一种新的正形置换构造方法

郑浩然; 张海模; 崔霆; 杜晓强

doi:10.3724/SP.J.1146.2008.00528

一种新的正形置换构造方法

doi: 10.3724/SP.J.1146.2008.00528

郑浩然^{①;张海模},
张海模,
崔霆,
杜晓强

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出版历程
- 收稿日期: 2008-04-28
- 修回日期: 2008-11-24
- 刊出日期: 2009-06-19

A New Method for Construction of Orthomorphic Permutations

摘要

摘要: 正形置换在密码体制设计中应用广泛。该文基于正形置换和正形拉丁方截集的一一对应关系，研究了正形置换的构造问题，给出了由n元正形置换构造n+1元正形置换的新方法，该方法利用正形拉丁方An的一个截集及其补序截集，扩展得到正形拉丁方An+1的一个复合截集，并由此构造出正形拉丁方An+1的截集。证明了按这种方法由任一n元正形置换可以构造出22n个n+1元正形置换。
- 密码学;正形置换;正形拉丁方;截集;复合截集
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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