In this work, we present an adaptively secure identity-based broadcast encryption system featuring constant sized ciphertext in the standard model. The size of the public key and the private keys of our system are both linear in the maximum number of receivers. Also, our system is fully collusion-resistant and has stateless receivers. Compared with the state-of-the-art, our scheme is well optimized for the broadcast encryption. The computational complexity of decryption of our scheme depends only on the number of receivers, not the maximum number of receivers of the system. Technically, we employ dual system encryption technique and our proposal offers adaptive security under the general subgroup decisional assumption. Our scheme demonstrates that the adaptive security of the schemes utilizing a composite order group can be proven under the general subgroup decisional assumption while many existing systems working in a composite order group are secure under multiple subgroup decision assumptions. We note that this finding is of an independent interest, which may be useful in other scenarios.