On the Fourier Spectra of the Infinite Families of Quadratic APN Functions

Details On the Fourier Spectra of the Infinite Families of Quadratic APN Functions On the Fourier Spectra of the Infinite Families of Quadratic APN Functions

2008-11-28

arxiv.org/abs/0811.4718v1

Computer Science

Information Theory

12 pages, submitted to Adavances in the Mathematics of communication

Scientific paper

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 new quadranomial family of APN functions. With this result, all known infinite families of APN functions now have their Fourier spectra and hence their nonlinearities computed.

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