Abstract: A group signature scheme allows members of a group to sign messages on the group’s behalf such that the resulting signature does not reveal their identity. Signature can be verified with respect to a single group public key. Only a designated group manager is able to identify the group member who issued a given signature. Previously proposed realizations of group signature schemes have the undesirable property that the length of the public key is linear in the size of the group and therefore the running time of the verification algorithm depends on the number of group members. In this paper a new group signature scheme is proposed, which overcome these problems. Furthermore, the scheme allows the group manager to add new members to the group without modifying the public key. The realization is based on the knowledge of signature of DSA.