In the VANET environment, the security of traffic information between vehicles is very important. The messages need to be real-time, and the complexity of authentication should be low. Our proposed method focus on the identity verification based on bilinear pairing, therefore, vehicles, roadside units (RSUs), central authorities (CAs) and trust authority (TA) can verify the identity of each other. After the identity authentication, RSUs will broadcast messages containing chameleon hashing values of verified vehicles, to the other RSUs and vehicles. In the future, vehicles can communicate with the verified vehicles, and verify the messages by these chameleon hashing values. The advantages of the propose method is mainly: 1. Based on the identity-based cryptography (i.e. IBC), the vehicles, RSUs, CAs and TA can verify the message each other. 2. The vehicles can verify the source and legitimacy of the public/private key. 3. The vehicles do not need to show any certificate to verify the identity, avoiding the certificate is exposed for a long time and causing attacks. 4. We can verify the messages through chameleon function and does not need to wait for RSU to verify, it would have good latency performance. 5. We don¡¦t need to re-verify the identity and consult the common keys when the vehicles hand off within the different cover ranges of the RSUs. 6. Not only within the RSUs, our proposal but also can execute in somewhere without RSU. Finally, our proposal method can fulfill the authentication, data integrity, non-repudiation, condition-privacy and untraceable.