Secret sharing on regular bipartite access structures

Bipartite secret sharing schemes realize access structures in which the participants are divided into two parts, and all the participants in the same part play an equivalent role. Such a bipartite structure can be described by the collection of its minimal points. The complexity of a scheme is the ratio between the maximum share size given to the participants and the secret size, and the Shannon complexity of a structure is the best lower bound provided by the entropy method. Within this work, we compute the Shannon complexity of regular bipartite structures and provide optimal constructions for some bipartite structures defined by 2 and 3 points.