摘要
运用存取结构与连通超图之间的关系,将7人参与的一类存取结构转化为连通超图中顶点数为7的一类共94种超图存取结构,研究了最优信息率及其所对应的完善秘密共享方案的构造.运用超图理论及方法对其中80种超图存取结构最优信息率的精确值进行了计算,并给出达到此信息率的秘密共享方案的具体构造方法;对其余的14种超图存取结构运用λ-分解等方法给出最优信息率的上下界.证明了具有n个顶点且秩为r的超图,其超边数至少为(n-r)/(r-1)+1条,至多为Cr n条;并从理论上证明了满足一定条件的顶点数为n(4≤n≤9),超边数为4且秩为3的非理想超图的最优信息率为2/3.
Abstract： Through transforming the access structures on seven participants to a total of 94 con- nected hypergraphs on seven vertices, the optimal information rate and the construction of perfect secret sharing schemes corresponding to these access structures are given in terms of the relation- ship between access structures and connected hypergraphs. The exact values for the optimal in- formation rate of the 80 access structures are computed by using hypergraph theory and method, and the relevant construction of perfect secret sharing schemes is discussed. The upper and lower bounds on the information rate of other 14 access structures based on hypergraphs are given by u- sing ;t-Decomposition method and so on. At the same time, it is shown that the hypergraph with n vertices and r rank has at least [（n--r）/（r--1）＋1 edges, and at most Cr edges, and that the optimal information rates of the non-ideal hypergraphs with n（4≤n≤9） vertices and r ranks are all equal to 2/3 if they meets certain conditions.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第1期1-6,共6页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(61373150)
陕西省科学技术研究发展计划工业攻关项目(2013K0611)
关键词
完善的秘密共享方案
存取结构
超图
超图存取结构
最优信息率
perfect secret sharing scheme
access structure
hypergraph
hypergraph accessstructure
optimal information rate
