Orthomorphism is a kind of important elementary permutation in symmetric cryptography, which is also a kind of complete mapping. Orthomorphism has been proved to have the perfectly balanced property. Construction and counting of orthomorphism has become one of the focal issues to Chinese and foreign scholars from 1995, however current researches on orthomorphisms pay little attention on their cryptographic properties, such as difference uniformity, nonlinearity and so on. Orthomorphisms with good cryptographic properties can be directly used to construct the cryptographic units in symmetric cryptographic algorithms. In this paper, firstly a problem in a conclusion about nonlinearity of composite functions is pointed out and corrected. Then several cryptographic properties against differential attack and linear attack of normal BDLL orthomorphism generator are analyzed, such as nonlinearity, algebraic degree and difference uniformity. Next, a modified orthomorphism generator based on composite functions is proposed. With the corrected conclusion of composite functions, the modified orthomorphism generator is proved to be able to construct nonlinear orthomorphisms with higher nonlinearity and algebraic degree than previous normal BDLL orthomorphism generators. And the numbers of orthomorphisms which can be derived from the modified orthomorphism generator is also proved to be bigger than that of previous normal BDLL orthomorphism generators.%作为一种完全映射,正形置换是对称密码体制中一类重要的基础置换.正形置换已经被证明拥有完全平衡性.自1995年以来,国内外学者对于正形置换的研究主要集中在构造与计数方面,但是对于正形置换的密码学性质,比如差分均匀度和非线性度等则相对关注得较少,而具有良好密码学性质的正形置换可以直接用来设计对称密码算法中的密码学部件.修正了一个关于复合函数密码学性质的结论中关于非线性度所存在的问题；接着分析了一般BDLL正形置换发生器的抗差分分析和抗线性分析的密码学性质；然后基于复合函数提出了一种改进的正形置换发生器,并结合修正后的复合函数结论证明了该正形置换发生器相比于一般BDLL正形置换发生器,能够生成数量更多、拥有更高非线性度和代数次数的非线性正形置换.
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