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.

Automated summary

This paper deals with monomial type GAPN functions, which are a generalization of APN functions in finite fields of odd characteristic p introduced in 2017. By connecting the GAPN property of a monomial function to the existence of suitable rational points on an algebraic curve, necessary conditions for a monomial function to be GAPN are provided.