Local do evento
We will show how curves over finite fields and their Jacobians are used in order to enforce the best current public key crypto-systems. We will see:
1) How to compute the order the order of rational points on the Jacobian (Schoof like algorithms).
2) How to perform fast operations on genus 2 curves using either Cantor algorithm or the Kummer surface.
3) Post-Quantum isogeny based schemes.
The accent will be more on the mathematical concepts than on the implementations details but we will try to program some functions in Magma for instance to gain some intution. Depending on the motivation of the audience, some recent articles may additionally be studied in a working group-style.