snarkjs/src/f2field.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 F2Field {
    constructor(F, nonResidue) {
        this.F = F;
        this.zero = [this.F.zero, this.F.zero];
        this.one = [this.F.one, 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])];
    }

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

    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])
        ];
    }

    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]);

        return [
            this.F.add( aA , this._mulByNonResidue(bB)),
            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))];
    }

    inverse(a) {
        const t0 = this.F.square(a[0]);
        const t1 = this.F.square(a[1]);
        const t2 = this.F.sub(t0, this._mulByNonResidue(t1));
        const t3 = this.F.inverse(t2);
        return [
            this.F.mul(a[0], t3),
            this.F.neg(this.F.mul( a[1], t3)) ];
    }

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

    square(a) {
        const ab = this.F.mul(a[0] , a[1]);

        /*
        [
            (a + b) * (a + non_residue * b) - ab - non_residue * ab,
            ab + ab
        ];
        */

        return [
            this.F.sub(
                this.F.mul(
                    this.F.add(a[0], a[1]) ,
                    this.F.add(
                        a[0] ,
                        this._mulByNonResidue(a[1]))),
                this.F.add(
                    ab,
                    this._mulByNonResidue(ab))),
            this.F.add(ab, ab)
        ];
    }

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

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

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

    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])} ]`;
    }
}

module.exports = F2Field;