Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## Multivariate cryptography and the complexity of solving a random polynomial system

Talk by Giulia Gaggero

**Date:** 23.11.22 **Time:** 16.30 - 17.30 **Room:**

A multivariate cryptograpic instance in practice is a multivariate polynomial system. So the security of a protocol rely on the complexity of solving a multivariate polynomial system. During this talk I will explain the invariant to which this complexity depends on: the solving degree. Unfortunately this invariant is hard to compute. We will talk about another invariant, the degree of regularity, that under certain condition, give us an upper bound on the solving degree. Finally we will talk about random polynomial systems and in particular what "random" means to us. We will give an upper bound on both the degree of regularity and the solving degree of such random systems.

(**This eSeminar will take place over Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact zita.fiquelideabreu@math.uzh.ch **)