**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

**Available format(s): **PDF | BibTeX Citation

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

**Short URL: **ia.cr/2010/472

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