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.
Type de document :
Article dans une revue
Mathematics of Computation / Mathematics of Computation, American Mathematical Society, 2010, 79, pp.1191-1208. 〈10.1090/S0025-5718-09-02295-9〉
https://hal.inria.fr/inria-00384128
Contributeur : Romain Cosset
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Soumis le : jeudi 14 mai 2009 - 14:29:54
Dernière modification le : mardi 13 décembre 2016 - 15:40:27
Document(s) archivé(s) le : lundi 15 octobre 2012 - 10:25:45
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〉
