# Is Vertical Logistic Regression Privacy-Preserving? A Comprehensive Privacy Analysis and Beyond

arXiv: https://arxiv.org/abs/2207.09087 · HTML: https://mlsanity.com/paper/2207.09087/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 80 references that are in the map.
- First posted on arXiv 19 Jul 2022.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [LEAF: A Benchmark for Federated Settings](https://mlsanity.com/paper/1812.01097/) (2018)
- [How To Backdoor Federated Learning](https://mlsanity.com/paper/1807.00459/) (2018)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [Federated Learning for Mobile Keyboard Prediction](https://mlsanity.com/paper/1811.03604/) (2018)
- [Federated Optimization: Distributed Machine Learning for On-Device Intelligence](https://mlsanity.com/paper/1610.02527/) (2016)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [Exploiting Unintended Feature Leakage in Collaborative Learning](https://mlsanity.com/paper/1805.04049/) (2018)
- [Differentially Private Federated Learning: A Client Level Perspective](https://mlsanity.com/paper/1712.07557/) (2017)
- [iDLG: Improved Deep Leakage from Gradients](https://mlsanity.com/paper/2001.02610/) (2020)
- [Analyzing Federated Learning through an Adversarial Lens](https://mlsanity.com/paper/1811.12470/) (2018)
- [Deep Models Under the GAN: Information Leakage from Collaborative Deep Learning](https://mlsanity.com/paper/1702.07464/) (2017)
- [See through Gradients: Image Batch Recovery via GradInversion](https://mlsanity.com/paper/2104.07586/) (2021)
- [A Little Is Enough: Circumventing Defenses For Distributed Learning](https://mlsanity.com/paper/1902.06156/) (2019)
- [Beyond Inferring Class Representatives: User-Level Privacy Leakage From Federated Learning](https://mlsanity.com/paper/1812.00535/) (2018)
- [A Hybrid Approach to Privacy-Preserving Federated Learning](https://mlsanity.com/paper/1812.03224/) (2018)
- [Private federated learning on vertically partitioned data via entity resolution and additively homomorphic encryption](https://mlsanity.com/paper/1711.10677/) (2017)
- [SecureBoost: A Lossless Federated Learning Framework](https://mlsanity.com/paper/1901.08755/) (2019)
- [A Survey on Homomorphic Encryption Schemes: Theory and Implementation](https://mlsanity.com/paper/1704.03578/) (2017)
- [Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds](https://mlsanity.com/paper/1405.7085/) (2014)
- [Feature Inference Attack on Model Predictions in Vertical Federated Learning](https://mlsanity.com/paper/2010.10152/) (2020)
- [A generic framework for privacy preserving deep learning](https://mlsanity.com/paper/1811.04017/) (2018)

## Built on by (most cited first, 7 of 7)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [Vertical Federated Learning for Effectiveness, Security, Applicability: A Survey](https://mlsanity.com/paper/2405.17495/) (2024)
- [FedPass: Privacy-Preserving Vertical Federated Deep Learning with Adaptive Obfuscation](https://mlsanity.com/paper/2301.12623/) (2023)
- [A Survey of Privacy Threats and Defense in Vertical Federated Learning: From Model Life Cycle Perspective](https://mlsanity.com/paper/2402.03688/) (2024)
- [Online Vertical Federated Learning for Cooperative Spectrum Sensing](https://mlsanity.com/paper/2312.11363/) (2023)
- [Mutual Information Regularization for Vertical Federated Learning](https://mlsanity.com/paper/2301.01142/) (2023)
- [Multimodal Federated Learning: A Survey through the Lens of Different FL Paradigms](https://mlsanity.com/paper/2505.21792/) (2025)

## Abstract (arXiv)

We consider vertical logistic regression (VLR) trained with mini-batch gradient descent -- a setting which has attracted growing interest among industries and proven to be useful in a wide range of applications including finance and medical research. We provide a comprehensive and rigorous privacy analysis of VLR in a class of open-source Federated Learning frameworks, where the protocols might differ between one another, yet a procedure of obtaining local gradients is implicitly shared. We first consider the honest-but-curious threat model, in which the detailed implementation of protocol is neglected and only the shared procedure is assumed, which we abstract as an oracle. We find that even under this general setting, single-dimension feature and label can still be recovered from the other party under suitable constraints of batch size, thus demonstrating the potential vulnerability of all frameworks following the same philosophy. Then we look into a popular instantiation of the protocol based on Homomorphic Encryption (HE). We propose an active attack that significantly weaken the constraints on batch size in the previous analysis via generating and compressing auxiliary ciphertext. To address the privacy leakage within the HE-based protocol, we develop a simple-yet-effective countermeasure based on Differential Privacy (DP), and provide both utility and privacy guarantees for the updated algorithm. Finally, we empirically verify the effectiveness of our attack and defense on benchmark datasets. Altogether, our findings suggest that all vertical federated learning frameworks that solely depend on HE might contain severe privacy risks, and DP, which has already demonstrated its power in horizontal federated learning, can also play a crucial role in the vertical setting, especially when coupled with HE or secure multi-party computation (MPC) techniques.