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| A New Method for Construction of Orthomorphic Permutations |
| Zheng Hao-ran①;Zhang Hai-mo②;Cui Ting①; Du Xiao-qiang① |
| ①Institute of Electronic Technology, Information Engineering University, Zhengzhou 450004, China; ②Huanghuai University, Zhumadian 463000, China |
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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.
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Received: 28 April 2008
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2009, Vol. 31 
