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Vehicular communications are envisioned to play a substantial role in providing safety in transportation by means of safety message exchange. However, the deployment of vehicular networks is strongly dependent on security and privacy features. In this paper, we present a Protocol for Anonymous Authentication in Vehicular Networks (PAAVE) to address the issue of privacy preservation with authority traceability in vehicular ad hoc networks (VANETs). The proposed protocol is based on smart cards to generate on-the-fly anonymous keys between vehicles and Roadside units (RSUs). PAAVE is lightweight and provides fast anonymous authentication and location privacy while requiring a vehicle to store one cryptographic key. We demonstrate the merits gained by the proposed protocol through extensive analysis and show that PAAVE outperforms existing schemes.