When Homomorphic Encryption Marries Secret Sharing: Secure Large-Scale Sparse Logistic Regression and Applications in Risk Control

Logistic Regression (LR) is the most widely used machine learning model in industry due to its efficiency, robustness, and interpretability. Meanwhile, with the problem of data isolation and the requirement of high model performance, building secure and efficient LR model for multi-parties becomes a hot topic for both academia and industry. Existing works mainly employ either Homomorphic Encryption (HE) or Secret Sharing (SS) to build secure LR. HE based methods can deal with high-dimensional sparse features, but they may suffer potential security risk. In contrast, SS based methods have provable security but they have efficiency issue under high-dimensional sparse features. In this paper, we first present CAESAR, which combines HE and SS to build seCure lArge-scalE SpArse logistic Regression model and thus has the advantages of both efficiency and security. We then present the distributed implementation of CAESAR for scalability requirement. We finally deploy CAESAR into a risk control task and conduct comprehensive experiments to study the efficiency of CAESAR.