关键词: 秘密共享方案, 完善的秘密共享方案, 单调的存取结构, 完全多划分图, 信息率

Abstract: Through transforming the access structures on eight participants to a total of 110 connected graphs on eight vertices, the paper studies the optimal information rate and the construction of perfect secret sharing schemes corresponding to these access structures are given in terms of the relationship between certain access structures and connected graphs. The exact values for the optimal information rate of the 101 access structures are computed and the relevant construction of perfect secret sharing schemes is discussed. At the same time, the upper and lower bounds for the information rate of other 9 access structures are computed and the upper bound on the information rate of connected graphs on eight vertices is proved.

Key words: secret sharing schemes, perfect secret sharing schemes, monotone access structure, complete multipartite graph, information rate