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Anonymity is an important feature in many two party communication systems. Its main meaning is that either the message sender or the receiver (or both) is unidentifiable to other users, even between themselves. Many mechanisms have been proposed to hide the identity of the sender, receiver, or both. Similarly, anonymity is an important feature in multi-party computing environments, but, little research has been conducted on this topic even though many secure group communication schemes have been proposed. In this paper, we highlight the concepts of anonymity for secure group communication and propose to extend a recently invented innovative group key management mechanism, Access Control Polynomial, to multiple-party group communication. This newly extended scheme can not only enforce anonymous group membership and group size but also implement secure and anonymous group communication. The experimental results and comparison with existing schemes show that the new scheme is elegant, flexible, efficient and practical. The paper also summarizes and classifies typical existing anonymous group communication schemes.