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Vehicular fog systems that are enabled by fifth-generation (5G) networks can significantly improve traffic safety and efficiency through vehicle-to-vehicle communication. Vehicles must have their legal status verified before they can join the network, as vehicular systems depend on open communication. Consequently, several anonymous authentication schemes have been created to withstand malicious vehicles, with the foundations being bilinear pairing or elliptic curve cryptography. But quantum attacks can easily defeat these schemes. To address this problem, this study introduces a 5G-supported vehicular fog system anonymous authentication strategy that makes use of lattice-based cryptography. The suggested system communicates with trusted authorities (TAs) and automobiles over the 5G-base station’s communication range, and it employs fog servers to authenticate vehicles and distribute anonymous …