Accusation probabilities in Tardos codes: beyond the Gaussian approximation

作者：Simone Antonino; Skoric Boris^*

来源：Designs, Codes and Cryptography, 2012, 63(3): 379-412.

DOI：10.1007/s10623-011-9563-4

• Traitor tracing
• Tardos fingerprinting
• Collusion resistance

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 %26apos;small parameter%26apos; 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 %26apos;shape%26apos; 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.

• 出版日期2012-6