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We study the effect of the noise distribution on the error probability of the detection test when a class of randomly rotated spherical fingerprints is used. The detection test is performed by a focused correlation detector, and the spherical codes studied here form a randomized orthogonal constellation. The colluders create a noise-free forgery by uniform averaging of their individual copies, and then add a noise sequence to form the actual forgery. We derive the noise distribution that maximizes the error probability of the detector under average and almost-sure distortion constraints. Moreover, we characterize the noise distribution that minimizes the decoder's error exponent under a large-deviations distortion constraint.