Investigation on Construction and Differential Property of a Class of Dynamic S-box

This paper discusses the dynamic S-boxes using the combination of inversion mapping and an affine transformation over the finite field. First, a definition of differential probability for dynamic S-box is provided. Necessary and sufficient conditions of impossible differentials in dynamic S-box and the number of impossible differentials are presented. Then, an upper bound on the maximum differential probability of dynamic S-box is proved, and the accessibility of this bound is presented. Finally, the differential properties of dynamic S-box consisting of randomly chosen S-boxes are researched by simulation experiments. The theoretical and experimental analyses show that dynamic S-box is better than single S-box in differential properties.