Distribution of the best nonzero differential and linear approximations of s-box functions

Abstract

In the paper the differential and the linear approximations of two classes of s-box functions are considered. The classes are the permutations and arbitrary functions with n binary inputs and m binary outputs, where 1≤n=m≤10. For randomly chosen functions from each of the classes, the two-dimensional distributions of the best nonzero approximations are investigated. The obtained results indicate that starting from some value of n, the linear approximation of s-box functions becomes more effective than the differential approximation. This advantage of the linear approximation rises with the increase of n and for DES size s-boxes is not yet visible.