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有限域上的正形置换具有良好密码学性质,被广泛应用.本文推广了正形置换的概念,得到了一般有限域上广义线性正形置换的计数公式和部分广义线性正形置换的生成算法.以2为特征的有限域上线性正形置换计数公式是本文公式的特例.本文生成的广义线性正形置换用于设计P-置换时,分支数可以达到最优.
The orthomorphic permutation over finite field has good cryptographic properties and is widely used.This paper generalizes the concept of orthomorphic permutation and obtains the generalized linear orthomorphic permutation counting formula and some generalized linear orthomorphic permutation algorithms The linear orthomorphic permutation and counting formula on finite field characterized by 2 is a special case of this paper.The generalized linear orthomorphic permutation generated in this paper can be used to optimize the number of branches when designing P-permutation.