In this paper, we analyze the conventional group signature schemes, and propose the notion of conflict of authenticated contents which implies the unconquerable drawbacks of the current group signature schemes and threshold signature schemes. We discuss an important problem of group signature, that is, whether the group signature is produced on behalf of the group or on behalf of its members, and consider that the group signatures should be produced on behalf of the group. A new kind of signature scheme, which is called anonymous signatures, has been proposed. And we indicate that the previously proposed group signature is actually a kind of anonymous signatures. In order to realize the anonymous signatures, we design two kinds of implementation schemes, whose performances are analyzed and compared. Finally, we introduce the new notion of real group signatures, describe its characteristics, present one realization based on pivot threshold scheme which we designed to solve the conflict of authenticated contents problem.