o1js-rsa/build/src/bigint.js

This repository exposes the API from the [o1js RSA example](https://github.com/o1-labs/o1js/tree/main/src/examples/crypto/rsa), making it importable and enabling RSA65537 signature verification on the Mina blockchain across various projects that utilize [

import { assert, Field, Provable } from 'o1js';
export { BigMultNoCarry };
function toNumber(x) {
    return Number(x.toBigInt());
}
// a and b have n-bit registers
// a has ka registers, each with NONNEGATIVE ma-bit values (ma can be > n)
// b has kb registers, each with NONNEGATIVE mb-bit values (mb can be > n)
// out has ka + kb - 1 registers, each with (ma + mb + ceil(log(max(ka, kb))))-bit values
function BigMultNoCarry(n, ma, mb, ka, kb, a, b) {
    assert(ma + mb <= 255);
    const out = Provable.witness(Provable.Array(Field, ka + kb - 1), () => {
        let prod_val = [];
        for (let i = 0; i < ka + kb - 1; i++) {
            prod_val[i] = 0;
        }
        for (let i = 0; i < ka; i++) {
            for (let j = 0; j < kb; j++) {
                prod_val[i + j] += toNumber(a[i]) * toNumber(b[j]);
            }
        }
        return prod_val.map(Field);
    });
    let a_poly = [];
    let b_poly = [];
    let out_poly = [];
    for (let i = 0; i < ka + kb - 1; i++) {
        out_poly[i] = Field(0);
        a_poly[i] = Field(0);
        b_poly[i] = Field(0);
        for (let j = 0; j < ka + kb - 1; j++) {
            out_poly[i] = out_poly[i].add(out[j].mul(i ** j));
        }
        for (let j = 0; j < ka; j++) {
            a_poly[i] = a_poly[i].add(a[j].mul(i ** j));
        }
        for (let j = 0; j < kb; j++) {
            b_poly[i] = b_poly[i].add(b[j].mul(i ** j));
        }
    }
    for (let i = 0; i < ka + kb - 1; i++) {
        out_poly[i].assertEquals(a_poly[i].mul(b_poly[i]));
    }
}
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