An insightful view into the design of traitor tracing codes should
necessarily consider the worst case attacks that the colluders can lead. This
paper takes an information-theoretic point of view where the worst case attack
is defined as the collusion strategy minimizing the achievable rate of the
traitor tracing code. Two different decoders are envisaged, the joint decoder
and the simple decoder, as recently defined by P. Moulin
\cite{Moulin08universal}. Several classes of colluders are defined with
increasing power. The worst case attack is derived for each class and each
decoder when applied to Tardos' codes and a probabilistic version of the
Boneh-Shaw construction. This contextual study gives the real rates achievable
by the binary probabilistic traitor tracing codes. Attacks usually considered
in literature, such as majority or minority votes, are indeed largely
suboptimal. This article also shows the utmost importance of the time-sharing
concept in a probabilistic codes.Comment: submitted to IEEE Trans. on Information Forensics and Securit