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Unlinkability is a privacy feature supported by those multi-party security protocols allowing anonymous users' credential exchanges among different organizations. Proper signature schemes, based on discrete logarithms, must be used in order to guarantee the above requirements as well as selective disclosure of information. In this paper, we highlight that whenever a concrete architecture based on the above protocols is implemented, some aspects concerning how to manage the association between bases of discrete logarithms and attributes used in attribute certificates should be carefully considered, in order to guarantee that unlinkability really holds. We show that the problem is concrete by testing that the state-of-the-art implementation suffers from the above problem. A general solution is also proposed.