Abbas Cheraghi,
Volume 14, Issue 2 (7-2014)
Abstract
Determining the Optimal Complexity of Bipartite Access Structures
Abbas Cneraghi
Abstract
Keywords: Complexity, Secret Sharing Scheme, Access structure.
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 Padro and Saez, but it is not known which is the optimal information rate of non ideal bipartite access structures. Determining the optimal complexity 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 complexity. Namely, by using the connection between secret sharing schemes and polymatroids, we show a linear programming problem that determines, for each access structure, a lower bound on the complexity. Moreover, we show new optimal constructions for certain bipartite access structures.
