# An Optimal Authentication Scheme through Dual Signature for the Internet of Medical Things
## 3 Related Work  
After its induction in the SET protocol, researchers have proposed various schemes based on dual signatures over the years. In 2008, [PERSON] et al. [17] put forward an offline micropayment mechanism based on the dual signature, in which they make sure a valid coin must be signed by both parties, i.e., issuers and coin owners. The limitation of this scheme is its high computational cost due to the employment of RSA encryption. An authentication scheme for the wireless network was proposed in [18], which comprises two stages, i.e., authentication in the Internet Key Exchange (IKE) based on a dual signature involves stage 1. In stage 2, a different session is generated between two wireless nodes without affecting stage 1. This scheme results in the sender's authentication, provides confidentiality of user sessions, and is resistant to replay attacks. The drawback of the designed approach is that authentication using the dual signature in stage 1 results in high computational overhead. A dual signature scheme based on the elliptic curve digital signature algorithm (ECDSA) in the SET protocol was proposed in [12]. This approach joins two messages that are meant for distinct recipients. One receiving party is unaware of the other recipient's information. However, it still suffers from high computational costs and the communication overhead due to the use of ECDSA. [PERSON] et al. [19] designed a multi-domain authentication protocol based on the dual signature, which allows direct authentication between two parties while excluding the need for a third party. The developed approach provides not only privacy but also secure authentication for multiple domains. Furthermore, this scheme provides faster access to resources, thereby solving bottleneck issues in the network and providing key escrow resilience in identity-based authentication protocols. This scheme's performance is its major drawback because it results in higher computational and communication costs. In [20], an online internet voting protocol scheme based on dual signature was put forth, enabling the voters to cast their ballot by simply scanning their thumbprint. Following the designed approach, once a voter has been successfully authenticated from the database, he can acquire a poll. When a voter submits a vote, the system performs these three operations (1) generates a dual signature (2) authenticates server envelope and (3) voting server envelope. The system sends an authentication server envelope concatenated with the voting server envelope to the authentication server, using the transmission link. The received envelope is validated by the authentication server, which then delivers it to the voting server for the final tally. This designed scheme provides key properties such as privacy, anonymity, eligibility, and verifiability, which are necessary constraints for any online voting system. Moreover, this approach is better than a blind signature regarding security and computational costs. However, this scheme's primary problem is the inability to display voting information that includes the voter's identity unless both the authentication server and the voting server desire to know this information. An elliptic curve digital signature algorithm (ECDSA) for IoMT based on dual signature was proposed by [PERSON] et al. [21] to ensure privacy and authentication. This scheme utilizes ECDSA to compute signatures and simplify the process; however, instead of IoMT devices, signature verification is performed by edge computing devices because it is a task that demands substantial computational resources. The advantage of this work is message authentication, data privacy, and security against data tampering. This work exhibits flaws in the form of high computational costs and communication overhead, and a lack of formal security validation. [PERSON] and [PERSON] [22] proposed a dual blind signature for quantum computing; however, the proposed scheme is not appropriate for IoMT devices with resource constraints. Similarly, [PERSON] et al.