## Section: New Results

### Estimating the minimal length of Tardos code

Participants : Frédéric Cérou, Arnaud Guyader.

This is a collaboration with Luis Pérez–Feire from GRADIANT (Galician R&D Center in Advanced Telecommunications, Vigo, Spain) and with Teddy Furon from INRIA Rennes Bretagne Atlantique (project–team TEMICS).

We are interested in the minimal length of a binary probabilistic traitor tracing code. We consider the code construction proposed by Gábor Tardos in 2003, with the symmetric accusation function as improved by Boris Škorić 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 constructed in order to estimate 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 [21] . This estimation is far lower than the known lower bounds.