@nori-zk/proof-conversion/build/src/towers/fp12.js

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

import { Struct } from 'o1js';
import { ATE_LOOP_COUNT } from './consts.js';
import { FpC } from './fp.js';
import { Fp2 } from './fp2.js';
import { Fp6 } from './fp6.js';
import { GAMMA_1S, GAMMA_2S, GAMMA_3S } from './precomputed.js';
// Fp6^2[w]/(w^2 - v)
class Fp12 extends Struct({ c0: Fp6, c1: Fp6 }) {
    static zero() {
        return new Fp12({ c0: Fp6.zero(), c1: Fp6.zero() });
    }
    static one() {
        return new Fp12({ c0: Fp6.one(), c1: Fp6.zero() });
    }
    neg() {
        return new Fp12({ c0: this.c0.neg(), c1: this.c1.neg() });
    }
    conjugate() {
        return new Fp12({ c0: this.c0, c1: this.c1.neg() });
    }
    assert_equals(rhs) {
        this.c0.assert_equals(rhs.c0);
        this.c1.assert_equals(rhs.c1);
    }
    inverse() {
        let t0 = this.c0.mul(this.c0);
        let t1 = this.c1.mul(this.c1);
        t0 = t0.sub(t1.mul_by_v());
        t1 = t0.inverse();
        const c0 = this.c0.mul(t1);
        const c1 = this.c1.neg().mul(t1);
        return new Fp12({ c0, c1 });
    }
    mul(rhs) {
        const t0 = this.c0.mul(rhs.c0);
        const t1 = this.c1.mul(rhs.c1);
        const c0 = t1.mul_by_v().add(t0);
        const a0_a1 = this.c0.add(this.c1);
        const b0_b1 = rhs.c0.add(rhs.c1);
        const c1 = a0_a1.mul(b0_b1).sub(t0).sub(t1);
        return new Fp12({ c0, c1 });
    }
    // rhs.c0 b00 + 0v + 0v^2
    // rhs.c1 b10 + b11v + 0v^2
    sparse_mul(rhs) {
        const t0 = this.c0.mul_by_fp2(rhs.c0.c0);
        const t1 = this.c1.mul_by_sparse_fp6(rhs.c1);
        const c0 = t0.add(t1.mul_by_v());
        const t2 = new Fp6({
            c0: rhs.c0.c0.add(rhs.c1.c0),
            c1: rhs.c1.c1,
            c2: Fp2.zero(),
        });
        let c1 = this.c0.add(this.c1).mul_by_sparse_fp6(t2);
        c1 = c1.sub(t0).sub(t1);
        return new Fp12({ c0, c1 });
    }
    square() {
        let c0 = this.c0.sub(this.c1);
        let c3 = this.c0.sub(this.c1.mul_by_v());
        let c2 = this.c0.mul(this.c1);
        c0 = c0.mul(c3).add(c2);
        const c1 = c2.mul_by_fp(FpC.from(2n));
        c2 = c2.mul_by_v();
        c0 = c0.add(c2);
        return new Fp12({ c0, c1 });
    }
    frobenius_pow_p() {
        const t1 = this.c0.c0.conjugate();
        let t2 = this.c1.c0.conjugate();
        let t3 = this.c0.c1.conjugate();
        let t4 = this.c1.c1.conjugate();
        let t5 = this.c0.c2.conjugate();
        let t6 = this.c1.c2.conjugate();
        t2 = t2.mul(GAMMA_1S[0]);
        t3 = t3.mul(GAMMA_1S[1]);
        t4 = t4.mul(GAMMA_1S[2]);
        t5 = t5.mul(GAMMA_1S[3]);
        t6 = t6.mul(GAMMA_1S[4]);
        const c0 = new Fp6({ c0: t1, c1: t3, c2: t5 });
        const c1 = new Fp6({ c0: t2, c1: t4, c2: t6 });
        return new Fp12({ c0, c1 });
    }
    frobenius_pow_p_with_gammas(gamma_1s) {
        const t1 = this.c0.c0.conjugate();
        let t2 = this.c1.c0.conjugate();
        let t3 = this.c0.c1.conjugate();
        let t4 = this.c1.c1.conjugate();
        let t5 = this.c0.c2.conjugate();
        let t6 = this.c1.c2.conjugate();
        t2 = t2.mul(gamma_1s[0]);
        t3 = t3.mul(gamma_1s[1]);
        t4 = t4.mul(gamma_1s[2]);
        t5 = t5.mul(gamma_1s[3]);
        t6 = t6.mul(gamma_1s[4]);
        const c0 = new Fp6({ c0: t1, c1: t3, c2: t5 });
        const c1 = new Fp6({ c0: t2, c1: t4, c2: t6 });
        return new Fp12({ c0, c1 });
    }
    frobenius_pow_p_squared() {
        const t1 = this.c0.c0;
        const t2 = this.c1.c0.mul(GAMMA_2S[0]);
        const t3 = this.c0.c1.mul(GAMMA_2S[1]);
        const t4 = this.c1.c1.mul(GAMMA_2S[2]);
        const t5 = this.c0.c2.mul(GAMMA_2S[3]);
        const t6 = this.c1.c2.mul(GAMMA_2S[4]);
        const c0 = new Fp6({ c0: t1, c1: t3, c2: t5 });
        const c1 = new Fp6({ c0: t2, c1: t4, c2: t6 });
        return new Fp12({ c0, c1 });
    }
    frobenius_pow_p_squared_with_gammas(gamma_2s) {
        const t1 = this.c0.c0;
        const t2 = this.c1.c0.mul(gamma_2s[0]);
        const t3 = this.c0.c1.mul(gamma_2s[1]);
        const t4 = this.c1.c1.mul(gamma_2s[2]);
        const t5 = this.c0.c2.mul(gamma_2s[3]);
        const t6 = this.c1.c2.mul(gamma_2s[4]);
        const c0 = new Fp6({ c0: t1, c1: t3, c2: t5 });
        const c1 = new Fp6({ c0: t2, c1: t4, c2: t6 });
        return new Fp12({ c0, c1 });
    }
    frobenius_pow_p_cubed() {
        const t1 = this.c0.c0.conjugate();
        let t2 = this.c1.c0.conjugate();
        let t3 = this.c0.c1.conjugate();
        let t4 = this.c1.c1.conjugate();
        let t5 = this.c0.c2.conjugate();
        let t6 = this.c1.c2.conjugate();
        t2 = t2.mul(GAMMA_3S[0]);
        t3 = t3.mul(GAMMA_3S[1]);
        t4 = t4.mul(GAMMA_3S[2]);
        t5 = t5.mul(GAMMA_3S[3]);
        t6 = t6.mul(GAMMA_3S[4]);
        const c0 = new Fp6({ c0: t1, c1: t3, c2: t5 });
        const c1 = new Fp6({ c0: t2, c1: t4, c2: t6 });
        return new Fp12({ c0, c1 });
    }
    frobenius_pow_p_cubed_with_gammas(gamma_3s) {
        const t1 = this.c0.c0.conjugate();
        let t2 = this.c1.c0.conjugate();
        let t3 = this.c0.c1.conjugate();
        let t4 = this.c1.c1.conjugate();
        let t5 = this.c0.c2.conjugate();
        let t6 = this.c1.c2.conjugate();
        t2 = t2.mul(gamma_3s[0]);
        t3 = t3.mul(gamma_3s[1]);
        t4 = t4.mul(gamma_3s[2]);
        t5 = t5.mul(gamma_3s[3]);
        t6 = t6.mul(gamma_3s[4]);
        const c0 = new Fp6({ c0: t1, c1: t3, c2: t5 });
        const c1 = new Fp6({ c0: t2, c1: t4, c2: t6 });
        return new Fp12({ c0, c1 });
    }
    // when this is not in cyclotomic group (i.e. x^(p^6 + 1) not 1 )
    pow(expBeWnaf) {
        let inv = this.inverse();
        let c = new Fp12({ c0: this.c0, c1: this.c1 });
        const n = expBeWnaf.length;
        for (let i = 1; i < n; i++) {
            c = c.square();
            if (expBeWnaf[i] == 1) {
                c = c.mul(this);
            }
            else if (expBeWnaf[i] == -1) {
                c = c.mul(inv);
            }
        }
        return c;
    }
    // e = 6x + 2 + p - p^2 + p^3
    exp_e() {
        const c0 = this.pow(ATE_LOOP_COUNT);
        const c1 = this.frobenius_pow_p();
        const c2 = this.frobenius_pow_p_squared().inverse();
        const c3 = this.frobenius_pow_p_cubed();
        return c0.mul(c1).mul(c2).mul(c3);
    }
    display(name) {
        console.log(`${name}.g00: `, this.c0.c0.c0.toBigInt());
        console.log(`${name}.g01: `, this.c0.c0.c1.toBigInt());
        console.log(`${name}.g10: `, this.c0.c1.c0.toBigInt());
        console.log(`${name}.g11: `, this.c0.c1.c1.toBigInt());
        console.log(`${name}.g20: `, this.c0.c2.c0.toBigInt());
        console.log(`${name}.g21: `, this.c0.c2.c1.toBigInt());
        console.log(`${name}.h00: `, this.c1.c0.c0.toBigInt());
        console.log(`${name}.h01: `, this.c1.c0.c1.toBigInt());
        console.log(`${name}.h10: `, this.c1.c1.c0.toBigInt());
        console.log(`${name}.h11: `, this.c1.c1.c1.toBigInt());
        console.log(`${name}.h20: `, this.c1.c2.c0.toBigInt());
        console.log(`${name}.h21: `, this.c1.c2.c1.toBigInt());
    }
    toJSON() {
        const f = {
            g00: this.c0.c0.c0.toBigInt().toString(),
            g01: this.c0.c0.c1.toBigInt().toString(),
            g10: this.c0.c1.c0.toBigInt().toString(),
            g11: this.c0.c1.c1.toBigInt().toString(),
            g20: this.c0.c2.c0.toBigInt().toString(),
            g21: this.c0.c2.c1.toBigInt().toString(),
            h00: this.c1.c0.c0.toBigInt().toString(),
            h01: this.c1.c0.c1.toBigInt().toString(),
            h10: this.c1.c1.c0.toBigInt().toString(),
            h11: this.c1.c1.c1.toBigInt().toString(),
            h20: this.c1.c2.c0.toBigInt().toString(),
            h21: this.c1.c2.c1.toBigInt().toString(),
        };
        return JSON.stringify(f);
    }
    static loadFromJSON(json) {
        const g00 = FpC.from(json.g00);
        const g01 = FpC.from(json.g01);
        const g0 = new Fp2({ c0: g00, c1: g01 });
        const g10 = FpC.from(json.g10);
        const g11 = FpC.from(json.g11);
        const g1 = new Fp2({ c0: g10, c1: g11 });
        const g20 = FpC.from(json.g20);
        const g21 = FpC.from(json.g21);
        const g2 = new Fp2({ c0: g20, c1: g21 });
        const g = new Fp6({ c0: g0, c1: g1, c2: g2 });
        const h00 = FpC.from(json.h00);
        const h01 = FpC.from(json.h01);
        const h0 = new Fp2({ c0: h00, c1: h01 });
        const h10 = FpC.from(json.h10);
        const h11 = FpC.from(json.h11);
        const h1 = new Fp2({ c0: h10, c1: h11 });
        const h20 = FpC.from(json.h20);
        const h21 = FpC.from(json.h21);
        const h2 = new Fp2({ c0: h20, c1: h21 });
        const h = new Fp6({ c0: h0, c1: h1, c2: h2 });
        return new Fp12({ c0: g, c1: h });
    }
}
export { Fp12 };
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