一类完善秘密共享方案的最优信息率

Optimal Information Rate of a Type of Perfect Secret Sharing Schemes

研究参与者人数为7的一类存取结构的完善秘密共享方案及其最优信息率。利用存取结构与连通图之间的关系,给出其对应的111种图存取结构。对其中的91种图存取结构计算它们最优信息率的精确值,并讨论达到此信息率的秘密共享方案的具体构造方法。对余下20种图存取结构给出最优信息率的上下界,并从理论上证明,满足一定条件且顶点数为7信息率的上界为3/5。

This paper studies the optimal information rate of perfect secret sharing schemes of a type of access structures on seven participants.Based on the relationship between these access structures and their connected graphs,111 connected graphs corresponding to these access structures are given.The exact values of the optimal information rate of 91 access structures based on graphs are computed and the secret sharing schemes attaining the optimal information rate are discussed in Table 1,where the upper and lower bounds on the information rate of the rest 20 are also calculated.The upper bound on the information rate of connected graphs on seven vertices is theoretically proved.