Regular Simplex Fingerprints and Their Optimality Properties

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 $Mleq N+1$ 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 rightarrow infty $. 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 $Kll sqrt N$. 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.