Privacy preservation is a crucial aspect of intelligent transportation systems, particularly in queries involving sensitive data stored in the Cloud. However, resource-constrained vehicles require security, privacy, and communication efficiency. To address these challenges, we propose an efficient and Privacy-Preserving Query (PPQ) scheme for intelligent transportation systems. The proposed scheme leverages matrix decomposition techniques to reorganize routes in a flexible manner. Additionally, all query operations are performed in the ciphertext state to protect the vehicle's route. Lightweight authentication is employed to ensure legitimate user access between vehicles and roadside units. Furthermore, security analysis confirms that the proposed scheme meets the security goals of privacy protection. Performance analysis demonstrates that the computational and communication overhead of the scheme are greatly improved compared to similar schemes. Therefore, the proposed solution is well-suited for resource-constrained vehicles.