On exceptional almost perfect non-linear functions

Official URL: https://risc01.sabanciuniv.edu/record=b2583800_(Table of contents)

In this master thesis, we study exceptional APN functions. We first give a detailed survey on exceptional APN monomials using the methods from algebraic geometry, especially algebraic curves over finite fields. We also collect recent results on exceptional APN polynomials, and we introduce a result for polynomials of Gold and Kasami-Welch types.