Union distinct families of sets, with an application to cryptography

Abstract

A family of sets is called K-union distinct if all unions involving K or fewer members thereof are distinct. If a family of sets is K-cover-free then it is K-union distinct. In this paper, we recognize that this is only a sufficient condition and, from this perspective, consider partially cover-free families of sets with a view to constructing union distinct families. The role of orthogonal arrays and related combinatorial structures is explored in this context. The results are applied to find efficient anti-collusion digital fingerprinting codes.