Algebraic techniques on searching linear diffusion layers in block cipher

Maximum branch number permutation plays an efficacious role in providing resistance against the most well-known attacks on block ciphers, such as differential cryptanalysis and linear cryptanalysis. In this paper, we propose algebraic techniques in searching permutations with maximal branch number, which can be employed as the linear diffusion layers in block ciphers. We focus on permutations composed of simple operations such as word-level XORs and rotations. Some necessary conditions are proposed to filter out linear permutations that cannot achieve the maximal branch number. With these conditions, the searching process of maximum permutation on 32-bit word can be finished in 1i¾źs, contrast to the previous searching method which spent several days on two computers. What is the most important is that it can be generalized to 64-bit word and show that there is no 8-byte word permutation, which is XOR of 9 right-rotations or 11 right-rotations with maximum branch number. Copyright © 2016 John Wiley & Sons, Ltd.

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