Tutte seminar - Gary McGuire

New Nonlinear Functions for S-Boxes in Cryptography and their Fourier Transform

Abstract:

Functions used in S-Boxes in block ciphers are required to be highly nonlinear in order to be resistant to linear cryptanalysis. This property is related to the Fourier spectrum of the function. The functions are also required to be resistant to differential cryptanalysis, and functions providing optimal resistance here are called perfect nonlinear. The two properties are different but curiously related. Few examples of these functions are known.
In this talk we will explain these concepts, and the relationships between them. We will then explain some recent constructions of new functions with optimal nonlinearity, and discuss their Fourier transforms.