Risk-distortion analysis for video collusion attack

Collusion attack is a cost-effective attack against digital fingerprint. To develop an efficient collusion-resistant fingerprint scheme, it is very important for the detector to study the behavior of the colluders and the performance of collusion attack. Although several prior works have been proposed in the literature to analyze the performance of collusion attack, few effort has been made to explicitly study the relationship between risk, i.e., the probability of the colluders to be detected, and distortion of collusion attack. In this paper, we investigate the risk-distortion relationship of the linear video collusion attack with Gaussian fingerprint. We formulate the optimal linear collusion attack as an optimization problem, where the colluders try to minimize the distortion subject to a risk constraint. For any fixed risk constraint, the optimal distortion can be found using numerical optimization methods. By varying the risk constraint, we can obtain the risk-distortion model. We also conduct experiments to verify the proposed risk-distortion model using real video data.