Everybody is cordially invited to our Seminar on Groups, Rings and Cryptography on the 4th of September, 14:00 - 16:30 in 6G.60

14:00-15:00 On the semidirect discrete logarithm problem

by Gabor Ivanyos (Institute for Computer Science and Control, Hungarian Academy of Sciences, Budapest, Hungary)

Abstract:

The semidirect discrete logarithm problem was introduced by Habib et al. in 2013 as the basis for a Diffie-Hellman-type key exchange protocol. In 2023, Battarbee et al. observed that the problem can be translated into a certain vectorization problem.

In this talk, we show how the SDLP arises from a quite natural vectorization problem and discuss efficient quantum algorithms to solve it in finite groups. This talk is mainly based on joint work with Muhammad Imran.

15:30-16:30 The Isomorphism Problem for group rings

by Angel del Rio (Department of Mathematics, University of Murcia, Spain)

Abstract:

The Isomorphism Problem for group rings is the following question where R is a ring and G and H are groups:

"Suppose that RG and RH are isomorphic as R-algebras. Are then G and H isomorphic as groups?"

In general the answer is negative, but many positive answers have been obtained in particular cases. We will present a panorama of the state of the art, including some recent results and open questions.