Secret sharing schemes for graph-based prohibited structures

A secret sharing scheme for the prohibited structure is a method of sharing a master key among a finite set of participants in such a way that only certain prespecified subsets of participants cannot recover the master key. A secret sharing scheme is called perfect, if any subset of participants who cannot recover the master key obtains no information regarding the master key. In this paper, we propose an efficient construction of perfect secret sharing schemes for graph-based prohibited structures where a vertex denotes a participant and an edge does a pair of participants who cannot recover the master key. The information rate of our scheme is 2/n, where n is the number of participants.