TernaryEllipticCurve.js: Technical Documentation

Overview

TernaryEllipticCurve.js implements elliptic curve cryptography over a ternary field GF(3^n). This unique implementation combines the security of elliptic curve cryptography with the efficiency of balanced ternary arithmetic, making it particularly suitable for quantum-resistant cryptographic operations.

Curve Equation

The curve implements the equation:

y² + xy = x³ + ax² + b

This is a special form of elliptic curve that's optimized for ternary field operations.

Usage Examples

1. Key Generation

const curve = new TernaryEllipticCurve(a, b, n);
const { privateKey, publicKey } = curve.generateKeyPair();

2. Point Operations

// Point addition
const sumPoint = curve.addPoints(point1, point2);

// Scalar multiplication
const resultPoint = curve.multiplyPoint(scalar, basePoint);

3. Signature Creation

function sign(message, privateKey) {
    const k = generateSecureRandom();
    const R = curve.multiplyPoint(k, curve.basePoint);
    const e = hash(message);
    const s = (k - privateKey * e) % curve.order;
    return { R, s };
}