This repository contains information and code to reproduce the results presented in the article
@article{kholod2026secure,
title={{S}ecure numerical simulations using fully homomorphic encryption},
author={Arseniy Kholod and Yuriy Polyakov and Michael Schlottke-Lakemper},
journal = {Computer Physics Communications},
volume = {318},
pages = {109868},
year={2026},
doi={10.1016/j.cpc.2025.109868},
eprint={2410.21824},
eprinttype={arxiv},
eprintclass={math.NA}
}If you find these results useful, please cite the article mentioned above. If you use the implementations provided here, please also cite this repository as
@misc{kholod2024secureRepro,
title={Reproducibility repository for
"{S}ecure numerical simulations using fully homomorphic encryption"},
author={Kholod, Arseniy and Polyakov, Yuriy and Schlottke-Lakemper, Michael},
year= {2024},
howpublished={\url{https://github.com/hpsc-lab/paper-2024-secure_numerical_simulations}},
doi={10.5281/zenodo.14003844}
}Data privacy is a significant concern when using numerical simulations for sensitive information such as medical, financial, or engineering data---especially in untrusted environments like public cloud infrastructures. Fully homomorphic encryption (FHE) offers a promising solution for achieving data privacy by enabling secure computations directly on encrypted data. Aimed at computational scientists, this work explores the viability of FHE-based, privacy-preserving numerical simulations of partial differential equations. The presented approach utilizes the Cheon-Kim-Kim-Song (CKKS) scheme, a widely used FHE method for approximate arithmetic on real numbers. Two Julia packages are introduced, OpenFHE.jl and SecureArithmetic.jl, which wrap the OpenFHE C++ library to provide a convenient interface for secure arithmetic operations. With these tools, the accuracy and performance of key FHE operations in OpenFHE are evaluated, and implementations of finite difference schemes for solving the linear advection equation with encrypted data are demonstrated. The results show that cryptographically secure numerical simulations are possible, but that careful consideration must be given to the computational overhead and the numerical errors introduced by using FHE. An analysis of the algorithmic restrictions imposed by FHE highlights potential challenges and solutions for extending the approach to other models and methods. While it remains uncertain how broadly the approach can be generalized to more complex algorithms due to CKKS limitations, these findings lay the groundwork for further research on privacy-preserving scientific computing.
The numerical experiments presented in the paper use SecureArithmetic.jl. To reproduce the numerical experiments using SecureArithmetic.jl, you need to install Julia.
The subfolder code of this repository contains a README.md file with
instructions to reproduce the numerical experiments.
Both subfolders also include the result data and scripts for postprocessing.
All numerical experiments were carried out using Julia v1.10.4.
- Arseniy Kholod (University of Augsburg, Germany)
- Yuriy Polyakov (Duality Technologies, Inc., United States)
- Michael Schlottke-Lakemper (University of Augsburg, Germany)
The contents of this repository are available under the MIT license. If you reuse our code or data, please also cite us (see above).
Everything is provided as is and without warranty. Use at your own risk!