Some Recent Results on Fourier Transforms of Boolean Functions

Gary McGuire
University College, Dublin


Abstract:
Various types of Boolean functions are used in coding and
cryptography.  In certain cryptosystems, Almost Perfect Nonlinear
functions provide the best resistance to certain types of attack. We
present some new APN functions. We will discuss recent calculations of
the Fourier spectrum of APN functions. Then we will talk about a
recent analysis of the Fourier spectrum of some monomial bent
functions using Stickelberger's theorem. Finally, if time permits we
discuss connections between bent functions and almost bent functions
via restriction.