AGROCAMPUS OUEST (Institut Supérieur des Sciences Agronomiques, Agroalimentaires, Horticoles et du Paysage - 65, rue de St Brieuc - CS 84215 - 35042 Rennes cedex - France)
Abstract : In this paper, we present a new approach based on theta functions to compute Weil and Tate pairings. A benefit of our method, which does not rely on the classical Miller's algorithm, is its generality since it extends to all abelian varieties the classical Weil and Tate pairing formulas. In the case of dimension $1$ and $2$ abelian varieties our algorithms lead to implementations which are efficient and naturally deterministic. We also introduce symmetric Weil and Tate pairings on Kummer varieties and explain how to compute them efficiently. We exhibit a nice algorithmic compatibility between some algebraic groups quotiented by the action of the automorphism $-1$, where the $\Z$-action can be computed efficiently with a Montgomery ladder type algorithm.
Type de document :
Communication dans un congrès
Guillaume Hanrot and François Morain and Emmanuel Thomé. ANTS IX - Algorithmic Number Theory 2010, Jul 2010, Nancy, France. Springer-Verlag, 6197, pp.251-269, 2010, Lecture Notes in Computer Science. <10.1007/978-3-642-14518-6_21>
https://hal.archives-ouvertes.fr/hal-00528944
Contributeur : Damien Robert <>
Soumis le : samedi 23 octobre 2010 - 00:38:04
Dernière modification le : mercredi 12 juillet 2017 - 01:15:17
Document(s) archivé(s) le : vendredi 26 octobre 2012 - 12:00:50
David Lubicz, Damien Robert. Efficient pairing computation with theta functions. Guillaume Hanrot and François Morain and Emmanuel Thomé. ANTS IX - Algorithmic Number Theory 2010, Jul 2010, Nancy, France. Springer-Verlag, 6197, pp.251-269, 2010, Lecture Notes in Computer Science. <10.1007/978-3-642-14518-6_21>. <hal-00528944>
