From c5e0e070d10182843bb078330c7292782b41a5bb Mon Sep 17 00:00:00 2001 From: Jack Lloyd Date: Thu, 24 Aug 2023 16:36:12 -0400 Subject: [PATCH] Complete BLS short signature support --- src/abstract/bls.ts | 62 ++++++++- src/bls12-381.ts | 38 +++++- test/bls12-381.test.js | 40 ++++++ test/bls12-381/bls12-381-g1-test-vectors.txt | 128 +++++++++++++++++++ 4 files changed, 266 insertions(+), 2 deletions(-) create mode 100644 test/bls12-381/bls12-381-g1-test-vectors.txt diff --git a/src/abstract/bls.ts b/src/abstract/bls.ts index ffc8192..f7c6c33 100644 --- a/src/abstract/bls.ts +++ b/src/abstract/bls.ts @@ -27,6 +27,12 @@ type Fp = bigint; // Can be different field? // prettier-ignore const _2n = BigInt(2), _3n = BigInt(3); +export type ShortSignatureCoder = { + fromHex(hex: Hex): ProjPointType; + toRawBytes(point: ProjPointType): Uint8Array; + toHex(point: ProjPointType): string; +}; + export type SignatureCoder = { fromHex(hex: Hex): ProjPointType; toRawBytes(point: ProjPointType): Uint8Array; @@ -35,6 +41,7 @@ export type SignatureCoder = { export type CurveType = { G1: Omit, 'n'> & { + ShortSignature: SignatureCoder; mapToCurve: htf.MapToCurve; htfDefaults: htf.Opts; }; @@ -70,10 +77,15 @@ export type CurveType = { export type CurveFn = { getPublicKey: (privateKey: PrivKey) => Uint8Array; + getPublicKeyForShortSignatures: (privateKey: PrivKey) => Uint8Array; sign: { (message: Hex, privateKey: PrivKey): Uint8Array; (message: ProjPointType, privateKey: PrivKey): ProjPointType; }; + signShortSignature: { + (message: Hex, privateKey: PrivKey): Uint8Array; + (message: ProjPointType, privateKey: PrivKey): ProjPointType; + }; verify: ( signature: Hex | ProjPointType, message: Hex | ProjPointType, @@ -97,11 +109,16 @@ export type CurveFn = { (signatures: Hex[]): Uint8Array; (signatures: ProjPointType[]): ProjPointType; }; + aggregateShortSignatures: { + (signatures: Hex[]): Uint8Array; + (signatures: ProjPointType[]): ProjPointType; + }; millerLoop: (ell: [Fp2, Fp2, Fp2][], g1: [Fp, Fp]) => Fp12; pairing: (P: ProjPointType, Q: ProjPointType, withFinalExponent?: boolean) => Fp12; G1: CurvePointsRes & ReturnType>; G2: CurvePointsRes & ReturnType>; Signature: SignatureCoder; + ShortSignature: ShortSignatureCoder; params: { x: bigint; r: bigint; @@ -238,6 +255,7 @@ export function bls( }) ); + const { ShortSignature } = CURVE.G1; const { Signature } = CURVE.G2; // Calculates bilinear pairing @@ -273,12 +291,18 @@ export function bls( : (G2.hashToCurve(ensureBytes('point', point), htfOpts) as G2); } - // Multiplies generator by private key. + // Multiplies generator (G1) by private key. // P = pk x G function getPublicKey(privateKey: PrivKey): Uint8Array { return G1.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true); } + // Multiplies generator (G2) by private key. + // P = pk x G + function getPublicKeyForShortSignatures(privateKey: PrivKey): Uint8Array { + return G2.ProjectivePoint.fromPrivateKey(privateKey).toRawBytes(true); + } + // Executes `hashToCurve` on the message and then multiplies the result by private key. // S = pk x H(m) function sign(message: Hex, privateKey: PrivKey, htfOpts?: htf.htfBasicOpts): Uint8Array; @@ -291,6 +315,24 @@ export function bls( return Signature.toRawBytes(sigPoint); } + function signShortSignature( + message: Hex, + privateKey: PrivKey, + htfOpts?: htf.htfBasicOpts + ): Uint8Array; + function signShortSignature(message: G1, privateKey: PrivKey, htfOpts?: htf.htfBasicOpts): G1; + function signShortSignature( + message: G1Hex, + privateKey: PrivKey, + htfOpts?: htf.htfBasicOpts + ): Uint8Array | G1 { + const msgPoint = normP1Hash(message, htfOpts); + msgPoint.assertValidity(); + const sigPoint = msgPoint.multiply(G1.normPrivateKeyToScalar(privateKey)); + if (message instanceof G1.ProjectivePoint) return sigPoint; + return ShortSignature.toRawBytes(sigPoint); + } + // Checks if pairing of public key & hash is equal to pairing of generator & signature. // e(P, H(m)) == e(G, S) function verify( @@ -361,6 +403,20 @@ export function bls( return Signature.toRawBytes(aggAffine); } + // Adds a bunch of signature points together. + function aggregateShortSignatures(signatures: Hex[]): Uint8Array; + function aggregateShortSignatures(signatures: G1[]): G1; + function aggregateShortSignatures(signatures: G1Hex[]): Uint8Array | G1 { + if (!signatures.length) throw new Error('Expected non-empty array'); + const agg = signatures.map(normP1).reduce((sum, s) => sum.add(s), G1.ProjectivePoint.ZERO); + const aggAffine = agg; //.toAffine(); + if (signatures[0] instanceof G1.ProjectivePoint) { + aggAffine.assertValidity(); + return aggAffine; + } + return ShortSignature.toRawBytes(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( @@ -403,17 +459,21 @@ export function bls( return { getPublicKey, + getPublicKeyForShortSignatures, sign, + signShortSignature, verify, verifyBatch, verifyShortSignature, aggregatePublicKeys, aggregateSignatures, + aggregateShortSignatures, millerLoop, pairing, G1, G2, Signature, + ShortSignature, fields: { Fr, Fp, diff --git a/src/bls12-381.ts b/src/bls12-381.ts index d4c7250..dc0e469 100644 --- a/src/bls12-381.ts +++ b/src/bls12-381.ts @@ -1023,6 +1023,18 @@ 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 +function signatureG1ToRawBytes(point: ProjPointType) { + point.assertValidity(); + const isZero = point.equals(bls12_381.G1.ProjectivePoint.ZERO); + const { x, y } = point.toAffine(); + 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); +} + function signatureG2ToRawBytes(point: ProjPointType) { // NOTE: by some reasons it was missed in bls12-381, looks like bug point.assertValidity(); @@ -1075,7 +1087,7 @@ export const bls12_381: CurveFn = bls({ ), a: Fp.ZERO, b: _4n, - htfDefaults: { ...htfDefaults, m: 1 }, + htfDefaults: { ...htfDefaults, m: 1, DST: 'BLS_SIG_BLS12381G1_XMD:SHA-256_SSWU_RO_NUL_' }, wrapPrivateKey: true, allowInfinityPoint: true, // Checks is the point resides in prime-order subgroup. @@ -1162,6 +1174,30 @@ export const bls12_381: CurveFn = bls({ } } }, + ShortSignature: { + fromHex(hex: Hex): ProjPointType { + const bytes = ensureBytes('signatureHex', hex, 48); + + const P = Fp.ORDER; + const compressedValue = bytesToNumberBE(bytes); + const bflag = bitGet(compressedValue, I_BIT_POS); + // Zero + if (bflag === _1n) return bls12_381.G1.ProjectivePoint.ZERO; + const x = Fp.create(compressedValue & Fp.MASK); + const right = Fp.add(Fp.pow(x, _3n), Fp.create(bls12_381.params.G1b)); // 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.neg(y); + return bls12_381.G1.ProjectivePoint.fromAffine({ x, y }); + }, + toRawBytes(point: ProjPointType) { + return signatureG1ToRawBytes(point); + }, + toHex(point: ProjPointType) { + return bytesToHex(signatureG1ToRawBytes(point)); + }, + }, }, // 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 diff --git a/test/bls12-381.test.js b/test/bls12-381.test.js index 5a914fa..6c7ff87 100644 --- a/test/bls12-381.test.js +++ b/test/bls12-381.test.js @@ -9,6 +9,10 @@ import { bls12_381 as bls } from '../esm/bls12-381.js'; import zkVectors from './bls12-381/zkcrypto/converted.json' assert { type: 'json' }; import pairingVectors from './bls12-381/go_pairing_vectors/pairing.json' assert { type: 'json' }; +const G1_VECTORS = readFileSync('./test/bls12-381/bls12-381-g1-test-vectors.txt', 'utf-8') + .trim() + .split('\n') + .map((l) => l.split(':')); const G2_VECTORS = readFileSync('./test/bls12-381/bls12-381-g2-test-vectors.txt', 'utf-8') .trim() .split('\n') @@ -852,6 +856,13 @@ describe('bls12-381/basic', () => { }); // should aggregate signatures + should(`produce correct short signatures (${G1_VECTORS.length} vectors)`, () => { + for (let vector of G1_VECTORS) { + const [priv, msg, expected] = vector; + const sig = bls.signShortSignature(msg, priv); + deepStrictEqual(bytesToHex(sig), expected); + } + }); should(`produce correct signatures (${G2_VECTORS.length} vectors)`, () => { for (let vector of G2_VECTORS) { const [priv, msg, expected] = vector; @@ -1182,6 +1193,35 @@ describe('verify()', () => { deepStrictEqual(res, false); } }); + should('verify signed message (short signatures)', () => { + for (let i = 0; i < NUM_RUNS; i++) { + const [priv, msg] = G1_VECTORS[i]; + const sig = bls.signShortSignature(msg, priv); + const pub = bls.getPublicKeyForShortSignatures(priv); + const res = bls.verifyShortSignature(sig, msg, pub); + deepStrictEqual(res, true, `${priv}-${msg}`); + } + }); + should('not verify signature with wrong message (short signatures)', () => { + for (let i = 0; i < NUM_RUNS; i++) { + const [priv, msg] = G1_VECTORS[i]; + const invMsg = G1_VECTORS[i + 1][1]; + const sig = bls.signShortSignature(msg, priv); + const pub = bls.getPublicKeyForShortSignatures(priv); + const res = bls.verifyShortSignature(sig, invMsg, pub); + deepStrictEqual(res, false); + } + }); + should('not verify signature with wrong key', () => { + for (let i = 0; i < NUM_RUNS; i++) { + const [priv, msg] = G1_VECTORS[i]; + const sig = bls.signShortSignature(msg, priv); + const invPriv = G1_VECTORS[i + 1][1].padStart(64, '0'); + const invPub = bls.getPublicKeyForShortSignatures(invPriv); + const res = bls.verifyShortSignature(sig, msg, invPub); + deepStrictEqual(res, false); + } + }); describe('batch', () => { should('verify multi-signature', () => { fc.assert( diff --git a/test/bls12-381/bls12-381-g1-test-vectors.txt b/test/bls12-381/bls12-381-g1-test-vectors.txt new file mode 100644 index 0000000..9fc6886 --- /dev/null +++ b/test/bls12-381/bls12-381-g1-test-vectors.txt @@ -0,0 +1,128 @@ +25d8cef413ba263e8d5732d3fca51fd369db74712655a5fd7b0b3a58d8095be8::800134e27aacc74dc91153a6bd65f96a5f8c8365c722da2f1e12eb048e0aed6987fa4168a51241ce41434fd05fd4bdd9 +611810ebd8f5a7faad47b2249f9d13be0506131db987b6948f1ca3194fa6b643:68:94250c0cc62ae9041c6f6e5042202b3c327991ce4b2841a4145d270f6c8311bc95673c826ada72a6d69e92a833d649e6 +419bb1de76e11a476f8d5cc5d85a648ec04f24bf75f6cf1f3fae43e57bf9a491:c8d0:898f660c5b26e8c9461ab3f42eb394465d5a115702c05d2a2bc761a8873ac0f33d21f9ea9cf4c435cd31391f5c8c0a91 +0d1bd9077705325666408124339dca98c0c842b35a90bc3cea8e0c36f2d35583:c43623:94f60dc44a4dbb2505befe346c0c143190fc877ded5e877418f0f890b8ae357a40e8fcc189139aaa509d2b6500f623a5 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