Simple-looking joint decoders for traitor tracing and group testing

The topic of this paper is collusion resistant watermarking, a.k.a. traitor tracing, in particular bias-based traitor tracing codes as introduced by G.Tardos in 2003. The past years have seen an ongoing effort to construct efficient high-performance decoders for these codes. In this paper we construct a score system from the Neyman-Pearson hypothesis test (which is known to be the most powerful test possible) into which we feed all the evidence available to the tracer, in particular the codewords of *all* users. As far as we know, until now similar efforts have taken into consideration only the codeword of a single user, namely the user under scrutiny. The Neyman-Pearson score needs as input the attack strategy of the colluders, which typically is not known to the tracer. We insert the Interleaving attack, which plays a very special role in the theory of bias-based traitor tracing by virtue of being part of the asymptotic (i.e. large coalition size) saddlepoint solution. The score system obtained in this way is universal: effective not only against the Interleaving attack, but against all other attack strategies as well. Our score function for one user depends on the other users' codewords in a very simple way: through the symbol tallies, which are easily computed. We present bounds on the False Positive and False Negative error probability, yielding a.o. a prescription for setting the accusation threshold. We investigate the probability distribution of the score. Finally we apply our construction to the area of (medical) Group Testing, which is related to traitor tracing. Keywords: traitor tracing, Tardos code, collusion, watermarking, group testing