On the Security of Rijndael-Like Structures against Differential and Linear Cryptanalysis

Rijndael-like structure is a special case of SPN structure. The linear transformation of Rijndael-like structures consists of linear transformations of two types, the one is byte permutation π and the other is linear transformation θ = (θ1,θ2,θ3,θ4), where each of θi separately operates on each of the four columns of a state. Furthermore, π and θ have some interesting properties. In this paper, we present a new method for upper bounding the maximum differential probability and the maximum linear hull probability for Rijndael-like structures. By applying our method to Rijndael, we obtain that the maximum differential probability and the maximum linear hull probability for 4 rounds of Rijndael are bounded by 1.06 × 2-96.