Hypothesis Testing and Advanced Distinguishers in Differential Cryptanalysis of Block Ciphers

Distinguishing distributions is a major part during cryptanalysis of symmetric block ciphers. The goal of the cryptanalyst is to distinguish two distributions; one that characterizes the number of certain events which occur totally at random and another one that characterizes same type of events but due to propagation inside the cipher. This can be realized as a hypothesis testing problem, where a source is used to generate independent random samples in some given finite set with some distribution P, which is either R or W, corresponding to propagation inside the cipher or a random permutation respectively. Distinguisher’s goal is to determine which one is most likely the one which was used to generate the sample. In this paper, we study a general hypothesis-testing based approach to construct statistical distinguishers using truncated differential properties. The observable variable in our case is the expected number of pairs that follow a certain truncated differential property of the form ΔX → ΔY after a certain number of rounds. As a proof of concept, we apply this methodology to GOST and SIMON64/128 block ciphers and present distinguishers on 20 and 22 rounds respectively.