Intelligent vehicles require to communicate with other vehicles as well as with the road-side infrastructure for gathering information such as traffic management, cooperative driving, telematics and road construction. However, vehicle-to vehicle (V2V) and vehicle to infrastructure (V2I) communications can impose some serious security threats against vehicles' safety and other sensitive information which can lead to catastrophic consequences. Therefore, there is a pressing need to develop appropriate security protocols facilitating V2I and V2V communication. This paper presents a model for smart traffic infrastructure consisting of numerous entities like smart sensors, intelligent vehicles, base stations along with a new user authentication and key-exchange protocol which aids in the establishment of a secure session for communication between the entities. In the proposed protocol, any SUF-CMA (Strong Unforgeable- Chosen Message Attack) secure digital signature algorithm can be used for authenticating the users and any NM-CCA2 (Non-Malleability Chosen Ciphertext Attack) secure algorithm can also be used for the challenge response phase between the users authenticating themselves.