Searching for impossible subspace trails and improved impossible differential characteristics for SIMON-like block ciphers

In this paper,we greatly increase the number of impossible differentials for SIMON and SIMECK by eliminating the 1-bit constraint in input/output difference,which is the precondition to ameliorate the complexity of attacks.We propose an algorithm which can greatly reduce the searching complexity to find such trails efficiently since the search space exponentially expands to find impossible differentials with multiple active bits.There is another situation leading to the contradiction in impossible differentials except for miss-in-the-middle.We show how the contradiction happens and conclude the precondition of it defined as miss-from-the-middle.It makes our results more comprehensive by applying these two approach simultaneously.This paper gives for the first time impossible differential characteristics with multiple active bits for SIMON and SIMECK,leading to a great increase in the number.The results can be verified not only by covering the state-of-art,but also by the MILP model.