The Internet of Medical Things (IoMT) overcomes the flaws in the traditional healthcare system by enabling remote administration, more effective use of resources, and the mobility of medical devices to fulfil the patient’s needs. The IoMT makes it simple to review the patient’s cloud-based medical history in addition to allowing the doctor to keep a close eye on the patient’s condition. However, any communication must be secure and dependable due to the private nature of patient medical records. In this paper, we proposed an authentication method for the IoMT based on hyperelliptic curves and featuring dual signatures. The decreased key size of hyperelliptic curves makes the proposed scheme efficient. Furthermore, security validation analysis is performed with the help of the formal verification tool called Scyther, which shows that the proposed scheme is secure against several types of attacks. A comparison of the proposed scheme’s computational and communication expenses with those of existing schemes reveals its efficiency.