748 lines
26 KiB
Plaintext
748 lines
26 KiB
Plaintext
/**
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* BLS != BLS.
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* The file implements BLS (Boneh-Lynn-Shacham) signatures.
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* Used in both BLS (Barreto-Lynn-Scott) and BN (Barreto-Naehrig)
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* families of pairing-friendly curves.
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* Consists of two curves: G1 and G2:
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* - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4.
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* - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1
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* - Gt, created by bilinear (ate) pairing e(G1, G2), consists of p-th roots of unity in
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* Fq^k where k is embedding degree. Only degree 12 is currently supported, 24 is not.
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* Pairing is used to aggregate and verify signatures.
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* There are two modes of operation:
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* - Long signatures: X-byte keys + 2X-byte sigs (G1 keys + G2 sigs).
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* - Short signatures: 2X-byte keys + X-byte sigs (G2 keys + G1 sigs).
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* @module
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**/
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/*! noble-curves - MIT License (c) 2022 Paul Miller (paulmillr.com) */
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import {
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abytes,
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ensureBytes,
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memoized,
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randomBytes,
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type CHash,
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type Hex,
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type PrivKey,
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} from '../utils.ts';
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import { normalizeZ } from './curve.ts';
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import {
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createHasher,
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type H2CHasher,
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type H2CHashOpts,
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type H2COpts,
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type H2CPointConstructor,
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type htfBasicOpts,
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type MapToCurve,
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} from './hash-to-curve.ts';
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import { getMinHashLength, mapHashToField, type IField } from './modular.ts';
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import type { Fp12, Fp12Bls, Fp2, Fp2Bls, Fp6Bls } from './tower.ts';
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import {
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_normFnElement,
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weierstrassPoints,
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type CurvePointsRes,
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type CurvePointsType,
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type WeierstrassPoint,
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type WeierstrassPointCons,
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} from './weierstrass.ts';
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type Fp = bigint; // Can be different field?
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// prettier-ignore
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const _0n = BigInt(0), _1n = BigInt(1), _2n = BigInt(2), _3n = BigInt(3);
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export type TwistType = 'multiplicative' | 'divisive';
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export type ShortSignatureCoder<Fp> = {
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fromBytes(bytes: Uint8Array): WeierstrassPoint<Fp>;
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fromHex(hex: Hex): WeierstrassPoint<Fp>;
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toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
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toHex(point: WeierstrassPoint<Fp>): string;
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/** @deprecated use `toBytes` */
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toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
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};
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export type SignatureCoder<Fp> = {
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fromBytes(bytes: Uint8Array): WeierstrassPoint<Fp>;
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fromHex(hex: Hex): WeierstrassPoint<Fp>;
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toBytes(point: WeierstrassPoint<Fp>): Uint8Array;
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toHex(point: WeierstrassPoint<Fp>): string;
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/** @deprecated use `toBytes` */
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toRawBytes(point: WeierstrassPoint<Fp>): Uint8Array;
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};
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export type BlsFields = {
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Fp: IField<Fp>;
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Fr: IField<bigint>;
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Fp2: Fp2Bls;
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Fp6: Fp6Bls;
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Fp12: Fp12Bls;
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};
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export type PostPrecomputePointAddFn = (
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Rx: Fp2,
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Ry: Fp2,
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Rz: Fp2,
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Qx: Fp2,
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Qy: Fp2
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) => { Rx: Fp2; Ry: Fp2; Rz: Fp2 };
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export type PostPrecomputeFn = (
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Rx: Fp2,
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Ry: Fp2,
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Rz: Fp2,
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Qx: Fp2,
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Qy: Fp2,
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pointAdd: PostPrecomputePointAddFn
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) => void;
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export type BlsPairing = {
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Fp12: Fp12Bls;
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calcPairingPrecomputes: (p: WeierstrassPoint<Fp2>) => Precompute;
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millerLoopBatch: (pairs: [Precompute, Fp, Fp][]) => Fp12;
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pairing: (P: WeierstrassPoint<Fp>, Q: WeierstrassPoint<Fp2>, withFinalExponent?: boolean) => Fp12;
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pairingBatch: (
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pairs: { g1: WeierstrassPoint<Fp>; g2: WeierstrassPoint<Fp2> }[],
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withFinalExponent?: boolean
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) => Fp12;
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};
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// TODO: replace CurveType with this? It doesn't contain r however and has postPrecompute
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export type BlsPairingParams = {
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// NOTE: MSB is always ignored and used as marker for length,
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// otherwise leading zeros will be lost.
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// Can be different from 'X' (seed) param!
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ateLoopSize: bigint;
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xNegative: boolean;
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twistType: TwistType; // BLS12-381: Multiplicative, BN254: Divisive
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// This is super ugly hack for untwist point in BN254 after miller loop
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postPrecompute?: PostPrecomputeFn;
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};
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export type CurveType = {
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G1: CurvePointsType<Fp> & {
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ShortSignature: SignatureCoder<Fp>;
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mapToCurve: MapToCurve<Fp>;
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htfDefaults: H2COpts;
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};
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G2: CurvePointsType<Fp2> & {
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Signature: SignatureCoder<Fp2>;
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mapToCurve: MapToCurve<Fp2>;
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htfDefaults: H2COpts;
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};
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fields: BlsFields;
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params: {
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// NOTE: MSB is always ignored and used as marker for length,
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// otherwise leading zeros will be lost.
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// Can be different from 'X' (seed) param!
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ateLoopSize: BlsPairingParams['ateLoopSize'];
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xNegative: BlsPairingParams['xNegative'];
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r: bigint; // TODO: remove
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twistType: BlsPairingParams['twistType']; // BLS12-381: Multiplicative, BN254: Divisive
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};
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htfDefaults: H2COpts;
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hash: CHash; // Because we need outputLen for DRBG
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randomBytes?: (bytesLength?: number) => Uint8Array;
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// This is super ugly hack for untwist point in BN254 after miller loop
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postPrecompute?: PostPrecomputeFn;
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};
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type PrecomputeSingle = [Fp2, Fp2, Fp2][];
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type Precompute = PrecomputeSingle[];
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/**
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* BLS consists of two curves: G1 and G2:
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* - G1 is a subgroup of (x, y) E(Fq) over y² = x³ + 4.
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* - G2 is a subgroup of ((x₁, x₂+i), (y₁, y₂+i)) E(Fq²) over y² = x³ + 4(1 + i) where i is √-1
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*/
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export interface BLSCurvePair {
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longSignatures: BLSSigs<bigint, Fp2>;
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shortSignatures: BLSSigs<Fp2, bigint>;
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millerLoopBatch: BlsPairing['millerLoopBatch'];
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pairing: BlsPairing['pairing'];
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pairingBatch: BlsPairing['pairingBatch'];
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G1: { Point: WeierstrassPointCons<bigint> } & H2CHasher<Fp>;
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G2: { Point: WeierstrassPointCons<Fp2> } & H2CHasher<Fp2>;
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fields: {
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Fp: IField<Fp>;
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Fp2: Fp2Bls;
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Fp6: Fp6Bls;
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Fp12: Fp12Bls;
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Fr: IField<bigint>;
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};
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utils: {
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randomSecretKey: () => Uint8Array;
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/** @deprecated use randomSecretKey */
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randomPrivateKey: () => Uint8Array;
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calcPairingPrecomputes: BlsPairing['calcPairingPrecomputes'];
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};
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}
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export type CurveFn = BLSCurvePair & {
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/** @deprecated use `longSignatures.getPublicKey` */
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getPublicKey: (secretKey: PrivKey) => Uint8Array;
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/** @deprecated use `shortSignatures.getPublicKey` */
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getPublicKeyForShortSignatures: (secretKey: PrivKey) => Uint8Array;
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/** @deprecated use `longSignatures.sign` */
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sign: {
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(message: Hex, secretKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;
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(
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message: WeierstrassPoint<Fp2>,
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secretKey: PrivKey,
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htfOpts?: htfBasicOpts
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): WeierstrassPoint<Fp2>;
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};
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/** @deprecated use `shortSignatures.sign` */
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signShortSignature: {
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(message: Hex, secretKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;
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(
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message: WeierstrassPoint<Fp>,
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secretKey: PrivKey,
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htfOpts?: htfBasicOpts
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): WeierstrassPoint<Fp>;
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};
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/** @deprecated use `longSignatures.verify` */
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verify: (
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signature: Hex | WeierstrassPoint<Fp2>,
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message: Hex | WeierstrassPoint<Fp2>,
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publicKey: Hex | WeierstrassPoint<Fp>,
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htfOpts?: htfBasicOpts
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) => boolean;
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/** @deprecated use `shortSignatures.verify` */
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verifyShortSignature: (
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signature: Hex | WeierstrassPoint<Fp>,
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message: Hex | WeierstrassPoint<Fp>,
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publicKey: Hex | WeierstrassPoint<Fp2>,
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htfOpts?: htfBasicOpts
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) => boolean;
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verifyBatch: (
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signature: Hex | WeierstrassPoint<Fp2>,
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messages: (Hex | WeierstrassPoint<Fp2>)[],
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publicKeys: (Hex | WeierstrassPoint<Fp>)[],
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htfOpts?: htfBasicOpts
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) => boolean;
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/** @deprecated use `longSignatures.aggregatePublicKeys` */
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aggregatePublicKeys: {
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(publicKeys: Hex[]): Uint8Array;
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(publicKeys: WeierstrassPoint<Fp>[]): WeierstrassPoint<Fp>;
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};
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/** @deprecated use `longSignatures.aggregateSignatures` */
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aggregateSignatures: {
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(signatures: Hex[]): Uint8Array;
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(signatures: WeierstrassPoint<Fp2>[]): WeierstrassPoint<Fp2>;
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};
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/** @deprecated use `shortSignatures.aggregateSignatures` */
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aggregateShortSignatures: {
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(signatures: Hex[]): Uint8Array;
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(signatures: WeierstrassPoint<Fp>[]): WeierstrassPoint<Fp>;
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};
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G1: CurvePointsRes<Fp> & H2CHasher<Fp>;
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G2: CurvePointsRes<Fp2> & H2CHasher<Fp2>;
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/** @deprecated use `longSignatures.Signature` */
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Signature: SignatureCoder<Fp2>;
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/** @deprecated use `shortSignatures.Signature` */
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ShortSignature: ShortSignatureCoder<Fp>;
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params: {
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ateLoopSize: bigint;
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r: bigint;
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twistType: TwistType;
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/** @deprecated */
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G1b: bigint;
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/** @deprecated */
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G2b: Fp2;
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};
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};
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type BLSInput = Hex | Uint8Array;
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export interface BLSSigs<P, S> {
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getPublicKey(secretKey: PrivKey): WeierstrassPoint<P>;
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sign(hashedMessage: WeierstrassPoint<S>, secretKey: PrivKey): WeierstrassPoint<S>;
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verify(
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signature: WeierstrassPoint<S> | BLSInput,
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message: WeierstrassPoint<S>,
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publicKey: WeierstrassPoint<P> | BLSInput
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): boolean;
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verifyBatch: (
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signature: WeierstrassPoint<S> | BLSInput,
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messages: WeierstrassPoint<S>[],
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publicKeys: (WeierstrassPoint<P> | BLSInput)[]
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) => boolean;
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aggregatePublicKeys(publicKeys: (WeierstrassPoint<P> | BLSInput)[]): WeierstrassPoint<P>;
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aggregateSignatures(signatures: (WeierstrassPoint<S> | BLSInput)[]): WeierstrassPoint<S>;
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hash(message: Uint8Array, DST?: string | Uint8Array, hashOpts?: H2CHashOpts): WeierstrassPoint<S>;
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Signature: SignatureCoder<S>;
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}
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// Not used with BLS12-381 (no sequential `11` in X). Useful for other curves.
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function NAfDecomposition(a: bigint) {
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const res = [];
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// a>1 because of marker bit
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for (; a > _1n; a >>= _1n) {
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if ((a & _1n) === _0n) res.unshift(0);
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else if ((a & _3n) === _3n) {
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res.unshift(-1);
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a += _1n;
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} else res.unshift(1);
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}
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return res;
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}
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function aNonEmpty(arr: any[]) {
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if (!Array.isArray(arr) || arr.length === 0) throw new Error('expected non-empty array');
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}
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// This should be enough for bn254, no need to export full stuff?
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function createBlsPairing(
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fields: BlsFields,
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G1: WeierstrassPointCons<Fp>,
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G2: WeierstrassPointCons<Fp2>,
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params: BlsPairingParams
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): BlsPairing {
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const { Fp2, Fp12 } = fields;
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const { twistType, ateLoopSize, xNegative, postPrecompute } = params;
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type G1 = typeof G1.BASE;
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type G2 = typeof G2.BASE;
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// Applies sparse multiplication as line function
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let lineFunction: (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) => Fp12;
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if (twistType === 'multiplicative') {
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lineFunction = (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) =>
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Fp12.mul014(f, c0, Fp2.mul(c1, Px), Fp2.mul(c2, Py));
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} else if (twistType === 'divisive') {
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// NOTE: it should be [c0, c1, c2], but we use different order here to reduce complexity of
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// precompute calculations.
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lineFunction = (c0: Fp2, c1: Fp2, c2: Fp2, f: Fp12, Px: Fp, Py: Fp) =>
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Fp12.mul034(f, Fp2.mul(c2, Py), Fp2.mul(c1, Px), c0);
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} else throw new Error('bls: unknown twist type');
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const Fp2div2 = Fp2.div(Fp2.ONE, Fp2.mul(Fp2.ONE, _2n));
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function pointDouble(ell: PrecomputeSingle, Rx: Fp2, Ry: Fp2, Rz: Fp2) {
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const t0 = Fp2.sqr(Ry); // Ry²
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const t1 = Fp2.sqr(Rz); // Rz²
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const t2 = Fp2.mulByB(Fp2.mul(t1, _3n)); // 3 * T1 * B
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const t3 = Fp2.mul(t2, _3n); // 3 * T2
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const t4 = Fp2.sub(Fp2.sub(Fp2.sqr(Fp2.add(Ry, Rz)), t1), t0); // (Ry + Rz)² - T1 - T0
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const c0 = Fp2.sub(t2, t0); // T2 - T0 (i)
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const c1 = Fp2.mul(Fp2.sqr(Rx), _3n); // 3 * Rx²
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const c2 = Fp2.neg(t4); // -T4 (-h)
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ell.push([c0, c1, c2]);
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Rx = Fp2.mul(Fp2.mul(Fp2.mul(Fp2.sub(t0, t3), Rx), Ry), Fp2div2); // ((T0 - T3) * Rx * Ry) / 2
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Ry = Fp2.sub(Fp2.sqr(Fp2.mul(Fp2.add(t0, t3), Fp2div2)), Fp2.mul(Fp2.sqr(t2), _3n)); // ((T0 + T3) / 2)² - 3 * T2²
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Rz = Fp2.mul(t0, t4); // T0 * T4
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return { Rx, Ry, Rz };
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}
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function pointAdd(ell: PrecomputeSingle, Rx: Fp2, Ry: Fp2, Rz: Fp2, Qx: Fp2, Qy: Fp2) {
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// Addition
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const t0 = Fp2.sub(Ry, Fp2.mul(Qy, Rz)); // Ry - Qy * Rz
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const t1 = Fp2.sub(Rx, Fp2.mul(Qx, Rz)); // Rx - Qx * Rz
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const c0 = Fp2.sub(Fp2.mul(t0, Qx), Fp2.mul(t1, Qy)); // T0 * Qx - T1 * Qy == Ry * Qx - Rx * Qy
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const c1 = Fp2.neg(t0); // -T0 == Qy * Rz - Ry
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const c2 = t1; // == Rx - Qx * Rz
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ell.push([c0, c1, c2]);
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const t2 = Fp2.sqr(t1); // T1²
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const t3 = Fp2.mul(t2, t1); // T2 * T1
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const t4 = Fp2.mul(t2, Rx); // T2 * Rx
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const t5 = Fp2.add(Fp2.sub(t3, Fp2.mul(t4, _2n)), Fp2.mul(Fp2.sqr(t0), Rz)); // T3 - 2 * T4 + T0² * Rz
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Rx = Fp2.mul(t1, t5); // T1 * T5
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Ry = Fp2.sub(Fp2.mul(Fp2.sub(t4, t5), t0), Fp2.mul(t3, Ry)); // (T4 - T5) * T0 - T3 * Ry
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Rz = Fp2.mul(Rz, t3); // Rz * T3
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return { Rx, Ry, Rz };
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}
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// Pre-compute coefficients for sparse multiplication
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// Point addition and point double calculations is reused for coefficients
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// pointAdd happens only if bit set, so wNAF is reasonable. Unfortunately we cannot combine
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// add + double in windowed precomputes here, otherwise it would be single op (since X is static)
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const ATE_NAF = NAfDecomposition(ateLoopSize);
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const calcPairingPrecomputes = memoized((point: G2) => {
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const p = point;
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const { x, y } = p.toAffine();
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// prettier-ignore
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const Qx = x, Qy = y, negQy = Fp2.neg(y);
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// prettier-ignore
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let Rx = Qx, Ry = Qy, Rz = Fp2.ONE;
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const ell: Precompute = [];
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for (const bit of ATE_NAF) {
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const cur: PrecomputeSingle = [];
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({ Rx, Ry, Rz } = pointDouble(cur, Rx, Ry, Rz));
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if (bit) ({ Rx, Ry, Rz } = pointAdd(cur, Rx, Ry, Rz, Qx, bit === -1 ? negQy : Qy));
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ell.push(cur);
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}
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if (postPrecompute) {
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const last = ell[ell.length - 1];
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postPrecompute(Rx, Ry, Rz, Qx, Qy, pointAdd.bind(null, last));
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}
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return ell;
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});
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// Main pairing logic is here. Computes product of miller loops + final exponentiate
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// Applies calculated precomputes
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type MillerInput = [Precompute, Fp, Fp][];
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function millerLoopBatch(pairs: MillerInput, withFinalExponent: boolean = false) {
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let f12 = Fp12.ONE;
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if (pairs.length) {
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const ellLen = pairs[0][0].length;
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for (let i = 0; i < ellLen; i++) {
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f12 = Fp12.sqr(f12); // This allows us to do sqr only one time for all pairings
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// NOTE: we apply multiple pairings in parallel here
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for (const [ell, Px, Py] of pairs) {
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for (const [c0, c1, c2] of ell[i]) f12 = lineFunction(c0, c1, c2, f12, Px, Py);
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}
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}
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}
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if (xNegative) f12 = Fp12.conjugate(f12);
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return withFinalExponent ? Fp12.finalExponentiate(f12) : f12;
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}
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|
type PairingInput = { g1: G1; g2: G2 };
|
|
// Calculates product of multiple pairings
|
|
// This up to x2 faster than just `map(({g1, g2})=>pairing({g1,g2}))`
|
|
function pairingBatch(pairs: PairingInput[], withFinalExponent: boolean = true) {
|
|
const res: MillerInput = [];
|
|
// Cache precomputed toAffine for all points
|
|
normalizeZ(
|
|
G1,
|
|
pairs.map(({ g1 }) => g1)
|
|
);
|
|
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: G1, P: G2, withFinalExponent: boolean = true): Fp12 {
|
|
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<P, S>(
|
|
blsPairing: BlsPairing,
|
|
PubCurve: CurvePointsRes<P> & H2CHasher<P>,
|
|
SigCurve: CurvePointsRes<S> & H2CHasher<S>,
|
|
SignatureCoder: SignatureCoder<S>,
|
|
isSigG1: boolean
|
|
): BLSSigs<P, S> {
|
|
const { Fp12, pairingBatch } = blsPairing;
|
|
type PubPoint = WeierstrassPoint<P>;
|
|
type SigPoint = WeierstrassPoint<S>;
|
|
function normPub(point: PubPoint | BLSInput): PubPoint {
|
|
return point instanceof PubCurve.Point ? (point as PubPoint) : PubCurve.Point.fromHex(point);
|
|
}
|
|
function normSig(point: SigPoint | BLSInput): SigPoint {
|
|
return point instanceof SigCurve.Point ? (point as SigPoint) : SigCurve.Point.fromHex(point);
|
|
}
|
|
function amsg(m: unknown): SigPoint {
|
|
if (!(m instanceof SigCurve.Point))
|
|
throw new Error(`expected valid message hashed to ${!isSigG1 ? 'G2' : 'G1'} curve`);
|
|
return m as SigPoint;
|
|
}
|
|
|
|
type G1 = CurvePointsRes<Fp>['Point']['BASE'];
|
|
type G2 = CurvePointsRes<Fp2>['Point']['BASE'];
|
|
type PairingInput = { g1: G1; g2: G2 };
|
|
// What matters here is what point pairing API accepts as G1 or G2, not actual size or names
|
|
const pair: (a: PubPoint, b: SigPoint) => PairingInput = !isSigG1
|
|
? (a: PubPoint, b: SigPoint) => ({ g1: a, g2: b }) as PairingInput
|
|
: (a: PubPoint, b: SigPoint) => ({ g1: b, g2: a }) as PairingInput;
|
|
return {
|
|
// P = pk x G
|
|
getPublicKey(secretKey: PrivKey): PubPoint {
|
|
// TODO: replace with
|
|
// const sec = PubCurve.Point.Fn.fromBytes(secretKey);
|
|
const sec = _normFnElement(PubCurve.Point.Fn, secretKey);
|
|
return PubCurve.Point.BASE.multiply(sec);
|
|
},
|
|
// S = pk x H(m)
|
|
sign(message: SigPoint, secretKey: PrivKey, unusedArg?: any): SigPoint {
|
|
if (unusedArg != null) throw new Error('sign() expects 2 arguments');
|
|
// TODO: replace with
|
|
// PubCurve.Point.Fn.fromBytes(secretKey)
|
|
const sec = _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: SigPoint | BLSInput,
|
|
message: SigPoint,
|
|
publicKey: PubPoint | BLSInput,
|
|
unusedArg?: any
|
|
): boolean {
|
|
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: SigPoint | BLSInput,
|
|
messages: SigPoint[],
|
|
publicKeys: (PubPoint | BLSInput)[]
|
|
): boolean {
|
|
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<SigPoint, PubPoint[]>();
|
|
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: (PubPoint | BLSInput)[]): PubPoint {
|
|
aNonEmpty(publicKeys);
|
|
publicKeys = publicKeys.map((pub) => normPub(pub));
|
|
const agg = (publicKeys as PubPoint[]).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: (SigPoint | BLSInput)[]): SigPoint {
|
|
aNonEmpty(signatures);
|
|
signatures = signatures.map((sig) => normSig(sig));
|
|
const agg = (signatures as SigPoint[]).reduce((sum, s) => sum.add(s), SigCurve.Point.ZERO);
|
|
agg.assertValidity();
|
|
return agg;
|
|
},
|
|
|
|
hash(messageBytes: Uint8Array, DST?: string | Uint8Array): SigPoint {
|
|
abytes(messageBytes);
|
|
const opts = DST ? { DST } : undefined;
|
|
return SigCurve.hashToCurve(messageBytes, opts) as SigPoint;
|
|
},
|
|
Signature: SignatureCoder,
|
|
};
|
|
}
|
|
|
|
// G1_Point: ProjConstructor<bigint>, G2_Point: ProjConstructor<Fp2>,
|
|
export function bls(CURVE: CurveType): CurveFn {
|
|
// 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_ = weierstrassPoints(CURVE.G1);
|
|
const G1 = Object.assign(
|
|
G1_,
|
|
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_ = weierstrassPoints(CURVE.G2);
|
|
const G2 = Object.assign(
|
|
G2_,
|
|
createHasher(G2_.Point as H2CPointConstructor<Fp2>, CURVE.G2.mapToCurve, {
|
|
...CURVE.htfDefaults,
|
|
...CURVE.G2.htfDefaults,
|
|
})
|
|
);
|
|
type G1 = typeof G1.Point.BASE;
|
|
type G2 = typeof G2.Point.BASE;
|
|
|
|
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 || randomBytes;
|
|
const randomSecretKey = (): Uint8Array => {
|
|
const length = getMinHashLength(Fr.ORDER);
|
|
return mapHashToField(rand(length), Fr.ORDER);
|
|
};
|
|
const utils = {
|
|
randomSecretKey,
|
|
randomPrivateKey: randomSecretKey,
|
|
calcPairingPrecomputes,
|
|
};
|
|
|
|
// LEGACY code
|
|
type G1Hex = Hex | G1;
|
|
type G2Hex = Hex | G2;
|
|
|
|
const { ShortSignature } = CURVE.G1;
|
|
const { Signature } = CURVE.G2;
|
|
|
|
function normP1Hash(point: G1Hex, htfOpts?: htfBasicOpts): G1 {
|
|
return point instanceof G1.Point
|
|
? point
|
|
: shortSignatures.hash(ensureBytes('point', point), htfOpts?.DST);
|
|
}
|
|
function normP2Hash(point: G2Hex, htfOpts?: htfBasicOpts): G2 {
|
|
return point instanceof G2.Point
|
|
? point
|
|
: longSignatures.hash(ensureBytes('point', point), htfOpts?.DST);
|
|
}
|
|
|
|
function getPublicKey(privateKey: PrivKey): Uint8Array {
|
|
return longSignatures.getPublicKey(privateKey).toBytes(true);
|
|
}
|
|
function getPublicKeyForShortSignatures(privateKey: PrivKey): Uint8Array {
|
|
return shortSignatures.getPublicKey(privateKey).toBytes(true);
|
|
}
|
|
function sign(message: Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array;
|
|
function sign(message: G2, privateKey: PrivKey, htfOpts?: htfBasicOpts): G2;
|
|
function sign(message: G2Hex, privateKey: PrivKey, htfOpts?: htfBasicOpts): Uint8Array | G2 {
|
|
const Hm = normP2Hash(message, htfOpts);
|
|
const S = longSignatures.sign(Hm, privateKey);
|
|
return message instanceof G2.Point ? S : Signature.toBytes(S);
|
|
}
|
|
function signShortSignature(
|
|
message: Hex,
|
|
privateKey: PrivKey,
|
|
htfOpts?: htfBasicOpts
|
|
): Uint8Array;
|
|
function signShortSignature(message: G1, privateKey: PrivKey, htfOpts?: htfBasicOpts): G1;
|
|
function signShortSignature(
|
|
message: G1Hex,
|
|
privateKey: PrivKey,
|
|
htfOpts?: htfBasicOpts
|
|
): Uint8Array | G1 {
|
|
const Hm = normP1Hash(message, htfOpts);
|
|
const S = shortSignatures.sign(Hm, privateKey);
|
|
return message instanceof G1.Point ? S : ShortSignature.toBytes(S);
|
|
}
|
|
function verify(
|
|
signature: G2Hex,
|
|
message: G2Hex,
|
|
publicKey: G1Hex,
|
|
htfOpts?: htfBasicOpts
|
|
): boolean {
|
|
const Hm = normP2Hash(message, htfOpts);
|
|
return longSignatures.verify(signature, Hm, publicKey);
|
|
}
|
|
function verifyShortSignature(
|
|
signature: G1Hex,
|
|
message: G1Hex,
|
|
publicKey: G2Hex,
|
|
htfOpts?: htfBasicOpts
|
|
): boolean {
|
|
const Hm = normP1Hash(message, htfOpts);
|
|
return shortSignatures.verify(signature, Hm, publicKey);
|
|
}
|
|
function aggregatePublicKeys(publicKeys: Hex[]): Uint8Array;
|
|
function aggregatePublicKeys(publicKeys: G1[]): G1;
|
|
function aggregatePublicKeys(publicKeys: G1Hex[]): Uint8Array | G1 {
|
|
const agg = longSignatures.aggregatePublicKeys(publicKeys);
|
|
return publicKeys[0] instanceof G1.Point ? agg : agg.toBytes(true);
|
|
}
|
|
function aggregateSignatures(signatures: Hex[]): Uint8Array;
|
|
function aggregateSignatures(signatures: G2[]): G2;
|
|
function aggregateSignatures(signatures: G2Hex[]): Uint8Array | G2 {
|
|
const agg = longSignatures.aggregateSignatures(signatures);
|
|
return signatures[0] instanceof G2.Point ? agg : Signature.toBytes(agg);
|
|
}
|
|
function aggregateShortSignatures(signatures: Hex[]): Uint8Array;
|
|
function aggregateShortSignatures(signatures: G1[]): G1;
|
|
function aggregateShortSignatures(signatures: G1Hex[]): Uint8Array | G1 {
|
|
const agg = shortSignatures.aggregateSignatures(signatures);
|
|
return signatures[0] instanceof G1.Point ? agg : ShortSignature.toBytes(agg);
|
|
}
|
|
function verifyBatch(
|
|
signature: G2Hex,
|
|
messages: G2Hex[],
|
|
publicKeys: G1Hex[],
|
|
htfOpts?: htfBasicOpts
|
|
): boolean {
|
|
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,
|
|
};
|
|
}
|