The recent improvement in VANET and cloud computing technology has developed the intelligent transportation systems, which raises security problems due to several violations of security policies. It is crucial to prevent vehicles to take in fact forged messages and to preserve the privacy of vehicles. Security and privacy are the major concern in vehicular cloud computing. In this paper, we propose an efficient authentication algorithm using Identifier-Based-Signature (IBS) scheme to provide vehicles' trustworthiness, secure communication and vehicles' privacy. Vehicles' privacy is preserved by using pseudonyms generated by the cloud instead of the real identifiers. V2R and V2V authentication is ensured by using the IBS signature scheme. The performance of our proposed algorithm is compared to recent schemes. Simulation results shows that our proposed algorithm provides secure communication among vehicles with less computation time.