Smart solutions are becoming increasingly popular, this is caused by both the increase in the quality and quantity of capabilities of Internet of Things devices, and the development of methods and approaches in organizing distributed networks, in addition, the demand for such solutions is also growing. When a solution such as a Smart City is fully developed, a large amount of confidential data or data of critical importance will be transmitted and processed in its network; if an intruder gains access to this data, or is able to change or destroy it, this can lead to various kinds of problems. In this paper, we investigate the fog computing network and its security, and it is established that fully homomorphic encryption schemes can be used to ensure the best data privacy. As a result, the architecture of a confidential data analysis system in a fog computing network for low-power devices based on the TFHE scheme was obtained, for this purpose, the quantization of values was investigated, as well as the logistic regression algorithm for confidential data processing.