# An Optimal Authentication Scheme through Dual Signature for the Internet of Medical Things
## 1 Introduction  
The Internet of Things (IoT) has attracted a lot of attention recently and can connect any device to any other device, anytime, anywhere, by using any communication channel or service [1, 2]. The IoT has many applications, as it is used in agriculture, smart homes, transportation, health care, etc. In this paper, we focus on healthcare because, due to the fast rise of the population, an IoT-based healthcare system will solve health-related issues in every person's life. Conventional healthcare systems cannot solve the demands of such a vast population [3], which necessitates additional resources and people. Due to manual management, there is always the possibility of a mistake that can be catastrophic for the patient [4]. The Internet of Medical Things (IoMT) offers a solution to these issues, which attempts to address the problems experienced by the traditional healthcare system by lowering manual involvement and increasing the system's precision and adaptability. The IoMT refers to the linking of healthcare equipment that can interact via a network without requiring human involvement [5]. As seen in Figure 1, the IoMT refers to the interconnection of medical equipment, such as wearables, smart chairs, smart belts, sphygromanometers, and diabetic devices, among others. Wearable gadgets consist of smartwatches, fitness trackers, and blood pressure monitoring devices, among others, that continuously measure the pulse, blood pressure, and other health data. In the event of a sudden drop in a patient's pulse or blood pressure, an alarm is transmitted to the caretaker, who then dispatches an ambulance to thepatient's residence [6]. The IoMT enables the use of chairs with integrated sensors capable of detecting movements and is especially good for older people, who are more susceptible to falling. If a patient exits the chair, the smart chair recognizes it and, based on a risk assessment, generates an alarm to notify the nursing staff [7]. Similarly, tracking sensors are incorporated into smart belts to monitor the mobility of elderly patients. Patients with diabetes and hypertension require continual glucose and blood pressure monitoring; so, IoT-based diabetes gadgets and sphygmomanometers make remote monitoring simple by measuring glucose and blood pressure and making the data accessible in real-time to doctors via health applications. Further, remote monitoring allows seriously ill individuals to avoid hospitalization; they can communicate with their doctor and obtain a prescription using the health application [8]. In addition to the above-mentioned benefits, the health applications continually transmit patient data to the hospital, where physicians evaluate it to identify variances, which can permit the physician to monitor the patient's status and expedite his recovery. Similarly, use of the IoMT decreases manual involvement while performing machine-to-machine communication; again, the diagnostic centre sends an electronic medical report to a patient's mobile phone [9; 10]. All IoMT devices are connected to cloud storage for data storage and subsequent analysis. Despite the numerous uses and benefits of the IoMT, there are a few issues, such as security, data privacy, and authentication, which must be handled. The above-mentioned problems can be solved through a dual digital signature, which can only authorize the legitimate user to access and use the health care data. A dual signature does not imply that there are two signatures; rather, it is a particular sort of signature that focuses on linking two distinct messages (information) meant for two separate recipients [11]. A dual-signature approach may be created using Rivest-Shamir-Adleman (RSA), elliptic-curve cryptography (ECC), and hyper elliptic-curve cryptography (HECC). Due to the 1024-bit key length, using a dual signature with RSA requires a lot of storage space, which can raise computation costs and communication overhead [12].