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In this paper we study a particular attack that may be launched by cooperating organisations in order to link the transactions and the pseudonyms of the users of an anonymous credential system. The results of our analysis are both positive and negative. The good (resp. bad) news, from a privacy protection (resp. evidence gathering) viewpoint, is that the attack may be computationally intensive. In particular, it requires solving a problem that is polynomial time equivalent to ALLSAT . The bad (resp. good) news is that a typical instance of this problem may be efficiently solvable.