functionalscript/crypto/secp/module.f.js

FunctionalScript is a purely functional subset of JavaScript

import { prime_field, sqrt } from "../prime_field/module.f.js";
import { repeat } from "../../types/monoid/module.f.js";
/**
 * Constructs an elliptic curve with the given initialization parameters.
 *
 * @example
 *
 * ```js
 * const curveParams = {
 *     p: 23n,
 *     a: [0n, 1n],
 *     g: [1n, 1n],
 *     n: 19n
 * };
 * const curveInstance = curve(curveParams);
 *
 * // Access curve operations
 * const point = curveInstance.add([1n, 1n])([2n, 5n]); // Add two points
 * const negPoint = curveInstance.neg([1n, 1n]); // Negate a point
 * const mulPoint = curveInstance.mul([1n, 1n])(3n); // Multiply a point by 3
 * ```
 */
export const curve = ({ p, a: [a0, a1], n }) => {
    const pf = prime_field(p);
    const { pow2, pow3, sub, add, mul, neg, div } = pf;
    const mul3 = mul(3n);
    const mul2 = mul(2n);
    const addA1 = add(a1);
    const mulA1 = mul(a1);
    const addA0 = add(a0);
    /**
     * y**2 = a1*x**3 + a0
     */
    const y2 = (x) => addA0(add(pow3(x))(mulA1(x)));
    const addPoint = p => q => {
        if (p === null) {
            return q;
        }
        if (q === null) {
            return p;
        }
        const [px, py] = p;
        const [qx, qy] = q;
        const md = px === qx
            // (3 * px ** 2 + a1) / (2 * py)
            ? py !== qy || py === 0n ? null : [addA1(mul3(pow2(px))), mul2(py)]
            // (py - qy) / (px - qx)
            : [sub(py)(qy), sub(px)(qx)];
        if (md === null) {
            return null;
        }
        const [ma, mb] = md;
        const m = div(ma)(mb);
        // m ** 2 - px - qx
        const rx = sub(pow2(m))(add(px)(qx));
        // [rx, m * (px - rx) - py]
        return [rx, sub(mul(m)(sub(px)(rx)))(py)];
    };
    const sqrt_p = sqrt(pf);
    return {
        pf,
        nf: prime_field(n),
        y2,
        y: x => sqrt_p(y2(x)),
        neg: p => {
            if (p === null) {
                return null;
            }
            const [x, y] = p;
            return [x, neg(y)];
        },
        add: addPoint,
        mul: repeat({ identity: null, operation: addPoint })
    };
};
export const eq = (a) => (b) => {
    if (a === null || b === null) {
        return a === b;
    }
    const [ax, ay] = a;
    const [bx, by] = b;
    return ax === bx && ay === by;
};
/**
 * https://neuromancer.sk/std/secg/secp192r1
 */
export const secp192r1 = {
    p: 0xfffffffffffffffffffffffffffffffeffffffffffffffffn,
    a: [
        0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1n,
        0xfffffffffffffffffffffffffffffffefffffffffffffffcn
    ],
    g: [
        0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012n,
        0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811n
    ],
    n: 0xffffffffffffffffffffffff99def836146bc9b1b4d22831n,
};
/**
 * https://en.bitcoin.it/wiki/Secp256k1
 * https://neuromancer.sk/std/secg/secp256k1
 */
export const secp256k1 = {
    p: 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2fn,
    a: [7n, 0n],
    g: [
        0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798n,
        0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8n
    ],
    n: 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141n,
};
/**
 * https://neuromancer.sk/std/secg/secp256r1
 */
export const secp256r1 = {
    p: 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffffn,
    a: [
        0x5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604bn, //< b
        0xffffffff00000001000000000000000000000000fffffffffffffffffffffffcn, //< a
    ],
    g: [
        0x6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296n, //< x
        0x4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5n, //< y
    ],
    n: 0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551n,
};
/**
 * https://neuromancer.sk/std/secg/secp384r1
 */
export const secp384r1 = {
    p: 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000ffffffffn,
    a: [
        0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aefn, //< b
        0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffeffffffff0000000000000000fffffffcn, //< a
    ],
    g: [
        0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7n, //< x
        0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5fn, //< y
    ],
    n: 0xffffffffffffffffffffffffffffffffffffffffffffffffc7634d81f4372ddf581a0db248b0a77aecec196accc52973n,
};
/**
 * https://neuromancer.sk/std/secg/secp521r1
 */
export const secp521r1 = {
    p: 0x01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffn,
    a: [
        0x0051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00n, //< b
        0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffcn, //< a
    ],
    g: [
        0x00c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66n,
        0x011839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650n,
    ],
    n: 0x01fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb71e91386409n
};