A Further Understanding of Differential-Linear Cryptanalysis

Differential-linear cryptanalysis has attracted much attention since proposed to attack DES in 1994, and then some generalized theories are developed to complement and unify the method. However, the links between differential-linear cryptanalysis and other important cryptanalysis methods have been still missing. The motivation is to fix the gap. By establishing some boolean equations, we propose the mathematical links among differential, linear and differential-linear attacks. We then generalise the definition of capacity and present some properties of the capacity of differential function. The links and properties are employed to explore the relationships between multidimensional differential-linear hulls and integral distinguishers. We show that a multidimensional differential-linear hull of certain correlation always implies the existence of an integral distinguisher and a zero-correlation linear hull, while a special integral distinguisher indicates the existence of a multidimensional differential-linear hull.