Smart wearable devices, as a popular mobile device, have a broad market. Smart wearable medical devices implemented in wearable health monitoring systems can monitor the data pertaining to a patient's body and let the patient know their own physical condition. In addition, these data can be stored, analyzed, and processed in the cloud to effectively prevent diseases. As an Internet-of-things technology, fog computing can process, store, and control data around devices in real time. However, the

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... distributed attributes of fog nodes make the monitored body data and medical reports at risk of privacy disclosure. In this paper, we propose a fog-driven secure authentication and key exchange scheme for wearable health monitoring systems. Furthermore, we conduct a formal analysis using the Real-Oracle-Random model, Burrows–Abadi–Needham logic, and ProVerif tools and an informal analysis to perform security verification. Finally, a performance comparison with other related schemes shows that the proposed scheme has the best advantages in terms of security, computing overhead, and communication cost.