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The focus of this paper is to design a dependable ID-based threshold broadcast encryption (TBE) scheme, by which a center can distribute keys over a network, so that a privileged subset of users can collaborate to jointly compute a specific key. Then a conventional secret-key cryptosystem, such as AES, can be used to encrypt the subsequent broadcast with the distributed key. Because a key distribution can be done in an encrypted broadcast without any key pre-distribution, re-keying protocols for group membership operations can be simplified, a center can use the ID-based TBE scheme to distribute new and random session key. We show that the proposed scheme is robust and secure under chosen-ciphertext attacks based on decisional bilinear Diffie-Hellman (DBDH) assumption. Compared with the previously proposed TBE schemes, our scheme needs only one exponentiation computation, which makes it be more efficient than those schemes.