Monomial generalized almost perfect nonlinear functions

Abstract

Generalized almost perfect nonlinear (GAPN) functions were defined to satisfy some generalizations of basic properties of almost perfect nonlinear (APN) functions for even characteristic. In this paper, we study monomial GAPN functions for odd characteristic. In particular, we give all monomial GAPN functions whose algebraic degree are maximum or minimum on a finite field of odd characteristic.