Factorization with genus 2 curves

Mathematics – Number Theory

Scientific paper

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Scientific paper

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.

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