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Abstract: In this paper, we propose a systematic method for finding impossible differentials for block cipher structures, which we call the unified impossible differential finding method or UID-method. It is more effective than the -method introduced by Kim et al. We apply the UID-method to some well-known block cipher structures. Using it, we find a 16-round impossible differential for Gen-Skipjack and a 19-round impossible differential for Gen-CAST256. By this result we can disprove Sung’s long standing conjecture that no such differential is possible for 16 or more rounds. On Gen-MARS and SMS4, the impossible differentials found by the UID-method are much longer than those found by the -method. On the Four-Cell and Gen-RC6 block ciphers, our results are the same as the best results previously obtained. [Copyright &y& Elsevier]