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
-
CryptoVerif: a computationally-sound security protocol verifier
Orateur : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
-