Optimum attack on digital watermarks and its defense

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 the 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.