Complementation-like and cyclic properties of AES round functions

Abstract

While it is known previously that the cycle lengths of individual components of the AES round function are very small, we demonstrate here that the cycle length of the S-box combined with the ShiftRow and MixColumn transformation is at least 10205. This result is obtained by providing new invariances of the complete AES round function without the key addition. Furthermore, we consider self-duality properties of the AES round function and derive a property analogous to the complementation property of the DES round function. These results confirm the assessments given in other publications that the AES components have several unexpected structural properties. © Springer-Verlag Berlin Heidelberg 2005.