Non-linearity of exponent permutations

Abstract

The paper deals with an examination of exponent permutations with respect to their non-linearity. The first part gives the necessary background to be able to determine permutation non-linearity. The second examines the interrelation between non-linearity and Walsh transform. The next part summarizes results gathered while experimenting with different binary fields. In the last part of the work, we discuss the results obtained and questions which are still open.