Two provably secure group identification schemes are presented in this report: 1) we extend De Santis, Crescenzo and Persiano's (SCP) anonymous group identification scheme to the discrete logarithm based case; then we provide a 3-move anonymous group identification scheme, which is more efficient than that presented in [SCPM, CDS], with the help of this basic scheme; 2) we also extend the original De Santis, Crescenzo and Persiano anonymous group identification scheme to the general case where each user holds public key which is chosen by herself independently. The communication cost for one round execution of the protocol is 2mk, where k is bit length of public key n and m is the number of users in the group.
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