**CCIS Seminar - Tuesday 11 January 2011 - CTL**

*14:00:00 - *__Salle de CTL__## Computing isogenies and applications in cryptography

**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.*

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