411 lines
17 KiB
JavaScript
411 lines
17 KiB
JavaScript
"use strict";
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Object.defineProperty(exports, "__esModule", { value: true });
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exports.bls = bls;
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/**
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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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const utils_ts_1 = require("../utils.js");
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const curve_ts_1 = require("./curve.js");
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const hash_to_curve_ts_1 = require("./hash-to-curve.js");
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const modular_ts_1 = require("./modular.js");
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const weierstrass_ts_1 = require("./weierstrass.js");
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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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// Not used with BLS12-381 (no sequential `11` in X). Useful for other curves.
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function NAfDecomposition(a) {
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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)
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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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}
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else
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res.unshift(1);
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}
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return res;
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}
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function aNonEmpty(arr) {
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if (!Array.isArray(arr) || arr.length === 0)
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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(fields, G1, G2, params) {
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const { Fp2, Fp12 } = fields;
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const { twistType, ateLoopSize, xNegative, postPrecompute } = params;
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// Applies sparse multiplication as line function
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let lineFunction;
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if (twistType === 'multiplicative') {
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lineFunction = (c0, c1, c2, f, Px, Py) => Fp12.mul014(f, c0, Fp2.mul(c1, Px), Fp2.mul(c2, Py));
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}
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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, c1, c2, f, Px, Py) => Fp12.mul034(f, Fp2.mul(c2, Py), Fp2.mul(c1, Px), c0);
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}
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else
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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, Rx, Ry, Rz) {
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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, Rx, Ry, Rz, Qx, Qy) {
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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 = (0, utils_ts_1.memoized)((point) => {
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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 = [];
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for (const bit of ATE_NAF) {
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const cur = [];
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({ Rx, Ry, Rz } = pointDouble(cur, Rx, Ry, Rz));
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if (bit)
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({ 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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function millerLoopBatch(pairs, withFinalExponent = 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])
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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)
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f12 = Fp12.conjugate(f12);
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return withFinalExponent ? Fp12.finalExponentiate(f12) : f12;
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}
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// Calculates product of multiple pairings
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// This up to x2 faster than just `map(({g1, g2})=>pairing({g1,g2}))`
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function pairingBatch(pairs, withFinalExponent = true) {
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const res = [];
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// Cache precomputed toAffine for all points
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(0, curve_ts_1.normalizeZ)(G1, pairs.map(({ g1 }) => g1));
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(0, curve_ts_1.normalizeZ)(G2, pairs.map(({ g2 }) => g2));
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for (const { g1, g2 } of pairs) {
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if (g1.is0() || g2.is0())
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throw new Error('pairing is not available for ZERO point');
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// This uses toAffine inside
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g1.assertValidity();
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g2.assertValidity();
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const Qa = g1.toAffine();
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res.push([calcPairingPrecomputes(g2), Qa.x, Qa.y]);
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}
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return millerLoopBatch(res, withFinalExponent);
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}
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// Calculates bilinear pairing
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function pairing(Q, P, withFinalExponent = true) {
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return pairingBatch([{ g1: Q, g2: P }], withFinalExponent);
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}
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return {
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Fp12, // NOTE: we re-export Fp12 here because pairing results are Fp12!
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millerLoopBatch,
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pairing,
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pairingBatch,
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calcPairingPrecomputes,
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};
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}
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function createBlsSig(blsPairing, PubCurve, SigCurve, SignatureCoder, isSigG1) {
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const { Fp12, pairingBatch } = blsPairing;
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function normPub(point) {
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return point instanceof PubCurve.Point ? point : PubCurve.Point.fromHex(point);
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}
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function normSig(point) {
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return point instanceof SigCurve.Point ? point : SigCurve.Point.fromHex(point);
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}
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function amsg(m) {
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if (!(m instanceof SigCurve.Point))
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throw new Error(`expected valid message hashed to ${!isSigG1 ? 'G2' : 'G1'} curve`);
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return m;
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}
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// What matters here is what point pairing API accepts as G1 or G2, not actual size or names
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const pair = !isSigG1
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? (a, b) => ({ g1: a, g2: b })
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: (a, b) => ({ g1: b, g2: a });
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return {
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// P = pk x G
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getPublicKey(secretKey) {
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// TODO: replace with
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// const sec = PubCurve.Point.Fn.fromBytes(secretKey);
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const sec = (0, weierstrass_ts_1._normFnElement)(PubCurve.Point.Fn, secretKey);
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return PubCurve.Point.BASE.multiply(sec);
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},
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// S = pk x H(m)
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sign(message, secretKey, unusedArg) {
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if (unusedArg != null)
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throw new Error('sign() expects 2 arguments');
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// TODO: replace with
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// PubCurve.Point.Fn.fromBytes(secretKey)
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const sec = (0, weierstrass_ts_1._normFnElement)(PubCurve.Point.Fn, secretKey);
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amsg(message).assertValidity();
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return message.multiply(sec);
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},
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// Checks if pairing of public key & hash is equal to pairing of generator & signature.
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// e(P, H(m)) == e(G, S)
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// e(S, G) == e(H(m), P)
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verify(signature, message, publicKey, unusedArg) {
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if (unusedArg != null)
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throw new Error('verify() expects 3 arguments');
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signature = normSig(signature);
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publicKey = normPub(publicKey);
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const P = publicKey.negate();
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const G = PubCurve.Point.BASE;
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const Hm = amsg(message);
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const S = signature;
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// This code was changed in 1.9.x:
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// Before it was G.negate() in G2, now it's always pubKey.negate
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// e(P, -Q)===e(-P, Q)==e(P, Q)^-1. Negate can be done anywhere (as long it is done once per pair).
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// We just moving sign, but since pairing is multiplicative, we doing X * X^-1 = 1
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const exp = pairingBatch([pair(P, Hm), pair(G, S)]);
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return Fp12.eql(exp, Fp12.ONE);
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},
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// https://ethresear.ch/t/fast-verification-of-multiple-bls-signatures/5407
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// e(G, S) = e(G, SUM(n)(Si)) = MUL(n)(e(G, Si))
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// TODO: maybe `{message: G2Hex, publicKey: G1Hex}[]` instead?
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verifyBatch(signature, messages, publicKeys) {
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aNonEmpty(messages);
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if (publicKeys.length !== messages.length)
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throw new Error('amount of public keys and messages should be equal');
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const sig = normSig(signature);
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const nMessages = messages;
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const nPublicKeys = publicKeys.map(normPub);
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// NOTE: this works only for exact same object
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const messagePubKeyMap = new Map();
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for (let i = 0; i < nPublicKeys.length; i++) {
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const pub = nPublicKeys[i];
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const msg = nMessages[i];
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let keys = messagePubKeyMap.get(msg);
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if (keys === undefined) {
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keys = [];
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messagePubKeyMap.set(msg, keys);
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}
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keys.push(pub);
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}
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const paired = [];
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const G = PubCurve.Point.BASE;
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try {
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for (const [msg, keys] of messagePubKeyMap) {
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const groupPublicKey = keys.reduce((acc, msg) => acc.add(msg));
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paired.push(pair(groupPublicKey, msg));
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}
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paired.push(pair(G.negate(), sig));
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return Fp12.eql(pairingBatch(paired), Fp12.ONE);
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}
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catch {
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return false;
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}
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},
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// Adds a bunch of public key points together.
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// pk1 + pk2 + pk3 = pkA
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aggregatePublicKeys(publicKeys) {
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aNonEmpty(publicKeys);
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publicKeys = publicKeys.map((pub) => normPub(pub));
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const agg = publicKeys.reduce((sum, p) => sum.add(p), PubCurve.Point.ZERO);
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agg.assertValidity();
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return agg;
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},
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// Adds a bunch of signature points together.
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// pk1 + pk2 + pk3 = pkA
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aggregateSignatures(signatures) {
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aNonEmpty(signatures);
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signatures = signatures.map((sig) => normSig(sig));
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const agg = signatures.reduce((sum, s) => sum.add(s), SigCurve.Point.ZERO);
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agg.assertValidity();
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return agg;
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},
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hash(messageBytes, DST) {
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(0, utils_ts_1.abytes)(messageBytes);
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const opts = DST ? { DST } : undefined;
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return SigCurve.hashToCurve(messageBytes, opts);
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},
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Signature: SignatureCoder,
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};
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}
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// G1_Point: ProjConstructor<bigint>, G2_Point: ProjConstructor<Fp2>,
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function bls(CURVE) {
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// Fields are specific for curve, so for now we'll need to pass them with opts
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const { Fp, Fr, Fp2, Fp6, Fp12 } = CURVE.fields;
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// Point on G1 curve: (x, y)
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const G1_ = (0, weierstrass_ts_1.weierstrassPoints)(CURVE.G1);
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const G1 = Object.assign(G1_, (0, hash_to_curve_ts_1.createHasher)(G1_.Point, CURVE.G1.mapToCurve, {
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...CURVE.htfDefaults,
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...CURVE.G1.htfDefaults,
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}));
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// Point on G2 curve (complex numbers): (x₁, x₂+i), (y₁, y₂+i)
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const G2_ = (0, weierstrass_ts_1.weierstrassPoints)(CURVE.G2);
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const G2 = Object.assign(G2_, (0, hash_to_curve_ts_1.createHasher)(G2_.Point, CURVE.G2.mapToCurve, {
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...CURVE.htfDefaults,
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...CURVE.G2.htfDefaults,
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}));
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const pairingRes = createBlsPairing(CURVE.fields, G1.Point, G2.Point, {
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...CURVE.params,
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postPrecompute: CURVE.postPrecompute,
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});
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const { millerLoopBatch, pairing, pairingBatch, calcPairingPrecomputes } = pairingRes;
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const longSignatures = createBlsSig(pairingRes, G1, G2, CURVE.G2.Signature, false);
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const shortSignatures = createBlsSig(pairingRes, G2, G1, CURVE.G1.ShortSignature, true);
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const rand = CURVE.randomBytes || utils_ts_1.randomBytes;
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const randomSecretKey = () => {
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const length = (0, modular_ts_1.getMinHashLength)(Fr.ORDER);
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return (0, modular_ts_1.mapHashToField)(rand(length), Fr.ORDER);
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};
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const utils = {
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randomSecretKey,
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randomPrivateKey: randomSecretKey,
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calcPairingPrecomputes,
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};
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const { ShortSignature } = CURVE.G1;
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const { Signature } = CURVE.G2;
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function normP1Hash(point, htfOpts) {
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return point instanceof G1.Point
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? point
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: shortSignatures.hash((0, utils_ts_1.ensureBytes)('point', point), htfOpts?.DST);
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}
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function normP2Hash(point, htfOpts) {
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return point instanceof G2.Point
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? point
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: longSignatures.hash((0, utils_ts_1.ensureBytes)('point', point), htfOpts?.DST);
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}
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function getPublicKey(privateKey) {
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return longSignatures.getPublicKey(privateKey).toBytes(true);
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}
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function getPublicKeyForShortSignatures(privateKey) {
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return shortSignatures.getPublicKey(privateKey).toBytes(true);
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}
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function sign(message, privateKey, htfOpts) {
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const Hm = normP2Hash(message, htfOpts);
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const S = longSignatures.sign(Hm, privateKey);
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return message instanceof G2.Point ? S : Signature.toBytes(S);
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}
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function signShortSignature(message, privateKey, htfOpts) {
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const Hm = normP1Hash(message, htfOpts);
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const S = shortSignatures.sign(Hm, privateKey);
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return message instanceof G1.Point ? S : ShortSignature.toBytes(S);
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}
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function verify(signature, message, publicKey, htfOpts) {
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const Hm = normP2Hash(message, htfOpts);
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return longSignatures.verify(signature, Hm, publicKey);
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}
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function verifyShortSignature(signature, message, publicKey, htfOpts) {
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const Hm = normP1Hash(message, htfOpts);
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return shortSignatures.verify(signature, Hm, publicKey);
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}
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function aggregatePublicKeys(publicKeys) {
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const agg = longSignatures.aggregatePublicKeys(publicKeys);
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return publicKeys[0] instanceof G1.Point ? agg : agg.toBytes(true);
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}
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function aggregateSignatures(signatures) {
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const agg = longSignatures.aggregateSignatures(signatures);
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return signatures[0] instanceof G2.Point ? agg : Signature.toBytes(agg);
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}
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function aggregateShortSignatures(signatures) {
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const agg = shortSignatures.aggregateSignatures(signatures);
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return signatures[0] instanceof G1.Point ? agg : ShortSignature.toBytes(agg);
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}
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function verifyBatch(signature, messages, publicKeys, htfOpts) {
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const Hm = messages.map((m) => normP2Hash(m, htfOpts));
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return longSignatures.verifyBatch(signature, Hm, publicKeys);
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}
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G1.Point.BASE.precompute(4);
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return {
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longSignatures,
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shortSignatures,
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millerLoopBatch,
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pairing,
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pairingBatch,
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verifyBatch,
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fields: {
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Fr,
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Fp,
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Fp2,
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Fp6,
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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
|