The main contributions of this dissertation are as follows : ( 1 ) the cryptographic properties of orthomorphic permutations in finite fields are studied ; the relationship between orthomorphic permutations and dbs . is studied , at same time , some cryptographic indices of some permutations used in dbs are analyzed and calculated , and furthermore it is presented that these indices are access to that of some orthomorphic permutations with same degree 本论文的主要工作和取得的研究成果如下： ( 1 )研究了有限域上的正形置换的密码学性质；并讨论了正形置换与典型分组密码des之间的关系，计算和分析了des中所使用的部分置换的密码指标值，指出这些指标与同阶的正形置换在密码性能上接近。
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And the cryptographic indices of non - linear orthomorphic permutations obtained are calculated . ( 7 ) the orthomorphic permutation polynomials in finite fields f8 are studied . we give all orthomorphic permutation polynomials in finite fields f8 , and the enumeration of orthomorphic permutation polynomials are obtained ( 7 )利用有限域上的多项式理论来研究具体的有限域凡上的正形置换多项式，给出了具体计算有限域上正形置换多项式的过程，得到了有限域fs上的正形置换多项式的具体形式及计数。
