On monomial generalized almost perfect nonlinear functions

Generalized almost perfect nonlinear (GAPN) functions are a generalization of APN functions to finite fields of odd characteristic p introduced in 2017 by Kuroda and Tsujie. In this paper we deal with GAPN functions of monomial type. To this aim, we connect the GAPN property for a monomial function over F-pn to the existence of suitable rational points of an algebraic curve defined over F-pn. We give necessary conditions for a monomial function to be GAPN, providing the converse of recent results by ozbudak and Salagean and by Zha, Hu and Zhang. (C) 2022 Elsevier Inc. All rights reserved.