On The Walsh Spectrum Of Almost Perfect Nonlinear Functions

Official URL: https://risc01.sabanciuniv.edu/record=b3205723

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.