Vehicular Ad Hoc Networks (VANETs) are crucial for intelligent transportation systems (ITS), yet they face significant security and privacy challenges. The open wireless environment makes VANETs vulnerable to attacks, and existing authentication protocols often have limitations, such as susceptibility to quantum threats or high communication overhead. In this paper, we propose an effective privacy-preserving authentication protocol using lattice-based group signatures for VANETs. Our protocol ensures quantum security and provides robust security features. It not only ensures privacy protection for vehicles but also enables efficient tracing of malicious signers when necessary. In addition, we show that the proposed protocol features small and fixed public key and signature sizes, independent of the number of members, and incurs low communication overhead.