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Many network applications are based on a group communications model where one party sends messages to a large number of authorized recipients and/or receives messages from multiple senders. In this paper we present a secure group communication scheme based on a new cryptosystem that admits a rigorous proof of security against adaptive chosen ciphertext attack (IND-CCA2). Our scheme is bi-directional, supporting both one-to-many and many-to-one communications. Compared with existing solutions, our scheme achieves the following improvements: (1) It guarantees data confidentiality and authenticity in both directions; (2) It is the most scalable solution so far among all existing schemes achieving (1). The group member storage overhead is constant while both the center storage and rekeying communication complexity are independent of group size. (3) It can be made to achieve higher level of security and hide even the information about the group dynamics. We show that this protection is more effective and more efficient than existing solutions.