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Digital fingerprinting is a method for protecting digital data in which fingerprints that are embedded in multimedia are capable of identifying unauthorized use of digital content. A powerful attack that can be employed to reduce this tracing capability is collusion, where several users combine their copies of the same content to attenuate/remove the original fingerprints. In this paper, we study the collusion resistance of a fingerprinting system employing Gaussian distributed fingerprints and orthogonal modulation. We introduce the maximum detector and the thresholding detector for colluder identification. We then analyze the collusion resistance of a system to the averaging collusion attack for the performance criteria represented by the probability of a false negative and the probability of a false positive. Lower and upper bounds for the maximum number of colluders Kmax are derived. We then show that the detectors are robust to different collusion attacks. We further study different sets of performance criteria, and our results indicate that attacks based on a few dozen independent copies can confound such a fingerprinting system. We also propose a likelihood-based approach to estimate the number of colluders. Finally, we demonstrate the performance for detecting colluders through experiments using real images.