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Fourier Spectra of Binomial APN Functions

Bracken, Carl and Byrne, Eimear and Markin, Nadya and McGuire, Gary (2009) Fourier Spectra of Binomial APN Functions. Siam Journal on Discrete Mathematics, 23 (2). pp. 596-608. ISSN 0895-4801

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Abstract

In this paper we compute the Fourier spectra of some recently discovered binomial APN functions. One consequence of this is the determination of the nonlinearity of the functions, which measures their resistance to linear cryptanalysis. Another consequence is that certain error-correcting codes related to these functions have the same weight distribution as the 2-error-correcting BCH code. Furthermore, for field extensions of F2 of odd degree, our results provide an alternative proof of the APN property of the functions.

Item Type: Article
Additional Information: Preprint version of original article © 2009 Society for Industrial and Applied Mathematics.
Keywords: almost perfect nonlinear; APN; Fourier spectrum;
Subjects: Science & Engineering > Mathematics
Item ID: 2703
Depositing User: Library Editor
Date Deposited: 09 Sep 2011 11:57
Journal or Publication Title: Siam Journal on Discrete Mathematics
Publisher: SIAM Society for Industrial and Applied Mathematics
Refereed: No
URI:

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