With the constant development of wireless communication technologies, the Vehicular Ad-hoc Networks (VANETs) will become an inevitable paradigm for intelligent transportation systems. Privacy-preserving and authentication security has been a core concern in VANETs, and pseudonym-based and group signature-based privacy-preserving authentication schemes have been widely proposed. However, most research schemes rely excessively on the Trusted Authority, and vehicle request and authentication information is almost transparent in front of TAs, while they cannot guarantee the security of vehicle request information after it is intercepted. To address these issues, this paper proposes a lightweight privacy-preserving authentication scheme that mitigates TA dependency, aiming to achieve mutual privacy protection and authentication between vehicles and TAs in VANETs by improving the oblivious transfer algorithm. The security analysis proves that this scheme has good privacy protection and attack resistance, and in addition, the performance simulation and evaluation show that this scheme spends lower computation and communication overheads while ensuring lower authentication delay and packet loss rate, which is a better overall performance compared with other schemes.