Sylow

Sylow (ˈsyːlɔv) is a comprehensive Rust library for elliptic curve cryptography, specifically tailored for the BN254 ( alt-bn128) curve. It provides a robust implementation of finite fields, elliptic curve groups, and pairing-based cryptography, making it an ideal choice for applications in blockchain, zero-knowledge proofs, and other cryptographic systems.

Features

• Finite Field Arithmetic: Efficient implementations of prime fields and their extensions 𝔽ₚ, 𝔽ₚ², 𝔽ₚ⁶, 𝔽ₚ¹²
• Elliptic Curve Groups: Complete support for operations on 𝔾₁, 𝔾₂, and 𝔾ₜ groups of the BN254 curve
• Pairing Operations: Optimized implementation of the optimal ate pairing
• Cryptographic Primitives:
  • Key generation
  • BLS signature generation and verification
  • Hash-to-curve functionality
• Compatibility: Designed to be compatible with Ethereum's precompiled contracts for BN254 operations and Warlock's SolBLS library.

Installation

Add this to your Cargo.toml:

[dependencies]
sylow = "0.1.0"

Usage

Here's a basic example demonstrating key generation, signing, and verification:

use sylow::{KeyPair, sign, verify};

fn main() {
    // Generate a new key pair
    let key_pair = KeyPair::generate();

    // Message to be signed
    let message = b"Hello, Sylow!";

    // Sign the message
    match sign(&key_pair.secret_key, message) {
        Ok(signature) => {
            // Verify the signature
            match verify(&key_pair.public_key, message, &signature) {
                Ok(is_valid) => {
                    assert!(is_valid, "Signature verification failed");
                    println!("Signature verified successfully!");
                }
                Err(e) => println!("Verification error: {:?}", e),
            }
        }
        Err(e) => println!("Signing error: {:?}", e),
    }
}

For more examples, please see the examples directory.

Core Concepts

• Finite fields: The foundation of the library, providing arithmetic operations in prime fields and their extensions.
• Elliptic Curve Groups: Implementations of the 𝔾₁, 𝔾₂, and 𝔾ₜ groups on the BN254 curve, supporting both affine and projective coordinates.
• Pairing: Efficient implementation of the optimal ate pairing, crucial for many cryptographic protocols.
• alt-bn128 (BN254) Curve: A pairing-friendly elliptic curve widely used in zkSNARKs and supported by Ethereum precompiles.

Advanced Features

• Customizable Hashing: Supports various hash functions through the Expander trait, such as the XMD and XOF algorithms on any hasher from sha3.
• Optimized Arithmetic: Utilizes Montgomery form for efficient modular arithmetic.
• Constant-time Operations: Implements algorithms resistant to timing attacks.
• Batch Verification: Verify multiple signatures in a single operation for improved performance.

Performance

Sylow is designed with performance in mind, leveraging optimized algorithms for j-invariant zero curves, the optimal ate pairing for efficient signature verification, as well as multiprecision Montgomery arithmetic.

Security

Sylow is designed in compliance with the recommendations set forth by Cloudflare in RFC 9380, especially regarding hashing an arbitrary byte array to an element of the curve. We provide multiple secure implementations of the hash_to_field standard and implement the Shallue-van de Woestijne encoding for elliptic curve points.

The multiprecision arithmetic operations are implemented in constant time, ensuring resistance to side-channel attacks. Constant-time operations are used whenever possible, and there are currently no variable-time functions used in Sylow.

If you discover any security issues, please report them to team@warlock.xyz.

Documentation

For detailed API documentation, please refer to docs.rs/sylow.

Contributing

We welcome contributions to Sylow! Whether it's bug reports, feature requests, or code contributions, please feel free to engage with the project by submitting issues, feature requests, or pull requests on the GitHub repository.

License

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

Contact

This project is maintained by:

• @trbritt - tristan@warlock.xyz
• @0xAlcibiades - alcibiades@warlock.xyz
• @merolish - michael@warlock.xyz

Warlock Labs - https://github.com/warlock-labs

Project Link: https://github.com/warlock-labs/sylow