Joint detection-estimation games for sensitivity analysis attacks

Sensitivity analysis attacks aim at estimating a watermark from multiple observations of the detector's output. Subsequently, the attacker removes the estimated watermark from the watermarked signal. In order to measure the vulnerability of a detector against such attacks, we evaluate the fundamental performance limits for the attacker's estimation problem. The inverse of the Fisher information matrix provides a bound on the covariance matrix of the estimation error. A general strategy for the attacker is to select the distribution of auxiliary test signals that minimizes the trace of the inverse Fisher information matrix. The watermark detector must trade off two conflicting requirements: (1) reliability, and (2) security against sensitivity attacks. We explore this tradeoff and design the detection function that maximizes the trace of the attacker's inverse Fisher information matrix while simultaneously guaranteeing a bound on the error probability. Game theory is the natural framework to study this problem, and considerable insights emerge from this analysis.