Graph eigenvalues and Walsh spectrum of Boolean functions
Pantelimon Stănică · 2012
In this paper we consider the Cayley graph Gf associated to a Boolean function f and we use it to investigate some of the cryptographic properties of f. We derive necessary (but not sufficient) conditions for a Boolean function to be bent. We also find a complete characterization of the propagation characteristics of f using the topology of its associated Cayley graph Gf. Finally, some inequalities between the cardinality of the spectrum of Gf and the Hamming weight of f are obtained, and some problems are raised.