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.