Computational aspects of the expected differential probability of 4-round AES and AES-like ciphers

In this paper we study the security of the Advanced Encryption Standard (AES) and AES-like block ciphers against differential cryptanalysis. Differential cryptanalysis is one of the most powerful methods for analyzing the security of block ciphers. Even though no formal proofs for the security of AES against differential cryptanalysis have been provided to date, some attempts to compute the maximum expected differential probability (MEDP) for two and four rounds of AES have been presented recently. In this paper, we will improve upon existing approaches in order to derive better bounds on the EDP for two and four rounds of AES based on a slightly simplified S-box. More precisely, we are able to provide the complete distribution of the EDP for two rounds of this AES variant with five active S-boxes and methods to improve the estimates for the EDP in the case of six active S-boxes.