Optimum attack on digital watermarks and its defense
J. K. Su, Joachim J. Eggers, Bernd Girod · 2002
We study the theoretical robustness of digital watermarks by viewing watermarking as communication over a hostile channel. Signals are modeled as stationary Gaussian random processes, and distortion is measured by frequency-weighted mean-squared error (MSE). The attack consists of linear shift-invariant filtering and additive Gaussian noise; it is optimized by selecting the filter and noise to minimize attacked-signal distortion under a capacity constraint. Then the defense is optimized by maximizing attacked-signal distortion under constraints on capacity and watermarked-signal distortion. We obtain performance limits and give rules-of-thumb for attack and defense. Experiments also show the influence of memory, suboptimality of additive-noise and effective white-noise attacks, and the effect of frequency-weighted distortion. 1. Introduction Digital watermarking is the imperceptible, robust, secure communication of information in which information is embedded in and retrieved from ot...