Two-Round AES Differentials

In this paper we study the probability of differentials and characteristics over 2 rounds of the AES with the objective to understand how the components of the AES round transformation interact. We extend and correct the analysis of the differential properties of the multiplicative inverse in GF(2) given in [17]. We show that AES has characteristics with a fixed-key probability that is many times larger than the EDP. For instance, in the case of 2-round AES, we measured factors up to 2. We study the number of characteristics with EDP > 0 whose probability adds up to the probability of a differential and derive formulas that allow to produce a close estimate of this number for any differential. We show how the properties discovered in our study can be used to explain the values of the differentials with the largest EDP values and to construct new distinguishers using truncated differentials.