Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## Gröbner Basis algorithms and applications in Multivariate Cryptography

Raffael Schüürmann talk

**Date:** 09.10.19 **Time:** 16.15 - 17.15 **Room:** Y27H28

Since the introduction of Buchberger's algorithm in 1965, Gröbner basis algorithms have attracted a lot of attention in computational algebra. During the years there were made several improvements on the the efficiency of such algorithms that compute a Gröbner basis for an ideal spanned by a set of multivariate polynomials. We will introduce and compare four of the most successful Gröbner basis algorithms including Buchberger's algorithm, Faugère's F4 algorithm, F5-like signature based algorithms and the most recent M4GB algorithm. Gröbner basis algorithms are fundamental, when solving multivariate polynomial systems. Therefore, the direct Gröbner basis attack is important for practical security analysis of Multivariate Cryptosystems. We will compare the performance of introduced Gröbner basis algorithms on instances of Multivariate Cryptosystems.