Spread-spectrum substitution watermarking game

In the integrity checking context of multimedia contents, a malicious user aims at devising a forged content in order to fool a watermarker by making him use as a genuine content. By considering that the watermark acts as an integrity stamp, the false-alarm probability to recover the watermark signature in a forged content is the criterion of interest. We study and solve a game for this criterion between a watermarker and a falsifier which is allowed to perform a substitution attack, i.e. replace the watermarked signal by a non-watermarked content. As for the watermarker, we are concerned with additive spread-spectrum (SS) embedding. Signals are modeled by parallel colored gaussian processes. Due to the intractability of the false-alarm probability, we resort to Chernoff bound as an alternative cost. Our study confirms some common heuristics: the best attacker choice is to substitute the watermarked host signal using a signal which has very close statistics to the original host signal. The best watermarker strategy is to embed the watermark into the weakest frequency power components of the host signal. We finally consider the consequences of these results in terms of frequency embedding domain for an image SS watermarking scheme which has to be robust to compression. This reveals notable differences with informed scalar quantized-based schemes.