Regular Simplex Fingerprints and Their Optimality Properties

• Published in: IEEE transactions on information forensics and security Vol. 4; no. 3; pp. 318 - 329
• Main Authors: Kiyavash, N., Moulin, P., Kalker, T.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2009; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additives; Collusion attacks; Copyright protection; Correlation; Data security; Detectors; Error detection; Fingerprint recognition; fingerprinting; Fingerprints; Gaussian; Gaussian noise; Noise; Nonuniform; Optimization; Performance evaluation; Reproduction; Signal detection; simplex codes; Testing; Vectors
• ISSN: 1556-6013; 1556-6021
• DOI: 10.1109/TIFS.2009.2025855

This paper addresses the design of additive fingerprints that are maximally resilient against linear collusion attacks on a focused correlation detector, as defined below. Let N be the length of the host vector and M les N + 1 the number of users. The focused detector performs a correlation test in order to decide whether a user of interest is among the colluders. Both the fingerprint embedder and the colluders are subject to squared-error distortion constraints. We show that simplex fingerprints maximize a geometric figure of merit for this detector. In that sense they outperform orthogonal fingerprints but the advantage vanishes as M rarr infin. They are also optimal in terms of minimizing the probability of error of the focused detector when the attack is a uniform averaging of the marked copies followed by the addition of white Gaussian noise. Reliable detection is guaranteed provided that the number of colluders K Lt radic( N ). Moreover, we study the probability of error performance of simplex fingerprints for the focused correlation detector when the colluders use nonuniform averaging plus white Gaussian noise attacks.