TernaryField.js: Technical Documentation

Overview

TernaryField.js implements a Galois Field of order 3^n (GF(3^n)), which is crucial for the balanced ternary arithmetic operations in our blockchain. This implementation provides the mathematical foundation for our ternary-based cryptographic operations.

Usage Examples

Basic Field Operations

const field = new TernaryField(3);  // GF(3³)

// Addition
const sum = field.add(7, 4);  // Operates in GF(27)

// Multiplication
const product = field.multiply(5, 3);

// Find inverse
const inv = field.inverse(5);

Cryptographic Application

// Generate key pair
const privateKey = field.generateRandom();
const publicKey = field.multiply(privateKey, generator);

// Sign message
const signature = field.sign(message, privateKey);

// Verify signature
const isValid = field.verify(message, signature, publicKey);