Classification of quadratic APN functions with coefficients in \(\mathbb{F}_2\) for dimensions up to 9
type: Item
instance of: scholarly article
title: Classification of quadratic APN functions with coefficients in \(\mathbb{F}_2\) for dimensions up to 9
zbMATH Open document ID: 1473.94180
author: Yuyin Yu
author: Nikolay Kaleyski
author: Lilya Budaghyan
author: Yongqiang Li
published in: Finite Fields and their Applications
publication date: 2021-02-18T00:00:00Z
review text: The classification of APN functions is a very difficult problem, even in a small number of variables \(n\). A complete classification (up to CCZ-equivalence) of APN functions on \(\mathbb{F}_{2^n}\) is known for dimension \(n\le 5\) [\textit{M. Brinkmann} and \textit{G. Leander}, Des. Codes Cryptography 49, No. 1--3, 273--288 (2008; Zbl 1184.94227)]. Further, some partial results for \(n=6\) are known. With a specialization of the construction method of quadratic APN functions via matrices in [\textit{Y. Yu} et al., Des. Codes Cryptography 73, No. 2, 587--600 (2014; Zbl 1320.11122)], by which a huge amount of quadratic APN functions can be generated, the authors present a complete classification (up to CCZ-equivalence) of quadratic APN functions on \(\mathbb{F}_{2^n}\), which have a representation as a polynomial with coefficients in \(\mathbb{F}_2\), up to dimension \(n =9\). Whereas in dimension \(6\le n \le 8\), all such quadratic APN functions are CCZ equivalent to already known APN functions, two new quadratic APN functions (not CCZ-equivalent to any earlier known function) in dimension \(n=9\) are discovered.
reviewed by: Wilfried Meidl
Mathematics Subject Classification ID: 94D10
Mathematics Subject Classification ID: 94A60
zbMATH DE Number: 7312715
zbMATH Keywords: Boolean functions
zbMATH Keywords: almost perfect nonlinear
zbMATH Keywords: almost bent
zbMATH Keywords: quadratic functions
MaRDI profile type: Publication
full work available at URL: j.ffa.2020.101733
OpenAlex ID: W3082441468
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DOI: 10.1016/J.FFA.2020.101733
description: scientific article; zbMATH DE number 7312715