一类图存取结构的最优信息率计算

Optimal Information Rate Calculation Based on a Class of Graph Access Structure

秘密共享为密钥管理提供了一个非常有效的途径,而存取结构的信息率为高效秘密共享方案的设计提供了理论保证。文章利用存取结构与连通图之间的关系,将参与者人数为8的一类存取结构转化为连通图中顶点数为8、边数为9且最大顶点度为3的一类共63种图存取结构,并分别通过分裂构造法、熵方法、顶点度定理、分解构造法、加权分解法对这63种图存取结构的最优信息率的准确值或上下界进行计算,得出其中30种图存取结构最优信息率的准确值和其余33种图存取结构最优信息率的上下界。

Secret sharing provides a very effective way for key management and the information rate of access structure provides a theoretical guarantee for the design of efficient secret sharing scheme.In this paper,by using the relationship between access structure and connected graph,a class of access structure with 8 participants is transformed into a class of 63 graph access structures with 8 vertices,9 edges and a maximum vertex degree of 3.The accurate value or upper and lower bounds of the optimal information rate of these 63 graph access structures are calculated by splitting construction method,entropy method,vertex degree theorem,decomposition construction method and weighted decomposition method.The accurate values of the optimal information rates of 30 graph access structures and the upper and lower bounds of the optimal information rates of the other 33 graph access structures are obtained.