Journal
FINITE FIELDS AND THEIR APPLICATIONS
Volume 82, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.ffa.2022.102050
Keywords
GAPN function; Monomial; Algebraic curve
Categories
Funding
- Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA-INdAM)
- Progetto Applicazioni di curve algebriche su campi finiti alla Teoria dei Codici e alla Crittografia, Fondo Ricerca di Base, 2019, Universite degli Studi di Perugia
- Progetto Strutture Geometriche, Combinatoria e loro Applicazioni, Fondo Ricerca di Base, 2019, Universite degli Studi di Perugia
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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.
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.
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