Recently, the application of fog-computing technology to vehicular ad hoc networks (VANETs) has rapidly advanced. Despite these advancements, challenges remain in ensuring efficient communication and security. Specifically, there are issues such as the high communication and computation load of authentications and insecure communication over public channels between fog nodes and vehicles. To address these problems, a lightweight and secure authenticated key agreement protocol for confidential communication is proposed. However, we found that the protocol does not offer perfect forward secrecy and is vulnerable to several attacks, such as privileged insider, ephemeral secret leakage, and stolen smart card attacks. Furthermore, their protocol excessively uses elliptic curve cryptography (ECC), resulting in delays in VANET environments where authentication occurs frequently. Therefore, this paper proposes a novel authentication protocol that outperforms other related protocols regarding security and performance. The proposed protocol reduced the usage frequency of ECC primarily using hash and exclusive OR operations. We analyzed the proposed protocol using informal and formal methods, including the real-or-random (RoR) model, Burrows–Abadi–Nikoogadam (BAN) logic, and automated validation of internet security protocols and applications (AVISPA) simulation to show that the proposed protocol is correct and secure against various attacks. Moreover, We compared the computational cost, communication cost, and security features of the proposed protocol with other related protocols and show that the proposed methods have better performance and security than other schemes. As a result, the proposed scheme is more secure and efficient for fog-based VANETs.
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