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扩散层是分组密码的一个重要组件,特别是SPN型结构的密码以及轮函数为SPN型的Feistel结构密码,都要用到一个非退化的线性变换作为其扩散层。好的分支数以及线性变换的对合性质对分组密码的扩散性以及实现效率都有很大的提高。本文基于循环移位和异或运算构造了三种线性变换。并证明了这三种线性变换是分支数为4的次最优的线性变换,同时在一定条件下,还证明了它们均是对合的线性变换。
Diffusion layer is an important component of block cipher. Especially SPN-type structure code and SPN-type Feistel structure code should use a non-degenerate linear transformation as its diffusion layer. The good number of branches and the nature of the nature of the linear transformation have greatly improved the diffusion and efficiency of the block cipher. This paper constructs three linear transformations based on cyclic shift and XOR. It is also proved that these three kinds of linear transformations are suboptimal linear transformations whose number of branches is four. At the same time, under certain conditions, it is also proved that they are both linear transformations of conjugation.