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We introduce an efficient conditional privacy preservation (ECPP) protocol in vehicular ad hoc networks (VANETs) to address the issue on anonymous authentication for safety messages with authority traceability. The proposed protocol is characterized by the generation of on-the-fly short-time anonymous keys between on-board units (OBUs) and roadside units (RSUs), which can provide fast anonymous authentication and privacy tracking while minimizing the required storage for short-time anonymous keys. We demonstrate the merits gained by the proposed protocol through extensive analysis.