Can Large Deviation Theory be Used for Estimating Data Complexity?
Recent block ciphers have been designed to be resistant against differential cryptanalysis. Nevertheless it has been shown that such resistance claims may not be as accurate as wished due to recent advances in this field. One of the main improvements to differential cryptanalysis is the use of many differentials to reduce the data complexity. In this paper we propose a general model for understanding multiple differential cryptanalysis and propose new attacks based on tools used in multidimensional linear cryptanalysis (namely LLR and χ statistical tests). Practical cases to evaluate different approaches for selecting and combining differentials are considered on a reduced version of the cipher PRESENT. We also consider the accuracy of the theoretical estimates corresponding to these attacks.