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In the VANET systems, the leakage of some sensitive data or communication information will cause heavy losses for life and property. Then, a higher security level is required in the VANET systems. Meanwhile, fast computation powers are needed by devices with limited computing resources. Thus, a secure and lightweight privacy-preserving protocol for VANETs is urgent. In this paper, we first propose an identity-based signature that achieves unforgeability against chosen-message attack without random oracle. In order to reduce the computational cost, we design two secure and efficient outsourcing algorithms for the exponential operations, where a homomorphic mapping based on matrices conjugate operation is used to achieve the security of both exponent and base numbers. Furthermore, we construct a privacy-preserving protocol for VANETs by using outsourcing computing and the proposed IBS, where a proxy re-signature scheme is presented for authentications. In the VANET privacy-preserving protocol, TA authorizes RSU to act as an agent and RUS converts OBU's signature into TA's signature, which effectively hides the real identity of vehicle OBU. Meanwhile, TAhas access to trace the real identity of OBUusing its secret key when malicious messages are found. Then, the protocol provides anonymity, traceability, and privacy. In addition, with respect to the efficiency, our scheme does not need pairing operations and exponential operations. Thus, the calculation burdens for the VANET system can be significantly reduced.
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