snarkjs/src/f3field.js

/*
    Copyright 2018 0kims association.

    This file is part of zksnark JavaScript library.

    zksnark JavaScript library is a free software: you can redistribute it and/or 
    modify it under the terms of the GNU General Public License as published by the 
    Free Software Foundation, either version 3 of the License, or (at your option) 
    any later version.

    zksnark JavaScript library is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 
    or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for 
    more details.

    You should have received a copy of the GNU General Public License along with 
    zksnark JavaScript library. If not, see <https://www.gnu.org/licenses/>.
*/

const fUtils = require("./futils.js");

class F3Field {
    constructor(F, nonResidue) {
        this.F = F;
        this.zero = [this.F.zero, this.F.zero, this.F.zero];
        this.one = [this.F.one, this.F.zero, this.F.zero];
        this.nonResidue = nonResidue;
    }

    _mulByNonResidue(a) {
        return this.F.mul(this.nonResidue, a);
    }

    copy(a) {
        return [this.F.copy(a[0]), this.F.copy(a[1]), this.F.copy(a[2])];
    }

    add(a, b) {
        return [
            this.F.add(a[0], b[0]),
            this.F.add(a[1], b[1]),
            this.F.add(a[2], b[2])
        ];
    }

    double(a) {
        return this.add(a,a);
    }

    sub(a, b) {
        return [
            this.F.sub(a[0], b[0]),
            this.F.sub(a[1], b[1]),
            this.F.sub(a[2], b[2])
        ];
    }

    neg(a) {
        return this.sub(this.zero, a);
    }

    mul(a, b) {

        const aA = this.F.mul(a[0] , b[0]);
        const bB = this.F.mul(a[1] , b[1]);
        const cC = this.F.mul(a[2] , b[2]);

        return [
            this.F.add(
                aA,
                this._mulByNonResidue(
                    this.F.sub(
                        this.F.mul(
                            this.F.add(a[1], a[2]),
                            this.F.add(b[1], b[2])),
                        this.F.add(bB, cC)))),    // aA + non_residue*((b+c)*(B+C)-bB-cC),

            this.F.add(
                this.F.sub(
                    this.F.mul(
                        this.F.add(a[0], a[1]),
                        this.F.add(b[0], b[1])),
                    this.F.add(aA, bB)),
                this._mulByNonResidue( cC)),   // (a+b)*(A+B)-aA-bB+non_residue*cC

            this.F.add(
                this.F.sub(
                    this.F.mul(
                        this.F.add(a[0], a[2]),
                        this.F.add(b[0], b[2])),
                    this.F.add(aA, cC)),
                bB)];                           // (a+c)*(A+C)-aA+bB-cC)
    }

    inverse(a) {
        const t0 = this.F.square(a[0]);             // t0 = a^2 ;
        const t1 = this.F.square(a[1]);             // t1 = b^2 ;
        const t2 = this.F.square(a[2]);             // t2 = c^2;
        const t3 = this.F.mul(a[0],a[1]);           // t3 = ab
        const t4 = this.F.mul(a[0],a[2]);           // t4 = ac
        const t5 = this.F.mul(a[1],a[2]);           // t5 = bc;
        // c0 = t0 - non_residue * t5;
        const c0 = this.F.sub(t0, this._mulByNonResidue(t5));
        // c1 = non_residue * t2 - t3;
        const c1 = this.F.sub(this._mulByNonResidue(t2), t3);
        const c2 = this.F.sub(t1, t4);              // c2 = t1-t4

        // t6 = (a * c0 + non_residue * (c * c1 + b * c2)).inverse();
        const t6 =
            this.F.inverse(
                this.F.add(
                    this.F.mul(a[0], c0),
                    this._mulByNonResidue(
                        this.F.add(
                            this.F.mul(a[2], c1),
                            this.F.mul(a[1], c2)))));

        return [
            this.F.mul(t6, c0),         // t6*c0
            this.F.mul(t6, c1),         // t6*c1
            this.F.mul(t6, c2)];        // t6*c2
    }

    div(a, b) {
        return this.mul(a, this.inverse(b));
    }

    square(a) {
        const s0 = this.F.square(a[0]);                   // s0 = a^2
        const ab = this.F.mul(a[0], a[1]);                // ab = a*b
        const s1 = this.F.add(ab, ab);                    // s1 = 2ab;
        const s2 = this.F.square(
            this.F.add(this.F.sub(a[0],a[1]), a[2]));     // s2 = (a - b + c)^2;
        const bc = this.F.mul(a[1],a[2]);                 // bc = b*c
        const s3 = this.F.add(bc, bc);                    // s3 = 2*bc
        const s4 = this.F.square(a[2]);                   // s4 = c^2


        return [
            this.F.add(
                s0,
                this._mulByNonResidue(s3)),           // s0 + non_residue * s3,
            this.F.add(
                s1,
                this._mulByNonResidue(s4)),           // s1 + non_residue * s4,
            this.F.sub(
                this.F.add( this.F.add(s1, s2) , s3 ),
                this.F.add(s0, s4))];                      // s1 + s2 + s3 - s0 - s4
    }

    isZero(a) {
        return this.F.isZero(a[0]) && this.F.isZero(a[1]) && this.F.isZero(a[2]);
    }

    equals(a, b) {
        return this.F.equals(a[0], b[0]) && this.F.equals(a[1], b[1]) && this.F.equals(a[2], b[2]);
    }

    affine(a) {
        return [this.F.affine(a[0]), this.F.affine(a[1]), this.F.affine(a[2])];
    }

    mulScalar(base, e) {
        return fUtils.mulScalar(this, base, e);
    }

    exp(base, e) {
        return fUtils.exp(this, base, e);
    }

    toString(a) {
        const cp = this.affine(a);
        return `[ ${this.F.toString(cp[0])} , ${this.F.toString(cp[1])}, ${this.F.toString(cp[2])} ]`;
    }
}

module.exports = F3Field;