Boolean functions form the backbone of modern cryptographic systems, serving as essential components in the design of stream ciphers, block ciphers, and other security protocols.

Beronika Daxner, Antoine Genitrini, Bernhard Gittenberger, Cécile Mailler, THE RELATION BETWEEN TREE SIZE COMPLEXITY AND PROBABILITY FOR BOOLEAN FUNCTIONS GENERATED BY UNIFORM RANDOM TREES, Applicable ...

In this paper we prove sharp thresholds for monotone functions taking values in an arbitrary finite set. We also provide examples of applications of the results to social choice and to random graph ...