inria-00107290, version 2
Index calculus in class groups of non-hyperelliptic curves of genus three
Claus Diem a, 1Emmanuel Thomé
b, 2
Journal of Cryptology 21, 4 (2008) 593-611
Résumé : We study an index calculus algorithm to solve the discrete logarithm problem (DLP) in degree~0 class groups of non-hyperelliptic curves of genus~3 over finite fields. We present a heuristic analysis of the algorithm which indicates that the DLP in degree~0 class groups of non-hyperelliptic curves of genus~3 can be solved in an expected time of soft-O(q). This heuristic result relies on one heuristic assumption which is studied experimentally. We also present experimental data which show that a variant of the algorithm is faster than the Rho method even for small group sizes, and we address practical limitations of the algorithm.
- a – Universität Leipzig
- b – INRIA
- 1 : Mathematischen Institut
- Universität Leipzig
- 2 : CACAO (INRIA Lorraine - LORIA)
- CNRS : UMR7503 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)
- Domaine : Informatique/Cryptographie et sécurité
- Commentaire : The original publication is available at www.springerlink.com
- Versions disponibles : v1 (17-10-2006) v2 (15-11-2007)
- inria-00107290, version 2
- http://hal.inria.fr/inria-00107290
- oai:hal.inria.fr:inria-00107290
- Contributeur : Emmanuel Thomé
- Soumis le : Jeudi 15 Novembre 2007, 11:12:51
- Dernière modification le : Vendredi 7 Novembre 2008, 09:45:14
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