TABLE OF CONTENTS San Ling and Huaxiong Wang
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University, Singapore
email: lingsan, hxwang@ntu.edu.sg
Chaoping Xing
Department of Mathematics
National University of Singapore, Singapore
email: matxcp@nus.edu.sg
Cover-free families are combinatorial objects that have been used in diverse applications such as information theory, communications, group testing, cryptography and information security. In this paper, we survey some mathematical results on cover-free families and present several interesting applications to topics in secure networks and distributed systems.
Cover-free families were first studied in terms of superimposed binary codes by Kautz and Singleton [21] in 1964. These codes are related to retrieval files, data communication and magnetic memories. In 1985 Erd s, Frankl and F redi [14] studied cover-free families as combinatorial objects, generalising the Sperner systems. Since then, they have been discussed by numerous researchers in the context of information theory, combinatorics, communication and cryptography and information security. In this paper we will present several interesting applications to topics in secure networks and distributed systems.
Definition 4.1. Let X be a set of N elements (points) and let 
be a set of T subsets (blocks) of X. Then ( X, ) is called an ( s, t) -cover-free family provided that, for any s
