有限域F_q～n上的广义线性正形置换计数

Numeration of generalized linear orthomorphisms over the galois field F_q～n

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 orthomorphisms have good cryptologic properties on the finite field and are widely used. This paper generalizes the concept of orthomorphisms, and obtains the counting formula on the generalized linear orthomorphisms over the Galois field with the arbitrary prime number pas the characteristic and the partial generation algorithm of generalized linear orthomorphisms. The counting formula of the linear orthomorphisms over the finite field with characteristic 2 is the spe- cial case in this paper. Furthermore, the generalized linear orthomorphisms that this paper has generated can gain the maximum branch number when they are designed as P-permutations.