Graph eigenvalues and Walsh spectrum of Boolean functions
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In this paper, we consider te Cayley graph Gf associated with 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 gind 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.
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