finitefields

Polynomials, Galois fields and Elliptic curves - in JS

• by @dr-Jonas-Birch

Installation

npm install finitefields

Examples

import { ecℤp, p256, type Coordinate, PrimeField, empty, fold } from 'finitefields';
import type { Point } from 'finitefields';

let f:PrimeField;
let c:ecℤp;
let g:Coordinate;
let mt:Coordinate;
let t:Point;

/*
 * initialization using Nist curve P256
 *   also available: birch17()
 */

// generate prime field
f = new PrimeField(p256().θ, p256().bitlen);
// generate curve
c = new ecℤp(f, p256());
// using the curve's standard P point as generator
g = c.p;

// point doubling, t=P+P
mt = c.double(g);

// point addition, t=P+Q
mt = c.add(g, c.q);

// point finding/scalar multiplication, t=5P
mt = c.find(5n, g);

// extract the values
if (empty(mt))
    console.log('infinity');
else {
    t = fold(mt);
    console.log(t);
}

console.log(mt.toString());

API

Initialization

p256() / birch17();

• Generate a 256bit standard Nist curve 'P256'
• or a (p=17) dr Birch curve 'birch17' (test curve)

let f:PrimeField;
f = new PrimeField(prime:bigint, bitlen:bigint);

• Generate a Galois field with a specified prime and bitlen

let c:ecℤp;
c = new ecℤp(field:PrimeField, curve:ECCurve);

• Generate a specific Elliptic curve over field

Point arithmetic

let mt:Coordinate;
mt = c.add(point1:Coordinate, point2:Coordinate);

• Point addition

mt = c.double(point:Coordinate);

• Point doubling

mt = c.find(scalar:bigint, generator:Coordinate);

• Point finding (scalar multiplication)

Misc

// generate your own random curve over a prime field
let curve:ECCurve;
curve = mkcurve(field:PrimeField);

// Maybe<a> datatype
let ms:Maybe<string>;
ms = nothing();
ms = just('hello world');

let s:string;
if (!empty(s))
  s = fold(ms);

// Polynomials
let pol:Polynomial;
pol = new Polynomial(src:Polysource, order:bigint);

type Polysource =
    | bigint
    | bigint[]
    | Tobject;

// more info about Polynomial methods, check the source code
interface Ipolynomial {
    fromarr(src:bigint[]): void;
    fromobj(src:Tobject): void;
    fromint(src:bigint): void;
    verifyorder(order:bigint): boolean;
    eval(): bigint;
    constructor: Function;
}

License

MIT

More info

Contact me [email protected], also check out my popular Youtube channel @dr-Jonas-Birch