On the Fourier spectra of the infinite families of quadratic APN functions

Carl Bracken; Zhengbang Zha

doi:10.3934/amc.2009.3.219

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2009, Volume 3, Issue 3: 219-226. Doi: 10.3934/amc.2009.3.219

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On the Fourier spectra of the infinite families of quadratic APN functions

Carl Bracken^1, and
Zhengbang Zha^2,

1.
Department of Mathematics, National University of Ireland Maynooth, Co. Kildare
2.
School of Mathematical Sciences, Luoyang Normal University, Luoyang 471022

Received: October 31, 2008

Revised: June 30, 2009

Published: July 2009

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Abstract

It is well known that a quadratic function defined on a finite field of odd degree is almost bent (AB) if and only if it is almost perfect nonlinear (APN). For the even degree case there is no apparent relationship between the values in the Fourier spectrum of a function and the APN property. In this article we compute the Fourier spectrum of the quadrinomial family of APN functions from [5]. With this result, all known infinite families of APN functions now have their Fourier spectra and hence their nonlinearities computed.

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Mathematics Subject Classification: 11T23, 11T71, 94B05.

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