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We show that equiangular tight frames (ETFs) are particularly well suited as additive fingerprint designs against Gaussian averaging collusion attacks when the number of users is less than the square of the signal dimension. The detector performs a binary hypothesis test in order to decide whether a user of interest is among the colluders. Given a maximum coalition size, we show that the geometric figure of merit of distance between the corresponding "guilty" and "not guilty" linear forgeries for each user is bounded away from zero. Moreover, we show that for a normalized correlation detector, reliable detection is guaranteed provided that the number of users is less than the square of the signal dimension. Moreover, we show that the coalition has the best chance of evading detection when it uses equal weights.