最大线性正形置换的刻画与计数

Characterization and Counting for Maximal Linear Orthomorphisms Permutations

最大线性正形置换可以用于密码体制中非线性置换的构造。利用有限域上的多项式理论给出了最大线性正形置换多项式的刻画与计数公式,并进一步结合1995年刘振华在成都研讨会上的结论,从理论上解决了全体最大线性正形置换的构造问题。

Maximal linear orthomorphism permutations can be used in the constructions for non-linear permutations in the cipher system. The characterization of and a counting formula for maximal linear orthomorphisms permutations are obtained by using polynomial theory in the finite fields. Furthermore, combining some conclusions of Mittenthal, the constructive problem for maximal linear orthormorphism permutations are also solved in theory.