Public key infrastructure (PKI) is the most widely used security mechanism for securing communications over the network. However, there are known performance issues, making it unsuitable for use in vehicular networks. In this paper, we propose a secure and authenticated key management protocol (SA-KMP) to overcome the shortcomings of the PKI. The SA-KMP scheme distributes repository containing the bindings of the entity's identity and its corresponding public key to each vehicle and road side unit. By doing so, certificate exchanges and certificate revocation lists are eliminated. Furthermore, the SA-KMP scheme uses symmetric keys derived based on a 3-D-matrix-based key agreement scheme to reduce the high computational costs of using asymmetric cryptography. We demonstrate the efficiency of the SA-KMP through performance evaluations in terms of transmission and storage overhead, network latency, and key generation time. Analytical results show that the SA-KMP is more scalable and outperforms the certificate-based PKI. Simulation results indicate that the key generation time of the SA-KMP scheme is less than that of the existing Elliptic Curve Diffie-Hellman and Diffie-Hellman protocols. In addition, we use Proverif to prove that the SA-KMP scheme is secure against an active attacker under the Dolev and Yao model and further show that the SA-KMP scheme is secure against denial of service, collusion attacks, and a wide range of other malicious attacks.