npm install @bradthomasbrown/finite-domain

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

sh

npm i @bradthomasbrown/finite-domain





Usage

js

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)