Performance of Random Fingerprinting Codes Under Arbitrary Nonlinear Attacks

This paper analyzes the performance of arbitrary nonlinear collusion attacks on random fingerprinting codes. We derive the error exponent of the fingerprinting system, which determines the exponential decay of the error probability. A Gaussian ensemble and an expurgated Gaussian ensemble of codes are considered. The collusion attacks include order-statistics attacks as special cases. In our model, a correlation detector is used. The colluders create a noise-free forgery by applying an arbitrary nonlinear mapping to their individual copies, and next they add a Gaussian noise sequence to form the final forgery. The colluders are subject to a mean-squared distortion constraint between host and forgery. We prove that the uniform linear averaging attack outperforms all others.