expected: '6b9a7312411d92f921c6f68ca0b6380730a1a4d982c507211a90964c394179ba', + }, + { + msg: 'abc', + len: 0x20, + expected: '0da749f12fbe5483eb066a5f595055679b976e93abe9be6f0f6318bce7aca8dc', + }, + { + msg: 'abcdef0123456789', + len: 0x20, + expected: '087e45a86e2939ee8b91100af1583c4938e0f5fc6c9db4b107b83346bc967f58', + }, + { + msg: + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', + len: 0x20, + expected: '7336234ee9983902440f6bc35b348352013becd88938d2afec44311caf8356b3', + }, + { + msg: + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', + len: 0x20, + expected: '57b5f7e766d5be68a6bfe1768e3c2b7f1228b3e4b3134956dd73a59b954c66f4', + }, + { + msg: '', + len: 0x80, + expected: + '41b037d1734a5f8df225dd8c7de38f851efdb45c372887be' + + '655212d07251b921b052b62eaed99b46f72f2ef4cc96bfaf254ebb' + + 'bec091e1a3b9e4fb5e5b619d2e0c5414800a1d882b62bb5cd1778f' + + '098b8eb6cb399d5d9d18f5d5842cf5d13d7eb00a7cff859b605da6' + + '78b318bd0e65ebff70bec88c753b159a805d2c89c55961', + }, + { + msg: 'abc', + len: 0x80, + expected: + '7f1dddd13c08b543f2e2037b14cefb255b44c83cc397c178' + + '6d975653e36a6b11bdd7732d8b38adb4a0edc26a0cef4bb4521713' + + '5456e58fbca1703cd6032cb1347ee720b87972d63fbf232587043e' + + 'd2901bce7f22610c0419751c065922b488431851041310ad659e4b' + + '23520e1772ab29dcdeb2002222a363f0c2b1c972b3efe1', + }, + { + msg: 'abcdef0123456789', + len: 0x80, + expected: + '3f721f208e6199fe903545abc26c837ce59ac6fa45733f1b' + + 'aaf0222f8b7acb0424814fcb5eecf6c1d38f06e9d0a6ccfbf85ae6' + + '12ab8735dfdf9ce84c372a77c8f9e1c1e952c3a61b7567dd069301' + + '6af51d2745822663d0c2367e3f4f0bed827feecc2aaf98c949b5ed' + + '0d35c3f1023d64ad1407924288d366ea159f46287e61ac', + }, + { + msg: + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq', + len: 0x80, + expected: + 'b799b045a58c8d2b4334cf54b78260b45eec544f9f2fb5bd' + + '12fb603eaee70db7317bf807c406e26373922b7b8920fa29142703' + + 'dd52bdf280084fb7ef69da78afdf80b3586395b433dc66cde048a2' + + '58e476a561e9deba7060af40adf30c64249ca7ddea79806ee5beb9' + + 'a1422949471d267b21bc88e688e4014087a0b592b695ed', + }, + { + msg: + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa', + len: 0x80, + expected: + '05b0bfef265dcee87654372777b7c44177e2ae4c13a27f10' + + '3340d9cd11c86cb2426ffcad5bd964080c2aee97f03be1ca18e30a' + + '1f14e27bc11ebbd650f305269cc9fb1db08bf90bfc79b42a952b46' + + 'daf810359e7bc36452684784a64952c343c52e5124cd1f71d474d5' + + '197fefc571a92929c9084ffe1112cf5eea5192ebff330b', + }, + ]; + for (let i = 0; i < VECTORS_SHA512.length; i++) { + const t = VECTORS_SHA512[i]; + should(`hash_to_field/expand_message_xmd(SHA-256) (long DST) (${i})`, async () => { + const p = await bls.utils.expandMessageXMD( + bls.utils.stringToBytes(t.msg), + bls.utils.stringToBytes(DST_512), + t.len, + sha512 + ); + deepStrictEqual(bls.utils.bytesToHex(p), t.expected); + }); + } + + // Point G1 + const VECTORS_G1 = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '0576730ab036cbac1d95b38dca905586f28d0a59048db4e8778782d89bff856ddef89277ead5a21e2975c4a6e3d8c79e' + + '1273e568bebf1864393c517f999b87c1eaa1b8432f95aea8160cd981b5b05d8cd4a7cf00103b6ef87f728e4b547dd7ae', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '061daf0cc00d8912dac1d4cf5a7c32fca97f8b3bf3f805121888e5eb89f77f9a9f406569027ac6d0e61b1229f42c43d6' + + '0de1601e5ba02cb637c1d35266f5700acee9850796dc88e860d022d7b9e7e3dce5950952e97861e5bb16d215c87f030d', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '0fb3455436843e76079c7cf3dfef75e5a104dfe257a29a850c145568d500ad31ccfe79be9ae0ea31a722548070cf98cd' + + '177989f7e2c751658df1b26943ee829d3ebcf131d8f805571712f3a7527ee5334ecff8a97fc2a50cea86f5e6212e9a57', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '0514af2137c1ae1d78d5cb97ee606ea142824c199f0f25ac463a0c78200de57640d34686521d3e9cf6b3721834f8a038' + + '047a85d6898416a0899e26219bca7c4f0fa682717199de196b02b95eaf9fb55456ac3b810e78571a1b7f5692b7c58ab6', + }, + ]; + for (let i = 0; i < VECTORS_G1.length; i++) { + const t = VECTORS_G1[i]; + should(`hashToCurve/G1 Killic (${i})`, async () => { + const p = await bls.G1.Point.hashToCurve(t.msg, { + DST: 'BLS12381G1_XMD:SHA-256_SSWU_RO_TESTGEN', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } + const VECTORS_G1_RO = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '052926add2207b76ca4fa57a8734416c8dc95e24501772c814278700eed6d1e4e8cf62d9c09db0fac349612b759e79a1' + + '08ba738453bfed09cb546dbb0783dbb3a5f1f566ed67bb6be0e8c67e2e81a4cc68ee29813bb7994998f3eae0c9c6a265', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '03567bc5ef9c690c2ab2ecdf6a96ef1c139cc0b2f284dca0a9a7943388a49a3aee664ba5379a7655d3c68900be2f6903' + + '0b9c15f3fe6e5cf4211f346271d7b01c8f3b28be689c8429c85b67af215533311f0b8dfaaa154fa6b88176c229f2885d', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '11e0b079dea29a68f0383ee94fed1b940995272407e3bb916bbf268c263ddd57a6a27200a784cbc248e84f357ce82d98' + + '03a87ae2caf14e8ee52e51fa2ed8eefe80f02457004ba4d486d6aa1f517c0889501dc7413753f9599b099ebcbbd2d709', + }, + { + msg: bls.utils.stringToBytes( + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + ), + expected: + '15f68eaa693b95ccb85215dc65fa81038d69629f70aeee0d0f677cf22285e7bf58d7cb86eefe8f2e9bc3f8cb84fac488' + + '1807a1d50c29f430b8cafc4f8638dfeeadf51211e1602a5f184443076715f91bb90a48ba1e370edce6ae1062f5e6dd38', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '082aabae8b7dedb0e78aeb619ad3bfd9277a2f77ba7fad20ef6aabdc6c31d19ba5a6d12283553294c1825c4b3ca2dcfe' + + '05b84ae5a942248eea39e1d91030458c40153f3b654ab7872d779ad1e942856a20c438e8d99bc8abfbf74729ce1f7ac8', + }, + ]; + for (let i = 0; i < VECTORS_G1_RO.length; i++) { + const t = VECTORS_G1_RO[i]; + should(`hashToCurve/G1 (BLS12381G1_XMD:SHA-256_SSWU_RO_) (${i})`, async () => { + const p = await bls.G1.Point.hashToCurve(t.msg, { + DST: 'QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_RO_', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } + const VECTORS_G1_NU = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '184bb665c37ff561a89ec2122dd343f20e0f4cbcaec84e3c3052ea81d1834e192c426074b02ed3dca4e7676ce4ce48ba' + + '04407b8d35af4dacc809927071fc0405218f1401a6d15af775810e4e460064bcc9468beeba82fdc751be70476c888bf3', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '009769f3ab59bfd551d53a5f846b9984c59b97d6842b20a2c565baa167945e3d026a3755b6345df8ec7e6acb6868ae6d' + + '1532c00cf61aa3d0ce3e5aa20c3b531a2abd2c770a790a2613818303c6b830ffc0ecf6c357af3317b9575c567f11cd2c', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '1974dbb8e6b5d20b84df7e625e2fbfecb2cdb5f77d5eae5fb2955e5ce7313cae8364bc2fff520a6c25619739c6bdcb6a' + + '15f9897e11c6441eaa676de141c8d83c37aab8667173cbe1dfd6de74d11861b961dccebcd9d289ac633455dfcc7013a3', + }, + { + msg: bls.utils.stringToBytes( + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + ), + expected: + '0a7a047c4a8397b3446450642c2ac64d7239b61872c9ae7a59707a8f4f950f101e766afe58223b3bff3a19a7f754027c' + + '1383aebba1e4327ccff7cf9912bda0dbc77de048b71ef8c8a81111d71dc33c5e3aa6edee9cf6f5fe525d50cc50b77cc9', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '0e7a16a975904f131682edbb03d9560d3e48214c9986bd50417a77108d13dc957500edf96462a3d01e62dc6cd468ef11' + + '0ae89e677711d05c30a48d6d75e76ca9fb70fe06c6dd6ff988683d89ccde29ac7d46c53bb97a59b1901abf1db66052db', + }, + ]; + for (let i = 0; i < VECTORS_G1_NU.length; i++) { + const t = VECTORS_G1_NU[i]; + should(`hashToCurve/G1 (BLS12381G1_XMD:SHA-256_SSWU_NU_) (${i})`, async () => { + const p = await bls.G1.Point.encodeToCurve(t.msg, { + DST: 'QUUX-V01-CS02-with-BLS12381G1_XMD:SHA-256_SSWU_NU_', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } + const VECTORS_ENCODE_G1 = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '1223effdbb2d38152495a864d78eee14cb0992d89a241707abb03819a91a6d2fd65854ab9a69e9aacb0cbebfd490732c' + + '0f925d61e0b235ecd945cbf0309291878df0d06e5d80d6b84aa4ff3e00633b26f9a7cb3523ef737d90e6d71e8b98b2d5', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '179d3fd0b4fb1da43aad06cea1fb3f828806ddb1b1fa9424b1e3944dfdbab6e763c42636404017da03099af0dcca0fd6' + + '0d037cb1c6d495c0f5f22b061d23f1be3d7fe64d3c6820cfcd99b6b36fa69f7b4c1f4addba2ae7aa46fb25901ab483e4', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '15aa66c77eded1209db694e8b1ba49daf8b686733afaa7b68c683d0b01788dfb0617a2e2d04c0856db4981921d3004af' + + '0952bb2f61739dd1d201dd0a79d74cda3285403d47655ee886afe860593a8a4e51c5b77a22d2133e3a4280eaaaa8b788', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '06328ce5106e837935e8da84bd9af473422e62492930aa5f460369baad9545defa468d9399854c23a75495d2a80487ee' + + '094bfdfe3e552447433b5a00967498a3f1314b86ce7a7164c8a8f4131f99333b30a574607e301d5f774172c627fd0bca', + }, + ]; + for (let i = 0; i < VECTORS_ENCODE_G1.length; i++) { + const t = VECTORS_ENCODE_G1[i]; + should(`hashToCurve/G1 (Killic, encodeToCurve) (${i})`, async () => { + const p = await bls.G1.Point.encodeToCurve(t.msg, { + DST: 'BLS12381G1_XMD:SHA-256_SSWU_NU_TESTGEN', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } + // Point G2 + const VECTORS_G2 = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '0fbdae26f9f9586a46d4b0b70390d09064ef2afe5c99348438a3c7d9756471e015cb534204c1b6824617a85024c772dc' + + '0a650bd36ae7455cb3fe5d8bb1310594551456f5c6593aec9ee0c03d2f6cb693bd2c5e99d4e23cbaec767609314f51d3' + + '02e5cf8f9b7348428cc9e66b9a9b36fe45ba0b0a146290c3a68d92895b1af0e1f2d9f889fb412670ae8478d8abd4c5aa' + + '0d8d49e7737d8f9fc5cef7c4b8817633103faf2613016cb86a1f3fc29968fe2413e232d9208d2d74a89bf7a48ac36f83', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '03578447618463deb106b60e609c6f7cc446dc6035f84a72801ba17c94cd800583b493b948eff0033f09086fdd7f6175' + + '1953ce6d4267939c7360756d9cca8eb34aac4633ef35369a7dc249445069888e7d1b3f9d2e75fbd468fbcbba7110ea02' + + '0184d26779ae9d4670aca9b267dbd4d3b30443ad05b8546d36a195686e1ccc3a59194aea05ed5bce7c3144a29ec047c4' + + '0882ab045b8fe4d7d557ebb59a63a35ac9f3d312581b509af0f8eaa2960cbc5e1e36bb969b6e22980b5cbdd0787fcf4e', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '195fad48982e186ce3c5c82133aefc9b26d55979b6f530992a8849d4263ec5d57f7a181553c8799bcc83da44847bdc8d' + + '17b461fc3b96a30c2408958cbfa5f5927b6063a8ad199d5ebf2d7cdeffa9c20c85487204804fab53f950b2f87db365aa' + + '005cdf3d984e3391e7e969276fb4bc02323c5924a4449af167030d855acc2600cf3d4fab025432c6d868c79571a95bef' + + '174a3473a3af2d0302b9065e895ca4adba4ece6ce0b41148ba597001abb152f852dd9a96fb45c9de0a43d944746f833e', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '123b6bd9feeba26dd4ad00f8bfda2718c9700dc093ea5287d7711844644eb981848316d3f3f57d5d3a652c6cdc816aca' + + '0a162306f3b0f2bb326f0c4fb0e1fea020019c3af796dcd1d7264f50ddae94cacf3cade74603834d44b9ab3d5d0a6c98' + + '05483f3b96d9252dd4fc0868344dfaf3c9d145e3387db23fa8e449304fab6a7b6ec9c15f05c0a1ea66ff0efcc03e001a' + + '15c1d4f1a685bb63ee67ca1fd96155e3d091e852a684b78d085fd34f6091e5249ddddbdcf2e7ec82ce6c04c63647eeb7', + }, + ]; + for (let i = 0; i < VECTORS_G2.length; i++) { + const t = VECTORS_G2[i]; + should(`hashToCurve/G2 Killic (${i})`, async () => { + const p = await bls.G2.Point.hashToCurve(t.msg, { + DST: 'BLS12381G2_XMD:SHA-256_SSWU_RO_TESTGEN', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } + const VECTORS_G2_RO = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '05cb8437535e20ecffaef7752baddf98034139c38452458baeefab379ba13dff5bf5dd71b72418717047f5b0f37da03d' + + '0141ebfbdca40eb85b87142e130ab689c673cf60f1a3e98d69335266f30d9b8d4ac44c1038e9dcdd5393faf5c41fb78a' + + '12424ac32561493f3fe3c260708a12b7c620e7be00099a974e259ddc7d1f6395c3c811cdd19f1e8dbf3e9ecfdcbab8d6' + + '0503921d7f6a12805e72940b963c0cf3471c7b2a524950ca195d11062ee75ec076daf2d4bc358c4b190c0c98064fdd92', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '139cddbccdc5e91b9623efd38c49f81a6f83f175e80b06fc374de9eb4b41dfe4ca3a230ed250fbe3a2acf73a41177fd8' + + '02c2d18e033b960562aae3cab37a27ce00d80ccd5ba4b7fe0e7a210245129dbec7780ccc7954725f4168aff2787776e6' + + '00aa65dae3c8d732d10ecd2c50f8a1baf3001578f71c694e03866e9f3d49ac1e1ce70dd94a733534f106d4cec0eddd16' + + '1787327b68159716a37440985269cf584bcb1e621d3a7202be6ea05c4cfe244aeb197642555a0645fb87bf7466b2ba48', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '190d119345b94fbd15497bcba94ecf7db2cbfd1e1fe7da034d26cbba169fb3968288b3fafb265f9ebd380512a71c3f2c' + + '121982811d2491fde9ba7ed31ef9ca474f0e1501297f68c298e9f4c0028add35aea8bb83d53c08cfc007c1e005723cd0' + + '0bb5e7572275c567462d91807de765611490205a941a5a6af3b1691bfe596c31225d3aabdf15faff860cb4ef17c7c3be' + + '05571a0f8d3c08d094576981f4a3b8eda0a8e771fcdcc8ecceaf1356a6acf17574518acb506e435b639353c2e14827c8', + }, + { + msg: bls.utils.stringToBytes( + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + ), + expected: + '0934aba516a52d8ae479939a91998299c76d39cc0c035cd18813bec433f587e2d7a4fef038260eef0cef4d02aae3eb91' + + '19a84dd7248a1066f737cc34502ee5555bd3c19f2ecdb3c7d9e24dc65d4e25e50d83f0f77105e955d78f4762d33c17da' + + '09bcccfa036b4847c9950780733633f13619994394c23ff0b32fa6b795844f4a0673e20282d07bc69641cee04f5e5662' + + '14f81cd421617428bc3b9fe25afbb751d934a00493524bc4e065635b0555084dd54679df1536101b2c979c0152d09192', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '11fca2ff525572795a801eed17eb12785887c7b63fb77a42be46ce4a34131d71f7a73e95fee3f812aea3de78b4d01569' + + '01a6ba2f9a11fa5598b2d8ace0fbe0a0eacb65deceb476fbbcb64fd24557c2f4b18ecfc5663e54ae16a84f5ab7f62534' + + '03a47f8e6d1763ba0cad63d6114c0accbef65707825a511b251a660a9b3994249ae4e63fac38b23da0c398689ee2ab52' + + '0b6798718c8aed24bc19cb27f866f1c9effcdbf92397ad6448b5c9db90d2b9da6cbabf48adc1adf59a1a28344e79d57e', + }, + ]; + for (let i = 0; i < VECTORS_G2_RO.length; i++) { + const t = VECTORS_G2_RO[i]; + should(`hashToCurve/G2 (BLS12381G2_XMD:SHA-256_SSWU_RO_) (${i})`, async () => { + const p = await bls.G2.Point.hashToCurve(t.msg, { + DST: 'QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_RO_', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } + const VECTORS_G2_NU = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '126b855e9e69b1f691f816e48ac6977664d24d99f8724868a184186469ddfd4617367e94527d4b74fc86413483afb35b' + + '00e7f4568a82b4b7dc1f14c6aaa055edf51502319c723c4dc2688c7fe5944c213f510328082396515734b6612c4e7bb7' + + '1498aadcf7ae2b345243e281ae076df6de84455d766ab6fcdaad71fab60abb2e8b980a440043cd305db09d283c895e3d' + + '0caead0fd7b6176c01436833c79d305c78be307da5f6af6c133c47311def6ff1e0babf57a0fb5539fce7ee12407b0a42', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '0296238ea82c6d4adb3c838ee3cb2346049c90b96d602d7bb1b469b905c9228be25c627bffee872def773d5b2a2eb57d' + + '108ed59fd9fae381abfd1d6bce2fd2fa220990f0f837fa30e0f27914ed6e1454db0d1ee957b219f61da6ff8be0d6441f' + + '153606c417e59fb331b7ae6bce4fbf7c5190c33ce9402b5ebe2b70e44fca614f3f1382a3625ed5493843d0b0a652fc3f' + + '033f90f6057aadacae7963b0a0b379dd46750c1c94a6357c99b65f63b79e321ff50fe3053330911c56b6ceea08fee656', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '0da75be60fb6aa0e9e3143e40c42796edf15685cafe0279afd2a67c3dff1c82341f17effd402e4f1af240ea90f4b659b' + + '038af300ef34c7759a6caaa4e69363cafeed218a1f207e93b2c70d91a1263d375d6730bd6b6509dcac3ba5b567e85bf3' + + '0492f4fed741b073e5a82580f7c663f9b79e036b70ab3e51162359cec4e77c78086fe879b65ca7a47d34374c8315ac5e' + + '19b148cbdf163cf0894f29660d2e7bfb2b68e37d54cc83fd4e6e62c020eaa48709302ef8e746736c0e19342cc1ce3df4', + }, + { + msg: bls.utils.stringToBytes( + 'q128_qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + + 'qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq' + ), + expected: + '12c8c05c1d5fc7bfa847f4d7d81e294e66b9a78bc9953990c358945e1f042eedafce608b67fdd3ab0cb2e6e263b9b1ad' + + '0c5ae723be00e6c3f0efe184fdc0702b64588fe77dda152ab13099a3bacd3876767fa7bbad6d6fd90b3642e902b208f9' + + '11c624c56dbe154d759d021eec60fab3d8b852395a89de497e48504366feedd4662d023af447d66926a28076813dd646' + + '04e77ddb3ede41b5ec4396b7421dd916efc68a358a0d7425bddd253547f2fb4830522358491827265dfc5bcc1928a569', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + + 'aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '1565c2f625032d232f13121d3cfb476f45275c303a037faa255f9da62000c2c864ea881e2bcddd111edc4a3c0da3e88d' + + '0ea4e7c33d43e17cc516a72f76437c4bf81d8f4eac69ac355d3bf9b71b8138d55dc10fd458be115afa798b55dac34be1' + + '0f8991d2a1ad662e7b6f58ab787947f1fa607fce12dde171bc17903b012091b657e15333e11701edcf5b63ba2a561247' + + '043b6f5fe4e52c839148dc66f2b3751e69a0f6ebb3d056d6465d50d4108543ecd956e10fa1640dfd9bc0030cc2558d28', + }, + ]; + for (let i = 0; i < VECTORS_G2_NU.length; i++) { + const t = VECTORS_G2_NU[i]; + should(`hashToCurve/G2 (BLS12381G2_XMD:SHA-256_SSWU_NU_) (${i})`, async () => { + const p = await bls.G2.Point.encodeToCurve(t.msg, { + DST: 'QUUX-V01-CS02-with-BLS12381G2_XMD:SHA-256_SSWU_NU_', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } + const VECTORS_ENCODE_G2 = [ + { + msg: bls.utils.stringToBytes(''), + expected: + '0d4333b77becbf9f9dfa3ca928002233d1ecc854b1447e5a71f751c9042d000f42db91c1d6649a5e0ad22bd7bf7398b8' + + '027e4bfada0b47f9f07e04aec463c7371e68f2fd0c738cd517932ea3801a35acf09db018deda57387b0f270f7a219e4d' + + '0cc76dc777ea0d447e02a41004f37a0a7b1fafb6746884e8d9fc276716ccf47e4e0899548a2ec71c2bdf1a2a50e876db' + + '053674cba9ef516ddc218fedb37324e6c47de27f88ab7ef123b006127d738293c0277187f7e2f80a299a24d84ed03da7', + }, + { + msg: bls.utils.stringToBytes('abc'), + expected: + '18f0f87b40af67c056915dbaf48534c592524e82c1c2b50c3734d02c0172c80df780a60b5683759298a3303c5d942778' + + '09349f1cb5b2e55489dcd45a38545343451cc30a1681c57acd4fb0a6db125f8352c09f4a67eb7d1d8242cb7d3405f97b' + + '10a2ba341bc689ab947b7941ce6ef39be17acaab067bd32bd652b471ab0792c53a2bd03bdac47f96aaafe96e441f63c0' + + '02f2d9deb2c7742512f5b8230bf0fd83ea42279d7d39779543c1a43b61c885982b611f6a7a24b514995e8a098496b811', + }, + { + msg: bls.utils.stringToBytes('abcdef0123456789'), + expected: + '19808ec5930a53c7cf5912ccce1cc33f1b3dcff24a53ce1cc4cba41fd6996dbed4843ccdd2eaf6a0cd801e562718d163' + + '149fe43777d34f0d25430dea463889bd9393bdfb4932946db23671727081c629ebb98a89604f3433fba1c67d356a4af7' + + '04783e391c30c83f805ca271e353582fdf19d159f6a4c39b73acbb637a9b8ac820cfbe2738d683368a7c07ad020e3e33' + + '04c0d6793a766233b2982087b5f4a254f261003ccb3262ea7c50903eecef3e871d1502c293f9e063d7d293f6384f4551', + }, + { + msg: bls.utils.stringToBytes( + 'a512_aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa' + ), + expected: + '0b8e0094c886487870372eb6264613a6a087c7eb9804fab789be4e47a57b29eb19b1983a51165a1b5eb025865e9fc63a' + + '0804152cbf8474669ad7d1796ab92d7ca21f32d8bed70898a748ed4e4e0ec557069003732fc86866d938538a2ae95552' + + '14c80f068ece15a3936bb00c3c883966f75b4e8d9ddde809c11f781ab92d23a2d1d103ad48f6f3bb158bf3e3a4063449' + + '09e5c8242dd7281ad32c03fe4af3f19167770016255fb25ad9b67ec51d62fade31a1af101e8f6172ec2ee8857662be3a', + }, + ]; + for (let i = 0; i < VECTORS_ENCODE_G2.length; i++) { + const t = VECTORS_ENCODE_G2[i]; + should(`hashToCurve/G2 (Killic, encodeToCurve) (${i})`, async () => { + const p = await bls.G2.Point.encodeToCurve(t.msg, { + DST: 'BLS12381G2_XMD:SHA-256_SSWU_NU_TESTGEN', + }); + deepStrictEqual(p.toHex(), t.expected); + }); + } +} +// Deterministic +{ + // NOTE: Killic returns all items in reversed order, which looks strange: + // instead of `Fp2(${this.c0} + ${this.c1}×i)`; it returns `Fp2(${this.c0}×i + ${this.c1})`; + const killicHex = (lst) => + Array.from(lst) + .reverse() + .reduce((acc, i) => acc + i); + + const Fp12 = bls.Fp12; + + should('Killic based/Pairing', () => { + const t = bls.pairing(bls.G1.Point.BASE, bls.G2.Point.BASE); + deepStrictEqual( + bls.utils.bytesToHex(Fp12.toBytes(t)), + killicHex([ + '0f41e58663bf08cf068672cbd01a7ec73baca4d72ca93544deff686bfd6df543d48eaa24afe47e1efde449383b676631', + '04c581234d086a9902249b64728ffd21a189e87935a954051c7cdba7b3872629a4fafc05066245cb9108f0242d0fe3ef', + '03350f55a7aefcd3c31b4fcb6ce5771cc6a0e9786ab5973320c806ad360829107ba810c5a09ffdd9be2291a0c25a99a2', + '11b8b424cd48bf38fcef68083b0b0ec5c81a93b330ee1a677d0d15ff7b984e8978ef48881e32fac91b93b47333e2ba57', + '06fba23eb7c5af0d9f80940ca771b6ffd5857baaf222eb95a7d2809d61bfe02e1bfd1b68ff02f0b8102ae1c2d5d5ab1a', + '19f26337d205fb469cd6bd15c3d5a04dc88784fbb3d0b2dbdea54d43b2b73f2cbb12d58386a8703e0f948226e47ee89d', + '018107154f25a764bd3c79937a45b84546da634b8f6be14a8061e55cceba478b23f7dacaa35c8ca78beae9624045b4b6', + '01b2f522473d171391125ba84dc4007cfbf2f8da752f7c74185203fcca589ac719c34dffbbaad8431dad1c1fb597aaa5', + '193502b86edb8857c273fa075a50512937e0794e1e65a7617c90d8bd66065b1fffe51d7a579973b1315021ec3c19934f', + '1368bb445c7c2d209703f239689ce34c0378a68e72a6b3b216da0e22a5031b54ddff57309396b38c881c4c849ec23e87', + '089a1c5b46e5110b86750ec6a532348868a84045483c92b7af5af689452eafabf1a8943e50439f1d59882a98eaa0170f', + '1250ebd871fc0a92a7b2d83168d0d727272d441befa15c503dd8e90ce98db3e7b6d194f60839c508a84305aaca1789b6', + ]) + ); + }); + should('Killic based/Pairing (big)', () => { + let p1 = bls.G1.Point.BASE; + let p2 = bls.G2.Point.BASE; + for (let v of pairingVectors) { + deepStrictEqual( + bls.utils.bytesToHex(Fp12.toBytes(bls.pairing(p1, p2))), + // Reverse order + v.match(/.{96}/g).reverse().join('') + ); + p1 = p1.add(bls.G1.Point.BASE); + p2 = p2.add(bls.G2.Point.BASE); + } + }); + + should(`zkcrypto/G1/compressed`, () => { + let p1 = bls.G1.Point.ZERO; + for (let i = 0; i < zkVectors.G1_Compressed.length; i++) { + const t = zkVectors.G1_Compressed[i]; + const P = bls.G1.Point.fromHex(t); + deepStrictEqual(P.toHex(true), t); + deepStrictEqual(P.equals(p1), true); + deepStrictEqual(p1.toHex(true), t); + p1 = p1.add(bls.G1.Point.BASE); + if (i) { + deepStrictEqual(bls.G1.Point.BASE.multiply(BigInt(i)).toHex(true), t); + deepStrictEqual(bls.G1.Point.BASE.multiplyUnsafe(BigInt(i)).toHex(true), t); + deepStrictEqual(bls.G1.Point.BASE.multiply(BigInt(i)).toHex(true), t); + } + } + }); + should(`zkcrypto/G1/uncompressed`, () => { + let p1 = bls.G1.Point.ZERO; + for (let i = 0; i < zkVectors.G1_Uncompressed.length; i++) { + const t = zkVectors.G1_Uncompressed[i]; + const P = bls.G1.Point.fromHex(t); + deepStrictEqual(P.toHex(), t); + deepStrictEqual(P.equals(p1), true); + deepStrictEqual(p1.toHex(), t); + p1 = p1.add(bls.G1.Point.BASE); + if (i) { + deepStrictEqual(bls.G1.Point.BASE.multiply(BigInt(i)).toHex(), t); + deepStrictEqual(bls.G1.Point.BASE.multiplyUnsafe(BigInt(i)).toHex(), t); + deepStrictEqual(bls.G1.Point.BASE.multiply(BigInt(i)).toHex(), t); + } + } + }); + should(`zkcrypto/G2/compressed`, () => { + let p1 = bls.G2.Point.ZERO; + for (let i = 0; i < zkVectors.G2_Compressed.length; i++) { + const t = zkVectors.G2_Compressed[i]; + const P = bls.G2.Point.fromHex(t); + deepStrictEqual(P.toHex(true), t); + deepStrictEqual(P.equals(p1), true); + deepStrictEqual(p1.toHex(true), t); + p1 = p1.add(bls.G2.Point.BASE); + if (i) { + deepStrictEqual(bls.G2.Point.BASE.multiply(BigInt(i)).toHex(true), t); + deepStrictEqual(bls.G2.Point.BASE.multiplyUnsafe(BigInt(i)).toHex(true), t); + deepStrictEqual(bls.G2.Point.BASE.multiply(BigInt(i)).toHex(true), t); + } + } + }); + should(`zkcrypto/G2/uncompressed`, () => { + let p1 = bls.G2.Point.ZERO; + for (let i = 0; i < zkVectors.G2_Uncompressed.length; i++) { + const t = zkVectors.G2_Uncompressed[i]; + const P = bls.G2.Point.fromHex(t); + deepStrictEqual(P.toHex(), t); + deepStrictEqual(P.equals(p1), true); + deepStrictEqual(p1.toHex(), t); + p1 = p1.add(bls.G2.Point.BASE); + if (i) { + deepStrictEqual(bls.G2.Point.BASE.multiply(BigInt(i)).toHex(), t); + deepStrictEqual(bls.G2.Point.BASE.multiplyUnsafe(BigInt(i)).toHex(), t); + deepStrictEqual(bls.G2.Point.BASE.multiply(BigInt(i)).toHex(), t); + } + } + }); +} + +// ESM is broken. +import url from 'url'; +if (import.meta.url === url.pathToFileURL(process.argv[1]).href) { + should.run(); +} + +// TODO: merge Fp tests with group tests in basic diff --git a/curve-definitions/test/bls12-381/bls12-381-g2-test-vectors.txt b/curve-definitions/test/bls12-381/bls12-381-g2-test-vectors.txt new file mode 100644 index 0000000..13e12ca --- /dev/null +++ b/curve-definitions/test/bls12-381/bls12-381-g2-test-vectors.txt @@ -0,0 +1,559 @@ +db29a6e1db5d6dcb485f26c174d11dd0ab1ecc54125e31dde2949b03e925ef23::8e49a02dc374bb1702ec4c8aa514c6d72e0884d3611334ae749462eb545a4d0a6086ef0a6b1bbc5db2934d297bf766c60dbe665dfc33d3aa765d071712075b4102a71f518e16376fc58c982d30a6196fdd8319090bcb2728c9bbbd8045fc7863 +28b90deaf189015d3a325908c5e0e4bf00f84f7e639b056ff82d7e70b6eede4c:09:8647aa9680cd0cdf065b94e818ff2bb948cc97838bcee987b9bc1b76d0a0a6e0d85db4e9d75aaedfc79d4ea2733a21ae0579014de7636dd2943d45b87c82b1c66a289006b0b9767921bb8edd3f6c5c5dec0d54cd65f61513113c50cc977849e5 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+984cfc344dd7da98dc2dcbcb8427e0195989e6b06380dd7dde4d73e289e1013c:093906e014849826bb:b74fbc224468498a680c923e1e9e8b90e7e55e44ffcb7cf1d2cf5bcbac1964e238025e30565325f2a1854244fa4ab233091c298fb9d5ba2525620f900960819e21f2e3d364eeac93f82c1303a141b883d29bbf4de2796daeb41f20cc05f0cd48 +ac47cf8395c7858c34896e1501c77b1028bb00f15721d92b4208a13cad2fbdac:3c65e5bd83d0464de9:9414a283286bb2eebde7e00e5510e406e96750a3595a104b0a003fa181ca8022eb688d6ed5363711b59d86f3f0cc696d08ee7c6939b9d7ec44a8d597880e15700d6cdff0fdd76ff814797b7b928f123a8dc22425333064821992559baf7f4b4c diff --git a/curve-definitions/test/bls12-381/bls12-381-scalar-test-vectors.txt b/curve-definitions/test/bls12-381/bls12-381-scalar-test-vectors.txt new file mode 100644 index 0000000..4b61819 --- /dev/null +++ b/curve-definitions/test/bls12-381/bls12-381-scalar-test-vectors.txt @@ -0,0 +1,3 @@ +:0000000000000000000000000000000000000000000000000000000000000000 +aaaaaabbbbbbccccccddddddeeeeeeffffffgggggghhhhhh:2228450bf55d8fe62395161bd3677ff6fc28e45b89bc87e02a818eda11a8c5da +111111222222333333444444555555666666777777888888:4aa543cbd2f0c8f37f8a375ce2e383eb343e7e3405f61e438b0a15fb8899d1ae diff --git a/curve-definitions/test/bls12-381/go_pairing_vectors/go.mod b/curve-definitions/test/bls12-381/go_pairing_vectors/go.mod new file mode 100644 index 0000000..46a9f26 --- /dev/null +++ b/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 +) diff --git a/curve-definitions/test/bls12-381/go_pairing_vectors/go.sum b/curve-definitions/test/bls12-381/go_pairing_vectors/go.sum new file mode 100644 index 0000000..8641410 --- /dev/null +++ b/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= diff --git a/curve-definitions/test/bls12-381/go_pairing_vectors/pairing.json b/curve-definitions/test/bls12-381/go_pairing_vectors/pairing.json new file mode 100644 index 0000000..f66d0f9 --- /dev/null +++ b/curve-definitions/test/bls12-381/go_pairing_vectors/pairing.json @@ -0,0 +1 @@ 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"] diff --git a/curve-definitions/test/bls12-381/go_pairing_vectors/t.go b/curve-definitions/test/bls12-381/go_pairing_vectors/t.go new file mode 100644 index 0000000..b6bd9a3 --- /dev/null +++ b/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)) + +} diff --git a/curve-definitions/test/bls12-381/zkcrypto/convert.js b/curve-definitions/test/bls12-381/zkcrypto/convert.js new file mode 100644 index 0000000..8295896 --- /dev/null +++ b/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)); +})(); diff --git a/curve-definitions/test/bls12-381/zkcrypto/converted.json b/curve-definitions/test/bls12-381/zkcrypto/converted.json new file mode 100644 index 0000000..8bf8bf2 --- /dev/null +++ b/curve-definitions/test/bls12-381/zkcrypto/converted.json @@ -0,0 +1 @@ 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diff --git a/curve-definitions/test/bls12-381/zkcrypto/g1_compressed_valid_test_vectors.dat b/curve-definitions/test/bls12-381/zkcrypto/g1_compressed_valid_test_vectors.dat new file mode 100644 index 0000000..ea8cd67 Binary files /dev/null and b/curve-definitions/test/bls12-381/zkcrypto/g1_compressed_valid_test_vectors.dat differ diff --git a/curve-definitions/test/bls12-381/zkcrypto/g1_uncompressed_valid_test_vectors.dat b/curve-definitions/test/bls12-381/zkcrypto/g1_uncompressed_valid_test_vectors.dat new file mode 100644 index 0000000..86abfba Binary files /dev/null and b/curve-definitions/test/bls12-381/zkcrypto/g1_uncompressed_valid_test_vectors.dat differ diff --git a/curve-definitions/test/bls12-381/zkcrypto/g2_compressed_valid_test_vectors.dat b/curve-definitions/test/bls12-381/zkcrypto/g2_compressed_valid_test_vectors.dat new file mode 100644 index 0000000..a40bbe2 Binary files /dev/null and b/curve-definitions/test/bls12-381/zkcrypto/g2_compressed_valid_test_vectors.dat differ diff --git a/curve-definitions/test/bls12-381/zkcrypto/g2_uncompressed_valid_test_vectors.dat b/curve-definitions/test/bls12-381/zkcrypto/g2_uncompressed_valid_test_vectors.dat new file mode 100644 index 0000000..92e4bc5 Binary files /dev/null and b/curve-definitions/test/bls12-381/zkcrypto/g2_uncompressed_valid_test_vectors.dat differ diff --git a/curve-definitions/test/index.test.js b/curve-definitions/test/index.test.js index 02022a5..5269ef2 100644 --- a/curve-definitions/test/index.test.js +++ b/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(); diff --git a/curve-definitions/test/nist.test.js b/curve-definitions/test/nist.test.js index 620a191..95e5ef9 100644 --- a/curve-definitions/test/nist.test.js +++ b/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 { diff --git a/curve-definitions/test/secp256k1.test.js b/curve-definitions/test/secp256k1.test.js index 699e1be..7637646 100644 --- a/curve-definitions/test/secp256k1.test.js +++ b/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]; diff --git a/package.json b/package.json index 431807e..4e4950f 100644 --- a/package.json +++ b/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", diff --git a/src/bls.ts b/src/bls.ts new file mode 100644 index 0000000..b0a2c85 --- /dev/null +++ b/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 = { + decode(hex: Hex): PointType; + encode(point: PointType): Uint8Array; +}; + +export type CurveType = { + r: bigint; + G1: Omit, 'n'>; + G2: Omit, 'n'> & { + Signature: SignatureCoder; + }; + x: bigint; + Fp: mod.Field; + Fr: mod.Field; + Fp2: mod.Field & { + reim: (num: Fp2) => { re: bigint; im: bigint }; + multiplyByB: (num: Fp2) => Fp2; + frobeniusMap(num: Fp2, power: number): Fp2; + }; + Fp6: mod.Field; + Fp12: mod.Field & { + 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 = { + CURVE: CurveType; + Fr: mod.Field; + Fp: mod.Field; + Fp2: mod.Field; + Fp6: mod.Field; + Fp12: mod.Field; + G1: CurvePointsRes; + G2: CurvePointsRes; + Signature: SignatureCoder; + millerLoop: (ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]) => Fp12; + calcPairingPrecomputes: (x: Fp2, y: Fp2) => [Fp2, Fp2, Fp2][]; + pairing: (P: PointType, Q: PointType, withFinalExponent?: boolean) => Fp12; + getPublicKey: (privateKey: PrivKey) => Uint8Array; + sign: { + (message: Hex, privateKey: PrivKey): Uint8Array; + (message: PointType, privateKey: PrivKey): PointType; + }; + verify: ( + signature: Hex | PointType, + message: Hex | PointType, + publicKey: Hex | PointType + ) => boolean; + aggregatePublicKeys: { + (publicKeys: Hex[]): Uint8Array; + (publicKeys: PointType[]): PointType; + }; + aggregateSignatures: { + (signatures: Hex[]): Uint8Array; + (signatures: PointType[]): PointType; + }; + verifyBatch: ( + signature: Hex | PointType, + messages: (Hex | PointType)[], + publicKeys: (Hex | PointType)[] + ) => 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( + CURVE: CurveType +): CurveFn { + // 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 = {}) => + 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, + }; +} diff --git a/src/edwards.ts b/src/edwards.ts index a7646de..b1b3c23 100644 --- a/src/edwards.ts +++ b/src/edwards.ts @@ -37,7 +37,7 @@ export type CHash = { create(): any; }; -export type CurveType = BasicCurve & { +export type CurveType = BasicCurve & { // 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; - invert: (number: bigint, modulo?: bigint) => bigint; + mod: (a: 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; + const Fp = CURVE.Fp as mod.Field; 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 modP = (a: bigint) => mod.mod(a, P); + const { randomBytes } = CURVE; + 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( - points.map((p) => p.z), - P - ); + const toInv = Fp.invertBatch(points.map((p) => p.z)); 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). diff --git a/src/group.ts b/src/group.ts index 7bb1735..710be5f 100644 --- a/src/group.ts +++ b/src/group.ts @@ -23,7 +23,6 @@ export function wNAF>(c: GroupConstructor, 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>(c: GroupConstructor, 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; diff --git a/src/hashToCurve.ts b/src/hashToCurve.ts new file mode 100644 index 0000000..e54969a --- /dev/null +++ b/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(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; +} diff --git a/src/modular.ts b/src/modular.ts index 0ff6208..43ded16 100644 --- a/src/modular.ts +++ b/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. - * `a/b mod p == a * invert(b) mod p` + * Calculates Legendre symbol (a | p), which denotes the value of a^((p-1)/2) (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: -// const FIELD = {add, pow, sqrt, mul}; -// Functions will take field elements, no need for an additional class -// 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); -// Could be insecure without shape check, so it needs to be done. -// Functions could be inlined by JIT. +// Currently completly inconsistent naming: +// - readable: add, mul, sqr, sqrt, inv, div, pow, eq, sub +// - unreadable mess: addition, multiply, square, squareRoot, inversion, divide, power, equals, subtract + +export interface Field { + ORDER: bigint; + 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(field: Field) { + 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(f: Field, 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(f: Field, 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(f: Field, 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> = {} +): Readonly> { + 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 = 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); + return Object.freeze(f); +} diff --git a/src/utils.ts b/src/utils.ts index 03c5e78..5690cbf 100644 --- a/src/utils.ts +++ b/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 = { // Field over which we'll do calculations (Fp) - P: bigint; + Fp: mod.Field; // 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; - Gy: bigint; + Gx: T; + Gy: T; + // Wrap private key by curve order (% CURVE.n instead of throwing error) + wrapPrivateKey?: boolean; + // Point at infinity is perfectly valid point, but not valid public key. + // Disabled by default because of compatibility reasons with @noble/secp256k1 + allowInfinityPoint?: boolean; }; -export function validateOpts(curve: T) { - for (const i of ['P', 'n', 'h', 'Gx', 'Gy'] as const) { +export function validateOpts(curve: BasicCurve & T) { + mod.validateField(curve.Fp); + for (const i of ['n', 'h'] as const) { if (typeof curve[i] !== 'bigint') throw new Error(`Invalid curve param ${i}=${curve[i]} (${typeof curve[i]})`); } + if (!curve.Fp.isValid(curve.Gx)) throw new Error('Invalid generator X coordinate Fp element'); + if (!curve.Fp.isValid(curve.Gy)) throw new Error('Invalid generator Y coordinate Fp element'); + for (const i of ['nBitLength', 'nByteLength'] as const) { if (curve[i] === undefined) continue; // Optional if (!Number.isSafeInteger(curve[i])) @@ -38,8 +58,6 @@ export function validateOpts(curve: T) { return Object.freeze({ ...nLength(curve.n, curve.nBitLength), ...curve } as const); } -import * as mod from './modular.js'; - const hexes = Array.from({ length: 256 }, (v, i) => i.toString(16).padStart(2, '0')); export function bytesToHex(uint8a: Uint8Array): string { if (!(uint8a instanceof Uint8Array)) throw new Error('Expected Uint8Array'); @@ -133,7 +151,6 @@ export function nLength(n: bigint, nBitLength?: number) { * @param hash hash output from sha512, or a similar function * @returns valid private scalar */ -const _1n = BigInt(1); export function hashToPrivateScalar(hash: Hex, CURVE_ORDER: bigint, isLE = false): bigint { hash = ensureBytes(hash); const orderLen = nLength(CURVE_ORDER).nByteLength; @@ -150,3 +167,21 @@ export function equalBytes(b1: Uint8Array, b2: Uint8Array) { for (let i = 0; i < b1.length; i++) if (b1[i] !== b2[i]) return false; return true; } + +// Bit operations + +// Amount of bits inside bigint (Same as n.toString(2).length) +export function bitLen(n: bigint) { + let len; + for (len = 0; n > 0n; n >>= _1n, len += 1); + return len; +} +// Gets single bit at position. NOTE: first bit position is 0 (same as arrays) +// Same as !!+Array.from(n.toString(2)).reverse()[pos] +export const bitGet = (n: bigint, pos: number) => (n >> BigInt(pos)) & 1n; +// Sets single bit at position +export const bitSet = (n: bigint, pos: number, value: boolean) => + n | ((value ? _1n : _0n) << BigInt(pos)); +// Return mask for N bits (Same as BigInt(`0b${Array(i).fill('1').join('')}`)) +// Not using ** operator with bigints for old engines. +export const bitMask = (n: number) => (_2n << BigInt(n - 1)) - _1n; diff --git a/src/weierstrass.ts b/src/weierstrass.ts index db6d0fb..1ed627d 100644 --- a/src/weierstrass.ts +++ b/src/weierstrass.ts @@ -19,74 +19,34 @@ import { hexToNumber, numberToHexUnpadded, hashToPrivateScalar, - BasicCurve, - validateOpts as utilOpts, Hex, PrivKey, } from './utils.js'; +import * as utils from './utils.js'; +import { hash_to_field, htfOpts, validateHTFOpts } from './hashToCurve.js'; import { Group, GroupConstructor, wNAF } from './group.js'; -export type CHash = { - (message: Uint8Array | string): Uint8Array; - blockLen: number; - outputLen: number; - create(): any; -}; type HmacFnSync = (key: Uint8Array, ...messages: Uint8Array[]) => Uint8Array; type EndomorphismOpts = { beta: bigint; splitScalar: (k: bigint) => { k1neg: boolean; k1: bigint; k2neg: boolean; k2: bigint }; }; - -export type CurveType = BasicCurve & { +export type BasicCurve = utils.BasicCurve & { // Params: a, b - a: bigint; - b: bigint; - // Default options - lowS?: boolean; - // Hashes - hash: CHash; // Because we need outputLen for DRBG - hmac: HmacFnSync; - randomBytes: (bytesLength?: number) => Uint8Array; - truncateHash?: (hash: Uint8Array, truncateOnly?: boolean) => bigint; - // Some fields can have specialized fast case - sqrtMod?: (n: bigint) => bigint; + a: T; + b: T; // TODO: move into options? + + normalizePrivateKey?: (key: PrivKey) => PrivKey; // Endomorphism options for Koblitz curves endo?: EndomorphismOpts; + // Torsions, can be optimized via endomorphisms + isTorsionFree?: (c: JacobianConstructor, point: JacobianPointType) => boolean; + clearCofactor?: (c: JacobianConstructor, point: JacobianPointType) => JacobianPointType; + // Hash to field opts + htfDefaults?: htfOpts; + mapToCurve?: (scalar: bigint[]) => { x: T; y: T }; }; - -// Should be separate from overrides, since overrides can use information about curve (for example nBits) -function validateOpts(curve: CurveType) { - const opts = utilOpts(curve); - if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen)) - throw new Error('Invalid hash function'); - if (typeof opts.hmac !== 'function') throw new Error('Invalid hmac function'); - if (typeof opts.randomBytes !== 'function') throw new Error('Invalid randomBytes function'); - - for (const i of ['a', 'b'] as const) { - if (typeof opts[i] !== 'bigint') - throw new Error(`Invalid curve param ${i}=${opts[i]} (${typeof opts[i]})`); - } - const endo = opts.endo; - if (endo) { - if (opts.a !== _0n) { - throw new Error('Endomorphism can only be defined for Koblitz curves that have a=0'); - } - if ( - typeof endo !== 'object' || - typeof endo.beta !== 'bigint' || - typeof endo.splitScalar !== 'function' - ) { - throw new Error('Expected endomorphism with beta: bigint and splitScalar: function'); - } - } - // Set defaults - return Object.freeze({ lowS: true, ...opts } as const); -} - -// TODO: convert bits to bytes aligned to 32 bits? (224 for example) - // DER encoding utilities class DERError extends Error { constructor(message: string) { @@ -163,6 +123,556 @@ type SignOpts = { lowS?: boolean; extraEntropy?: Entropy }; * TODO: https://www.typescriptlang.org/docs/handbook/release-notes/typescript-2-7.html#unique-symbol */ +// Instance +export interface JacobianPointType extends Group> { + readonly x: T; + readonly y: T; + readonly z: T; + multiply(scalar: number | bigint, affinePoint?: PointType): JacobianPointType; + multiplyUnsafe(scalar: bigint): JacobianPointType; + toAffine(invZ?: T): PointType; +} +// Static methods +export interface JacobianConstructor extends GroupConstructor> { + new (x: T, y: T, z: T): JacobianPointType; + fromAffine(p: PointType): JacobianPointType; + toAffineBatch(points: JacobianPointType[]): PointType[]; + normalizeZ(points: JacobianPointType[]): JacobianPointType[]; +} +// Instance +export interface PointType extends Group> { + readonly x: T; + readonly y: T; + _setWindowSize(windowSize: number): void; + hasEvenY(): boolean; + toRawBytes(isCompressed?: boolean): Uint8Array; + toHex(isCompressed?: boolean): string; + assertValidity(): void; + multiplyAndAddUnsafe(Q: PointType, a: bigint, b: bigint): PointType | undefined; +} +// Static methods +export interface PointConstructor extends GroupConstructor> { + new (x: T, y: T): PointType; + fromHex(hex: Hex): PointType; + fromPrivateKey(privateKey: PrivKey): PointType; + hashToCurve(msg: Hex, options?: Partial): PointType; + encodeToCurve(msg: Hex, options?: Partial): PointType; +} + +export type CurvePointsType = BasicCurve & { + // Bytes + fromBytes: (bytes: Uint8Array) => { x: T; y: T }; + toBytes: (c: PointConstructor, point: PointType, compressed: boolean) => Uint8Array; +}; + +function validatePointOpts(curve: CurvePointsType) { + const opts = utils.validateOpts(curve); + const Fp = opts.Fp; + for (const i of ['a', 'b'] as const) { + if (!Fp.isValid(curve[i])) + throw new Error(`Invalid curve param ${i}=${opts[i]} (${typeof opts[i]})`); + } + for (const i of ['isTorsionFree', 'clearCofactor', 'mapToCurve'] as const) { + if (curve[i] === undefined) continue; // Optional + if (typeof curve[i] !== 'function') throw new Error(`Invalid ${i} function`); + } + const endo = opts.endo; + if (endo) { + if (!Fp.equals(opts.a, Fp.ZERO)) { + throw new Error('Endomorphism can only be defined for Koblitz curves that have a=0'); + } + if ( + typeof endo !== 'object' || + typeof endo.beta !== 'bigint' || + typeof endo.splitScalar !== 'function' + ) { + throw new Error('Expected endomorphism with beta: bigint and splitScalar: function'); + } + } + if (typeof opts.fromBytes !== 'function') throw new Error('Invalid fromBytes function'); + if (typeof opts.toBytes !== 'function') throw new Error('Invalid fromBytes function'); + // Requires including hashToCurve file + if (opts.htfDefaults !== undefined) validateHTFOpts(opts.htfDefaults); + // Set defaults + return Object.freeze({ ...opts } as const); +} + +export type CurvePointsRes = { + Point: PointConstructor; + JacobianPoint: JacobianConstructor; + normalizePrivateKey: (key: PrivKey) => bigint; + weierstrassEquation: (x: T) => T; + isWithinCurveOrder: (num: bigint) => boolean; +}; + +export function weierstrassPoints(opts: CurvePointsType) { + const CURVE = validatePointOpts(opts); + const Fp = CURVE.Fp; + // Lengths + // All curves has same field / group length as for now, but it can be different for other curves + const { nByteLength, nBitLength } = CURVE; + const groupLen = nByteLength; + + // Not using ** operator with bigints for old engines. + // 2n ** (8n * 32n) == 2n << (8n * 32n - 1n) + //const FIELD_MASK = _2n << (_8n * BigInt(fieldLen) - _1n); + // function numToFieldStr(num: bigint): string { + // if (typeof num !== 'bigint') throw new Error('Expected bigint'); + // if (!(_0n <= num && num < FIELD_MASK)) throw new Error(`Expected number < 2^${fieldLen * 8}`); + // return num.toString(16).padStart(2 * fieldLen, '0'); + // } + + /** + * y² = x³ + ax + b: Short weierstrass curve formula + * @returns y² + */ + function weierstrassEquation(x: T): T { + const { a, b } = CURVE; + const x2 = Fp.square(x); // x * x + const x3 = Fp.multiply(x2, x); // x2 * x + return Fp.add(Fp.add(x3, Fp.multiply(x, a)), b); // x3 + a * x + b + } + + function isWithinCurveOrder(num: bigint): boolean { + return _0n < num && num < CURVE.n; + } + + function normalizePrivateKey(key: PrivKey): bigint { + if (typeof CURVE.normalizePrivateKey === 'function') { + key = CURVE.normalizePrivateKey(key); + } + let num: bigint; + if (typeof key === 'bigint') { + num = key; + } else if (typeof key === 'number' && Number.isSafeInteger(key) && key > 0) { + num = BigInt(key); + } else if (typeof key === 'string') { + if (key.length !== 2 * groupLen) throw new Error(`Expected ${groupLen} bytes of private key`); + num = hexToNumber(key); + } else if (key instanceof Uint8Array) { + if (key.length !== groupLen) throw new Error(`Expected ${groupLen} bytes of private key`); + num = bytesToNumberBE(key); + } else { + throw new TypeError('Expected valid private key'); + } + if (CURVE.wrapPrivateKey) num = mod.mod(num, CURVE.n); + if (!isWithinCurveOrder(num)) throw new Error('Expected private key: 0 < key < n'); + return num; + } + + function normalizeScalar(num: number | bigint): bigint { + if (typeof num === 'number' && Number.isSafeInteger(num) && num > 0) return BigInt(num); + if (typeof num === 'bigint' && isWithinCurveOrder(num)) return num; + throw new TypeError('Expected valid private scalar: 0 < scalar < curve.n'); + } + + /** + * Jacobian Point works in 3d / jacobi coordinates: (x, y, z) ∋ (x=x/z², y=y/z³) + * Default Point works in 2d / affine coordinates: (x, y) + * We're doing calculations in jacobi, because its operations don't require costly inversion. + */ + class JacobianPoint implements JacobianPointType { + constructor(readonly x: T, readonly y: T, readonly z: T) {} + + static readonly BASE = new JacobianPoint(CURVE.Gx, CURVE.Gy, Fp.ONE); + static readonly ZERO = new JacobianPoint(Fp.ZERO, Fp.ONE, Fp.ZERO); + + static fromAffine(p: Point): JacobianPoint { + if (!(p instanceof Point)) { + throw new TypeError('JacobianPoint#fromAffine: expected Point'); + } + // fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0) + if (p.equals(Point.ZERO)) return JacobianPoint.ZERO; + return new JacobianPoint(p.x, p.y, Fp.ONE); + } + + /** + * Takes a bunch of Jacobian Points but executes only one + * invert on all of them. invert is very slow operation, + * so this improves performance massively. + */ + static toAffineBatch(points: JacobianPoint[]): Point[] { + const toInv = Fp.invertBatch(points.map((p) => p.z)); + return points.map((p, i) => p.toAffine(toInv[i])); + } + + static normalizeZ(points: JacobianPoint[]): JacobianPoint[] { + return JacobianPoint.toAffineBatch(points).map(JacobianPoint.fromAffine); + } + + /** + * Compare one point to another. + */ + equals(other: JacobianPoint): boolean { + if (!(other instanceof JacobianPoint)) throw new TypeError('JacobianPoint expected'); + const { x: X1, y: Y1, z: Z1 } = this; + const { x: X2, y: Y2, z: Z2 } = other; + const Z1Z1 = Fp.square(Z1); // Z1 * Z1 + const Z2Z2 = Fp.square(Z2); // Z2 * Z2 + const U1 = Fp.multiply(X1, Z2Z2); // X1 * Z2Z2 + const U2 = Fp.multiply(X2, Z1Z1); // X2 * Z1Z1 + const S1 = Fp.multiply(Fp.multiply(Y1, Z2), Z2Z2); // Y1 * Z2 * Z2Z2 + const S2 = Fp.multiply(Fp.multiply(Y2, Z1), Z1Z1); // Y2 * Z1 * Z1Z1 + return Fp.equals(U1, U2) && Fp.equals(S1, S2); + } + + /** + * Flips point to one corresponding to (x, -y) in Affine coordinates. + */ + negate(): JacobianPoint { + return new JacobianPoint(this.x, Fp.negate(this.y), this.z); + } + + // Fast algo for doubling 2 Jacobian Points. + // From: https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl + // Cost: 1M + 8S + 1*a + 10add + 2*2 + 1*3 + 1*8. + double(): JacobianPoint { + const { x: X1, y: Y1, z: Z1 } = this; + const { a } = CURVE; + // Faster algorithm: when a=0 + // From: https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l + // Cost: 2M + 5S + 6add + 3*2 + 1*3 + 1*8. + if (Fp.isZero(a)) { + const A = Fp.square(X1); // X1 * X1 + const B = Fp.square(Y1); // Y1 * Y1 + const C = Fp.square(B); // B * B + const x1b = Fp.addN(X1, B); // X1 + B + const D = Fp.multiply(Fp.subtractN(Fp.subtractN(Fp.square(x1b), A), C), _2n); // ((x1b * x1b) - A - C) * 2 + const E = Fp.multiply(A, _3n); // A * 3 + const F = Fp.square(E); // E * E + const X3 = Fp.subtract(F, Fp.multiplyN(D, _2n)); // F - 2 * D + const Y3 = Fp.subtract(Fp.multiplyN(E, Fp.subtractN(D, X3)), Fp.multiplyN(C, _8n)); // E * (D - X3) - 8 * C; + const Z3 = Fp.multiply(Fp.multiplyN(Y1, _2n), Z1); // 2 * Y1 * Z1 + return new JacobianPoint(X3, Y3, Z3); + } + const XX = Fp.square(X1); // X1 * X1 + const YY = Fp.square(Y1); // Y1 * Y1 + const YYYY = Fp.square(YY); // YY * YY + const ZZ = Fp.square(Z1); // Z1 * Z1 + const tmp1 = Fp.add(X1, YY); // X1 + YY + const S = Fp.multiply(Fp.subtractN(Fp.subtractN(Fp.square(tmp1), XX), YYYY), _2n); // 2*((X1+YY)^2-XX-YYYY) + const M = Fp.add(Fp.multiplyN(XX, _3n), Fp.multiplyN(Fp.square(ZZ), a)); // 3 * XX + a * ZZ^2 + const T = Fp.subtract(Fp.square(M), Fp.multiplyN(S, _2n)); // M^2-2*S + const X3 = T; + const Y3 = Fp.subtract(Fp.multiplyN(M, Fp.subtractN(S, T)), Fp.multiplyN(YYYY, _8n)); // M*(S-T)-8*YYYY + const y1az1 = Fp.add(Y1, Z1); // (Y1+Z1) + const Z3 = Fp.subtract(Fp.subtractN(Fp.square(y1az1), YY), ZZ); // (Y1+Z1)^2-YY-ZZ + return new JacobianPoint(X3, Y3, Z3); + } + + // Fast algo for adding 2 Jacobian Points. + // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-1998-cmo-2 + // Cost: 12M + 4S + 6add + 1*2 + // Note: 2007 Bernstein-Lange (11M + 5S + 9add + 4*2) is actually 10% slower. + add(other: JacobianPoint): JacobianPoint { + if (!(other instanceof JacobianPoint)) throw new TypeError('JacobianPoint expected'); + const { x: X1, y: Y1, z: Z1 } = this; + const { x: X2, y: Y2, z: Z2 } = other; + if (Fp.isZero(X2) || Fp.isZero(Y2)) return this; + if (Fp.isZero(X1) || Fp.isZero(Y1)) return other; + // We're using same code in equals() + const Z1Z1 = Fp.square(Z1); // Z1Z1 = Z1^2 + const Z2Z2 = Fp.square(Z2); // Z2Z2 = Z2^2; + const U1 = Fp.multiply(X1, Z2Z2); // X1 * Z2Z2 + const U2 = Fp.multiply(X2, Z1Z1); // X2 * Z1Z1 + const S1 = Fp.multiply(Fp.multiply(Y1, Z2), Z2Z2); // Y1 * Z2 * Z2Z2 + const S2 = Fp.multiply(Fp.multiply(Y2, Z1), Z1Z1); // Y2 * Z1 * Z1Z1 + const H = Fp.subtractN(U2, U1); // H = U2 - U1 + const r = Fp.subtractN(S2, S1); // S2 - S1 + // H = 0 meaning it's the same point. + if (Fp.isZero(H)) return Fp.isZero(r) ? this.double() : JacobianPoint.ZERO; + const HH = Fp.square(H); // HH = H2 + const HHH = Fp.multiply(H, HH); // HHH = H * HH + const V = Fp.multiply(U1, HH); // V = U1 * HH + const X3 = Fp.subtract(Fp.subtractN(Fp.squareN(r), HHH), Fp.multiplyN(V, _2n)); // X3 = r^2 - HHH - 2 * V; + const Y3 = Fp.subtract(Fp.multiplyN(r, Fp.subtractN(V, X3)), Fp.multiplyN(S1, HHH)); // Y3 = r * (V - X3) - S1 * HHH; + const Z3 = Fp.multiply(Fp.multiply(Z1, Z2), H); // Z3 = Z1 * Z2 * H; + return new JacobianPoint(X3, Y3, Z3); + } + + subtract(other: JacobianPoint) { + return this.add(other.negate()); + } + + /** + * Non-constant-time multiplication. Uses double-and-add algorithm. + * It's faster, but should only be used when you don't care about + * an exposed private key e.g. sig verification, which works over *public* keys. + */ + multiplyUnsafe(scalar: bigint): JacobianPoint { + const P0 = JacobianPoint.ZERO; + if (typeof scalar === 'bigint' && scalar === _0n) return P0; + // Will throw on 0 + let n = normalizeScalar(scalar); + if (n === _1n) return this; + + if (!CURVE.endo) return wnaf.unsafeLadder(this, n); + + // Apply endomorphism + let { k1neg, k1, k2neg, k2 } = CURVE.endo.splitScalar(n); + let k1p = P0; + let k2p = P0; + let d: JacobianPoint = this; + while (k1 > _0n || k2 > _0n) { + if (k1 & _1n) k1p = k1p.add(d); + if (k2 & _1n) k2p = k2p.add(d); + d = d.double(); + k1 >>= _1n; + k2 >>= _1n; + } + if (k1neg) k1p = k1p.negate(); + if (k2neg) k2p = k2p.negate(); + k2p = new JacobianPoint(Fp.multiply(k2p.x, CURVE.endo.beta), k2p.y, k2p.z); + return k1p.add(k2p); + } + + /** + * Implements w-ary non-adjacent form for calculating ec multiplication. + */ + private wNAF(n: bigint, affinePoint?: Point): { p: JacobianPoint; f: JacobianPoint } { + if (!affinePoint && this.equals(JacobianPoint.BASE)) affinePoint = Point.BASE; + const W = (affinePoint && affinePoint._WINDOW_SIZE) || 1; + // Calculate precomputes on a first run, reuse them after + let precomputes = affinePoint && pointPrecomputes.get(affinePoint); + if (!precomputes) { + precomputes = wnaf.precomputeWindow(this, W) as JacobianPoint[]; + if (affinePoint && W !== 1) { + precomputes = JacobianPoint.normalizeZ(precomputes); + pointPrecomputes.set(affinePoint, precomputes); + } + } + return wnaf.wNAF(W, precomputes, n); + } + + /** + * Constant time multiplication. + * Uses wNAF method. Windowed method may be 10% faster, + * but takes 2x longer to generate and consumes 2x memory. + * @param scalar by which the point would be multiplied + * @param affinePoint optional point ot save cached precompute windows on it + * @returns New point + */ + multiply(scalar: number | bigint, affinePoint?: Point): JacobianPoint { + let n = normalizeScalar(scalar); + + // Real point. + let point: JacobianPoint; + // Fake point, we use it to achieve constant-time multiplication. + let fake: JacobianPoint; + if (CURVE.endo) { + const { k1neg, k1, k2neg, k2 } = CURVE.endo.splitScalar(n); + let { p: k1p, f: f1p } = this.wNAF(k1, affinePoint); + let { p: k2p, f: f2p } = this.wNAF(k2, affinePoint); + k1p = wnaf.constTimeNegate(k1neg, k1p); + k2p = wnaf.constTimeNegate(k2neg, k2p); + k2p = new JacobianPoint(Fp.multiply(k2p.x, CURVE.endo.beta), k2p.y, k2p.z); + point = k1p.add(k2p); + fake = f1p.add(f2p); + } else { + const { p, f } = this.wNAF(n, affinePoint); + point = p; + fake = f; + } + // Normalize `z` for both points, but return only real one + return JacobianPoint.normalizeZ([point, fake])[0]; + } + + // Converts Jacobian point to affine (x, y) coordinates. + // Can accept precomputed Z^-1 - for example, from invertBatch. + // (x, y, z) ∋ (x=x/z², y=y/z³) + // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#scaling-z + toAffine(invZ?: T): Point { + const { x, y, z } = this; + const is0 = this.equals(JacobianPoint.ZERO); + // If invZ was 0, we return zero point. However we still want to execute + // all operations, so we replace invZ with a random number, 1. + if (invZ == null) invZ = is0 ? Fp.ONE : Fp.invert(z); + const iz1 = invZ; + const iz2 = Fp.square(iz1); // iz1 * iz1 + const iz3 = Fp.multiply(iz2, iz1); // iz2 * iz1 + const ax = Fp.multiply(x, iz2); // x * iz2 + const ay = Fp.multiply(y, iz3); // y * iz3 + const zz = Fp.multiply(z, iz1); // z * iz1 + if (is0) return Point.ZERO; + if (!Fp.equals(zz, Fp.ONE)) throw new Error('invZ was invalid'); + return new Point(ax, ay); + } + isTorsionFree(): boolean { + if (CURVE.h === _1n) return true; // No subgroups, always torsion fee + if (CURVE.isTorsionFree) return CURVE.isTorsionFree(JacobianPoint, this); + // is multiplyUnsafe(CURVE.n) is always ok, same as for edwards? + throw new Error('Unsupported!'); + } + // Clear cofactor of G1 + // https://eprint.iacr.org/2019/403 + clearCofactor(): JacobianPoint { + if (CURVE.h === _1n) return this; // Fast-path + if (CURVE.clearCofactor) return CURVE.clearCofactor(JacobianPoint, this) as JacobianPoint; + return this.multiplyUnsafe(CURVE.h); + } + } + const wnaf = wNAF(JacobianPoint, CURVE.endo ? nBitLength / 2 : nBitLength); + // Stores precomputed values for points. + const pointPrecomputes = new WeakMap(); + + /** + * Default Point works in default aka affine coordinates: (x, y) + */ + class Point implements PointType { + /** + * Base point aka generator. public_key = Point.BASE * private_key + */ + static BASE: Point = new Point(CURVE.Gx, CURVE.Gy); + /** + * Identity point aka point at infinity. point = point + zero_point + */ + static ZERO: Point = new Point(Fp.ZERO, Fp.ZERO); + + // We calculate precomputes for elliptic curve point multiplication + // using windowed method. This specifies window size and + // stores precomputed values. Usually only base point would be precomputed. + _WINDOW_SIZE?: number; + + constructor(readonly x: T, readonly y: T) {} + + // "Private method", don't use it directly + _setWindowSize(windowSize: number) { + this._WINDOW_SIZE = windowSize; + pointPrecomputes.delete(this); + } + + // Checks for y % 2 == 0 + hasEvenY(): boolean { + if (Fp.isOdd) return !Fp.isOdd(this.y); + throw new Error("Field doesn't support isOdd"); + } + + /** + * Converts hash string or Uint8Array to Point. + * @param hex short/long ECDSA hex + */ + static fromHex(hex: Hex): Point { + const { x, y } = CURVE.fromBytes(ensureBytes(hex)); + const point = new Point(x, y); + point.assertValidity(); + return point; + } + + // Multiplies generator point by privateKey. + static fromPrivateKey(privateKey: PrivKey) { + return Point.BASE.multiply(normalizePrivateKey(privateKey)); + } + + toRawBytes(isCompressed = false): Uint8Array { + this.assertValidity(); + return CURVE.toBytes(Point, this, isCompressed); + } + + toHex(isCompressed = false): string { + return bytesToHex(this.toRawBytes(isCompressed)); + } + // A point on curve is valid if it conforms to equation. + assertValidity(): void { + // Zero is valid point too! + if (this.equals(Point.ZERO)) { + if (CURVE.allowInfinityPoint) return; + throw new Error('Point is infinity'); + } + // Some 3rd-party test vectors require different wording between here & `fromCompressedHex` + const msg = 'Point is not on elliptic curve'; + const { x, y } = this; + if (!Fp.isValid(x) || !Fp.isValid(y)) throw new Error(msg); + const left = Fp.square(y); + const right = weierstrassEquation(x); + if (!Fp.equals(left, right)) throw new Error(msg); + // TODO: flag to disable this? + if (!this.isTorsionFree()) throw new Error('Point must be of prime-order subgroup'); + } + + equals(other: Point): boolean { + if (!(other instanceof Point)) throw new TypeError('Point#equals: expected Point'); + return Fp.equals(this.x, other.x) && Fp.equals(this.y, other.y); + } + + // Returns the same point with inverted `y` + negate() { + return new Point(this.x, Fp.negate(this.y)); + } + + // Adds point to itself + double() { + return JacobianPoint.fromAffine(this).double().toAffine(); + } + + // Adds point to other point + add(other: Point) { + return JacobianPoint.fromAffine(this).add(JacobianPoint.fromAffine(other)).toAffine(); + } + + // Subtracts other point from the point + subtract(other: Point) { + return this.add(other.negate()); + } + + multiply(scalar: number | bigint) { + return JacobianPoint.fromAffine(this).multiply(scalar, this).toAffine(); + } + + multiplyUnsafe(scalar: bigint) { + return JacobianPoint.fromAffine(this).multiplyUnsafe(scalar).toAffine(); + } + clearCofactor() { + return JacobianPoint.fromAffine(this).clearCofactor().toAffine(); + } + + isTorsionFree(): boolean { + return JacobianPoint.fromAffine(this).isTorsionFree(); + } + + /** + * Efficiently calculate `aP + bQ`. + * Unsafe, can expose private key, if used incorrectly. + * TODO: Utilize Shamir's trick + * @returns non-zero affine point + */ + multiplyAndAddUnsafe(Q: Point, a: bigint, b: bigint): Point | undefined { + const P = JacobianPoint.fromAffine(this); + const aP = + a === _0n || a === _1n || this !== Point.BASE ? P.multiplyUnsafe(a) : P.multiply(a); + const bQ = JacobianPoint.fromAffine(Q).multiplyUnsafe(b); + const sum = aP.add(bQ); + return sum.equals(JacobianPoint.ZERO) ? undefined : sum.toAffine(); + } + + // Encodes byte string to elliptic curve + // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-11#section-3 + static hashToCurve(msg: Hex, options?: Partial) { + if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve'); + msg = ensureBytes(msg); + const u = hash_to_field(msg, 2, { ...CURVE.htfDefaults, ...options } as htfOpts); + const { x: x0, y: y0 } = CURVE.mapToCurve(u[0]); + const { x: x1, y: y1 } = CURVE.mapToCurve(u[1]); + const p = new Point(x0, y0).add(new Point(x1, y1)).clearCofactor(); + return p; + } + // https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-hash-to-curve-16#section-3 + static encodeToCurve(msg: Hex, options?: Partial) { + if (!CURVE.mapToCurve) throw new Error('No mapToCurve defined for curve'); + msg = ensureBytes(msg); + const u = hash_to_field(msg, 1, { ...CURVE.htfDefaults, ...options } as htfOpts); + const { x, y } = CURVE.mapToCurve(u[0]); + return new Point(x, y).clearCofactor(); + } + } + return { + Point: Point as PointConstructor, + JacobianPoint: JacobianPoint as JacobianConstructor, + normalizePrivateKey, + weierstrassEquation, + isWithinCurveOrder, + }; +} + // Instance export interface SignatureType { readonly r: bigint; @@ -172,7 +682,7 @@ export interface SignatureType { copyWithRecoveryBit(recovery: number): SignatureType; hasHighS(): boolean; normalizeS(): SignatureType; - recoverPublicKey(msgHash: Hex): PointType; + recoverPublicKey(msgHash: Hex): PointType; // DER-encoded toDERRawBytes(isCompressed?: boolean): Uint8Array; toDERHex(isCompressed?: boolean): string; @@ -186,41 +696,27 @@ export type SignatureConstructor = { fromDER(hex: Hex): SignatureType; }; -// Instance -export interface JacobianPointType extends Group { - readonly x: bigint; - readonly y: bigint; - readonly z: bigint; - multiply(scalar: number | bigint, affinePoint?: PointType): JacobianPointType; - multiplyUnsafe(scalar: bigint): JacobianPointType; - toAffine(invZ?: bigint): PointType; -} -// Static methods -export interface JacobianPointConstructor extends GroupConstructor { - new (x: bigint, y: bigint, z: bigint): JacobianPointType; - fromAffine(p: PointType): JacobianPointType; - toAffineBatch(points: JacobianPointType[]): PointType[]; - normalizeZ(points: JacobianPointType[]): JacobianPointType[]; -} -// Instance -export interface PointType extends Group { - readonly x: bigint; - readonly y: bigint; - _setWindowSize(windowSize: number): void; - hasEvenY(): boolean; - toRawBytes(isCompressed?: boolean): Uint8Array; - toHex(isCompressed?: boolean): string; - assertValidity(): void; - multiplyAndAddUnsafe(Q: PointType, a: bigint, b: bigint): PointType | undefined; -} -// Static methods -export interface PointConstructor extends GroupConstructor { - new (x: bigint, y: bigint): PointType; - fromHex(hex: Hex): PointType; - fromPrivateKey(privateKey: PrivKey): PointType; -} +export type PubKey = Hex | PointType; -export type PubKey = Hex | PointType; +export type CurveType = BasicCurve & { + // Default options + lowS?: boolean; + // Hashes + hash: utils.CHash; // Because we need outputLen for DRBG + hmac: HmacFnSync; + randomBytes: (bytesLength?: number) => Uint8Array; + truncateHash?: (hash: Uint8Array, truncateOnly?: boolean) => bigint; +}; + +function validateOpts(curve: CurveType) { + const opts = utils.validateOpts(curve); + if (typeof opts.hash !== 'function' || !Number.isSafeInteger(opts.hash.outputLen)) + throw new Error('Invalid hash function'); + if (typeof opts.hmac !== 'function') throw new Error('Invalid hmac function'); + if (typeof opts.randomBytes !== 'function') throw new Error('Invalid randomBytes function'); + // Set defaults + return Object.freeze({ lowS: true, ...opts } as const); +} export type CurveFn = { CURVE: ReturnType; @@ -235,8 +731,8 @@ export type CurveFn = { lowS?: boolean; } ) => boolean; - Point: PointConstructor; - JacobianPoint: JacobianPointConstructor; + Point: PointConstructor; + JacobianPoint: JacobianConstructor; Signature: SignatureConstructor; utils: { mod: (a: bigint, b?: bigint) => bigint; @@ -244,7 +740,7 @@ export type CurveFn = { _bigintToBytes: (num: bigint) => Uint8Array; _bigintToString: (num: bigint) => string; _normalizePrivateKey: (key: PrivKey) => bigint; - _normalizePublicKey: (publicKey: PubKey) => PointType; + _normalizePublicKey: (publicKey: PubKey) => PointType; _isWithinCurveOrder: (num: bigint) => boolean; _isValidFieldElement: (num: bigint) => boolean; _weierstrassEquation: (x: bigint) => bigint; @@ -304,80 +800,67 @@ class HmacDrbg { // whether bigints are removed even if you clean Uint8Arrays. } -// Use only input from curveOpts! export function weierstrass(curveDef: CurveType): CurveFn { const CURVE = validateOpts(curveDef) as ReturnType; const CURVE_ORDER = CURVE.n; - // Lengths - // All curves has same field / group length as for now, but it can be different for other curves - const groupLen = CURVE.nByteLength; - const fieldLen = CURVE.nByteLength; // 32 (length of one field element) - if (fieldLen > 2048) throw new Error('Field lengths over 2048 are not supported'); - - const compressedLen = fieldLen + 1; // 33 - const uncompressedLen = 2 * fieldLen + 1; // 65 - // Not using ** operator with bigints for old engines. - // 2n ** (8n * 32n) == 2n << (8n * 32n - 1n) - const FIELD_MASK = _2n << (_8n * BigInt(fieldLen) - _1n); - function numToFieldStr(num: bigint): string { - if (typeof num !== 'bigint') throw new Error('Expected bigint'); - if (!(_0n <= num && num < FIELD_MASK)) throw new Error(`Expected number < 2^${fieldLen * 8}`); - return num.toString(16).padStart(2 * fieldLen, '0'); - } - - function numToField(num: bigint): Uint8Array { - const b = hexToBytes(numToFieldStr(num)); - if (b.length !== fieldLen) throw new Error(`Error: expected ${fieldLen} bytes`); - return b; - } - - function modP(n: bigint, m = CURVE.P) { - return mod.mod(n, m); - } - - /** - * y² = x³ + ax + b: Short weierstrass curve formula - * @returns y² - */ - function weierstrassEquation(x: bigint): bigint { - const { a, b } = CURVE; - const x2 = modP(x * x); - const x3 = modP(x2 * x); - return modP(x3 + a * x + b); - } - - function isWithinCurveOrder(num: bigint): boolean { - return _0n < num && num < CURVE.n; - } + const Fp = CURVE.Fp; + const compressedLen = Fp.BYTES + 1; // 33 + const uncompressedLen = 2 * Fp.BYTES + 1; // 65 function isValidFieldElement(num: bigint): boolean { - return _0n < num && num < CURVE.P; + // 0 is disallowed by arbitrary reasons. Probably because infinity point? + return _0n < num && num < Fp.ORDER; } - function normalizePrivateKey(key: PrivKey): bigint { - let num: bigint; - if (typeof key === 'bigint') { - num = key; - } else if (typeof key === 'number' && Number.isSafeInteger(key) && key > 0) { - num = BigInt(key); - } else if (typeof key === 'string') { - key = key.padStart(2 * groupLen, '0'); // Eth-like hexes - if (key.length !== 2 * groupLen) throw new Error(`Expected ${groupLen} bytes of private key`); - num = hexToNumber(key); - } else if (key instanceof Uint8Array) { - if (key.length !== groupLen) throw new Error(`Expected ${groupLen} bytes of private key`); - num = bytesToNumberBE(key); - } else { - throw new TypeError('Expected valid private key'); - } - if (!isWithinCurveOrder(num)) throw new Error('Expected private key: 0 < key < n'); - return num; + const { Point, JacobianPoint, normalizePrivateKey, weierstrassEquation, isWithinCurveOrder } = + weierstrassPoints({ + ...CURVE, + toBytes(c, point, isCompressed: boolean): Uint8Array { + if (isCompressed) { + return concatBytes(new Uint8Array([point.hasEvenY() ? 0x02 : 0x03]), Fp.toBytes(point.x)); + } else { + return concatBytes(new Uint8Array([0x04]), Fp.toBytes(point.x), Fp.toBytes(point.y)); + } + }, + fromBytes(bytes: Uint8Array) { + const len = bytes.length; + const header = bytes[0]; + // this.assertValidity() is done inside of fromHex + if (len === compressedLen && (header === 0x02 || header === 0x03)) { + const x = bytesToNumberBE(bytes.subarray(1)); + if (!isValidFieldElement(x)) throw new Error('Point is not on curve'); + const y2 = weierstrassEquation(x); // y² = x³ + ax + b + let y = Fp.sqrt(y2); // y = y² ^ (p+1)/4 + const isYOdd = (y & _1n) === _1n; + // ECDSA + const isFirstByteOdd = (bytes[0] & 1) === 1; + if (isFirstByteOdd !== isYOdd) y = Fp.negate(y); + return { x, y }; + } else if (len === uncompressedLen && header === 0x04) { + const x = Fp.fromBytes(bytes.subarray(1, Fp.BYTES + 1)); + const y = Fp.fromBytes(bytes.subarray(Fp.BYTES + 1, 2 * Fp.BYTES + 1)); + return { x, y }; + } else { + throw new Error( + `Point.fromHex: received invalid point. Expected ${compressedLen} compressed bytes or ${uncompressedLen} uncompressed bytes, not ${len}` + ); + } + }, + }); + type Point = typeof Point.BASE; + + // Do we need these functions at all? + function numToField(num: bigint): Uint8Array { + if (typeof num !== 'bigint') throw new Error('Expected bigint'); + if (!(_0n <= num && num < Fp.MASK)) throw new Error(`Expected number < 2^${Fp.BYTES * 8}`); + return Fp.toBytes(num); } + const numToFieldStr = (num: bigint): string => bytesToHex(numToField(num)); /** * Normalizes hex, bytes, Point to Point. Checks for curve equation. */ - function normalizePublicKey(publicKey: PubKey): Point { + function normalizePublicKey(publicKey: PubKey): PointType { if (publicKey instanceof Point) { publicKey.assertValidity(); return publicKey; @@ -396,14 +879,6 @@ export function weierstrass(curveDef: CurveType): CurveFn { return isBiggerThanHalfOrder(s) ? mod.mod(-s, CURVE_ORDER) : s; } - function normalizeScalar(num: number | bigint): bigint { - if (typeof num === 'number' && Number.isSafeInteger(num) && num > 0) return BigInt(num); - if (typeof num === 'bigint' && isWithinCurveOrder(num)) return num; - throw new TypeError('Expected valid private scalar: 0 < scalar < curve.n'); - } - - const sqrtModCurve = CURVE.sqrtMod || mod.sqrt; - // Ensures ECDSA message hashes are 32 bytes and < curve order function _truncateHash(hash: Uint8Array, truncateOnly = false): bigint { const { n, nBitLength } = CURVE; @@ -416,396 +891,6 @@ export function weierstrass(curveDef: CurveType): CurveFn { } const truncateHash = CURVE.truncateHash || _truncateHash; - /** - * Jacobian Point works in 3d / jacobi coordinates: (x, y, z) ∋ (x=x/z², y=y/z³) - * Default Point works in 2d / affine coordinates: (x, y) - * We're doing calculations in jacobi, because its operations don't require costly inversion. - */ - class JacobianPoint implements JacobianPointType { - constructor(readonly x: bigint, readonly y: bigint, readonly z: bigint) {} - - static readonly BASE = new JacobianPoint(CURVE.Gx, CURVE.Gy, _1n); - static readonly ZERO = new JacobianPoint(_0n, _1n, _0n); - - static fromAffine(p: Point): JacobianPoint { - if (!(p instanceof Point)) { - throw new TypeError('JacobianPoint#fromAffine: expected Point'); - } - // fromAffine(x:0, y:0) would produce (x:0, y:0, z:1), but we need (x:0, y:1, z:0) - if (p.equals(Point.ZERO)) return JacobianPoint.ZERO; - return new JacobianPoint(p.x, p.y, _1n); - } - - /** - * Takes a bunch of Jacobian Points but executes only one - * invert on all of them. invert is very slow operation, - * so this improves performance massively. - */ - static toAffineBatch(points: JacobianPoint[]): Point[] { - const toInv = mod.invertBatch( - points.map((p) => p.z), - CURVE.P - ); - return points.map((p, i) => p.toAffine(toInv[i])); - } - - static normalizeZ(points: JacobianPoint[]): JacobianPoint[] { - return JacobianPoint.toAffineBatch(points).map(JacobianPoint.fromAffine); - } - - /** - * Compare one point to another. - */ - equals(other: JacobianPoint): boolean { - if (!(other instanceof JacobianPoint)) throw new TypeError('JacobianPoint expected'); - const { x: X1, y: Y1, z: Z1 } = this; - const { x: X2, y: Y2, z: Z2 } = other; - const Z1Z1 = modP(Z1 * Z1); - const Z2Z2 = modP(Z2 * Z2); - const U1 = modP(X1 * Z2Z2); - const U2 = modP(X2 * Z1Z1); - const S1 = modP(modP(Y1 * Z2) * Z2Z2); - const S2 = modP(modP(Y2 * Z1) * Z1Z1); - return U1 === U2 && S1 === S2; - } - - /** - * Flips point to one corresponding to (x, -y) in Affine coordinates. - */ - negate(): JacobianPoint { - return new JacobianPoint(this.x, modP(-this.y), this.z); - } - - // Fast algo for doubling 2 Jacobian Points. - // From: https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl - // Cost: 1M + 8S + 1*a + 10add + 2*2 + 1*3 + 1*8. - double(): JacobianPoint { - const { x: X1, y: Y1, z: Z1 } = this; - const { a } = CURVE; - - // Faster algorithm: when a=0 - // From: https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l - // Cost: 2M + 5S + 6add + 3*2 + 1*3 + 1*8. - if (a === _0n) { - const A = modP(X1 * X1); - const B = modP(Y1 * Y1); - const C = modP(B * B); - const x1b = X1 + B; - const D = modP(_2n * (modP(x1b * x1b) - A - C)); - const E = modP(_3n * A); - const F = modP(E * E); - const X3 = modP(F - _2n * D); - const Y3 = modP(E * (D - X3) - _8n * C); - const Z3 = modP(_2n * Y1 * Z1); - return new JacobianPoint(X3, Y3, Z3); - } - const XX = modP(X1 * X1); - const YY = modP(Y1 * Y1); - const YYYY = modP(YY * YY); - const ZZ = modP(Z1 * Z1); - const tmp1 = modP(X1 + YY); - const S = modP(_2n * (modP(tmp1 * tmp1) - XX - YYYY)); // 2*((X1+YY)^2-XX-YYYY) - const M = modP(_3n * XX + a * modP(ZZ * ZZ)); - const T = modP(modP(M * M) - _2n * S); // M^2-2*S - const X3 = T; - const Y3 = modP(M * (S - T) - _8n * YYYY); // M*(S-T)-8*YYYY - const y1az1 = modP(Y1 + Z1); // (Y1+Z1) - const Z3 = modP(modP(y1az1 * y1az1) - YY - ZZ); // (Y1+Z1)^2-YY-ZZ - return new JacobianPoint(X3, Y3, Z3); - } - - // Fast algo for adding 2 Jacobian Points. - // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#addition-add-1998-cmo-2 - // Cost: 12M + 4S + 6add + 1*2 - // Note: 2007 Bernstein-Lange (11M + 5S + 9add + 4*2) is actually 10% slower. - add(other: JacobianPoint): JacobianPoint { - if (!(other instanceof JacobianPoint)) throw new TypeError('JacobianPoint expected'); - const { x: X1, y: Y1, z: Z1 } = this; - const { x: X2, y: Y2, z: Z2 } = other; - if (X2 === _0n || Y2 === _0n) return this; - if (X1 === _0n || Y1 === _0n) return other; - // We're using same code in equals() - const Z1Z1 = modP(Z1 * Z1); // Z1Z1 = Z1^2 - const Z2Z2 = modP(Z2 * Z2); // Z2Z2 = Z2^2; - const U1 = modP(X1 * Z2Z2); // X1 * Z2Z2 - const U2 = modP(X2 * Z1Z1); // X2 * Z1Z1 - const S1 = modP(modP(Y1 * Z2) * Z2Z2); // Y1 * Z2 * Z2Z2 - const S2 = modP(modP(Y2 * Z1) * Z1Z1); // Y2 * Z1 * Z1Z1 - const H = modP(U2 - U1); // H = U2 - U1 - const r = modP(S2 - S1); // S2 - S1 - // H = 0 meaning it's the same point. - if (H === _0n) return r === _0n ? this.double() : JacobianPoint.ZERO; - const HH = modP(H * H); // HH = H2 - const HHH = modP(H * HH); // HHH = H * HH - const V = modP(U1 * HH); // V = U1 * HH - const X3 = modP(r * r - HHH - _2n * V); // X3 = r^2 - HHH - 2 * V; - const Y3 = modP(r * (V - X3) - S1 * HHH); // Y3 = r * (V - X3) - S1 * HHH; - const Z3 = modP(Z1 * Z2 * H); // Z3 = Z1 * Z2 * H; - return new JacobianPoint(X3, Y3, Z3); - } - - subtract(other: JacobianPoint) { - return this.add(other.negate()); - } - - /** - * Non-constant-time multiplication. Uses double-and-add algorithm. - * It's faster, but should only be used when you don't care about - * an exposed private key e.g. sig verification, which works over *public* keys. - */ - multiplyUnsafe(scalar: bigint): JacobianPoint { - const P0 = JacobianPoint.ZERO; - if (typeof scalar === 'bigint' && scalar === _0n) return P0; - // Will throw on 0 - let n = normalizeScalar(scalar); - if (n === _1n) return this; - - if (!CURVE.endo) return wnaf.unsafeLadder(this, n); - - // Apply endomorphism - let { k1neg, k1, k2neg, k2 } = CURVE.endo.splitScalar(n); - let k1p = P0; - let k2p = P0; - let d: JacobianPoint = this; - while (k1 > _0n || k2 > _0n) { - if (k1 & _1n) k1p = k1p.add(d); - if (k2 & _1n) k2p = k2p.add(d); - d = d.double(); - k1 >>= _1n; - k2 >>= _1n; - } - if (k1neg) k1p = k1p.negate(); - if (k2neg) k2p = k2p.negate(); - k2p = new JacobianPoint(modP(k2p.x * CURVE.endo.beta), k2p.y, k2p.z); - return k1p.add(k2p); - } - - /** - * Implements w-ary non-adjacent form for calculating ec multiplication. - */ - private wNAF(n: bigint, affinePoint?: Point): { p: JacobianPoint; f: JacobianPoint } { - if (!affinePoint && this.equals(JacobianPoint.BASE)) affinePoint = Point.BASE; - const W = (affinePoint && affinePoint._WINDOW_SIZE) || 1; - // Calculate precomputes on a first run, reuse them after - let precomputes = affinePoint && pointPrecomputes.get(affinePoint); - if (!precomputes) { - precomputes = wnaf.precomputeWindow(this, W) as JacobianPoint[]; - if (affinePoint && W !== 1) { - precomputes = JacobianPoint.normalizeZ(precomputes); - pointPrecomputes.set(affinePoint, precomputes); - } - } - return wnaf.wNAF(W, precomputes, n); - } - - /** - * Constant time multiplication. - * Uses wNAF method. Windowed method may be 10% faster, - * but takes 2x longer to generate and consumes 2x memory. - * @param scalar by which the point would be multiplied - * @param affinePoint optional point ot save cached precompute windows on it - * @returns New point - */ - multiply(scalar: number | bigint, affinePoint?: Point): JacobianPoint { - let n = normalizeScalar(scalar); - - // Real point. - let point: JacobianPoint; - // Fake point, we use it to achieve constant-time multiplication. - let fake: JacobianPoint; - if (CURVE.endo) { - const { k1neg, k1, k2neg, k2 } = CURVE.endo.splitScalar(n); - let { p: k1p, f: f1p } = this.wNAF(k1, affinePoint); - let { p: k2p, f: f2p } = this.wNAF(k2, affinePoint); - k1p = wnaf.constTimeNegate(k1neg, k1p); - k2p = wnaf.constTimeNegate(k2neg, k2p); - k2p = new JacobianPoint(modP(k2p.x * CURVE.endo.beta), k2p.y, k2p.z); - point = k1p.add(k2p); - fake = f1p.add(f2p); - } else { - const { p, f } = this.wNAF(n, affinePoint); - point = p; - fake = f; - } - // Normalize `z` for both points, but return only real one - return JacobianPoint.normalizeZ([point, fake])[0]; - } - - // Converts Jacobian point to affine (x, y) coordinates. - // Can accept precomputed Z^-1 - for example, from invertBatch. - // (x, y, z) ∋ (x=x/z², y=y/z³) - // https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#scaling-z - toAffine(invZ?: bigint): Point { - const { x, y, z } = this; - const is0 = this.equals(JacobianPoint.ZERO); - // If invZ was 0, we return zero point. However we still want to execute - // all operations, so we replace invZ with a random number, 8. - if (invZ == null) invZ = is0 ? _8n : mod.invert(z, CURVE.P); - const iz1 = invZ; - const iz2 = modP(iz1 * iz1); - const iz3 = modP(iz2 * iz1); - const ax = modP(x * iz2); - const ay = modP(y * iz3); - const zz = modP(z * iz1); - if (is0) return Point.ZERO; - if (zz !== _1n) throw new Error('invZ was invalid'); - return new Point(ax, ay); - } - } - const wnaf = wNAF(JacobianPoint, CURVE.endo ? CURVE.nBitLength / 2 : CURVE.nBitLength); - // Stores precomputed values for points. - const pointPrecomputes = new WeakMap(); - - /** - * Default Point works in default aka affine coordinates: (x, y) - */ - class Point implements PointType { - /** - * Base point aka generator. public_key = Point.BASE * private_key - */ - static BASE: Point = new Point(CURVE.Gx, CURVE.Gy); - /** - * Identity point aka point at infinity. point = point + zero_point - */ - static ZERO: Point = new Point(_0n, _0n); - - // We calculate precomputes for elliptic curve point multiplication - // using windowed method. This specifies window size and - // stores precomputed values. Usually only base point would be precomputed. - _WINDOW_SIZE?: number; - - constructor(readonly x: bigint, readonly y: bigint) {} - - // "Private method", don't use it directly - _setWindowSize(windowSize: number) { - this._WINDOW_SIZE = windowSize; - pointPrecomputes.delete(this); - } - - // Checks for y % 2 == 0 - hasEvenY() { - return this.y % _2n === _0n; - } - - /** - * Supports compressed ECDSA points - * @returns Point instance - */ - private static fromCompressedHex(bytes: Uint8Array) { - const P = CURVE.P; - const x = bytesToNumberBE(bytes.subarray(1)); - if (!isValidFieldElement(x)) throw new Error('Point is not on curve'); - const y2 = weierstrassEquation(x); // y² = x³ + ax + b - let y = sqrtModCurve(y2, P); // y = y² ^ (p+1)/4 - const isYOdd = (y & _1n) === _1n; - // ECDSA - const isFirstByteOdd = (bytes[0] & 1) === 1; - if (isFirstByteOdd !== isYOdd) y = modP(-y); - const point = new Point(x, y); - point.assertValidity(); - return point; - } - - private static fromUncompressedHex(bytes: Uint8Array) { - const x = bytesToNumberBE(bytes.subarray(1, fieldLen + 1)); - const y = bytesToNumberBE(bytes.subarray(fieldLen + 1, 2 * fieldLen + 1)); - const point = new Point(x, y); - point.assertValidity(); - return point; - } - - /** - * Converts hash string or Uint8Array to Point. - * @param hex short/long ECDSA hex - */ - static fromHex(hex: Hex): Point { - const bytes = ensureBytes(hex); - const len = bytes.length; - const header = bytes[0]; - // this.assertValidity() is done inside of those two functions - if (len === compressedLen && (header === 0x02 || header === 0x03)) - return this.fromCompressedHex(bytes); - if (len === uncompressedLen && header === 0x04) return this.fromUncompressedHex(bytes); - throw new Error( - `Point.fromHex: received invalid point. Expected ${compressedLen} compressed bytes or ${uncompressedLen} uncompressed bytes, not ${len}` - ); - } - - // Multiplies generator point by privateKey. - static fromPrivateKey(privateKey: PrivKey) { - return Point.BASE.multiply(normalizePrivateKey(privateKey)); - } - - toRawBytes(isCompressed = false): Uint8Array { - return hexToBytes(this.toHex(isCompressed)); - } - - toHex(isCompressed = false): string { - const x = numToFieldStr(this.x); - if (isCompressed) { - const prefix = this.hasEvenY() ? '02' : '03'; - return `${prefix}${x}`; - } else { - return `04${x}${numToFieldStr(this.y)}`; - } - } - - // A point on curve is valid if it conforms to equation. - assertValidity(): void { - // Some 3rd-party test vectors require different wording between here & `fromCompressedHex` - const msg = 'Point is not on elliptic curve'; - const { x, y } = this; - if (!isValidFieldElement(x) || !isValidFieldElement(y)) throw new Error(msg); - const left = modP(y * y); - const right = weierstrassEquation(x); - if (modP(left - right) !== _0n) throw new Error(msg); - } - - equals(other: Point): boolean { - if (!(other instanceof Point)) throw new TypeError('Point#equals: expected Point'); - return this.x === other.x && this.y === other.y; - } - - // Returns the same point with inverted `y` - negate() { - return new Point(this.x, modP(-this.y)); - } - - // Adds point to itself - double() { - return JacobianPoint.fromAffine(this).double().toAffine(); - } - - // Adds point to other point - add(other: Point) { - return JacobianPoint.fromAffine(this).add(JacobianPoint.fromAffine(other)).toAffine(); - } - - // Subtracts other point from the point - subtract(other: Point) { - return this.add(other.negate()); - } - - multiply(scalar: number | bigint) { - return JacobianPoint.fromAffine(this).multiply(scalar, this).toAffine(); - } - - /** - * Efficiently calculate `aP + bQ`. - * Unsafe, can expose private key, if used incorrectly. - * TODO: Utilize Shamir's trick - * @returns non-zero affine point - */ - multiplyAndAddUnsafe(Q: Point, a: bigint, b: bigint): Point | undefined { - const P = JacobianPoint.fromAffine(this); - const aP = - a === _0n || a === _1n || this !== Point.BASE ? P.multiplyUnsafe(a) : P.multiply(a); - const bQ = JacobianPoint.fromAffine(Q).multiplyUnsafe(b); - const sum = aP.add(bQ); - return sum.equals(JacobianPoint.ZERO) ? undefined : sum.toAffine(); - } - } - /** * ECDSA signature with its (r, s) properties. Supports DER & compact representations. */ @@ -916,8 +1001,8 @@ export function weierstrass(curveDef: CurveType): CurveFn { } const utils = { - mod: modP, - invert: (n: bigint, m: bigint = CURVE.P) => mod.invert(n, m), + mod: (n: bigint, modulo = Fp.ORDER) => mod.mod(n, modulo), + invert: Fp.invert, isValidPrivateKey(privateKey: PrivKey) { try { normalizePrivateKey(privateKey); @@ -943,7 +1028,7 @@ export function weierstrass(curveDef: CurveType): CurveFn { * Produces cryptographically secure private key from random of size (nBitLength+64) * as per FIPS 186 B.4.1 with modulo bias being neglible. */ - randomPrivateKey: (): Uint8Array => utils.hashToPrivateKey(CURVE.randomBytes(fieldLen + 8)), + randomPrivateKey: (): Uint8Array => utils.hashToPrivateKey(CURVE.randomBytes(Fp.BYTES + 8)), /** * 1. Returns cached point which you can use to pass to `getSharedSecret` or `#multiply` by it. @@ -1003,7 +1088,7 @@ export function weierstrass(curveDef: CurveType): CurveFn { // RFC6979 methods function bits2int(bytes: Uint8Array) { - const slice = bytes.length > fieldLen ? bytes.slice(0, fieldLen) : bytes; + const slice = bytes.length > Fp.BYTES ? bytes.slice(0, Fp.BYTES) : bytes; return bytesToNumberBE(slice); } function bits2octets(bytes: Uint8Array): Uint8Array { @@ -1025,9 +1110,9 @@ export function weierstrass(curveDef: CurveType): CurveFn { const seedArgs = [int2octets(d), bits2octets(h1)]; // RFC6979 3.6: additional k' could be provided if (extraEntropy != null) { - if (extraEntropy === true) extraEntropy = CURVE.randomBytes(fieldLen); + if (extraEntropy === true) extraEntropy = CURVE.randomBytes(Fp.BYTES); const e = ensureBytes(extraEntropy); - if (e.length !== fieldLen) throw new Error(`sign: Expected ${fieldLen} bytes of extra data`); + if (e.length !== Fp.BYTES) throw new Error(`sign: Expected ${Fp.BYTES} bytes of extra data`); seedArgs.push(e); } // seed is constructed from private key and message