446 lines
14 KiB
JavaScript
446 lines
14 KiB
JavaScript
/*
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Copyright 2018 0kims association.
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This file is part of snarkjs.
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snarkjs is a free software: you can redistribute it and/or
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modify it under the terms of the GNU General Public License as published by the
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Free Software Foundation, either version 3 of the License, or (at your option)
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any later version.
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snarkjs is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
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more details.
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You should have received a copy of the GNU General Public License along with
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snarkjs. If not, see <https://www.gnu.org/licenses/>.
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*/
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const bigInt = require("./bigint.js");
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const F1Field = require("./zqfield.js");
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const F2Field = require("./f2field.js");
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const F3Field = require("./f3field.js");
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const GCurve = require("./gcurve.js");
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class BN128 {
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constructor() {
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this.q = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208583");
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this.r = bigInt("21888242871839275222246405745257275088548364400416034343698204186575808495617");
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this.g1 = [ bigInt(1), bigInt(2), bigInt(1)];
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this.g2 = [
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[
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bigInt("10857046999023057135944570762232829481370756359578518086990519993285655852781"),
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bigInt("11559732032986387107991004021392285783925812861821192530917403151452391805634")
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],
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[
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bigInt("8495653923123431417604973247489272438418190587263600148770280649306958101930"),
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bigInt("4082367875863433681332203403145435568316851327593401208105741076214120093531")
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],
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[
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bigInt("1"),
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bigInt("0")
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]
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];
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this.nonResidueF2 = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582");
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this.nonResidueF6 = [ bigInt("9"), bigInt("1") ];
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this.F1 = new F1Field(this.q);
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this.F2 = new F2Field(this.F1, this.nonResidueF2);
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this.G1 = new GCurve(this.F1, this.g1);
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this.G2 = new GCurve(this.F2, this.g2);
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this.F6 = new F3Field(this.F2, this.nonResidueF6);
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this.F12 = new F2Field(this.F6, this.nonResidueF6);
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this.Fr = new F1Field(this.r);
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const self = this;
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this.F12._mulByNonResidue = function(a) {
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return [self.F2.mul(this.nonResidue, a[2]), a[0], a[1]];
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};
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this._preparePairing();
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}
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_preparePairing() {
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this.loopCount = bigInt("29793968203157093288");// CONSTANT
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// Set loopCountNeg
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if (this.loopCount.isNegative()) {
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this.loopCount = this.loopCount.neg();
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this.loopCountNeg = true;
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} else {
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this.loopCountNeg = false;
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}
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// Set loop_count_bits
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let lc = this.loopCount;
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this.loop_count_bits = []; // Constant
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while (!lc.isZero()) {
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this.loop_count_bits.push( lc.isOdd() );
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lc = lc.shr(1);
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}
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this.two_inv = this.F1.inverse(bigInt(2));
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this.coef_b = bigInt(3);
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this.twist = [bigInt(9) , bigInt(1)];
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this.twist_coeff_b = this.F2.mulScalar( this.F2.inverse(this.twist), this.coef_b );
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this.frobenius_coeffs_c1_1 = bigInt("21888242871839275222246405745257275088696311157297823662689037894645226208582");
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this.twist_mul_by_q_X =
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[
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bigInt("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
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bigInt("10307601595873709700152284273816112264069230130616436755625194854815875713954")
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];
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this.twist_mul_by_q_Y =
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[
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bigInt("2821565182194536844548159561693502659359617185244120367078079554186484126554"),
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bigInt("3505843767911556378687030309984248845540243509899259641013678093033130930403")
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];
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this.final_exponent = bigInt("552484233613224096312617126783173147097382103762957654188882734314196910839907541213974502761540629817009608548654680343627701153829446747810907373256841551006201639677726139946029199968412598804882391702273019083653272047566316584365559776493027495458238373902875937659943504873220554161550525926302303331747463515644711876653177129578303191095900909191624817826566688241804408081892785725967931714097716709526092261278071952560171111444072049229123565057483750161460024353346284167282452756217662335528813519139808291170539072125381230815729071544861602750936964829313608137325426383735122175229541155376346436093930287402089517426973178917569713384748081827255472576937471496195752727188261435633271238710131736096299798168852925540549342330775279877006784354801422249722573783561685179618816480037695005515426162362431072245638324744480");
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}
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pairing(p1, p2) {
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const pre1 = this.precomputeG1(p1);
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const pre2 = this.precomputeG2(p2);
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const r1 = this.millerLoop(pre1, pre2);
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const res = this.finalExponentiation(r1);
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return res;
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}
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precomputeG1(p) {
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const Pcopy = this.G1.affine(p);
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const res = {};
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res.PX = Pcopy[0];
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res.PY = Pcopy[1];
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return res;
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}
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precomputeG2(p) {
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const Qcopy = this.G2.affine(p);
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const res = {
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QX: Qcopy[0],
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QY: Qcopy[1],
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coeffs: []
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};
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const R = {
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X: Qcopy[0],
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Y: Qcopy[1],
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Z: this.F2.one
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};
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let c;
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for (let i = this.loop_count_bits.length-2; i >= 0; --i)
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{
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const bit = this.loop_count_bits[i];
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c = this._doubleStep(R);
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res.coeffs.push(c);
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if (bit)
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{
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c = this._addStep(Qcopy, R);
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res.coeffs.push(c);
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}
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}
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const Q1 = this.G2.affine(this._g2MulByQ(Qcopy));
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if (!this.F2.equals(Q1[2], this.F2.one))
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{
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throw new Error("Expected values are not equal");
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}
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const Q2 = this.G2.affine(this._g2MulByQ(Q1));
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if (!this.F2.equals(Q2[2], this.F2.one))
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{
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throw new Error("Expected values are not equal");
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}
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if (this.loopCountNeg)
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{
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R.Y = this.F2.neg(R.Y);
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}
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Q2[1] = this.F2.neg(Q2[1]);
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c = this._addStep(Q1, R);
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res.coeffs.push(c);
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c = this._addStep(Q2, R);
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res.coeffs.push(c);
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return res;
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}
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millerLoop(pre1, pre2) {
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let f = this.F12.one;
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let idx = 0;
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let c;
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for (let i = this.loop_count_bits.length-2; i >= 0; --i)
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{
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const bit = this.loop_count_bits[i];
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/* code below gets executed for all bits (EXCEPT the MSB itself) of
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alt_bn128_param_p (skipping leading zeros) in MSB to LSB
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order */
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c = pre2.coeffs[idx++];
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f = this.F12.square(f);
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f = this._mul_by_024(
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f,
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c.ell_0,
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this.F2.mulScalar(c.ell_VW , pre1.PY),
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this.F2.mulScalar(c.ell_VV , pre1.PX));
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if (bit)
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{
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c = pre2.coeffs[idx++];
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f = this._mul_by_024(
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f,
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c.ell_0,
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this.F2.mulScalar(c.ell_VW, pre1.PY),
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this.F2.mulScalar(c.ell_VV, pre1.PX));
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}
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}
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if (this.loopCountNeg)
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{
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f = this.F12.inverse(f);
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}
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c = pre2.coeffs[idx++];
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f = this._mul_by_024(
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f,
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c.ell_0,
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this.F2.mulScalar(c.ell_VW, pre1.PY),
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this.F2.mulScalar(c.ell_VV, pre1.PX));
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c = pre2.coeffs[idx++];
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f = this._mul_by_024(
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f,
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c.ell_0,
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this.F2.mulScalar(c.ell_VW, pre1.PY),
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this.F2.mulScalar(c.ell_VV, pre1.PX));
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return f;
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}
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finalExponentiation(elt) {
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// TODO: There is an optimization in FF
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const res = this.F12.exp(elt,this.final_exponent);
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return res;
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}
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_doubleStep(current) {
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const X = current.X;
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const Y = current.Y;
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const Z = current.Z;
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const A = this.F2.mulScalar(this.F2.mul(X,Y), this.two_inv); // A = X1 * Y1 / 2
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const B = this.F2.square(Y); // B = Y1^2
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const C = this.F2.square(Z); // C = Z1^2
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const D = this.F2.add(C, this.F2.add(C,C)); // D = 3 * C
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const E = this.F2.mul(this.twist_coeff_b, D); // E = twist_b * D
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const F = this.F2.add(E, this.F2.add(E,E)); // F = 3 * E
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const G =
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this.F2.mulScalar(
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this.F2.add( B , F ),
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this.two_inv); // G = (B+F)/2
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const H =
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this.F2.sub(
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this.F2.square( this.F2.add(Y,Z) ),
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this.F2.add( B , C)); // H = (Y1+Z1)^2-(B+C)
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const I = this.F2.sub(E, B); // I = E-B
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const J = this.F2.square(X); // J = X1^2
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const E_squared = this.F2.square(E); // E_squared = E^2
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current.X = this.F2.mul( A, this.F2.sub(B,F) ); // X3 = A * (B-F)
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current.Y =
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this.F2.sub(
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this.F2.sub( this.F2.square(G) , E_squared ),
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this.F2.add( E_squared , E_squared )); // Y3 = G^2 - 3*E^2
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current.Z = this.F2.mul( B, H ); // Z3 = B * H
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const c = {
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ell_0 : this.F2.mul( I, this.twist), // ell_0 = xi * I
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ell_VW: this.F2.neg( H ), // ell_VW = - H (later: * yP)
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ell_VV: this.F2.add( J , this.F2.add(J,J) ) // ell_VV = 3*J (later: * xP)
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};
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return c;
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}
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_addStep(base, current) {
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const X1 = current.X;
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const Y1 = current.Y;
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const Z1 = current.Z;
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const x2 = base[0];
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const y2 = base[1];
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const D = this.F2.sub( X1, this.F2.mul(x2,Z1) ); // D = X1 - X2*Z1
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// console.log("Y: "+ A[0].affine(this.q).toString(16));
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const E = this.F2.sub( Y1, this.F2.mul(y2,Z1) ); // E = Y1 - Y2*Z1
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const F = this.F2.square(D); // F = D^2
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const G = this.F2.square(E); // G = E^2
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const H = this.F2.mul(D,F); // H = D*F
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const I = this.F2.mul(X1,F); // I = X1 * F
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const J =
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this.F2.sub(
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this.F2.add( H, this.F2.mul(Z1,G) ),
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this.F2.add( I, I )); // J = H + Z1*G - (I+I)
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current.X = this.F2.mul( D , J ); // X3 = D*J
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current.Y =
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this.F2.sub(
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this.F2.mul( E , this.F2.sub(I,J) ),
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this.F2.mul( H , Y1)); // Y3 = E*(I-J)-(H*Y1)
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current.Z = this.F2.mul(Z1,H);
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const c = {
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ell_0 :
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this.F2.mul(
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this.twist,
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this.F2.sub(
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this.F2.mul(E , x2),
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this.F2.mul(D , y2))), // ell_0 = xi * (E * X2 - D * Y2)
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ell_VV : this.F2.neg(E), // ell_VV = - E (later: * xP)
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ell_VW : D // ell_VW = D (later: * yP )
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};
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return c;
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}
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_mul_by_024(a, ell_0, ell_VW, ell_VV) {
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// Old implementation
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/*
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const b = [
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[ell_0, this.F2.zero, ell_VV],
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[this.F2.zero, ell_VW, this.F2.zero]
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];
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return this.F12.mul(a,b);
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*/
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// This is a new implementation,
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// But it does not look worthy
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// at least in javascript.
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let z0 = a[0][0];
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let z1 = a[0][1];
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let z2 = a[0][2];
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let z3 = a[1][0];
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let z4 = a[1][1];
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let z5 = a[1][2];
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const x0 = ell_0;
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const x2 = ell_VV;
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const x4 = ell_VW;
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const D0 = this.F2.mul(z0, x0);
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const D2 = this.F2.mul(z2, x2);
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const D4 = this.F2.mul(z4, x4);
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const t2 = this.F2.add(z0, z4);
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let t1 = this.F2.add(z0, z2);
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const s0 = this.F2.add(this.F2.add(z1,z3),z5);
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// For z.a_.a_ = z0.
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let S1 = this.F2.mul(z1, x2);
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let T3 = this.F2.add(S1, D4);
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let T4 = this.F2.add( this.F2.mul(this.nonResidueF6, T3),D0);
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z0 = T4;
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// For z.a_.b_ = z1
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T3 = this.F2.mul(z5, x4);
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S1 = this.F2.add(S1, T3);
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T3 = this.F2.add(T3, D2);
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T4 = this.F2.mul(this.nonResidueF6, T3);
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T3 = this.F2.mul(z1, x0);
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S1 = this.F2.add(S1, T3);
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T4 = this.F2.add(T4, T3);
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z1 = T4;
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// For z.a_.c_ = z2
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let t0 = this.F2.add(x0, x2);
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T3 = this.F2.sub(
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this.F2.mul(t1, t0),
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this.F2.add(D0, D2));
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T4 = this.F2.mul(z3, x4);
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S1 = this.F2.add(S1, T4);
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// For z.b_.a_ = z3 (z3 needs z2)
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t0 = this.F2.add(z2, z4);
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z2 = this.F2.add(T3, T4);
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t1 = this.F2.add(x2, x4);
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T3 = this.F2.sub(
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this.F2.mul(t0,t1),
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this.F2.add(D2, D4));
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T4 = this.F2.mul(this.nonResidueF6, T3);
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T3 = this.F2.mul(z3, x0);
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S1 = this.F2.add(S1, T3);
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T4 = this.F2.add(T4, T3);
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z3 = T4;
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// For z.b_.b_ = z4
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T3 = this.F2.mul(z5, x2);
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S1 = this.F2.add(S1, T3);
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T4 = this.F2.mul(this.nonResidueF6, T3);
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t0 = this.F2.add(x0, x4);
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T3 = this.F2.sub(
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this.F2.mul(t2,t0),
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this.F2.add(D0, D4));
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T4 = this.F2.add(T4, T3);
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z4 = T4;
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// For z.b_.c_ = z5.
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t0 = this.F2.add(this.F2.add(x0, x2), x4);
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T3 = this.F2.sub(this.F2.mul(s0, t0), S1);
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z5 = T3;
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return [
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[z0, z1, z2],
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[z3, z4, z5]
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];
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}
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_g2MulByQ(p) {
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const fmx = [p[0][0], this.F1.mul(p[0][1], this.frobenius_coeffs_c1_1 )];
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const fmy = [p[1][0], this.F1.mul(p[1][1], this.frobenius_coeffs_c1_1 )];
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const fmz = [p[2][0], this.F1.mul(p[2][1], this.frobenius_coeffs_c1_1 )];
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return [
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this.F2.mul(this.twist_mul_by_q_X , fmx),
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this.F2.mul(this.twist_mul_by_q_Y , fmy),
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fmz
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];
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}
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}
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module.exports = BN128;
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