对合型列混合变换的研究

Research on Involution-typed Mixcolumn Transform

基于S-P网络中P置换的重要性和加解密的一致性,本文提出了对合型列混合变换的概念,并对其代数结构、枝数和计数问题进行了深入地研究和分析.本文从列混合变换的代数结构入手,证明了枝数达到最大与其对合特性是相互制约的两个因素,解决了对合型列混合变换的计数问题,并给出了对合型列混合变换中固定多项式c(x)的重量与其枝数之间的精确关系.最后针对有关分组密码编码环节的设计问题进行了讨论,从而为分组密码的设计与分析提供重要的依据和支持.

Based on the importance of P transform and coherence in encryption-decryption in the S-P networks,we put forward the definition of involution-typed mixcolumn transform. Algebraic structure, branch and enumeration of involution-typed mixcolumn transform are researched deeply in this paper. It is shown that the maximum of branch and property of involution are restricted each other using algebraic structure of mixcolumn trausform. Enumeration of involution-typed mixcolumn transform is solved and the relation between the weight of polynomial c（x） and the branch is given. In conclusion, some discussion of the design of block cipher are given and this provides a significant basis for the design and analysis of block cipher.