Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## Master's Thesis Defense: Nexuses of Uniforms: A Family of Uniform Hypergraphs Representing Ideal Access Structures

Talk by Sascha Hoppler

**Date:** 02.03.22 **Time:** 15.00 - 16.00 **Room:** Y27H25

Secret sharing is a cryptographical tool to split a piece of information called secret among several participants such that only certain qualified subsets of them can reconstruct the initial secret. The collection of these qualified sets is called access structure and can be represented by hypergraphs, where vertices correspond to participants and hyperedges correspond to minimal qualified sets.
It is desirable that not much data needs to be transferred to the participants of such a scheme. In particular, a secret sharing scheme is called ideal if each share has the same size as the secret, and a hypergraph representing an access structure which can be realized by an ideal scheme is called ideal.
We introduce an operation on hypergraphs preserving idealness and then define a family of ideal uniform hypergraphs called Nexuses of Uniforms. We eventually focus on 3-uniform hypergraphs and analyze for which of them we can determine whether they are ideal or non-ideal.

(**This eSeminar will also be live-streamed on Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact simran.tinani@math.uzh.ch **)