Differential distribution properties of the SIMON block cipher family

SIMON is a family of the lightweight block ciphers designed by the U.S National Security Agency in 2013 which is a classical Feistel scheme. The round function uses bitwise AND, rotation and XOR operations. This paper studies on differential distribution properties of the general SIMON-like round function F[a, b, c](x) = (x ⋘a) ⊙(x⋘)⊕(x⋘c) It gives the relationship between the differential probability and the hamming weight of the input difference, and solves the constructing and counting issue of the corresponding input and output differences when the differential probabilities are 1/2, 1/4, 1/8, 1/16, 1/2⁽ⁿ⁻¹⁾, and also proposes a fast algorithm to compute the combined differential (α→ β)·p(α→ β) of the iterative differential characteristic with a computation complexity of O(2^r n³). It provides theoretical guidance for the differential cryptanalysis and design of SIMON family.