AbstractSustainable Computing has advanced the technological evolution of the Internet and information-based communication technology. It is nowadays emerging in the form of the Cloud of Medical Things (CoMT) to develop smart healthcare systems. The academic community has lately made great strides for the development of security for the CoMT based application systems, such as e-healthcare systems, industrial automation systems, military surveillance systems, and so on. To the architecture of CoMT based Smart Environment, Chebyshev Chaotic-Map based single-user sign-in (S-USI) is found as a significant security-control mechanism. To ensure the fidelity, the S-USI assigns a unary-token to the legal users to access the various services, provided by a service provider over an IP-enabled distributed networks. Numerous authentication mechanisms have been presented for the cloud-based distributed networks. However, most of the schemes are still persuasible to security threats, such as user-anonymity, privileged-insider, mutual authentication, and replay type of attacks. This paper applies a sensor/sensor-tag based smart healthcare environment that uses S-USI to provide security and privacy. To strengthen the authentication process, a robust secure based S-USI mechanism and a well-formed coexistence protocol proof for pervasive services in the cloud are proposed. Using the formal security analysis, the prominence of the proposed strategies is proven to show the security efficiency of proposed S-USI. From the formal verification, the comparison results demonstrate that the proposed S-USI consumes less computation overhead; and thus it can be more suitable for the telecare medical information systems.