Designs, Codes and Cryptography

, Volume 63, Issue 3, pp 379-412

Open Access This content is freely available online to anyone, anywhere at any time.

Accusation probabilities in Tardos codes: beyond the Gaussian approximation

  • Antonino SimoneAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of Technology
  • , Boris ŠkorićAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of Technology Email author 


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.


Traitor tracing Tardos fingerprinting Collusion resistance

Mathematics Subject Classification (2000)

94B60 60G35 60G50