Study of the AES-like Super Boxes in LED and PHOTON

In this paper we investigate the choice of S-box and MDS-matrix in AES-like super box structures. Before giving the theory, we first study the super boxes of the led block cipher and the photon hash function and compute the distribution of all two-round characteristics when there is a key addition in the round function. Then, we compare these results with a fixed key (i.e. using the given constant values) in the round function. We observe that the results are consistent with the theory (following the approach of plateau characteristics) except for some extreme cases. Next, we discuss the effect of the S-box size for a fixed size super box. We show that the number of right pairs increases if the size of S-box decreases. Moreover, we study the effect of MDS-matrix with the previous setting by using a circulant matrix and the special MDS-matrix used in the design of led.