Exceptional crooked functions
type: Item
instance of: scholarly article
title: Exceptional crooked functions
author: Daniele Bartoli
author: Marco Calderini
author: Marco Timpanella
published in: Finite Fields and their Applications
publication date: 2022-10-12T00:00:00Z
review text: In this paper, the authors investigate conditions on the shape of a polynomial to be crooked (it is already known that the only monomial and binomial crooked functions are quadratic). The notion of exceptional crooked is introduced, similarly to those of APN or PN exceptional functions. Via a connection with algebraic varieties over finite fields, the authors provide non-existence results of exceptional crooked functions (functions that are crooked over infinitely many extensions of \(\mathbb{F}_2\)). Their approach is based on an attaching of algebraic variety \(W_f\) defined by a given affine equation to a function \(f:\mathbb{F}_{2^n} \rightarrow \mathbb{F}_{2^n}\) with \(f(0) = 0\).
Mathematics Subject Classification ID: 11T71
Mathematics Subject Classification ID: 94A60
Mathematics Subject Classification ID: 94D10
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 11T06
zbMATH DE Number: 7600478
zbMATH Keywords: crooked functions
zbMATH Keywords: algebraic varieties over finite fields
zbMATH Keywords: APN functions
reviewed by: Zlatko Varbanov
MaRDI profile type: Publication
full work available at URL: j.ffa.2022.102109
OpenAlex ID: W4296070754
Wikidata QID: Q114179429
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DOI: 10.1016/J.FFA.2022.102109
description: scientific article; zbMATH DE number 7600478