Are you threatening me? Towards smart detectors in watermarking

We revisit the well-known watermarking detection problem, also known as one-bit watermarking, in the presence of an oracle attack. In the absence of an adversary, the design of the detector generally relies on probabilistic formulations (e. g., Neyman-Pearson's lemma) or on ad-hoc solutions. When there is an adversary trying to minimize the probability of correct detection, game-theoretic approaches are possible. However, they usually assume that the attacker cannot learn the secret parameters used in detection. This is no longer the case when the adversary launches an oracle-based attack, which turns out to be extremely effective. In this paper, we discuss how the detector can learn whether it is being subject to such an attack, and take proper measures. We present two approaches based on different attacker models. The first model is very general and makes minimum assumptions on attacker's beaver. The second model is more specific since it assumes that the oracle attack follows a weel-defined path. In all cases, a few observations are sufficient to the watermark detector to understand whether an oracle attack is on going.