基于通用攻击结构的秘密共享方案及其化简

借助集合论的相关概念设计了一种基于通用攻击结构的秘密共享方案,证明了该方案满足秘密共享所要求的秘密重构及完善保密两个基本特性。整个方案运行过程中只需执行简单的模加和模减运算,有着很高的计算性能。最后,又在参与方集合上定义了一种关于攻击结构的等价关系并给出了相应的化简方案,分析显示简化后的方案保持了原方案的基本特性。

An Efficient Secret Sharing Realizing Generalized Adversary Structure and Its Reduction

This paper proposes an efficient secret sharing scheme realizing generalized adversary structure, and proves that the scheme satisfies both reconstruction and perfect properties of the secret sharing. The major feature of this scheme is that it performs modular additions and subtractions only, and each share appears in multiple share sets and thus is replicated. This makes the scheme have the advantages over those available of low computational complexity and high recoverability. Also, the reduction on the scheme is achieved by defining an equivalence relation to adversary structure. Analysis shows that reduced scheme still preserves the properties of original one