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.

翻译：推荐系统的普及也给用户和商家带来了隐私担忧，因为中心化平台会尽可能多地收集他们的数据。为了保护数据隐私，我们提出了PADER：一种基于Paillier的安全去中心化社交推荐系统。在该系统中，用户和商家作为节点构成去中心化网络。推荐模型的训练和推理以安全、去中心化的方式执行，无需中心化平台的参与。为此，我们将Paillier密码系统应用于SoReg（社交正则化）模型，该模型同时利用用户评分和社交关系。我们将SoReg模型视为一个两方安全多项式求值问题，并观察到简单的二分计算可能导致效率低下。为了提高效率，我们设计了安全加法和乘法协议以支持对任意算术电路的安全计算，同时提出了一种适用于实值多项式计算的最优数据打包方案。实验结果表明，我们的方法仅需约一秒即可完成对拥有数百条评分记录的单个用户的一次迭代，且使用约50万条评分数据进行一轮训练仅需不到3小时，这证明该方法在实际应用中具有可行性。代码发布于 https://github.com/GarminQ/PADER。