Secure multicast communication provides an efficient way to deliver data to a large group of recipients. Scalability, efficiency and authenticity are the key challenges for secure multicast. In this paper, we propose a novel group key agreement scheme called logical identity hierarchy(LIH) for multicast to support secure communications for large and dynamic groups, which is based on bilinear pairing. Compared with the previous tree-based schemes, LIH provides dual authentication between group controller(GC) and group members and hierarchical authentication among group members. GC and all the users do not need to execute any encryption/decryption process during the rekeying operation. Moreover, in LIH, the group members can be stateless receivers, who do not need to update their state during the protocol execution. Using a public board, GC does not need to multicast any rekeying message when a user joins/leaves the communication group. Security analysis shows that LIH satisfies both backward secrecy and forward secrecy.