On The Walsh Spectrum Of Almost Perfect Nonlinear Functions

Sak, Yağmur (2023) On The Walsh Spectrum Of Almost Perfect Nonlinear Functions. [Thesis]

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In this thesis, we study the Walsh spectrum of "Almost Perfect Nonlinear" (APN) functions over finite fields of characteristic 2. We first give a characterization of APN functions in terms of the Walsh spectrum. We also gather recent characterization results of APN functions. Then, we give upper bounds for the Walsh spectrum of two families of biprojective APN functions, which have been recently introduced by Göloğlu. As a result, we obtain lower bounds for the nonlinearity of those APN functions. Our method is based on Bezout’s theorem, i.e., the intersection theory of two projective plane curves.
Item Type: Thesis
Uncontrolled Keywords: APN functions, Walsh spectrum, Biprojective polynomials, Nonlinearity, Finite fields. -- APN fonksiyoları, Walsh spektrum, Biprojektif polinomlar, Doğrusal olmama, Sonlu cisimler.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Dila Günay
Date Deposited: 21 Dec 2023 14:13
Last Modified: 21 Dec 2023 14:13
URI: https://research.sabanciuniv.edu/id/eprint/48858

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