| Orthomorphic permutation is both a complete mapping and a special Boolean permutation, it has good cryptographic properties such as full balance, input output is evenly distributed and so on. There are important applications in block cipher design,Therefore, the study of positive displacement has important theoretical significance and practical application value. The construction and counting of conformal displacement is one of the main contents of the study, This paper mainly studies the construction and application of orthomorphic permutation, and the main work is as follows:1. This paper introduce the relative concepts and properties of orthomorphic permutation, narrate the basic idea of the existing orthomorphic permutation construction method. This article presents the definitions and theorems of Boolean permutation, positive displacement, conformal Latin square and replacement polynomial, introduces the basic method of constructing orthomorphic permutation,and illustrates the process and characteristics of each constructional method using examples.2. This paper presents a way for constructing the orthomorphic permutation with Boolean function groups, and the corresponding counting result. The basic idea:Using m(2≤m≤n-2)variate orthomorphic permutation and n-m variate orthomorphic per-mutation, management some techniques, Construct an n variate orthomorphic perm?utation. In this paper, we obtain a new method of constructing n variate orthomor:phic permutation, and presents the corresponding counting result.3. This paper introduces the practical application of orthomorphic permutation in modern cryptography. Orthomorphic permutation is applied in cryptographic design, Special applications in the design of cipher algorithm SMS4 design and sequential cipher design. This paper also describes the principle of constructing cryptographic functions by using orthomorphic permutation, and finally introduces the application of orthomorphic permutation polynomial in cryptography. |
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