quadratic-sieve

A Java math library focused on number theory and integer factorization in particular.

R Package for Factoring Big Integers using the C Library GMP (GNU Multiple Precision Arithmetic)

High-performance integer factorization suite implementing GNFS, MPQS, and QS algorithms with optimized lattice reduction, vectorization, GPU acceleration, and tensor-based linear algebra. Features automatic algorithm selection, NUMA-aware scheduling, and checkpoint/restore for computational number theory research and cryptanalytic analysis.

An efficient implementation of Quadratic Sieve in Java

A collection of Integer factorization algorithms

Quadratic Sieve integer factorization method for JavaScript bigints

Write ups on Mathematical Cryptography

A Practical Study and Comparison of Integer Factorization Methods

naive quadratic sieve implementation https://www.ams.org/notices/199612/pomerance.pdf

The frontier of pure-Rust Quadratic Sieve integer factorization, portable to WASM (wasm32-unknown-unknown).

From-scratch RSA implementation paired with a Quadratic Sieve factorization attack — empirically demonstrates why RSA security scales with modulus size, extrapolated out to 2048-bit.

Browser-based integer factorization demo — trial division, Fermat, Pollard rho (Brent), Pollard p−1, Williams p+1, Lenstra ECM and the quadratic sieve over real BigInt N, each keyed to the RSA key-generation rule that closes it. Obey every rule and rho and ECM still factor it: only size defeats them, and nothing defeats Shor.

A breakthrough optimization framework for the Multiple Polynomial Quadratic Sieve (MPQS) using deterministic geometric filters derived from the Pisano Period. Architected by Jacopo Liberati.

A C implementation of the Quadratic sieve for factoring large integers.

COL759 Assignment-2

This quadratic sieve implementation is a part of the coursework for MATH 404 Mathematical Cryptography with Prof. Samit Dasgupta at Duke University.

Quadratic Sieve implementation for large integer factorization using GMP for arbitrary precision arithmetic and MPI for parallel distributed sieving. Includes smooth relation collection, Gaussian elimination over GF(2), and non-trivial factor extraction on 40–50 digit numbers.

Implementation of some basic algorithms relevant for cryptography.