Modern machine and deep learning systems are becoming part of high-performance cloud services and technologies. It is extremely important to understand that in systems such as recommendation systems, data is stored on local machines, and the trained system (matrix) is located in the cloud vendor, for example, in AWS or Google Cloud. Data on local machines can be updated or deleted. Local machines are often networked, which requires the use of synchronization methods and specialized protocols for the exchange of such information. And the central server is used as a single computer center for machine learning tasks. At the same time, it is necessary to control both the integrity of local data and their relevance with respect to other local machines. An important aspect is that the data center in the cloud should not know about our data, that is, we must be able to transmit them in encrypted form. At the same time, the deep learning model should be able to work with such encrypted data and send us the answers in encrypted form too. All this should be calculated in polynomial time, that is, quickly enough. For encryption purposes, it is proposed to use homomorphic algorithms. This report attempts to combine two promising modern paradigms for solving similar problems: machine intelligence and distributed ledger. For the purposes of distributed deep learning in relation to recommender systems, this symbiosis shows very serious practical prospects.