Resistance of Digital Watermarks to Collusive Attacks

Abstract:

In many schemes for digital watermarking, an
attacker in possession of a small fixed number of differently marked
copies of a single document can easily produce an unmarked copy.
In contrast, we show in this paper that if the watermarks have a component-wise
normal distribution, then $Omega ig( {sqrt{n/ln m}},/ig)$
differently marked copies are required to
successfully erase any mark with non-negligible probability.
Here n is the dimensionality of the
watermarks, and m is the number of differently marked copies distributed.
This result holds in a specific but natural statistical model of watermarking.