Impossible Differential Cryptanalysis for SPN Cipher Structure and Advanced Encryption Standard

In this correspondence, we examine the security of block ciphers referred to as substitution-permutation networks (SPN) by considering the impossible differential characteristics of given S-boxes. When the SPN has 2-round, we obtain a new upper bound on the maximum impossible differential probability MIDP. Moreover, when using a recursive technique, we obtain a general result for the MIDP of r (rges8) rounds SPN ciphers. Furthermore, when our result applies to r (rges8) rounds AES, it is shown that the upper bound of MIDP is up to 1, which means AES may be existence of characteristics with differential probability 0 in high rounds