A characterization of a class of maximum nonlinear functions

Abstract

Maximum nonlinear functions on finite fields are widely used in cryptography because the coordinate functions have large distance to linear functions. More precisely, the Hamming distance to the characteristic functions of hyperplanes is large. One class of maximum nonlinear functions are the Gold power functions We characterize these functions in terms of the distance of their coordinate functions to characteristic functions of subspaces of codimension 2.