基于帕特里亚加密的去中心化推荐系统，保护用户隐私且高效。

The prevalence of recommendation systems also brings privacy concerns to both the users and the sellers, as centralized platforms collect as much data as possible from them. To keep the data private, we propose PADER: a Paillier-based secure decentralized social recommendation system. In this system, the users and the sellers are nodes in a decentralized network. The training and inference of the recommendation model are carried out securely in a decentralized manner, without the involvement of a centralized platform. To this end, we apply the Paillier cryptosystem to the SoReg (Social Regularization) model, which exploits both user's ratings and social relations. We view the SoReg model as a two-party secure polynomial evaluation problem and observe that the simple bipartite computation may result in poor efficiency. To improve efficiency, we design secure addition and multiplication protocols to support secure computation on any arithmetic circuit, along with an optimal data packing scheme that is suitable for the polynomial computations of real values. Experiment results show that our method only takes about one second to iterate through one user with hundreds of ratings, and training with ~500K ratings for one epoch only takes <3 hours, which shows that the method is practical in real applications. The code is available at https://github.com/GarminQ/PADER.