N个Shamir门限秘密共享方案组合的通用可验证性设计

Universal Verifiability Design for the Combination of N Shamir Threshold Secret Sharing Schemes

摘要: 秘密共享方案的可验证性是安全多方计算协议中重要的一个研究方向，该领域的研究可以作为安全计算的公平性、安全性、正确性研究基础。本文设计了一种n个Shamir门限秘密共享方案组合的通用可验证性，该方案与已有的Shamir门限秘密共享方案不同，本文将每个参与者分享的秘密数扩展到个，即个Shamir门限的组合，而不是单单的对于一个秘密的分享，使其应用的方面更加广泛；同时，弥补了现有通用方法在输入阶段和计算阶段的验证性的不足，最后实现了每个阶段、每个步骤可验证性的连续性、传递性。

Abstract: The verifiability of secret sharing scheme is an important research direction in secure multi-party computing protocols. The research in this field can be used as the basis for the fairness, security and correctness of security computing. This paper designed that a universal verifiability of a n-shamir threshold secret sharing scheme is different from the existing shamir threshold secret sharing scheme. This paper extends the secret number shared by each participant to n, i.e. the combination of n-shamir thresholds, rather than a single secret sharing, makes its application more extensive; at the same time, it makes up for the lack of verification of the existing general methods in the input phase and the computing phase. Finally, the continuity and transitivity of the verifiability of each stage and every step are achieved.