# Residue-based Label Protection Mechanisms in Vertical Logistic Regression

arXiv: https://arxiv.org/abs/2205.04166 · HTML: https://mlsanity.com/paper/2205.04166/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 9 May 2022.

## Builds on (most cited first, 10 of 10)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [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)
- [Feature Inference Attack on Model Predictions in Vertical Federated Learning](https://mlsanity.com/paper/2010.10152/) (2020)
- [Label Leakage and Protection in Two-party Split Learning](https://mlsanity.com/paper/2102.08504/) (2021)
- [Parallel Distributed Logistic Regression for Vertical Federated Learning without Third-Party Coordinator](https://mlsanity.com/paper/1911.09824/) (2019)
- [Collecting and Analyzing Multidimensional Data with Local Differential Privacy](https://mlsanity.com/paper/1907.00782/) (2019)
- [Asymmetrical Vertical Federated Learning](https://mlsanity.com/paper/2004.07427/) (2020)
- [Collecting and Analyzing Data from Smart Device Users with Local Differential Privacy](https://mlsanity.com/paper/1606.05053/) (2016)
- [Additively Homomorphical Encryption based Deep Neural Network for Asymmetrically Collaborative Machine Learning](https://mlsanity.com/paper/2007.06849/) (2020)

## Built on by (most cited first, 10 of 10)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [FedSDG-FS: Efficient and Secure Feature Selection for Vertical Federated Learning](https://mlsanity.com/paper/2302.10417/) (2023)
- [A Framework for Evaluating Privacy-Utility Trade-off in Vertical Federated Learning](https://mlsanity.com/paper/2209.03885/) (2022)
- [A Survey of Privacy Threats and Defense in Vertical Federated Learning: From Model Life Cycle Perspective](https://mlsanity.com/paper/2402.03688/) (2024)
- [Eliminating Label Leakage in Tree-Based Vertical Federated Learning](https://mlsanity.com/paper/2307.10318/) (2023)
- [Hyperparameter Optimization for SecureBoost via Constrained Multi-Objective Federated Learning](https://mlsanity.com/paper/2404.04490/) (2024)
- [SecureBoost Hyperparameter Tuning via Multi-Objective Federated Learning](https://mlsanity.com/paper/2307.10579/) (2023)
- [Multimodal Federated Learning: A Survey through the Lens of Different FL Paradigms](https://mlsanity.com/paper/2505.21792/) (2025)
- [VTarbel: Targeted Label Attack with Minimal Knowledge on Detector-enhanced Vertical Federated Learning](https://mlsanity.com/paper/2507.14625/) (2025)
- [LEA: Label Enumeration Attack in Vertical Federated Learning](https://mlsanity.com/paper/2603.03777/) (2026)

## Abstract (arXiv)

Federated learning (FL) enables distributed participants to collaboratively learn a global model without revealing their private data to each other. Recently, vertical FL, where the participants hold the same set of samples but with different features, has received increased attention. This paper first presents one label inference attack method to investigate the potential privacy leakages of the vertical logistic regression model. Specifically, we discover that the attacker can utilize the residue variables, which are calculated by solving the system of linear equations constructed by local dataset and the received decrypted gradients, to infer the privately owned labels. To deal with this, we then propose three protection mechanisms, e.g., additive noise mechanism, multiplicative noise mechanism, and hybrid mechanism which leverages local differential privacy and homomorphic encryption techniques, to prevent the attack and improve the robustness of the vertical logistic regression. model. Experimental results show that both the additive noise mechanism and the multiplicative noise mechanism can achieve efficient label protection with only a slight drop in model testing accuracy, furthermore, the hybrid mechanism can achieve label protection without any testing accuracy degradation, which demonstrates the effectiveness and efficiency of our protection techniques