# Efficient Batch Homomorphic Encryption for Vertically Federated XGBoost

arXiv: https://arxiv.org/abs/2112.04261 · HTML: https://mlsanity.com/paper/2112.04261/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 11 of 11)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [The Future of Digital Health with Federated Learning](https://mlsanity.com/paper/2003.08119/) (2020)
- [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019)
- [TernGrad: Ternary Gradients to Reduce Communication in Distributed Deep Learning](https://mlsanity.com/paper/1705.07878/) (2017)
- [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)
- [Federated Forest](https://mlsanity.com/paper/1905.10053/) (2019)
- [A Quasi-Newton Method Based Vertical Federated Learning Framework for Logistic Regression](https://mlsanity.com/paper/1912.00513/) (2019)
- [Federated Doubly Stochastic Kernel Learning for Vertically Partitioned Data](https://mlsanity.com/paper/2008.06197/) (2020)
- [Privacy-Preserving Gradient Boosting Decision Trees](https://mlsanity.com/paper/1911.04209/) (2019)
- [SecureGBM: Secure Multi-Party Gradient Boosting](https://mlsanity.com/paper/1911.11997/) (2019)

## Built on by (most cited first, 6 of 6)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [URVFL: Undetectable Data Reconstruction Attack on Vertical Federated Learning](https://mlsanity.com/paper/2404.19582/) (2024)
- [Vertical Federated Learning Hybrid Local Pre-training](https://mlsanity.com/paper/2405.11884/) (2024)
- [DictPFL: Efficient and Private Federated Learning on Encrypted Gradients](https://mlsanity.com/paper/2510.21086/) (2025)
- [SenseCrypt: Sensitivity-guided Selective Homomorphic Encryption for Joint Federated Learning in Cross-Device Scenarios](https://mlsanity.com/paper/2508.04100/) (2025)
- [Exploring New Frontiers in Vertical Federated Learning: the Role of Saddle Point Reformulation](https://mlsanity.com/paper/2602.15996/) (2026)

## Abstract (arXiv)

More and more orgainizations and institutions make efforts on using external data to improve the performance of AI services. To address the data privacy and security concerns, federated learning has attracted increasing attention from both academia and industry to securely construct AI models across multiple isolated data providers. In this paper, we studied the efficiency problem of adapting widely used XGBoost model in real-world applications to vertical federated learning setting. State-of-the-art vertical federated XGBoost frameworks requires large number of encryption operations and ciphertext transmissions, which makes the model training much less efficient than training XGBoost models locally. To bridge this gap, we proposed a novel batch homomorphic encryption method to cut the cost of encryption-related computation and transmission in nearly half. This is achieved by encoding the first-order derivative and the second-order derivative into a single number for encryption, ciphertext transmission, and homomorphic addition operations. The sum of multiple first-order derivatives and second-order derivatives can be simultaneously decoded from the sum of encoded values. We are motivated by the batch idea in the work of BatchCrypt for horizontal federated learning, and design a novel batch method to address the limitations of allowing quite few number of negative numbers. The encode procedure of the proposed batch method consists of four steps, including shifting, truncating, quantizing and batching, while the decoding procedure consists of de-quantization and shifting back. The advantages of our method are demonstrated through theoretical analysis and extensive numerical experiments.