Paper 2010/472

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

A. Simone and B. Skoric


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.

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Publication info
Published elsewhere. Unknown where it was published
traitor tracingforensic watermarkingTardos fingerprinting
Contact author(s)
b skoric @ tue nl
2010-09-08: received
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Creative Commons Attribution


      author = {A.  Simone and B.  Skoric},
      title = {Accusation probabilities in Tardos codes: the Gaussian approximation is better than we thought},
      howpublished = {Cryptology ePrint Archive, Paper 2010/472},
      year = {2010},
      note = {\url{}},
      url = {}
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