Abstract: A hierarchical threshold scheme is used to solve the secret sharing with a hierarchical access structure where participants are partitioned into different levels. In a hierarchical access structure, the participants group is divided into different levels based on the privilege, and a certain number of participants from each level are required to recover the secret. In the past hierarchical threshold schemes, participants are partitioned based on a single attribute. But in practice, each participant always has several attributes, and the group of participants always should be partitioned based on different attributes to satisfy the security requirements. Even though hierarchical threshold schemes have been studied extensively in the past years, few of the existing solutions can solve the above problem. A reusable multi-attributes hierarchical threshold scheme based on Tassa’s scheme which uses Birkhoff interpolation, and Mignotte’s scheme which uses Chinese Remainder Theorem, is proposed to solve this problem in this paper.

Key words: multi-attributes, hierarchical threshold scheme, Birkhoff interpolation, Chinese Remainder Theorem

摘要： 多等级门限秘密共享策略是用来解决具有多等级访问结构的秘密共享问题。多等级访问结构是将所有参与者根据其权限或职位高低分割成不同的层次，并在恢复秘密时，对各等级参与人数都有一定门限要求的结构。在以前的多等级门限策略中，划分参与者集合都是基于单一的用户属性。在实际情况中，参与者通常会有多种属性，并且为了满足一些更高级别的安全需求，系统更希望基于多种属性对参与者集合进行划分。虽然对多等级秘密共享策略的研究已经非常深入，但是现存的秘密共享策略几乎无法解决上述问题。基于Tassa提出的基于Birkhoff插值法的多等级门限秘密共享策略和Mignotte提出的基于中国剩余定理的秘密共享策略，提出了一种用户秘密份额可重复使用的基于多属性划分的多等级门限秘密共享策略。

关键词: 多属性, 多等级门限策略, Birkhoff插值法, 中国剩余定理