Arithmetic on abelian varieties and related topics

Vortrag von Dr. Damien Robert

Datum: 03.03.14  Zeit: 13.00 - 14.00  Raum:

A natural generalisation of elliptic curve cryptography consists of looking at Jacobian of curves, which associate a commutative group (scheme) to a curve; these Jacobians are themselves a particular example of abelian varieties.

In this talk, I will discuss the use of abelian varieties in cryptography. One important question is how to compute (efficiently) the addition law when we can't rely on the geometry of the curve in the case of an abelian variety that is not a Jacobian.

Interlocked to this topic are the questions of the explicit computation of pairings (which have a lot of applications in public key cryptography) and isogenies between abelian varieties.

I will present these three topics, explain their relationships and describe related algorithms.