## 1 Introduction  
With the development of computing technologies and the expansion of smart-devices and inter-network protocols, hospitals and healthcare organizations are adopting the Telecare Medical Information System (TMIS). The medical identification process has become more resourceful, trustworthy, and efficient by using TMIS. Some Telecare services have been projected in the modern age to ease the workload on the professionals, for example, by methods such as automated healthcare devices, distant health nursing, and patient's health monitoring for remote areas. It is considered as a time-saving, economical, and easy way to access health care facilities remotely. TMIS can lower societal and medical operating cost with improved quality and efficiency [1]. Patient authentication is mandatory to guard against data forgery, misuse, and falsifying the original information by unauthorized active or passive parties. In TMIS, a trusted medical server is responsible for registering all participants, including doctors, nursing staff, and patients, as illustrated in Figure 1. The remote healthcare server keeps the advanced clinical information of the register patients and gives different administrations like healthcare education, doctors, doctor's facilities, remote medical aid, general healthcare, private care benefit, and the most important is medical prescription. Registered TMIS users for medical services can utilize smart cards to access medical devices and transmit collected statistics to the medical server using a public channel. An intruder may likewise find access over the public open channel. The adversary can eavesdrop, block service, modify, delete records, and can also reply to a message broadcasted over an open channel. Therefore, authentication is mandatory for providing information security, records honesty, and confidentiality of data. It is necessary to overcome all existing threats that are major hurdles and make TMIS trustworthy. A session key must be established for a short-time secure communication between two parties where a new key is established for every new session. We have considered various advanced cryptographic calculations like non-revertible one-way hash function, Rivest-Shamir-Adelman (RSA), Elliptic Curve Cryptography (ECC), and chaotic maps cryptosystem. Despite the fact that both ECC and RSA cryptosystems offer an equal level of security, ECC is additionally advantageous as compared to RSA with respect to computational efficiency [2]. An Internet of Things (IoT) is composed of a vast number of small and large devices that are using the internet for sharing data across the nodes of different networks. In an IoT environment, TMIS can serve patients to save time by remotely accessing consultants and doctors by using the new generation of internet. IoT supports a collection of objects, devices, and networks in surroundings to develop a large number of smart applications. It can undeniably improve the identification and dissemination of information regarding emergency situations where appropriate medical aid is mandatory to save precious lives. IoT can also support integration mechanisms for all physical objects with embedded systems or cyber physical systems for monitoring patients at distant locations. It improves diagnosis at the patient's home for better usefulness and effectiveness regarding medical services [3]. IoT promises an attractive future networking prototype. Secure authentication and session key establishment schemes enable secure communication for health care services. A three-party password authentication key exchange (3-PAKE) scheme provides mutual authentication between doctor-patient-TS at the same time and hides identities from the adversary [4]. It helps in maintaining a secure link by using a common session key for specific communication.