Enumeration of Generalized Linear Orthomorphism in the Vector Space F_q^n  

作　　者：HAN Haiqing LI Qin TONG Yan LIU Xiusheng 

机构地区：[1]. School of Mathematics and Physics, Huangshi Institute ofTechnology, Huangshi 435003, Hubei, China [2]Department of Normal, Huangshi Institute of Technology,Huangshi 435003, Hubei, China

出　　处：《Wuhan University Journal of Natural Sciences》2012年第1期43-47,共5页武汉大学学报（自然科学英文版）

基　　金：Supported by the National Natural Science Foundation of China (60970115, 91018008)

摘　　要：The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the characteristic is obtained. Thus, the partial generation algorithm of generalized linear orthomorphism is achieved. The counting formula of the linear orthomorphism in the vector space over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphism generated and discussed in this paper can gain the maximum branch number when they are designed as P-permutations.The conception of orthomorphism has been generalized in this paper, and a counting formula on the generalized linear orthomorphism in the vector space over the Galois field with the arbitrary prime number p as the characteristic is obtained. Thus, the partial generation algorithm of generalized linear orthomorphism is achieved. The counting formula of the linear orthomorphism in the vector space over the finite field with characteristic 2 is the special case in our results. Furthermore, the generalized linear orthomorphism generated and discussed in this paper can gain the maximum branch number when they are designed as P-permutations.

关 键 词：block cipher P-permutation generalized linear orthomorphism the branch number counting formula 

分 类 号：TP918[自动化与计算机技术]