Notation and their description.

The role that vehicular fog computing based on the Fifth Generation (5G) can play in improving traffic management and motorist safety is growing quickly. The use of wireless technology within a vehicle raises issues of confidentiality and safety. Such concerns are optimal targets for conditional privacy-preserving authentication (CPPA) methods. However, current CPPA-based systems face a challenge when subjected to attacks from quantum computers. Because of the need for security and anti-piracy features in fog computing when using a 5G-enabled vehicle system, the L-CPPA scheme is proposed in this article. Using a fog server, secret keys are generated and transmitted to each registered car via a 5G-Base Station (5G-BS) in the proposed L-CPPA system. In the proposed L-CPPA method, the trusted authority, rather than the vehicle’s Onboard Unit (OBU), stores the vehicle’s master secret data to each fog server. Finally, the computation cost of the suggested L-CPPA system regards message signing, single verification and batch verification is 694.161 ms, 60.118 ms, and 1348.218 ms, respectively. Meanwhile, the communication cost is 7757 bytes.