There are many generalizations of the classical Boolean bent functions. Let G, H be finite groups and let X be a finite G-set. G-perfect nonlinear functions from X to H have been studied in several papers. They are generalizations of perfect nonlinear functions from G itself to H. By introducing the concept of a (G,H)-related difference family of X, we obtain a characterization of G-perfect nonlinear functions on X in terms of a (G,H)-related difference family. When G is abelian, we prove that there is a normalized G-dual set X^ of X, and chara...
