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

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