Provable security against impossible differential and zero correlation linear cryptanalysis of some feistel structures

Abstract

Impossible differential and zero correlation linear cryptanalysis are two important cryptanalytic methods. In this paper, we study the security of some Feistel structures against these two cryptanalytic methods. Throughout this paper, we consider the impossible differential and zero correlation linear hull that are independent of the choices of the non-linear parts. Based on that, a method is introduced to estimate the number of rounds that the longest impossible differential could cover for one kind of Feistel-SP structure. Fortunately, our method also applies to some generalized Feistel structures, such as the Type-2 generalized Feistel structure. Then we project our results to zero correlation by the links between impossible differential and zero correlation linear hull. Lastly, as an application of our method, we prove that there do not exist 15-round impossible differential and zero correlation linear hull for LBlock and TWINE.