An Upper Bound of the Longest Impossible Differentials of Several Block Ciphers

Impossible differential cryptanalysis is an essential cryptanalytic technique and its key point is whether there is an impossible differential path. The main factor of influencing impossible differential cryptanalysis is the length of the rounds of the impossible differential trail because the attack will be more close to the real encryption algorithm with the number becoming longer. We provide the upper bound of the longest impossible differential trails of several important block ciphers. We first analyse the national standard of the Russian Federation in 2015, Kuznyechik, which utilizes the 16-byte LFSR to achieve the linear transformation. We conclude that there is no any 3-round impossible differential trail of the Kuznyechik without the consideration of the specific S-boxes. Then we ascertain the longest impossible differential paths of several other important block ciphers by using the matrix method which can be extended to many other block ciphers. As a result, we show that, unless considering the details of the S-boxes, there is no any more than or equal to 5-round, 7-round and 9-round impossible differential paths for KLEIN, Midori64 and MIBS respectively.