Accusation probabilities in Tardos codes : the Gaussian approximation is better than we thought

We study the probability distribution of user accusations in the q-ary Tardos fingerprinting system under the Marking Assumption, in the restricted digit model. In particular, we look at the applicability of the so-called Gaussian approximation, which states that accusation probabilities tend to the normal distribution when the fingerprinting code is long. We introduce a novel parametrization of the attack strategy which enables a significant speedup of numerical evaluations. We set up a method, based on power series expansions, to systematically compute the probability of accusing innocent users. The 'small parameter' in the power series is 1/m, where m is the code length. We use our method to semi-analytically study the performance of the Tardos code against majority voting and interleaving attacks. The bias function 'shape' parameter kappa strongly influences the distance between the actual probabilities and the asymptotic Gaussian curve. The impact on the collusion-reslilience of the code is shown. For some realistic parameter values, the false accusation probability is even lower than the Gaussian approximation predicts. Keywords: traitor tracing, forensic watermarking, Tardos fingerprinting.