Accusation probabilities in Tardos codes: beyond the Gaussian approximation

Abstract

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-resilience of the code is shown. For some realistic parameter values, the false accusation probability is even lower than the Gaussian approximation predicts.