MAK Crypto Seminar: Michael Bamiloshin and Victor Peña-Macias

TALK #1:

By: Michael Olugbenga Bamiloshin, URV Tarragona

Title: Common Information, Matroid Representation, and Secret Sharing for Matroid Ports

Abstract: A secret sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret. The information ratio of a secret sharing scheme is the size in bits of the largest share of the scheme divided by the size of the secret. Farràs, Kaced, Martín and Padró presented an improvement in the linear programming technique to derive lower bounds on the information ratio of the schemes for an access structure that use the Ahlswede-Körner lemma and the common information of random variables, avoiding the use of explicit non-Shannon information inequalities (EUROCRYPT 2018). In this work we apply this linear programming technique to the classification of matroids on eight and nine points. Namely, we apply this technique to check if a matroid is multilinearly representable, algebraic or almost entropic. We also present some hitherto unknown non-representable matroids and new bounds on the information ratio of schemes for ports of non-representable matroids.

This is a joint work with Aner Ben-Efraim, Oriol Farràs and Carles Padró.

TALK #2:

By: Victor Peña-Macias, Universidad Nacional de Colombia

Title: Characteristic-Dependent Linear Rank Inequalities and Applications to Network Coding

Abstract: In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over fields with other characteristic. In this talk, we show a new method to produce these inequalities. We also discuss some results of application to Network Coding, among these, for each finite or co-finite set of primes P, we show that there exists a sequence of networks (N(t)) in which each member is linearly solvable over a field if and only if the characteristic of the field is in P; and the linear capacity, over fields whose characteristic is not in P, tends to 0 as t tends to infinity.