Abstract : We describe a fast algorithm for counting points on elliptic curves defined over finite fields of small characteristic, following Satoh. Our main contribution is an extension to characteristics two and three. We give a detailed description with the optimisations necessary for an efficient implementation. Finally we give the number of points we have computed on a ``random'' curve defined over the field Fq with q=2^8009.
Type de document :
Article dans une revue
Journal of the Ramanujan Mathematical Society, Ramanujan Mathematical Society, 2000, 15, pp.281-318
https://hal.inria.fr/inria-00512791
Contributeur : Pierrick Gaudry
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Soumis le : mardi 31 août 2010 - 15:56:56
Dernière modification le : vendredi 25 mai 2018 - 12:02:03
Document(s) archivé(s) le : mercredi 1 décembre 2010 - 02:52:34
Mireille Fouquet, Pierrick Gaudry, Robert Harley. An extension of Satoh's algorithm and its implementation. Journal of the Ramanujan Mathematical Society, Ramanujan Mathematical Society, 2000, 15, pp.281-318. 〈inria-00512791〉
