Description
Isogenies are an important tool in the study of elliptic curves. As such their applications in Elliptic Curve Cryptography are numerous, ranging from point counting to new cryptographic schemes.<br/> The problem of finding explicit formulae expressing an isogeny between two elliptic curves has been studied by many. Vélu gave formulae for the case where the curves are defined over C; these formulae have been extended in works by Morain, Atkin and Charlap, Coley & Robbins to compute isogenies in the case where the characteristic of the field is larger than the degree of the isogeny.<br/> The small characteristic case requires another treatment. Algorithms by Couveignes, Lercier, Joux & Lercier, Lercier & Sirvent give solutions to different instances of the problem. We review these strategies, then we present an improved algorithm based over Couveignes' ideas and we compare its performance to the other ones.
Prochains exposés
-
Schéma de signature à clé publique : Frobénius-UOV
Orateur : Gilles Macario-Rat - Orange
L'exposé présente un schéma de signature à clé publique post-quantique inspiré du schéma UOV et introduisant un nouvel outil : les formes de Frobénius. L'accent est mis sur le rôle et les propriétés des formes de Frobénius dans ce nouveau schéma : la simplicité de description, la facilité de mise en oeuvre et le gain inédit sur les tailles de signature et de clé qui bat RSA-2048 au niveau de[…] -
Yoyo tricks with a BEANIE
Orateur : Xavier Bonnetain - Inria
TBD-
Cryptography
-
Symmetrical primitive
-