A high-performance Rust library for lattice-based cryptography and algebra, providing efficient implementations of polynomial rings, matrices, and vector operations over finite fields.

• Polynomial Rings: Efficient implementation of polynomial rings over finite fields

  • FFT-based polynomial multiplication (O(n log n) complexity)
  • Generic polynomial operations (addition, multiplication, division)
  • Support for polynomial rings with degree bounds

• Matrix Operations: Generic matrix implementation supporting various element types

  • Basic matrix operations (addition, multiplication, transposition)
  • Matrix-vector operations
  • Efficient storage and computation
  • Support for different matrix types (ring matrices, polynomial matrices)

• Vector Arithmetic: Efficient vector operations for cryptographic applications

  • Generic vector implementation with type-safe operations
  • Support for various element types (rings, polynomials)
  • Vector operations (inner product, Hadamard product)
  • Efficient random vector generation

• Rust 1.70.0 or later
• Dependencies:
  • rand = "0.9.1"
  • rustfft = "6.3.0"
  • serde = { version = "1.0.216", features = ["derive"] }

Add this to your Cargo.toml:

[dependencies]
lattice-algebra-rs = "0.1.0"

Basic example:

use lattice_algebra_rs::ring::Zq17;
use lattice_algebra_rs::matrix::vector_arithmatic::GenericVector;
use lattice_algebra_rs::poly::UniPolynomial;

// Create a vector over Zq17
let v = GenericVector::new(vec![Zq17::new(1), Zq17::new(2), Zq17::new(3)]);

// Perform vector operations
let a = GenericVector::new(vec![Zq17::new(1), Zq17::new(2)]);
let b = GenericVector::new(vec![Zq17::new(3), Zq17::new(4)]);
let sum = a.clone() + b.clone();
assert_eq!(sum, GenericVector::new(vec![Zq17::new(4), Zq17::new(6)]));
let dot = a.inner_product(&b);
assert_eq!(dot, Zq17::new(11));

Contributions are welcome! Please feel free to submit a Pull Request. For major changes, please open an issue first to discuss what you would like to change.

• Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)

This project is inspired by various lattice-based cryptography implementations:

• rustfft
• condor-rs
• Lazarus
• latticefold
• larkworks