An efficient construction of perfect secret sharing schemes for graph-based structures

Abstract

In this paper, we propose an efficient construction of perfect secret sharing schemes for graph-based access structures where a vertex denotes a participant and an edge does a qualified pair of participants. The secret sharing scheme is based on the assumptions that the pairs of participants corresponding to edges in the graph can compute the master key but the pairs of participants corresponding to nonedges in the graph cannot. The information rate of our scheme is 1/(n - 1), where n is the number of participants. We also present an application of our scheme to the reduction of storage and computation loads on the communication granting server in a secure network.