Cryptology ePrint Archive: Report 2010/472

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

A. Simone and B. Skoric

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

Category / Keywords: traitor tracing, forensic watermarking, Tardos fingerprinting

Date: received 6 Sep 2010

Contact author: b skoric at tue nl

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Version: 20100908:181150 (All versions of this report)

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