"use strict"; Object.defineProperty(exports, "__esModule", { value: true }); exports.bls = bls; /** * BLS != BLS. * The file implements BLS (Boneh-Lynn-Shacham) signatures. * Used in both BLS (Barreto-Lynn-Scott) and BN (Barreto-Naehrig) * families of pairing-friendly curves. * Consists of two curves: G1 and G2: * - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4. * - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1 * - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in * Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not. * Pairing is used to aggregate and verify signatures. * There are two modes of operation: * - Long signatures: X-byte keys + 2X-byte sigs (G1 keys + G2 sigs). * - Short signatures: 2X-byte keys + X-byte sigs (G2 keys + G1 sigs). * @module **/ /*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */ const utils_ts_1 = require("../utils.js"); const curve_ts_1 = require("./curve.js"); const hash_to_curve_ts_1 = require("./hash-to-curve.js"); const modular_ts_1 = require("./modular.js"); const weierstrass_ts_1 = require("./weierstrass.js"); // prettier-ignore const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3); // Not used with BLS12-381 (no sequential `11` in X). Useful for other curves. function NAfDecomposition(a) { const res = []; // a>1 because of marker bit for (; a > _1n; a >>= _1n) { if ((a & _1n) === _0n) res.unshift(0); else if ((a & _3n) === _3n) { res.unshift(-1); a += _1n; } else res.unshift(1); } return res; } function aNonEmpty(arr) { if (!Array.isArray(arr) || arr.length === 0) throw new Error('expected non-empty array'); } // This should be enough for bn254, no need to export full stuff? function createBlsPairing(fields, G1, G2, params) { const { Fp2, Fp12 } = fields; const { twistType, ateLoopSize, xNegative, postPrecompute } = params; // Applies sparse multiplication as line function let lineFunction; if (twistType === 'multiplicative') { lineFunction = (c0, c1, c2, f, Px, Py) => Fp12.mul014(f, c0, Fp2.mul(c1, Px), Fp2.mul(c2, Py)); } else if (twistType === 'divisive') { // NOTE: it should be [c0, c1, c2], but we use different order here to reduce complexity of // precompute calculations. lineFunction = (c0, c1, c2, f, Px, Py) => Fp12.mul034(f, Fp2.mul(c2, Py), Fp2.mul(c1, Px), c0); } else throw new Error('bls: unknown twist type'); const Fp2div2 = Fp2.div(Fp2.ONE, Fp2.mul(Fp2.ONE, _2n)); function pointDouble(ell, Rx, Ry, Rz) { const t0 = Fp2.sqr(Ry); // Ry² const t1 = Fp2.sqr(Rz); // Rz² const t2 = Fp2.mulByB(Fp2.mul(t1, _3n)); // 3 * T1 * B const t3 = Fp2.mul(t2, _3n); // 3 * T2 const t4 = Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0 const c0 = Fp2.sub(t2, t0); // T2 - T0 (i) const c1 = Fp2.mul(Fp2.sqr(Rx), _3n); // 3 * Rx² const c2 = Fp2.neg(t4); // -T4 (-h) ell.push([c0, c1, c2]); Rx = Fp2.mul(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), Fp2div2); // ((T0 - T3) * Rx * Ry) / 2 Ry = Fp2.sub(Fp2.sqr(Fp2.mul(Fp2.add(t0, t3), Fp2div2)), Fp2.mul(Fp2.sqr(t2), _3n)); // ((T0 + T3) / 2)² - 3 * T2² Rz = Fp2.mul(t0, t4); // T0 * T4 return { Rx, Ry, Rz }; } function pointAdd(ell, Rx, Ry, Rz, Qx, Qy) { // Addition const t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz const t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz const c0 = Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)); // T0 * Qx - T1 * Qy == Ry * Qx - Rx * Qy const c1 = Fp2.neg(t0); // -T0 == Qy * Rz - Ry const c2 = t1; // == Rx - Qx * Rz ell.push([c0, c1, c2]); const t2 = Fp2.sqr(t1); // T1² const t3 = Fp2.mul(t2, t1); // T2 * T1 const t4 = Fp2.mul(t2, Rx); // T2 * Rx const t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, _2n)), Fp2.mul(Fp2.sqr(t0), Rz)); // T3 - 2 * T4 + T0² * Rz Rx = Fp2.mul(t1, t5); // T1 * T5 Ry = Fp2.sub(Fp2.mul(Fp2.sub(t4, t5), t0), Fp2.mul(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry Rz = Fp2.mul(Rz, t3); // Rz * T3 return { Rx, Ry, Rz }; } // Pre-compute coefficients for sparse multiplication // Point addition and point double calculations is reused for coefficients // pointAdd happens only if bit set, so wNAF is reasonable. Unfortunately we cannot combine // add + double in windowed precomputes here, otherwise it would be single op (since X is static) const ATE_NAF = NAfDecomposition(ateLoopSize); const calcPairingPrecomputes = (0, utils_ts_1.memoized)((point) => { const p = point; const { x, y } = p.toAffine(); // prettier-ignore const Qx = x, Qy = y, negQy = Fp2.neg(y); // prettier-ignore let Rx = Qx, Ry = Qy, Rz = Fp2.ONE; const ell = []; for (const bit of ATE_NAF) { const cur = []; ({ Rx, Ry, Rz } = pointDouble(cur, Rx, Ry, Rz)); if (bit) ({ Rx, Ry, Rz } = pointAdd(cur, Rx, Ry, Rz, Qx, bit === -1 ? negQy : Qy)); ell.push(cur); } if (postPrecompute) { const last = ell[ell.length - 1]; postPrecompute(Rx, Ry, Rz, Qx, Qy, pointAdd.bind(null, last)); } return ell; }); function millerLoopBatch(pairs, withFinalExponent = false) { let f12 = Fp12.ONE; if (pairs.length) { const ellLen = pairs[0][0].length; for (let i = 0; i < ellLen; i++) { f12 = Fp12.sqr(f12); // This allows us to do sqr only one time for all pairings // NOTE: we apply multiple pairings in parallel here for (const [ell, Px, Py] of pairs) { for (const [c0, c1, c2] of ell[i]) f12 = lineFunction(c0, c1, c2, f12, Px, Py); } } } if (xNegative) f12 = Fp12.conjugate(f12); return withFinalExponent ? Fp12.finalExponentiate(f12) : f12; } // Calculates product of multiple pairings // This up to x2 faster than just `map(({g1, g2})=>pairing({g1,g2}))` function pairingBatch(pairs, withFinalExponent = true) { const res = []; // Cache precomputed toAffine for all points (0, curve_ts_1.normalizeZ)(G1, pairs.map(({ g1 }) => g1)); (0, curve_ts_1.normalizeZ)(G2, pairs.map(({ g2 }) => g2)); for (const { g1, g2 } of pairs) { if (g1.is0() || g2.is0()) throw new Error('pairing is not available for ZERO point'); // This uses toAffine inside g1.assertValidity(); g2.assertValidity(); const Qa = g1.toAffine(); res.push([calcPairingPrecomputes(g2), Qa.x, Qa.y]); } return millerLoopBatch(res, withFinalExponent); } // Calculates bilinear pairing function pairing(Q, P, withFinalExponent = true) { return pairingBatch([{ g1: Q, g2: P }], withFinalExponent); } return { Fp12, // NOTE: we re-export Fp12 here because pairing results are Fp12! millerLoopBatch, pairing, pairingBatch, calcPairingPrecomputes, }; } function createBlsSig(blsPairing, PubCurve, SigCurve, SignatureCoder, isSigG1) { const { Fp12, pairingBatch } = blsPairing; function normPub(point) { return point instanceof PubCurve.Point ? point : PubCurve.Point.fromHex(point); } function normSig(point) { return point instanceof SigCurve.Point ? point : SigCurve.Point.fromHex(point); } function amsg(m) { if (!(m instanceof SigCurve.Point)) throw new Error(`expected valid message hashed to ${!isSigG1 ? 'G2' : 'G1'} curve`); return m; } // What matters here is what point pairing API accepts as G1 or G2, not actual size or names const pair = !isSigG1 ? (a, b) => ({ g1: a, g2: b }) : (a, b) => ({ g1: b, g2: a }); return { // P = pk x G getPublicKey(secretKey) { // TODO: replace with // const sec = PubCurve.Point.Fn.fromBytes(secretKey); const sec = (0, weierstrass_ts_1._normFnElement)(PubCurve.Point.Fn, secretKey); return PubCurve.Point.BASE.multiply(sec); }, // S = pk x H(m) sign(message, secretKey, unusedArg) { if (unusedArg != null) throw new Error('sign() expects 2 arguments'); // TODO: replace with // PubCurve.Point.Fn.fromBytes(secretKey) const sec = (0, weierstrass_ts_1._normFnElement)(PubCurve.Point.Fn, secretKey); amsg(message).assertValidity(); return message.multiply(sec); }, // Checks if pairing of public key & hash is equal to pairing of generator & signature. // e(P, H(m)) == e(G, S) // e(S, G) == e(H(m), P) verify(signature, message, publicKey, unusedArg) { if (unusedArg != null) throw new Error('verify() expects 3 arguments'); signature = normSig(signature); publicKey = normPub(publicKey); const P = publicKey.negate(); const G = PubCurve.Point.BASE; const Hm = amsg(message); const S = signature; // This code was changed in 1.9.x: // Before it was G.negate() in G2, now it's always pubKey.negate // e(P, -Q)===e(-P, Q)==e(P, Q)^-1. Negate can be done anywhere (as long it is done once per pair). // We just moving sign, but since pairing is multiplicative, we doing X * X^-1 = 1 const exp = pairingBatch([pair(P, Hm), pair(G, S)]); return Fp12.eql(exp, Fp12.ONE); }, // https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407 // e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si)) // TODO: maybe `{message: G2Hex, publicKey: G1Hex}[]` instead? verifyBatch(signature, messages, publicKeys) { aNonEmpty(messages); if (publicKeys.length !== messages.length) throw new Error('amount of public keys and messages should be equal'); const sig = normSig(signature); const nMessages = messages; const nPublicKeys = publicKeys.map(normPub); // NOTE: this works only for exact same object const messagePubKeyMap = new Map(); for (let i = 0; i < nPublicKeys.length; i++) { const pub = nPublicKeys[i]; const msg = nMessages[i]; let keys = messagePubKeyMap.get(msg); if (keys === undefined) { keys = []; messagePubKeyMap.set(msg, keys); } keys.push(pub); } const paired = []; const G = PubCurve.Point.BASE; try { for (const [msg, keys] of messagePubKeyMap) { const groupPublicKey = keys.reduce((acc, msg) => acc.add(msg)); paired.push(pair(groupPublicKey, msg)); } paired.push(pair(G.negate(), sig)); return Fp12.eql(pairingBatch(paired), Fp12.ONE); } catch { return false; } }, // Adds a bunch of public key points together. // pk1 + pk2 + pk3 = pkA aggregatePublicKeys(publicKeys) { aNonEmpty(publicKeys); publicKeys = publicKeys.map((pub) => normPub(pub)); const agg = publicKeys.reduce((sum, p) => sum.add(p), PubCurve.Point.ZERO); agg.assertValidity(); return agg; }, // Adds a bunch of signature points together. // pk1 + pk2 + pk3 = pkA aggregateSignatures(signatures) { aNonEmpty(signatures); signatures = signatures.map((sig) => normSig(sig)); const agg = signatures.reduce((sum, s) => sum.add(s), SigCurve.Point.ZERO); agg.assertValidity(); return agg; }, hash(messageBytes, DST) { (0, utils_ts_1.abytes)(messageBytes); const opts = DST ? { DST } : undefined; return SigCurve.hashToCurve(messageBytes, opts); }, Signature: SignatureCoder, }; } // G1_Point: ProjConstructor, G2_Point: ProjConstructor, function bls(CURVE) { // Fields are specific for curve, so for now we'll need to pass them with opts const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE.fields; // Point on G1 curve: (x, y) const G1_ = (0, weierstrass_ts_1.weierstrassPoints)(CURVE.G1); const G1 = Object.assign(G1_, (0, hash_to_curve_ts_1.createHasher)(G1_.Point, CURVE.G1.mapToCurve, { ...CURVE.htfDefaults, ...CURVE.G1.htfDefaults, })); // Point on G2 curve (complex numbers): (x₁, x₂+i), (y₁, y₂+i) const G2_ = (0, weierstrass_ts_1.weierstrassPoints)(CURVE.G2); const G2 = Object.assign(G2_, (0, hash_to_curve_ts_1.createHasher)(G2_.Point, CURVE.G2.mapToCurve, { ...CURVE.htfDefaults, ...CURVE.G2.htfDefaults, })); const pairingRes = createBlsPairing(CURVE.fields, G1.Point, G2.Point, { ...CURVE.params, postPrecompute: CURVE.postPrecompute, }); const { millerLoopBatch, pairing, pairingBatch, calcPairingPrecomputes } = pairingRes; const longSignatures = createBlsSig(pairingRes, G1, G2, CURVE.G2.Signature, false); const shortSignatures = createBlsSig(pairingRes, G2, G1, CURVE.G1.ShortSignature, true); const rand = CURVE.randomBytes || utils_ts_1.randomBytes; const randomSecretKey = () => { const length = (0, modular_ts_1.getMinHashLength)(Fr.ORDER); return (0, modular_ts_1.mapHashToField)(rand(length), Fr.ORDER); }; const utils = { randomSecretKey, randomPrivateKey: randomSecretKey, calcPairingPrecomputes, }; const { ShortSignature } = CURVE.G1; const { Signature } = CURVE.G2; function normP1Hash(point, htfOpts) { return point instanceof G1.Point ? point : shortSignatures.hash((0, utils_ts_1.ensureBytes)('point', point), htfOpts?.DST); } function normP2Hash(point, htfOpts) { return point instanceof G2.Point ? point : longSignatures.hash((0, utils_ts_1.ensureBytes)('point', point), htfOpts?.DST); } function getPublicKey(privateKey) { return longSignatures.getPublicKey(privateKey).toBytes(true); } function getPublicKeyForShortSignatures(privateKey) { return shortSignatures.getPublicKey(privateKey).toBytes(true); } function sign(message, privateKey, htfOpts) { const Hm = normP2Hash(message, htfOpts); const S = longSignatures.sign(Hm, privateKey); return message instanceof G2.Point ? S : Signature.toBytes(S); } function signShortSignature(message, privateKey, htfOpts) { const Hm = normP1Hash(message, htfOpts); const S = shortSignatures.sign(Hm, privateKey); return message instanceof G1.Point ? S : ShortSignature.toBytes(S); } function verify(signature, message, publicKey, htfOpts) { const Hm = normP2Hash(message, htfOpts); return longSignatures.verify(signature, Hm, publicKey); } function verifyShortSignature(signature, message, publicKey, htfOpts) { const Hm = normP1Hash(message, htfOpts); return shortSignatures.verify(signature, Hm, publicKey); } function aggregatePublicKeys(publicKeys) { const agg = longSignatures.aggregatePublicKeys(publicKeys); return publicKeys[0] instanceof G1.Point ? agg : agg.toBytes(true); } function aggregateSignatures(signatures) { const agg = longSignatures.aggregateSignatures(signatures); return signatures[0] instanceof G2.Point ? agg : Signature.toBytes(agg); } function aggregateShortSignatures(signatures) { const agg = shortSignatures.aggregateSignatures(signatures); return signatures[0] instanceof G1.Point ? agg : ShortSignature.toBytes(agg); } function verifyBatch(signature, messages, publicKeys, htfOpts) { const Hm = messages.map((m) => normP2Hash(m, htfOpts)); return longSignatures.verifyBatch(signature, Hm, publicKeys); } G1.Point.BASE.precompute(4); return { longSignatures, shortSignatures, millerLoopBatch, pairing, pairingBatch, verifyBatch, fields: { Fr, Fp, Fp2, Fp6, Fp12, }, params: { ateLoopSize: CURVE.params.ateLoopSize, twistType: CURVE.params.twistType, // deprecated r: CURVE.params.r, G1b: CURVE.G1.b, G2b: CURVE.G2.b, }, utils, // deprecated getPublicKey, getPublicKeyForShortSignatures, sign, signShortSignature, verify, verifyShortSignature, aggregatePublicKeys, aggregateSignatures, aggregateShortSignatures, G1, G2, Signature, ShortSignature, }; } //# sourceMappingURL=bls.js.map