一种改进的非线性正形置换构造方法及其性能分析

An improved method of constructing nonlinear orthomorphic permutations with the analysis of its property

对Ｌ．Ｍｉｔｅｎｔｈａｌ提出的非线性正形置换的构造方法进行了改进，指出了原方法中存在的问题．通过改进一个最大线性正形置换方法得到了非线性正形置换的个数下限．最后，引入了差值非线性度的概念。

This paper not only improves the method of constructing nonlinear orthomorphic permutations presented by L.Mittenthal, but points out some problems existing in the original one. Meanwhile, the number of the nonlinear orthomorphic permutations derived from a maximal linear orthomophic permutation is given by our improved method. Moreover, the concept of differential nonlinearity is introduced. Finally, the cryptographic property of nonlinear orthomorphic permutations generated in this way is evaluated with the concept above.