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Nowadays, recommendation systems are widely used, and it is a very difficult issue to solve the cold-start problem. Recent studies shows that the introduction of social network relationships can alleviate the cold-start problem of the recommendation system. However, some of these algorithms have higher requirements for implementation scenarios, and some cannot guarantee user information security. In our study, we propose a matrix factorization recommendation system method based on homomorphic encryption and social network. The method introduces the sum of preference information of cold-start user neighbors as prior knowledge into the recommendation system to solved the problem of insufficient information for cold start users. In addition, the method uses Pallier homomorphic encryption algorithm to ensure the security of user information and improve computational efficiency. Experiments on three real …