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Applicable Algebra in Engineering, Communication and Computing

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01-08-2014 | Original Paper

New constructions of APN polynomial functions in odd characteristic

Authors: Zhengbang Zha, Lei Hu, Siwei Sun, Yao Sun

Published in: Applicable Algebra in Engineering, Communication and Computing | Issue 4/2014

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Abstract

A general construction of APN polynomial functions of the form \(c_{30}x^3+c_{03}x^{3q}+\sum \nolimits _{i=0}^2\sum \nolimits _{j=0}^2c_{ij}x^{i+qj}\) over a finite field \(\mathbb {F}_{q^2}\) of odd characteristic is proposed, and some variants of this construction are also presented. As a consequence, new APN polynomial functions such as ones over \(\mathbb {F}_{3^{2m}}\) and \(\mathbb {F}_{11^2}\) which are CCZ-inequivalent to known APN functions are obtained.

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Title: New constructions of APN polynomial functions in odd characteristic
Authors: Zhengbang Zha
Lei Hu
Siwei Sun
Yao Sun
Publication date: 01-08-2014
Publisher: Springer Berlin Heidelberg
Published in: Applicable Algebra in Engineering, Communication and Computing / Issue 4/2014
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI: https://doi.org/10.1007/s00200-014-0227-2

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