Efficient Dynamic Traitor Tracing

Abstract

The notion of traitor tracing was introduced by Chor, Fiat, and Naor [Tracing Traitors, Lecture Notes in Comput. Sci. 839, 1994, pp. 257--270] in order to combat piracy scenarios. Recently, Fiat and Tassa [ Tracing Traitors, Lecture Notes in Comput. Sci. 1666, 1999, pp. 354--371] proposed a dynamic traitor tracing scenario, in which the algorithm adapts dynamically according to the responses of the pirate. Let n be the number of users and p the number of traitors. Our main result is an algorithm which locates p traitors, even if p is unknown, using a watermarking alphabet of size p+1 and an optimal number of $\Theta(p^2 + p\log n)$ rounds. This improves the exponential number of rounds achieved by Fiat and Tassa in this case. We also present two algorithms that use a larger alphabet: for an alphabet of size p+c+1, $c\geq1$, an algorithm that uses O(p2 /c+ p log n) rounds; for an alphabet of size pc+1, an algorithm that uses O(p logcn ) rounds. Our final result is a lower bound of $\Omega(p^2/c+p\log_{c+1}n)$ rounds for any algorithm that uses an alphabet of size p+c, assuming that p is not known in advance.