Fourier Spectra of Binomial APN Functions

2008/03/26 by Carl Bracken, Eimear Byrne, Bracken, Carl +5
Computer Science · #Chaos-based Image/Signal Encryption #Coding theory and cryptography #Cryptographic Implementations and Security #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.0803.3781

openalex publication_date 2008/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 fields of odd degree, our results provide an alternative proof of the APN property of the functions.

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