Relations between classes of bent functions and some results on correlation immunity

In this talk we will consider the class membership problem for the secondary classes of bent functions C and D. We will present a  characterization of the intersection between D_0 and the completed Maiorana-McFarland class M^#, give some sufficient conditions for functions in C to be outside M^#, and show that asymptotically the classes C and PS_ap are disjoint. We will also investigate another cryptographically significant property of Boolean functions called correlation-immunity (CI). Two efficient constructions of CI functions will be presented which are well-suited for designing CI functions with low Hamming weight. Finally, we will consider the O’Donnell conjecture about the sum of Walsh coefficients of CI functions.

Everyone is welcome and encouraged to attend.