# Neural Network Training With Homomorphic Encryption

arXiv: https://arxiv.org/abs/2012.13552 · HTML: https://mlsanity.com/paper/2012.13552/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2020.

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

- [SoK: Privacy-preserving Deep Learning with Homomorphic Encryption](https://mlsanity.com/paper/2112.12855/) (2021)
- [Wildest Dreams: Reproducible Research in Privacy-preserving Neural Network Training](https://mlsanity.com/paper/2403.03592/) (2024)
- [ReBoot: Encrypted Training of Deep Neural Networks with CKKS Bootstrapping](https://mlsanity.com/paper/2506.19693/) (2025)
- [SoK: Data Minimization in Machine Learning](https://mlsanity.com/paper/2508.10836/) (2025)
- [N-Parties Private Structure and Parameter Learning for Sum-Product Networks](https://mlsanity.com/paper/2510.05946/) (2025)
- [Revisiting ML Training under Fully Homomorphic Encryption: Convergence Guarantees, Differential Privacy, and Efficient Algorithms](https://mlsanity.com/paper/2605.27782/) (2026)

## Abstract (arXiv)

We introduce a novel method and implementation architecture to train neural networks which preserves the confidentiality of both the model and the data. Our method relies on homomorphic capability of lattice based encryption scheme. Our procedure is optimized for operations on packed ciphertexts in order to achieve efficient updates of the model parameters. Our method achieves a significant reduction of computations due to our way to perform multiplications and rotations on packed ciphertexts from a feedforward network to a back-propagation network. To verify the accuracy of the training model as well as the implementation feasibility, we tested our method on the Iris data set by using the CKKS scheme with Microsoft SEAL as a back end. Although our test implementation is for simple neural network training, we believe our basic implementation block can help the further applications for more complex neural network based use cases.