Logistic Regression (LR) is the mos

Logistic Regression (LR) is the most widely used machine learning model in industry for its efficiency, robustness, and interpretability. Due to the problem of data isolation and the requirement of high model performance, many applications in industry call for building a secure and efficient LR model for multiple parties. Most existing work uses either Homomorphic Encryption (HE) or Secret Sharing (SS) to build secure LR. HE based methods can deal with high-dimensional sparse features, but they incur potential security risks. 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 achieves both efficiency and security. We then present the distributed implementation of CAESAR for scalability requirement. We have deployed CAESAR in a risk control task and conducted comprehensive experiments. Our experimental results show that CAESAR improves the state-of-the-art model by around 130 times.