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 Fpjavax.xml.bind.JAXBElement@7f2e9ed8 to the existence of suitable rational points of an algebraic curve defined over Fpjavax.xml.bind.JAXBElement@425705. We give necessary conditions for a monomial function to be GAPN, providing the converse of recent results by Özbudak and Sălăgean and by Zha, Hu and Zhang.
On monomial generalized almost perfect nonlinear functions / Bartoli, D.; Giulietti, M.; Peraro, G.; Zini, G.. - In: FINITE FIELDS AND THEIR APPLICATIONS. - ISSN 1071-5797. - 82:(2022), pp. 1-14. [10.1016/j.ffa.2022.102050]
On monomial generalized almost perfect nonlinear functions
Zini G.
2022
Abstract
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 Fpjavax.xml.bind.JAXBElement@7f2e9ed8 to the existence of suitable rational points of an algebraic curve defined over Fpjavax.xml.bind.JAXBElement@425705. We give necessary conditions for a monomial function to be GAPN, providing the converse of recent results by Özbudak and Sălăgean and by Zha, Hu and Zhang.
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