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In this paper, we propose a new privacy preservation scheme, named pseudonymous authentication-based conditional privacy (PACP), which allows vehicles in a vehicular ad hoc network (VANET) to use pseudonyms instead of their true identity to obtain provably good privacy. In our scheme, vehicles interact with roadside units to help them generate pseudonyms for anonymous communication. In our setup, the pseudonyms are only known to the vehicles but have no other entities in the network. In addition, our scheme provides an efficient revocation mechanism that allows vehicles to be identified and revoked from the network if needed. Thus, we provide conditional privacy to the vehicles in the system, that is, the vehicles will be anonymous in the network until they are revoked, at which point, they cease to be anonymous.