Regular Simplex Fingerprints and Their Optimality Properties

• Published in: Digital Watermarking pp. 97 - 109
• Main Authors: Kiyavash, Negar, Moulin, Pierre
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005
• Series: Lecture Notes in Computer Science
• Subjects: Error exponents; Fingerprinting; Simplex codes
• ISBN: 354028768X; 9783540287681
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11551492_8

This paper addresses the design of additive fingerprints that are maximally resilient against Gaussian averaging collusion attacks. The detector performs a binary hypothesis test in order to decide whether a user of interest is among the colluders. The encoder (fingerprint designer) is to imbed additive fingerprints that minimize the probability of error of the test. Both the encoder and the attackers are subject to squared-error distortion constraints. We show that n-simplex fingerprints are optimal in sense of maximizing a geometric figure of merit for the detection test; these fingerprints outperform orthogonal fingerprints. They are also optimal in terms of maximizing the error exponent of the detection test, and maximizing the deflection criteria at the detector when the attacker’s noise is non-Gaussian. Reliable detection is guaranteed provided that the number of colluders $K \ll \sqrt{N}$ , where N is the length of the host vector.