Detection-theoretic analysis of desynchronization attacks in watermarking

This paper studies the effects of desynchronization attacks such as delay and warping on the performance of blind watermark detection systems. Detection performance is measured using a probability-of-error criterion. Evaluation of the optimal likelihood ratio test is often computationally expensive, so as a practical alternative, we propose a family of quadratic detectors and construct the detector and family of watermarks that maximize the deflection criterion. For delay attacks, the deflection criterion is shown to increase quadratically with the duration of the host signal. For warping attacks, the deflection criterion increases proportionally to the duration of the signal and proportionally to the correlation time of the warping function. Piecewise-sinusoidal watermarks are shown to be nearly optimal in that case. Some examples are presented.