Facta Universitatis Series Mathematics and Informatics

NEW METHOD TO COMPUTE BOUNDS ON THE OPTIMAL INFORMATION RATE OF SECRET SHARING SCHEMES

Abbas Cheraghi

Published Nov 21, 2025• 0 citations

Abstract

In a bipartite secret sharing scheme, the set of participants is divided into two parts, and all participants in each part play an equivalent role. The ideal bipartite access structures were characterized by Padr´o and S´aez, but it is not known which is the optimal information rate of non ideal bipartite access structures. Determining the optimal information rate of general access structures is one of the major problems in secret sharing. We study this open problem restricted to the bipartite access structures, obtaining a new method to compute bounds on the optimal information rate. Namely, by using the connection between secret sharing schemes and polymatroids, we show a linear programming problem that determines, for each access structure, an upper bound on the information rate. Moreover, we show new optimal constructions for certain bipartite access structures.

DOI: 10.22190/fumi240824056c

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