Secure message transmission in vehicular communications in smart cities is still a challenging task. Most of the related work employed the Public Key Infrastructure, Certification Revocation Lists (CRLs) for ensuring security, privacy. However, these work suffered from some issues such as: 1) the time-consuming checking process, huge size of CRLs, 2) traceability attacks by linking unencrypted Basic Safety Messages (BSMs), 3) extracting secret keys from the storage of parked vehicles or road-side units (RSU) by an adversary. To address the aforementioned issues, we thus propose a physically secure privacy-preserving message authentication protocol using Physical Unclonable Function (PUF), Secret Sharing. The proposed protocol guarantees security, privacy against passive, active attacks even under memory leakage. The entities (i.e., vehicles, RSU) make use of their PUF to reconstruct a secret polynomial-share so that pairwise temporal secret keys (PTKs) can be established with other entities. Unlike existing protocols, BSMs are also encrypted in our protocol (by PTKs) to provide a higher level of security, thwart vehicles traceability attacks. To revoke a vehicle, RSU needs not broadcast CRLs. Instead, RSU distributes only a secure offset key using threshold Secret Sharing. Consequently, our revocation checking process has computation complexity $\mathcal {O}(1)$ . Our protocol also eliminates the need for a third party in Vehicle-to-Vehicle communication to ensure expeditious transmission. Security analysis, performance evaluation show that our proposed protocol outperforms existing schemes in terms of security features, computation, communication cost.