The vehicular ad-hoc network relies on wireless communication, thus exposing security and privacy-related issues. The primary security requirements in a vehicular network are vehicle authentication, message integrity, and privacy preservation. Most of the existing state-of-the-art security schemes heavily relied on infrastructural entities such as roadside units and trusted authorities to achieve authentication. Typically, frequent authentication involving infrastructural entities increases communication overhead. Besides, the existing solutions assume the usage of ideal tamper-proof devices for storing sensitive data, which is prone to physical and cloning attacks. In this context, we present a Physically Unclonable Function based Lightweight Authentication Scheme with privacy preservation for vehicle-to-vehicle communication in the vehicular network. Physically unclonable function adds an extra layer of security from cloning and physical attacks. The proposed method uses a two-tier approach consisting of trusted authority and vehicles for achieving authentication using lightweight bitwise XOR operations and one-way hash functions. The proposed scheme reduces the burden on infrastructural entities by performing authentication through vehicle-to-vehicle communication. Compared with state-of-the-art schemes, the proposed scheme's security and performance analysis demonstrates its effectiveness in meeting various security requirements while ensuring resilience against various known attacks and competitive communication and computation cost. © 2022 Elsevier Ltd