Graph Eigenvalues and Walsh Spectrum of Boolean Functions.

摘要

In this paper we consider the Cayley graph G(f) 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 G(f) . Finally, some inequalities between the cardinality of the spectrum of G(f) and the Hamming weight of functions are obtained, and some problems are raised.