/*
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Copyright 2018 0kims association
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This file is part of zksnark javascript library.
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zksnark javascript library is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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zksnark javascript library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with zksnark javascript library. If not, see <https://www.gnu.org/licenses/>.
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*/
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const fUtils = require("./futils.js");
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class F3Field {
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constructor(F, nonResidue) {
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this.F = F;
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this.zero = [this.F.zero, this.F.zero, this.F.zero];
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this.one = [this.F.one, this.F.zero, this.F.zero];
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this.nonResidue = nonResidue;
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}
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_mulByNonResidue(a) {
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return this.F.mul(this.nonResidue, a);
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}
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copy(a) {
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return [this.F.copy(a[0]), this.F.copy(a[1]), this.F.copy(a[2])];
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}
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add(a, b) {
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return [
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this.F.add(a[0], b[0]),
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this.F.add(a[1], b[1]),
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this.F.add(a[2], b[2])
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];
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}
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double(a) {
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return this.add(a,a);
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}
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sub(a, b) {
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return [
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this.F.sub(a[0], b[0]),
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this.F.sub(a[1], b[1]),
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this.F.sub(a[2], b[2])
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];
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}
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neg(a) {
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return this.sub(this.zero, a);
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}
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mul(a, b) {
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const aA = this.F.mul(a[0] , b[0]);
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const bB = this.F.mul(a[1] , b[1]);
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const cC = this.F.mul(a[2] , b[2]);
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return [
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this.F.add(
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aA,
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this._mulByNonResidue(
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this.F.sub(
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this.F.mul(
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this.F.add(a[1], a[2]),
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this.F.add(b[1], b[2])),
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this.F.add(bB, cC)))), // aA + non_residue*((b+c)*(B+C)-bB-cC),
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this.F.add(
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this.F.sub(
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this.F.mul(
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this.F.add(a[0], a[1]),
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this.F.add(b[0], b[1])),
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this.F.add(aA, bB)),
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this._mulByNonResidue( cC)), // (a+b)*(A+B)-aA-bB+non_residue*cC
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this.F.add(
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this.F.sub(
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this.F.mul(
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this.F.add(a[0], a[2]),
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this.F.add(b[0], b[2])),
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this.F.add(aA, cC)),
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bB)]; // (a+c)*(A+C)-aA+bB-cC)
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}
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inverse(a) {
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const t0 = this.F.square(a[0]); // t0 = a^2 ;
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const t1 = this.F.square(a[1]); // t1 = b^2 ;
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const t2 = this.F.square(a[2]); // t2 = c^2;
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const t3 = this.F.mul(a[0],a[1]); // t3 = ab
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const t4 = this.F.mul(a[0],a[2]); // t4 = ac
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const t5 = this.F.mul(a[1],a[2]); // t5 = bc;
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// c0 = t0 - non_residue * t5;
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const c0 = this.F.sub(t0, this._mulByNonResidue(t5));
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// c1 = non_residue * t2 - t3;
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const c1 = this.F.sub(this._mulByNonResidue(t2), t3);
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const c2 = this.F.sub(t1, t4); // c2 = t1-t4
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// t6 = (a * c0 + non_residue * (c * c1 + b * c2)).inverse();
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const t6 =
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this.F.inverse(
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this.F.add(
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this.F.mul(a[0], c0),
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this._mulByNonResidue(
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this.F.add(
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this.F.mul(a[2], c1),
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this.F.mul(a[1], c2)))));
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return [
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this.F.mul(t6, c0), // t6*c0
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this.F.mul(t6, c1), // t6*c1
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this.F.mul(t6, c2)]; // t6*c2
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}
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div(a, b) {
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return this.mul(a, this.inverse(b));
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}
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square(a) {
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const s0 = this.F.square(a[0]); // s0 = a^2
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const ab = this.F.mul(a[0], a[1]); // ab = a*b
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const s1 = this.F.add(ab, ab); // s1 = 2ab;
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const s2 = this.F.square(
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this.F.add(this.F.sub(a[0],a[1]), a[2])); // s2 = (a - b + c)^2;
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const bc = this.F.mul(a[1],a[2]); // bc = b*c
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const s3 = this.F.add(bc, bc); // s3 = 2*bc
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const s4 = this.F.square(a[2]); // s4 = c^2
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return [
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this.F.add(
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s0,
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this._mulByNonResidue(s3)), // s0 + non_residue * s3,
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this.F.add(
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s1,
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this._mulByNonResidue(s4)), // s1 + non_residue * s4,
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this.F.sub(
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this.F.add( this.F.add(s1, s2) , s3 ),
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this.F.add(s0, s4))]; // s1 + s2 + s3 - s0 - s4
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}
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isZero(a) {
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return this.F.isZero(a[0]) && this.F.isZero(a[1]) && this.F.isZero(a[2]);
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}
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equals(a, b) {
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return this.F.equals(a[0], b[0]) && this.F.equals(a[1], b[1]) && this.F.equals(a[2], b[2]);
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}
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affine(a) {
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return [this.F.affine(a[0]), this.F.affine(a[1]), this.F.affine(a[2])];
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}
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mulScalar(base, e) {
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return fUtils.mulScalar(this, base, e);
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}
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exp(base, e) {
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return fUtils.exp(this, base, e);
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}
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toString(a) {
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const cp = this.affine(a);
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return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])}, ${this.F.toString(cp[2])} ]`;
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}
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}
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module.exports = F3Field;
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