finite-domain

This is a simple, minimal implementation of elliptic curve domain parameters in TypeScript/JavaScript.

Why?

There is surprisingly little information on all aspects of the "cryptographic stack" in JavaScript and elsewhere that is simple and minimal. This repository is part of a series of repositories that builds up this stack from first principles, including:

• Finite field arithmetic
• Elliptic curves over finite fields
• Sponge constructions and Keccak
• Elliptic curve domain parameters (this library)
• ECDSA
• Interacting with EVM nodes
• And potentially more

Dependencies

These should be installed when you install the finite-domain package, but this is listed here for completeness.

• @bradthomasbrown/finite-field
• @bradthomasbrown/finite-curve

Installation

npm i @bradthomasbrown/finite-domain

Usage

import { FiniteField } from "@bradthomasbrown/finite-field";
import { FiniteCurve, FinitePoint } from "@bradthomasbrown/finite-curve";
import { FiniteDomain } from "@bradthomasbrown/finite-domain.js";

let secp256k1:FiniteDomain;
{
    const p =
          (1n << 256n)
        - (1n << 32n)
        - 977n;
    const F = new FiniteField(p);
    const E = new FiniteCurve(F, 0, 7);
    const G = new FinitePoint(
        0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798n,
        0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8n
    );
    const n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141n;
    const h = 1;
    secp256k1 = new FiniteDomain(E, G, n, h);
}

// this should be the same as the example from `finite-curve`, but a bit simpler
const P = secp256k1.divide(new FinitePoint(), 2, secp256k1.G);
console.log({ x: P.x, y: P.y });
// x: 86918276961810349294276103416548851884759982251107n
// y: 87194829221142880348582938487511785107150118762739500766654458540580527283772n
// # note the relatively extremely low value of x after halving the generator point,
// # a characteristic of SEC 2 curves (https://bitcoin.stackexchange.com/a/113122)