Abstract: Vehicular ad hoc network is the foundation of the intelligent transportation system, which can effectively improve traffic efficiency and enhance road safety. However, due to the openness of its wireless communication environment, the edge nodes in vehicular ad hoc networks are vulnerable to various external attacks. In order to balance privacy protection and traceability, also ensure secure authentication, an effective method is to adopt the conditional privacy-preserving authentication scheme in vehicular ad hoc networks. Although various privacy-preserving authentication schemes have been proposed successively, the security of these schemes almost all rely on the difficult assumptions of traditional number theory, and it is difficult to have post-quantum security characteristics. Therefore, aiming at the security and efficiency problems of existing lattice-based conditional privacy-preserving authentication schemes in vehicular ad hoc networks, and in order to solve the key escrowing problem, by leveraging the decisional learning with errors over rings (RLWE) hardness assumption and the ring-learning with errors (RLWE) small integer solution (SIS) hardness assumption on structured lattices, and combining with the rejection sampling technique, a lattice-based sampling-free conditional privacy preserving aggregate authentication scheme is designed. It is proved that the proposed scheme can achieve adaptive security in the random oracle. In addition, the performance evaluation shows that the proposed scheme is superior to the scheme based on the general lattice in terms of computation cost.