@kotevode/ffjavascript/src/f2field.js

Finite Field Library in Javascript

/*
    Copyright 2018 0kims association.

    This file is part of snarkjs.

    snarkjs 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.

    snarkjs 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
    snarkjs. If not, see <https://www.gnu.org/licenses/>.
*/

import * as fUtils from "./futils.js";
import buildSqrt from "./fsqrt.js";

export default class F2Field {
    constructor(F, nonResidue) {
        this.type="F2";
        this.F = F;
        this.zero = [this.F.zero, this.F.zero];
        this.one = [this.F.one, this.F.zero];
        this.negone = this.neg(this.one);
        this.nonResidue = nonResidue;
        this.m = F.m*2;
        this.p = F.p;
        this.n64 = F.n64*2;
        this.n32 = this.n64*2;
        this.n8 = this.n64*8;

        buildSqrt(this);
    }

    _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);
    }

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

    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))];
    }

    inv(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.inv(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.inv(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]);
    }

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

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

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

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

    toString(a) {
        return `[ ${this.F.toString(a[0])} , ${this.F.toString(a[1])} ]`;
    }

    fromRng(rng) {
        const c0 = this.F.fromRng(rng);
        const c1 = this.F.fromRng(rng);
        return [c0, c1];
    }

    gt(a, b) {
        if (this.F.gt(a[0], b[0])) return true;
        if (this.F.gt(b[0], a[0])) return false;
        if (this.F.gt(a[1], b[1])) return true;
        return false;
    }

    geq(a, b) {
        return this.gt(a, b) || this.eq(a, b);
    }

    lt(a, b) {
        return !this.geq(a,b);
    }

    leq(a, b) {
        return !this.gt(a,b);
    }

    neq(a, b) {
        return !this.eq(a,b);
    }

    random() {
        return [this.F.random(), this.F.random()];
    }


    toRprLE(buff, o, e) {
        this.F.toRprLE(buff, o, e[0]);
        this.F.toRprLE(buff, o+this.F.n8, e[1]);
    }

    toRprBE(buff, o, e) {
        this.F.toRprBE(buff, o, e[1]);
        this.F.toRprBE(buff, o+this.F.n8, e[0]);
    }

    toRprLEM(buff, o, e) {
        this.F.toRprLEM(buff, o, e[0]);
        this.F.toRprLEM(buff, o+this.F.n8, e[1]);
    }


    toRprBEM(buff, o, e) {
        this.F.toRprBEM(buff, o, e[1]);
        this.F.toRprBEM(buff, o+this.F.n8, e[0]);
    }

    fromRprLE(buff, o) {
        o = o || 0;
        const c0 = this.F.fromRprLE(buff, o);
        const c1 = this.F.fromRprLE(buff, o+this.F.n8);
        return [c0, c1];
    }

    fromRprBE(buff, o) {
        o = o || 0;
        const c1 = this.F.fromRprBE(buff, o);
        const c0 = this.F.fromRprBE(buff, o+this.F.n8);
        return [c0, c1];
    }

    fromRprLEM(buff, o) {
        o = o || 0;
        const c0 = this.F.fromRprLEM(buff, o);
        const c1 = this.F.fromRprLEM(buff, o+this.F.n8);
        return [c0, c1];
    }

    fromRprBEM(buff, o) {
        o = o || 0;
        const c1 = this.F.fromRprBEM(buff, o);
        const c0 = this.F.fromRprBEM(buff, o+this.F.n8);
        return [c0, c1];
    }

    toObject(a) {
        return a;
    }

}