Factorization with genus 2 curves

TL;DR

This paper introduces GMP-HECM, a hyperelliptic curve-based factorization method that outperforms traditional elliptic curve methods in speed for large number factorization.

Contribution

It presents a novel implementation using genus 2 hyperelliptic curves and Kummer surfaces to improve factorization efficiency over existing elliptic curve methods.

Findings

GMP-HECM is faster than GMP-ECM for large numbers

Special hyperelliptic curves reduce algorithm complexity

Implementation demonstrates practical speed improvements

Abstract

The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to reduce the complexity of the algorithm. Our implementation GMP-HECM is faster than GMP-ECM for factoring big numbers.