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引入了一个新的代数系统——称为密码协议代数(cryptographic protocolalgebra,CPA),刻画具有多种密码运算的消息代数性质,并基于CPA提出了一个新的密码协议代数模型.模型中,用子代数、自由生成元和多项式代数等概念刻画主体的知识扩张过程,并用类似于代数中的正合序列概念描述了密码协议的攻击过程,从而为密码协议的安全性分析建立了一种数学方法.基于这个模型,利用代数的技巧证明了对于具有一定对称性的协议,任意多主体参与运行的协议安全性分析可归结为几个主体与攻击者参与的协议安全性分析.研究了密码协议安全的一致性问题,给出了两个协议合成保持安全性的一个充分条件,并提供两个安全的密码协议的合成安全的例子,推广了相关工作.
A new algebraic system called cryptographic protocolalgebra (CPA) is introduced to characterize the algebraic properties of messages with various cryptographic operations and a new cryptographic protocol algebraic model based on CPA is proposed. In the model, Algebra, Free Generators and Polynomial Algebra are used to describe the process of knowledge expansions and describe the attack process of cryptographic protocols in a similar way to the concept of positive coincidence sequences in algebra. Thus, a mathematical method is established for the security analysis of cryptographic protocols. Based on this model, the algebraic technique is used to prove that for a symmetric protocol, the protocol security analysis of any multi-principal involved in running can be attributed to the protocol security analysis involving several subjects and attackers.The security of the cryptographic protocol Consistency problem, a sufficient condition for the security of the two protocols to be synthesized is given, and examples of the security of the synthesis of two secure cryptographic protocols are provided to promote the related work.