On applicability of chaos game method for block cipher randomness analysis

Block cipher can be considered as a random permutation function which maps a set of plaintext character P to a set of ciphertext character C. Block cipher is designed in a way that the effort to distinguish it from a random permutation function will be very difficult or computationally infeasible. It this paper, block cipher randomness analysis is performed by using chaos game method. The method treats block cipher as a mapping function of a discrete time dynamical system. The system is used to generate a random sequence. Next, chaos game method analyzes the sequence in order to reveal its characteristics or regularities. The applicability of the method to reveal some characteristics of a block cipher is verified by using it for comparing the randomness of three-round and four-round SPN-network and distinguishing them from each other. So, the method can role as a distinguisher.