Secure frameproof codes, key distribution patterns, group testing algorithms and related structures

• Published in: Journal of statistical planning and inference Vol. 86; no. 2; pp. 595 - 617
• Main Authors: Stinson, D.R., van Trung, Tran, Wei, R.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 01.05.2000; New York,NY Elsevier Science; Amsterdam
• Subjects: Applied sciences; Coding, codes; Combinatorics; Combinatorics. Ordered structures; Designs and configurations; Exact sciences and technology; Group theory; Group theory and generalizations; Information, signal and communications theory; Manifolds and cell complexes; Mathematics; Sciences and techniques of general use; Signal and communications theory; Telecommunications and information theory; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Frameproof code; Key distribution pattern; Secure frameproof code; Combinatorial problem; Code; Group testing algorithm
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(99)00131-7

Frameproof codes were introduced by Boneh and Shaw as a method of “digital fingerprinting” which prevents a coalition of a specified size c from framing a user not in the coalition. Stinson and Wei then gave a combinatorial formulation of the problem in terms of certain types of extremal set systems. In this paper, we study frameproof codes that provide a certain (weak) form of traceability. We extend our combinatorial formulation to address this stronger requirement, and show that the problem is solved by using ( i, j)-separating systems, as defined by Friedman, Graham and Ullman. Using constructions based on perfect hash families, we give the first efficient explicit constructions for these objects for general values of i and j. We also review nonconstructive existence results that are based on probabilistic arguments. Then we look at two other, related concepts, namely key distribution patterns and nonadaptive group testing algorithms. We again approach these problems from the point of view of extremal set systems, and we describe a natural common setting in which these two problems are complementary special cases. This approach also demonstrates a close relationship between these two problems and frameproof codes. Explicit constructions are given, and some nonconstructive existence results are reviewed. In the case of key distribution patterns, our explicit constructions are the most efficient ones known.