## 2 Related Works  
E2E communication security has been discussed in many research papers. In 2012, [PERSON] et al. [9] introduced a design of E2E key exchange and encryption protocol for accelerated satellite networks. Another E2E authentication scheme for wearable health monitoring systems proposed by [PERSON] et al. [10] could assure a secure communication environment for patients and service providers. In [PERSON] et al. 's [11] work, a session key agreement scheme was proposed for E2E security in time-synchronized networks. [PERSON] et al. [12] also conducted research on E2E security authentication protocol of narrowband internet of things (NB-IoT) for a smart grid based on the physical unclonable function. [PERSON] [13] presented a two-factor authentication mechanism for E2E healthcare communications in wireless body sensor networks (WBSNs). [PERSON] et al. [14] proposed a client-server E2E key exchange solution for IoT communications in the application layer. A multi-data multi-user E2E encryption scheme designed by [PERSON] and [PERSON] [15] provided an access control mechanism for electronic health records stored in clouds. In general, there was no secure cross-server solution for E2E user communications introduced in these works. In recent years, security issues and authentication solutions in the healthcare systems have become prevalent and have attracted a lot of attention from the scientific community [16]. [PERSON] and [PERSON] [17] designed a mutual authentication protocol for cloud-based medical healthcare systems, which addresses several security issues found in Ref. [18], such as smart device stolen attack, server spoofing attack, etc. In another work, a multi-factor fast authentication protocol with patient privacy protection for telecare medical information systems (TMISs) was proposed by [PERSON] et al. [19]. [PERSON] et al. [20] presented an improved authentication protocol, which resolved some weaknesses of [PERSON] et al. 's [21] scheme for smart healthcare in WBSNs. Recently, [PERSON] et al. [22] proposed a three-factor key agreement scheme for multiple healthcare services in 6G networks. Although the work was proven to withstand multiple well-known attacks, I found it was designed without the biometrics update function. The Rabin decryption operation in their protocol was no faster than the one of the RSA cryptosystem [23]. [PERSON] et al. [24] proposed another anonymous three-factor authentication protocol with costly fuzzy extraction operation employed. [PERSON] et al. [25] introduced a multi-server key agreement protocol with patient anonymity for 5G IoT healthcare systems. In the protocol, I found that a public parameter (\(N_{i}\)) of the first conveyed transcript was revealed to the public. There was also no timestamp employed in their work, which is not free from denial of service (DoS) attacks. [PERSON] et al. [26] proposed a password-based user authentication scheme using a smart card based on extended chaotic maps. The server in their protocol stores an additional value (\(SB_{i}\)) after the authentication procedure is complete. This would not be robust against desynchronization problems. Although [PERSON] et al. [25] and [PERSON] et al. [26] can provide user anonymity, their works cannot achieve user untraceability, as the messages in their proposals contain some fixed parameters; the adversaries may guess the identity of the user based on these values. In addition, [PERSON] et al. [25] cannot prevent lost smart card attacks, as unmasked user credentials are stored on smart cards directly. [PERSON] and [PERSON] [27] designed a secure ECC-based two-factor remote authentication protocol for cyber-physical system applications. The two-factor authentication mechanism in the protocol presented some security concerns that need addressing. The communication efficiency of their design is not very high considering the four message transcripts conveyed during the login and authentication process.