The MARS-like structure is a generalised Feistel structure. Unified impossible differential (UID) method is an effective method to discover impossible differential characteristics for block cipher structures. In this study, for a specific kind of MARS-like structure, the authors use UID to show that when n, the number of subblocks, is even, there always exist 3n − 1 rounds impossible differentials. Moreover, the authors prove that when n is odd, the MARS-like structure has impossible differentials for any number of rounds, which is a clear but interesting result.
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Abstract-Unified Impossible Differential (UID) cryptanalysis is a systematic method to find impossible differentials for block ciphers and there are large amount of cryptanalysis results coming out by using it. ARIA is a Korean block cipher expecting no impossible differential chains on four or more rounds. In this paper, we apply UID to ARIA and 89136 four rounds impossible differential chains are found. With the optimization of the conflict searching algorithms, UID gets better results compared with former cryptanalysis results. Moreover, we conclude that no impossible differential chains with number of rounds larger than four can be found by the UID method.
Differential cryptanalysis is an effective tool in modern cryptanalysis. The differential chain of a Markov cipher forms a Markov chain, and the second largest eigenvalue (SLE) of the transition matrix determines the number of iterations such that the Markov cipher can resist differential cryptanalysis. Owing to the huge scale of the transition matrix, it is infeasible to compute the SLE. Thus, an estimation method would be desirable. We find two methods to estimate the SLE by using the elements of the row-stochastic matrix in the literature. Their advantage is parallel computing, without generating the complete matrix. We apply these two methods to the transition matrix of International Data Encryption Algorithm(8) and investigate the accuracy of such estimation. Because the International Data Encryption Algorithm is a primitive Markov cipher, its transition matrix will converge to a uniform distribution. We use the power of the initial transition matrix to estimate the SLE for different number of rounds and compare the results. The errors of the estimation will be acceptable after several rounds when there are less zero elements in the transition matrix and the distribution is more uniform. Moreover, we present a simple relation between the SLE and the number of iterations that the Markov cipher requires against differential cryptanalysis and show the necessary condition of the matrix decomposition method.
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