基于Birkhoff插值的可验证多等级秘密共享算法

Birkhoff interpolation-based verifiable hierarchical threshold secret sharing algorithm

分布式密钥生成(DKG)协议是分布式加密系统的重要组成部分,其允许一群参与者共同产生私钥和公钥,但只有授权的参与者子集才能重构私钥。然而,现有的基于DKG协议均是假定参与者等级相同。为此,提出基于Birkhoff插值的可验证多等级秘密共享BI-VHTSS算法。BI-VHTSS算法考虑了DKG问题,并由等级门限访问结构定义授权子集。利用Birkhoff插值和离数对数问题,验证了BI-VHTSS算法的正确性和安全性。

A Distributed Key Generation（ DKG） protocol is a central component in distributed cryptosystems,it allows a group of participants to jointly generate private key and public key,but only authorised subgroups of participants are able to reconstruct private key. However,the existing literatures based on DKG protocol assume equal authority for participants.Therefore,Birkhoff Interpolation-based Verifiable Hierarchical Threshold Secret Sharing（ BI-VHTSS） algorithm was proposed. Considering the problem of DKG,authorized subsets were defined by a hierarchical threshold access structure in BIVHTSS algorithm. On the basis of intractability of the Discrete Logarithm Problem（ DLP） and Birkhoff interpolation,the correctness and security of the proposed algorithm were also proved.