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In this paper, a secure and efficient protocol for vehicular ad hoc networks has been proposed that ensures both message authentication and privacy preservation. As safety related message may contain life critical information, it is a necessity that the sender as well as the message are authentic. The proposed scheme is based on a secure elliptic curve digital signature algorithm approach. The proposed scheme supports conditional privacy, where the user's location can be revealed at the willingness of the user. Apart from this, the scheme is secure against attacks like DoS, Sybil and Grey/Black Hole attacks. From the comparison with previously proposed schemes, it is found that the proposed scheme as based on elliptic curve discrete logarithmic problem, outperforms existing algorithms based on integer factoring and discrete logarithmic problem.