摘要： 具有n个参与者形成的存取结构集合与具有n个顶点的超图集合之间存在一一对应关系。定义一类超图,即r－一致完全k分超图,运用向量空间构造法证明该类超图对应的存取结构是理想的,进而利用组合数学知识计算出该类超图存取结构的数目。在有限域F7上给出参与者人数为4,5,6的所有r－一致完全k分超图存取结构。验证结果表明,相比(r,n)门限存取结构和完全k分图存取结构,该类理想的超图存取结构更为一般化,应用更为广泛。
关键词:
超图,
完全k分超图,
存取结构,
理想存取结构,
向量空间构造
Abstract: There exists a one-to-one correspondence between the set of access structures with n participants and that of hypergraphs with n vertices.This paper proposes a type of hypergraph,i.e.,r-uniform hypergraphs with complete k-partition.It proves that the type of hypergraph access structures is ideal by using vector space construction.The paper gives the number of this type of ideal hypergraph access structures using combinatorial mathematics,and gives all the ideal access structures with the number of participants (or vertices) 4,5,6 over a finite field F7 based on the r-uniform hypergraph with complete k-partition.Test results show that,compared with (r,n) threshold access structures and completek-partition graph access structures,the proposed ideal access structures are more vivid,and can be extensively applied in practice.
Key words:
hypergraph,
complete k-partition hypergraph,
access structure,
ideal access structure,
vector space construction
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