@nori-zk/proof-conversion/build/src/ec/g2.js

Verifying zkVM proofs inside o1js circuits, to generate Mina compatible proof

import { Struct } from 'o1js';
import { FpC, Fp2, Fp6, Fp12 } from '../towers/index.js';
import { GAMMA_1S, NEG_GAMMA_13 } from '../towers/precomputed.js';
class G2Affine extends Struct({ x: Fp2, y: Fp2 }) {
    equals(rhs) {
        let same_x = this.x.equals(rhs.x);
        let same_y = this.y.equals(rhs.y);
        return same_x.mul(same_y);
    }
    neg() {
        return new G2Affine({ x: this.x, y: this.y.neg() });
    }
    // a = 0 for bn
    computeLambdaSame() {
        // λ = 3x^2 / 2y
        let num = this.x.square().mul_by_fp(FpC.from(3n));
        let denom = this.y.mul_by_fp(FpC.from(2n)).inverse();
        return num.mul(denom);
    }
    computeLambdaDiff(rhs) {
        // λ = (y2 - y1) / (x2 - x1)
        let num = rhs.y.sub(this.y);
        let denom = rhs.x.sub(this.x).inverse();
        return num.mul(denom);
    }
    computeMu(lambda) {
        return this.y.sub(this.x.mul(lambda));
    }
    // assumes that this and rhs are not 0 points
    add(rhs) {
        const eq = this.equals(rhs);
        let lambda;
        if (eq.toBigInt() === 1n) {
            lambda = this.computeLambdaSame();
        }
        else {
            lambda = this.computeLambdaDiff(rhs);
        }
        const x_3 = lambda.square().sub(this.x).sub(rhs.x);
        const y_3 = lambda.mul(this.x.sub(x_3)).sub(this.y);
        return new G2Affine({ x: x_3, y: y_3 });
    }
    double_from_line(lambda) {
        const x_3 = lambda.square().sub(this.x).sub(this.x); // x_3 = λ^2 - 2x_1
        const y_3 = lambda.mul(this.x.sub(x_3)).sub(this.y); // y_3 = λ(x_1 - x_3) - y_1
        return new G2Affine({ x: x_3, y: y_3 });
    }
    add_from_line(lambda, rhs) {
        const x_3 = lambda.square().sub(this.x).sub(rhs.x); // x_3 = λ^2 - x_1 - x_2
        const y_3 = lambda.mul(this.x.sub(x_3)).sub(this.y); // y_3 = λ(x_1 - x_3) - y_1
        return new G2Affine({ x: x_3, y: y_3 });
    }
    frobenius() {
        const x = this.x.conjugate().mul(GAMMA_1S[1]);
        const y = this.y.conjugate().mul(GAMMA_1S[2]);
        return new G2Affine({ x, y });
    }
    frobFromInputs(g1, g2) {
        const x = this.x.conjugate().mul(g1);
        const y = this.y.conjugate().mul(g2);
        return new G2Affine({ x, y });
    }
    negative_frobenius() {
        const x = this.x.conjugate().mul(GAMMA_1S[1]);
        const y = this.y.conjugate().mul(NEG_GAMMA_13);
        return new G2Affine({ x, y });
    }
    negFrobFromInputs(g1, g2) {
        const x = this.x.conjugate().mul(g1);
        const y = this.y.conjugate().mul(g2);
        return new G2Affine({ x, y });
    }
    // g + hw = g0 + h0W + g1W^2 + h1W^3 + g2W^4 + h2W^5
    // PSI: (x, y) -> (w^2x, w^3y)
    hom() {
        const x_g = new Fp6({ c0: Fp2.zero(), c1: this.x, c2: Fp2.zero() });
        const x_h = Fp6.zero();
        const x = new Fp12({ c0: x_g, c1: x_h });
        const y_g = Fp6.zero();
        const y_h = new Fp6({ c0: Fp2.zero(), c1: this.y, c2: Fp2.zero() });
        const y = new Fp12({ c0: y_g, c1: y_h });
        return [x, y];
    }
}
export { G2Affine };
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