*CTL*

11 January 2011 - 14h00

Computing isogenies and applications in cryptography

by Damien Robert from INRIA

Résumé : Elliptic curves provide an efficient public-key cryptosystem. An

important tool in the study of elliptic curves is Vélu's formulas which

allow to compute explicit isogenies between them. In this talk, I will

explain how to generalize Vélu's formulas to abelian varieties (this is a

joint work with Romain Cosset and David Lubicz). I will then describe

AVIsogenies, a full open source implementation of isogeny computation

between Jacobians of genus 2 curves. The interest for cryptography is that

genus 2 curves allow to work over fields of half the size for the same

security as with elliptic curves.