摘要： 在一般存取结构上，通过建立存取结构与超图之间的一一对应关系，提出基于特殊超图-非循环超图的一个秘密共享方案。采用向量空间构造法和(t, t)门限体制相结合的思想设计分发算法和重构算法。找出非循环超图的最大路径，增加图中2-区域的顶点个数，并在图中不断添加耳朵来完成方案的构造。该方案的信息率可达到最大值1。

关键词: 理想秘密共享方案, 存取结构, 非循环超图, 最长路径, 2-区域, 向量空间构造, (t, t)门限体制

Abstract: On the general access structures, this paper presents an ideal secret sharing scheme on a special type of hypergraphs by establishing a one-to-one correspondence between access structures and hypergraphs. The designed distribution algorithm and reconstruction algorithm are mainly based on the thought of vector space construction and (t, t) threshold scheme. Find the longest path in the given acyclic hypergraphs, increase the number of vertex in 2-regions, add the ears onto the hypergraphs, and finish the construction of the scheme. Meanwhile, the information rate of the scheme can reach its maximum 1.

Key words: ideal secret sharing scheme, access structure, acyclic hypergraph, the longest hyperpath, 2-region, vector space construction, (t, t) threshold scheme

中图分类号: 

• TP309