A Framework for Optimizing Nonlinear Collusion Attacks on Fingerprinting Systems

Negar Kiyavash and Pierre Moulin

This paper develops a mathematical analysis of the performance of order statistic collusion attacks on Gaussian fingerprinting
systems. The attacks considered include the popular memoryless averaging and median attacks as special cases. In this model, the
colluders create a noise-free forgery by applying an order statistic mapping to each sample of their individual copies, and next
they add a Gaussian noise sequence to form the final forgery. The choice of the mapping may be time-dependent and/or random. The
performance of a strategy is evaluated in terms of the resulting probability of error of a correlation focused detector, and in
terms of the mean-squared distortion between host and forgery. We prove the surprising fact that all the nonlinear attacks
considered result in the same detection performance. Moreover, the linear averaging attack outperforms the other ones in the
sense of minimizing mean-squared distortion.