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 large numbers.
https://hal.inria.fr/inria-00384128
Contributor : Romain Cosset
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Submitted on : Thursday, May 14, 2009 - 2:29:54 PM
Last modification on : Tuesday, December 18, 2018 - 4:18:25 PM
Document(s) archivé(s) le : Monday, October 15, 2012 - 10:25:45 AM
Romain Cosset. Factorization with genus 2 curves. Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2010, 79, pp.1191-1208. ⟨10.1090/S0025-5718-09-02295-9⟩. ⟨inria-00384128⟩
