Abstract:Orthomorphic permutations have important application in the design of cryptosystems. Based on the one-to-one corresponding relationship between orthomorphic permutations and transversals of orthomorphic Latin square, the construction issue for orthomorphic permutations is studied, a new construction method is proposed to construct a (n+1)-bit orthomorphic permutation from a n-bit one where n>1. The method extends to obtain a composite transversal of orthomorphic Latin square An+1 by employing a transversal of orthomorphic Latin square An and its supplementary sequence transversal, based on composite transversal of , An+1 transversal of An+1 is constructed. Using the method, 22n (n+1)-bit orthomorphic permutations from a n-bit one can be obtained.
郑浩然; 张海模; 崔 霆; 杜晓强. 一种新的正形置换构造方法[J]. 电子与信息学报, 2009, 31(6): 1438-1441 .
Zheng Hao-ran①;Zhang Hai-mo②;Cui Ting①; Du Xiao-qiang①. A New Method for Construction of Orthomorphic Permutations. , 2009, 31(6): 1438-1441 .