The smart city environment includes dozens or even hundreds of various services in various areas of interest to users and aimed at improving the standard of living. These include services related to very sensitive aspects such as health, education, banking, and services that have a secret aspect. Cloud service providers need user data in order to be able to authenticate him in order to be able to access and access the desired service. Therefore, confidentiality, privacy and security are essential conditions for this type of communication. This type of complex and intrusive services leads to the need to provide effective solutions and mechanisms for authentication processes based on digital identity information. The process of building and managing trust between service providers and users needs a system of standards, so this paper provides a framework based on the archived behavior of users and cloud service providers operating within the approved trust circle in a smart environment based on the blockchain and its advantages in reliability, transparency and decentralization, while providing a mathematical model for evaluating and calculating trust standards for all subscribers as a basis for completing the authentication process and accessing services. © 2023 IEEE.