functionalscript/crypto/prime_field/module.f.js

FunctionalScript is a purely functional subset of JavaScript

import { repeat } from "../../types/monoid/module.f.js";
/**
 * Creates a prime field with the specified prime modulus and associated operations.
 *
 * @param p - A prime number to define the field.
 * @returns The prime field object.
 */
export const prime_field = (p) => {
    const sub = a => b => {
        const r = a - b;
        return r < 0 ? r + p : r;
    };
    const mul = a => b => a * b % p;
    const reciprocal = a => {
        if (a === 0n) {
            throw '1/0';
        }
        let a1 = a;
        let a0 = p;
        let f0 = 0n;
        let f1 = 1n;
        while (a1 !== 1n) {
            const q = a0 / a1;
            const a2 = a0 % a1;
            a0 = a1;
            a1 = a2;
            const f2 = sub(f0)(mul(f1)(q));
            f0 = f1;
            f1 = f2;
        }
        return f1;
    };
    const middle = p >> 1n;
    const pow2 = a => mul(a)(a);
    const pow = repeat({ identity: 1n, operation: mul });
    return {
        p,
        middle,
        max: p - 1n,
        neg: a => a === 0n ? 0n : p - a,
        sub,
        add: a => b => {
            const r = a + b;
            return r < p ? r : r - p;
        },
        abs: a => middle < a ? p - a : a,
        mul,
        reciprocal,
        div: a => b => mul(a)(reciprocal(b)),
        pow,
        pow2,
        pow3: a => mul(a)(pow2(a))
    };
};
/**
 * Computes the square root of a number in a prime field.
 *
 * @throws If the prime modulus `p` does not satisfy `p % 4 == 3`.
 *
 * @example
 *
 * ```js
 * const field = prime_field(7n);
 * const root = sqrt(field)(4n);
 * if (root !== 2n) { throw root }
 * ```
 */
export const sqrt = ({ p, mul, pow }) => {
    if ((p & 3n) !== 3n) {
        throw 'sqrt';
    }
    const sqrt_k = (p + 1n) >> 2n;
    return a => {
        const result = pow(a)(sqrt_k);
        return mul(result)(result) === a ? result : null;
    };
};