抗合谋攻击的多变量群签名方案

摘要

多变量公钥密码体制能抵御量子计算机的攻击,被认为是后量子时代的一种安全的密码体制备选方案.提出了一种基于多变量公钥密码体制的群签名设计模型,同时在分析该方案时,提出了一种合谋攻击方案,可以有若干合谋攻击者对群签名体制进行伪造签名攻击.随后,给出了一种新的矩阵乘法定义,以及素矩阵等概念,并提出了一种可以抵抗合谋攻击的基于多变量公钥密码体制的群签名设计模型.分析结果表明:该方案不仅能够从根本上抵抗合谋攻击和伪造签名攻击,而且在保证匿名性的前提下,能够真正实现签名成员身份的可追查性,同时通过构造安全的密钥生成协议保证群签名私钥的不可知性,因此具有更高的安全性.%Multivariate public key encryption scheme which can resist attacks by quantum computer is believed to be an alternative security cryptography scheme in the post-quantum age. A multivariate group signature scheme was proposed. After an analysis of the scheme, a conspiracy attack scheme which could offer forgery attacks to the signature system was proposed. Then, a new matrix multiplication definition and prime matrix concept were given, and a conspiracy attack immune group signature scheme was proposed. Analysis shows that the scheme can not only fundamentally withstand conspiracy and forgery attacks, but trace the identity of signature members anonymously. Meanwhile, it can realize the unknown ability of group signature secret keys by constructing a secure distributed key generation protocol, thus greatly enhancing group signature security.