Most security- and privacy-preserving protocols in vehicular ad hoc networks (VANETs) heavily rely on time-consuming cryptographic operations which produce a huge volume of cryptographic data. These data are usually employed for many kinds of decisions, which poses the challenge of processing the received cryptographic data fast enough to avoid unaffordable reaction delay. To meet that challenge, we propose a vehicular authentication protocol referred to as APPA. It guarantees trustworthiness of vehicular communications and privacy of vehicles, and enables vehicles to react to vehicular reports containing cryptographic data within a very short delay. Moreover, using our protocol, the seemingly random cryptographic data can be securely and substantially compressed so that the storage space of a vehicle can be greatly saved. Finally, our protocol does not heavily rely on roadside units (RSUs) and it can work to some extent even if the VANET infrastructure is incomplete. These features distinguish our proposal from others and make it attractive in various secure VANET scenarios.