Damien Robert

In the use of elliptic curve and abelian varieties for public key cryptography, the speed of the arithmetic play a preponderent role in the
efficiency of the cryptosystem. Currently it seems that Kummer surfaces (represented by a theta model of level 2) have a slight edge against elliptic curves.

In this talk I will discuss the arithmetic of Abelian and Kummer varieties in the theta models of level 4 and 2. In the first part I will
give a brief review of Mumford's theory of algebraic theta functions and explain how the fact that a model is projectively normal can help for the arithmetic. In the second part I will adopt a more elementary point of view to explain how one can speed-up the arithmetic of Kummer and Abelian varieties.

This is a joint work with David Lubicz.