Pedersen Commitment Library

This library provides an implementation of Pedersen Commitments, a cryptographic technique widely used for creating non-interactive commitments with strong security properties like homomorphic addition, subtraction, and multiplication.

Features

• Miller-Rabin Primality Test: Ensures prime numbers are correctly identified.
• Pedersen Parameters Generation: Generates valid Pedersen parameters including prime, generator, and secondary generator.
• Homomorphic Properties: Supports operations like addition, subtraction, and multiplication of commitments.
• Secure Randomness: Utilizes Node.js crypto module to generate secure random values for blinding.

Installation

To use this library, you need to have Node.js installed. Run the following command to install the package:

npm install bigint-pedersen

Usage

Here is a simple example to demonstrate how to create a Pedersen Commitment and use its homomorphic sum property:

Creating a Commitment

import pedersen from 'bigint-pedersen';

// Generate Pedersen parameters
const parans = await pedersen.generator(2048); // 2048-bit safety

// Create a commitment for a message
const message1 = 42n;
const randomness1 = pedersen.randomBlinding();
const commitment1 = pedersen.commitment(message1, randomness1, parans);

console.log(`Commitment1: ${commitment1}`);

Homomorphic Sum of Commitments

Here is how you can sum two commitments homomorphically:

// Create a second commitment
const message2 = 58n;
const randomness2 = pedersen.randomBlinding();
const commitment2 = pedersen.commitment(message2, randomness2, parans);

console.log(`Commitment2: ${commitment2}`);

// Sum the commitments
const commitmentSum = pedersen.sum(commitment1, commitment2, parans);

console.log(`Sum of Commitments: ${commitmentSum}`);

In this example, the result commitmentSum is a valid commitment of the sum of the original messages (message1 + message2), demonstrating the library's homomorphic properties.

API Reference

Functions

• isPrimeMillerRabin(n: bigint, k?: number): boolean
  Performs the Miller-Rabin primality test on n.

• generator(bits: number): Promise<PedersenParameters>
  Generates Pedersen parameters including a prime p and generators g and h.

• commitment(m: bigint, r: bigint, parans: PedersenParameters): bigint
  Computes a Pedersen commitment for the message m and randomness r.

• sum(C1: bigint, C2: bigint, parans: PedersenParameters): bigint
  Computes the sum of two commitments C1 and C2.

• sub(C1: bigint, C2: bigint, parans: PedersenParameters): bigint
  Computes the difference between two commitments C1 and C2.

• multiply(C: bigint, scalar: bigint, parans: PedersenParameters): bigint
  Multiplies a commitment C by a scalar value.

Tests

To run the tests for this project, use the following command:

npm run test

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgements

• Utilizes the Node.js crypto module for random value generation.
• Implementation inspired by cryptographic primitives common in privacy-preserving protocols.