This paper presents a proposal for an authentication scheme for smart building systems and environments based on blockchain, its positive features, and fog computing. The most important feature that can be distinguished in the submitted proposal is its adoption of the principle of decentralization in contrast to traditional centralized documentation protocols, i.e. the proposed authentication system in which users and smart devices are implemented in a distributed and decentralized manner on the blockchain,  that will provide a solution to a significant problem of low overall efficiency of the authentication process caused by a bottleneck in such important areas as computing capacity as well as centralized storage of a single authentication authority in the traditional model. There are also benefits from adding fog computing, and because it has higher computing and storage capabilities, it makes the data processing process more efficient, faster, more streamlined, and in line with the common necessities of the real-time IoT environment. The proposed scheme also provides solutions to protect the privacy of user data and increase the level of confidentiality, protection, and security, since a mysterious extractor was used to increase the confidentiality of the proposed model of the authentication system. Comparing a set of security schemes and conducting a security and performance analysis of the proposed scheme, the comparisons showed that the scheme can be characterized as having a good security level and an important efficiency level. The paper focused on specific aspects design of the authentication system, such as the registration and authentication process of all network entities, regardless of the specifics of the implementation of blockchain smart contracts.