On the combinatorial approaches of computing upper bounds on the information rate of secret sharing schemes

Authors:
Zhanfei Zhou
Affiliations:
State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing, China
Venue:
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Year:
2010

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Abstract

Computing the information rate of access structures is an important part of the research of secret sharing schemes. In this paper, we investigate two combinatorial approaches of computing upper bounds on the information rate of access structures - the Csirmaz's polymatroid approach and the independent sequence approach. We prove that the Csirmaz's polymatroid approach is only a special variant of the independent sequence approach, and finding an independent sequence with respect to a graph-based access structure with maximum length is equivalent to finding a maximum alternating cycle-free matching in a bipartite graph, which is a NP hard problem.