Speaker: Gaetan Bisson
Date, Time: Fri, 21 Oct 2011 15:00
Elliptic curves have become an important building block in asymmetric
cryptography as they provide featureful cryptosystems with short keys.
Isogenies, that is, morphisms between such curves, must be carefully
studied as they permit to reduce the security of a curve to that of
We will first give a high-level description of the structure of the graph of isogenies, and then explain its relationship to the endomorphism rings of the curves. Later, we will present a fast algorithm for computing the location of a given curve in that graph, that is, computing its endomorphism ring. This exploits complex multiplication theory and a few other ingredients from computational number theory which we will introduce along the way.