Amidst the rapid development of the Internet of Things (IoT), Vehicular Ad-Hoc NETwork (VANET), a typical IoT application, are bringing an ever-larger number of intelligent and convenient services to the daily lives of individuals. However, there remain challenges for VANETs in preserving privacy and security. In this paper, we propose the first lattice-based Double-Authentication-Preventing Ring Signature (DAPRS) and adopt it to propose a novel privacy-preserving authentication scheme for VANETs, offering the potential for security against quantum computers. The new construction is proven secure against chosen message attacks. Our scheme is more efficient than other ring signature in terms of the time cost of the message signing phase and verification phase, and also in terms of signature length. Analyses of security and efficiency demonstrate that our proposed scheme is provably secure and efficient in the application.