The rapid expansion of Vehicle-to-Everything (V2X) networks within the Internet of Vehicles (IoV) demands secure and efficient authentication to support high-speed, high-density and mobility-challenged environments. This paper presents a privacy-preserving authentication scheme that incorporates batch authentication, mutual authentication, and secure key establishment, enabling users to authenticate one another without a central authority. Our proposed scheme facilitates simultaneous multi-user authentication, significantly enhancing scalability, robustness and security in dynamic IoV networks. Results from realistic implementations show that our method achieves average authentication and verification times of 10.61 ms and 1.78 ms, respectively, for a fleet of 100 vehicles, outperforming existing methods. Scalability tests demonstrate efficient processing for larger groups of up to 500 vehicles, where average authentication times remain low, establishing our scheme as a robust solution for secure communication in IoV systems.