Efficient Traitor Tracing Algorithms Using List Decoding

We apply powerful, recently discovered techniques for the list decoding of error-correcting codes to the problem of efficiently tracing traitors. Much work has focused on methods for constructing such traceability schemes, but the complexity of the traitor tracing algorithms has received little attention. A widely used traitor tracing algorithm, the TA algorithm, has a runtime of O(N) in general, where N is the number of sets in the system (e.g., the number of copies of a software CD, or the number of smartcards for decrypting pay-TV), and therefore is inefficient for large populations. In this paper we use a coding theoretic approach to produce traceability schemes for which the TA algorithm is very fast. The IPP algorithm is another traitor tracing algorithm that has garnered attention recently. It is less efficient than the TA algorithm, but has the interesting feature that it accumulates important additional piracy information, namely, a list of all coalitions capable of constructing a given pirate. We give evidence that when a natural algebraic structure is used to construct traceability schemes, the ability to trace with the IPP algorithm implies the ability to trace with the TA algorithm. Thus if the goal is to find a traitor, it is unlikely that IPP codes offer efficiency advantages. In addition, we show that the error-correcting code approach can be used to construct traceability schemes with an algorithm that finds all possible traitor coalitions faster than the brute force approach of the IPP algorithm. Both of these results address open issues raised in [37]. Finally, we suggest the use of other decoding techniques to trace traitors when additional information about the behavior of the traitors is known.