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Secret sharing in 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 pre-specified 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 obtain 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 denotes 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.