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Internet of Vehicles(IoV) is increasingly used as a medium to propagate critical information via establishing connections between entities such as vehicles and infrastructures. During message transmission, privacy-preserving authentication is considered as the first line of defence against attackers and malicious information. To achieve a more secure and stable communication environment, ever-increasing numbers of blockchain-based authentication schemes are proposed. At first glance, existing approaches provide robust architectures and achieve transparent authentication. However, in these schemes, verifiers must connect to the blockchain network in advance and accomplish the authentication with smart contracts, which prolongs the latency. To remedy this limit, we propose a privacy-preserving blockchain-based authentication protocol(PBAG), where Root Authority(RA) generates a unique evaluation proof corresponding to the issued certificate for each authorized vehicle. Meanwhile, RA broadcasts a public global commitment based on all valid certificates. Instead of querying certificates stored in the blockchain, the vehicle will be efficiently proved to be an authorized user by utilizing the global commitment through bilinear pairing. Moreover, our scheme can prevent vehicles equipped with invalid certificates from accomplishing the authentication, thus avoiding the time-consuming for checking Certificate Revocation List (CRL). Finally, our scheme provides privacy properties such as anonymity and unlinkability. It allows anonymous authentication based on evaluation proofs and achieves traceability of identity in the event of a dispute. The simulation demonstrates that the average time of verification is 0.36ms under the batch-enabled mechanism, outperforming existing schemes by at least 63.7%.