Privacy-related issues are crucial for the wide diffusion of Vehicular Communications (VC). In particular, traffic analysis is one of the subtler threats to privacy in VC. In this paper we first briefly review current work in literature addressing privacy issues and survey vehicular mobility models. Then we present VIPER: a Vehicle-to-Infrastructure communication Privacy Enforcement pRotocol. VIPER is inspired to solutions provided for the Internet-mix-and cryptography-universal re-encryption. The protocol is shown to be resilient to traffic analysis attacks and analytical results suggest that it also performs well with respect to key performance indicators: queue occupancy, message path length and message delivery time; simulation results support our analytical findings. Finally, a comprehensive analysis has been performed to assess the overhead introduced by our mechanism. Simulation results show that the overhead introduced by VIPER in terms of extra bits required, computations, time delay, and message overhead is feasible even for increasing requirements on the security of the underlying cryptographic mechanisms.