Generalization of differential criteria for Sboxes

Linear and differential cryptanalysis and their generalizations, are the most important tools in statistical analysis of symmetric ciphers. These attacks make use of linear and differential properties of Sboxes or symmetric cipher components. In ISCISC´12 we generalized linear criteria for Sboxes. In this paper, we examine differential properties of Sboxes and symmetric cipher components. We generalize differential properties for Sboxes in arbitrary groups and based on that, we study generalized differential criteria for them. Then, we verify differential-linear properties of Sboxes. At last, we study (nonlinear) two-dimensional criteria for Sboxes and symmetric cipher components.