Conference "Algorithms and Arithmetic"
with applications to cryptography

Computing isogenies between abelian varieties

Damien Robert (LORIA, Metz)

Tuesday, May 18, 11:30 - 12:30

Abstract

Isogenies are an essential tool in Elliptic Curves cryptography, where they are used in a wide variety of area: fast point counting, complex multiplication methods... Vélu's formulas give an efficient method for computing such isogenies, but there were no known formulas for computing isogenies for hyperelliptic curves of higher genus, except in particuliar cases. In this talk, we will show how the framework of theta structures, developped by Mumford in 1967, allows us to give a generalization of Vélu's formulas for any abelian variety. This is a joint work with David Lubicz.