A Note on the Limits of Collusion - ResistantWatermarksFunda Ergun ?

In one proposed use of digital watermarks, the owner of a document D sells slightly diierent documents, D 1 ; D 2 ; : : : to each buyer; if a buyer posts his/her document D i to the web, the owner can identify the source of the leak. More general attacks are however possible in which k buyers create some composite document D ; the goal of the owner is to identify at least one of the conspirators. We show, for a reasonable model of digital watermarks, fundamental limits on their eecacy against collusive attacks. In particular, if the eeective document length is n, then at most O(p n= ln n) adversaries can defeat any watermarking scheme. Our attack is, in the theoretical model, oblivious to the watermarking scheme being used; in practice, it uses very little information about the watermarking scheme. Thus, using a proprietary system seems to give only a very weak defense.