Estimating the minimal length of Tardos code

Teddy Furon (1) , Luis Pérez-Freire (2, 3) , Arnaud Guyader (4, 5, 6) , Frédéric Cérou (4)

1 TEMICS - Digital image processing, modeling and communication
2 Thomson Multimedia R&D France
3 Gradiant - Centro Tecnoloxico de Telecomunicacions de Galicia
4 ASPI - Applications of interacting particle systems to statistics
5 MASS - Département Mathématiques appliquées et sciences sociales - Rennes 2
6 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Teddy Furon, Luis Pérez-Freire, Arnaud Guyader, Frédéric Cérou. Estimating the minimal length of Tardos code. Information Hiding, Jun 2009, Darmstadt, Germany. ⟨inria-00505882⟩