Reserch On Several Tranformations In Block Cipher Design

Design transformation in block cipher is one of the most important questions which attractthe cryptanalysts’attension. The transformation will affect both security level and theimplementation performance of block cipher. In this paper, we mainly study on several commontechnologies in block cipher design, then we analyed the security level of a kind of unbalancedFeistel structure.1. We study on the construction of diffusion layer: firstly, we improved a constructionmethod which is used to design a kind of “almost involutory”Cauchy matrices, and weprovide the algorithm, then we prove that this kind of matrices can always transform intoinvolutory MDS matrices. Secondly, we prove the conditions of the branch number of bit-wisediffusion layer reaches the maximum value. Finally, we provide a new design of SPN cipher, thenested-SPN. Compared with traditional SPN structures, this kind of design can provide higherimmunity against differential/linear attack, and increases tiny cost.2. This paper studies the construction of orthomorphic permutation based on some popularblock cipher structures. we proved that when F layer is designed as a bijection, Feistel structure,SMS4structure, CAST256structure and MARS structure are all orthomorphic permutations.3. We further focus on the “structural” construction of orthomorphic permutation. Weintroduce the tranformation matrix to describe the structure of a tranformation, and by using thismatrix, we transform the judgement of orthomorphic permutation into the reversible oftranformation matrix M and M E. Finally, we provide the sufficient condition of thereversible of tranformation matrix.4. Then we extend the DSM mechanism used for Feistel structure, we obtain the result onunbalanced Feistel structures, we prove the number of active S-boxes in this kind of unbalancedFeistel structure. We prove that this kind of unbalanced Feistel structure can provide moresecurity than the traditional unbalanced Feistel strucuture.