Estimating the minimal length of Tardos code

Abstract : This paper estimates the minimal length of a binary proba- bilistic traitor tracing code. We consider the code construction proposed by G. Tardos in 2003, with the symmetric accusation function as im- proved by B. Skoric et al. The length estimation is based on two pillars. First, we consider the Worst Case Attack that a group of c colluders can lead. This attack minimizes the mutual information between the code sequence of a colluder and the pirated sequence. Second, an algorithm pertaining to the field of rare event analysis is presented in order to es- timate the probabilities of error: the probability that an innocent user is framed, and the probabilities that all colluders are missed. Therefore, for a given collusion size, we are able to estimate the minimal length of the code satisfying some error probabilities constraints. This estimation is far lower than the known lower bounds.
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Teddy Furon, Luis Pérez-Freire, Arnaud Guyader, Frédéric Cérou. Estimating the minimal length of Tardos code. Information Hiding, Jun 2009, Darmstadt, Germany. ⟨inria-00505882⟩

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