A unified method for finding impossible differentials of block cipher structures

In this paper, we propose a systematic method for finding impossible differentials for block cipher structures, better than the Umethod introduced by Kim et al [4]. It is referred as a unified impossible differential finding method (UID-method). We apply the UID-method to some popular block ciphers such as Gen-Skipjack, Gen-CAST256, GenMARS, Gen-RC6, Four-Cell, SMS4 and give the detailed impossible differentials. By the UID-method, we find a 16-round impossible differential on Gen-Skipjack and a 19-round impossible differential on Gen-CAST256. Thus we disprove the Conjecture 2 proposed in Asiacrypt’00 [9] and the theorem in FSE’09 rump session presentation [8]. On Gen-MARS and SMS4, the impossible differentials find by the UID-method are much longer than that found by the U-method. On the Four-Cell block cipher, our result is the same as the best result previously obtained by case-bycase treatment.