Authentication is one of the essential security services in Wireless Sensor Networks (WSNs) for ensuring secure data sessions. Sensor node authentication ensures the confidentiality and validity of data collected by the sensor node, whereas user authentication guarantees that only legitimate users can access the sensor data. In a mobile WSN, sensor and user nodes move across the network and exchange data with multiple nodes, thus experiencing the authentication process multiple times. The integration of WSNs with Internet of Things (IoT) brings forth a new kind of WSN architecture along with stricter security requirements; for instance, a sensor node or a user node may need to establish multiple concurrent secure data sessions. With concurrent data sessions, the frequency of the re-authentication process increases in proportion to the number of concurrent connections. Moreover, to establish multiple data sessions, it is essential that a protocol participant have the capability of running multiple instances of the protocol run, which makes the security issue even more challenging. The currently available authentication protocols were designed for the autonomous WSN and do not account for the above requirements. Hence, ensuring a lightweight and efficient authentication protocol has become more crucial. In this paper, we present a novel, lightweight and efficient key exchange and authentication protocol suite called the Secure Mobile Sensor Network (SMSN) Authentication Protocol. In the SMSN a mobile node goes through an initial authentication procedure and receives a re-authentication ticket from the base station. Later a mobile node can use this re-authentication ticket when establishing multiple data exchange sessions and/or when moving across the network. This scheme reduces the communication and computational complexity of the authentication process. We proved the strength of our protocol with rigorous security analysis (including formal analysis using the BAN-logic) and simulated the SMSN and previously proposed schemes in an automated protocol verifier tool. Finally, we compared the computational complexity and communication cost against well-known authentication protocols.