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

arXiv: https://arxiv.org/abs/2008.08753 · HTML: https://mlsanity.com/paper/2008.08753/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2020.

## Built on by (most cited first, 30 of 32)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [FATE-LLM: A Industrial Grade Federated Learning Framework for Large Language Models](https://mlsanity.com/paper/2310.10049/) (2023)
- [A Survey on Vertical Federated Learning: From a Layered Perspective](https://mlsanity.com/paper/2304.01829/) (2023)
- [A Survey of Trustworthy Federated Learning with Perspectives on Security, Robustness, and Privacy](https://mlsanity.com/paper/2302.10637/) (2023)
- [Reducing Communication for Split Learning by Randomized Top-k Sparsification](https://mlsanity.com/paper/2305.18469/) (2023)
- [Exploiting Data Sparsity in Secure Cross-Platform Social Recommendation](https://mlsanity.com/paper/2202.07253/) (2022)
- [A Hybrid Self-Supervised Learning Framework for Vertical Federated Learning](https://mlsanity.com/paper/2208.08934/) (2022)
- [A Survey for Federated Learning Evaluations: Goals and Measures](https://mlsanity.com/paper/2308.11841/) (2023)
- [A Framework for Evaluating Privacy-Utility Trade-off in Vertical Federated Learning](https://mlsanity.com/paper/2209.03885/) (2022)
- [BadVFL: Backdoor Attacks in Vertical Federated Learning](https://mlsanity.com/paper/2304.08847/) (2023)
- [Is Vertical Logistic Regression Privacy-Preserving? A Comprehensive Privacy Analysis and Beyond](https://mlsanity.com/paper/2207.09087/) (2022)
- [A Survey of Privacy Threats and Defense in Vertical Federated Learning: From Model Life Cycle Perspective](https://mlsanity.com/paper/2402.03688/) (2024)
- [Towards Secure and Practical Machine Learning via Secret Sharing and Random Permutation](https://mlsanity.com/paper/2108.07463/) (2021)
- [EFMVFL: An Efficient and Flexible Multi-party Vertical Federated Learning without a Third Party](https://mlsanity.com/paper/2201.06244/) (2022)
- [Privacy-Preserving Diffusion Model Using Homomorphic Encryption](https://mlsanity.com/paper/2403.05794/) (2024)
- [Vertical Federated Learning in Practice: The Good, the Bad, and the Ugly](https://mlsanity.com/paper/2502.08160/) (2025)
- [UniFed: All-In-One Federated Learning Platform to Unify Open-Source Frameworks](https://mlsanity.com/paper/2207.10308/) (2022)
- [Tree-based Models for Vertical Federated Learning: A Survey](https://mlsanity.com/paper/2504.02285/) (2025)
- [From Risk to Resilience: Towards Assessing and Mitigating the Risk of Data Reconstruction Attacks in Federated Learning](https://mlsanity.com/paper/2512.15460/) (2025)
- [SecureBoost+: Large Scale and High-Performance Vertical Federated Gradient Boosting Decision Tree](https://mlsanity.com/paper/2110.10927/) (2021)
- [Exploiting Unstructured Sparsity in Fully Homomorphic Encrypted DNNs](https://mlsanity.com/paper/2503.09184/) (2025)
- [Hybrid FedGraph: An efficient hybrid federated learning algorithm using graph convolutional neural network](https://mlsanity.com/paper/2404.09443/) (2024)
- [PackVFL: Efficient HE Packing for Vertical Federated Learning](https://mlsanity.com/paper/2405.00482/) (2024)
- [Scalable and Sparsity-Aware Privacy-Preserving K-means Clustering with Application to Fraud Detection](https://mlsanity.com/paper/2208.06093/) (2022)
- [HGV4Risk: Hierarchical Global View-guided Sequence Representation Learning for Risk Prediction](https://mlsanity.com/paper/2211.07956/) (2022)
- [Active-Passive Federated Learning for Vertically Partitioned Multi-view Data](https://mlsanity.com/paper/2409.04111/) (2024)
- [Stalactite: Toolbox for Fast Prototyping of Vertical Federated Learning Systems](https://mlsanity.com/paper/2409.15558/) (2024)
- [VTarbel: Targeted Label Attack with Minimal Knowledge on Detector-enhanced Vertical Federated Learning](https://mlsanity.com/paper/2507.14625/) (2025)
- [Secure Sparse Matrix Multiplications and their Applications to Privacy-Preserving Machine Learning](https://mlsanity.com/paper/2510.14894/) (2025)
- [Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation](https://mlsanity.com/paper/2602.15996/) (2026)

## Abstract (arXiv)

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.