Technical Report TR-98-17B, LCIS, Tamkang University, Taiwan, R.O.C., November 1998.

Abstract. Very recently, Ateniese and Tsudik suggested two nice and practical group signature schemes allowing members of a group to sign on behalf of the group in such a way that the signer's identity can be recovered by the group manager in case of abuse. Their first scheme does not address hostile coalition of group members while the second one is supposed to be coalition-resistant. This report shows that this additional property is not satisfied: two colluding group members can produce untraceable group signatures.