Initial import

Author: sloede

.gitignore

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+**/*.pdf

.zenodo.json

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+{
+    "license": "MIT",
+    "title": "Reproducibility repository for Secure numerical simulations using fully homomorphic encryption",
+    "upload_type": "software",
+    "creators": [
+        {
+            "affiliation": "High-Performance Scientific Computing, University of Augsburg, Germany",
+            "name": "Kholod, Arseniy",
+            "orcid": "0009-0002-9457-4867"
+        },
+        {
+            "affiliation": "Duality Technologies, Inc., United States",
+            "name": "Polyakov, Yuriy",
+            "orcid": "0000-0002-5566-3763"
+        },
+        {
+            "affiliation": "High-Performance Scientific Computing, University of Augsburg, Germany",
+            "name": "Schlottke-Lakemper, Michael",
+            "orcid": "0000-0002-3195-2536"
+        }
+    ],
+    "access_right": "open"
+}
+

LICENSE.md

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+MIT License
+
+Copyright (c) 2024 Arseniy Kholod, Yuriy Polyakov, Michael Schlottke-Lakemper
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

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+# Secure numerical simulations using fully homomorphic encryption 
+
+[![License: MIT](https://img.shields.io/badge/License-MIT-success.svg)](https://opensource.org/licenses/MIT)
+[![DOI](https://zenodo.org/badge/DOI/10.5281/zenodo.TODO.svg)](https://doi.org/10.5281/zenodo.TODO)
+
+This repository contains information and code to reproduce the results presented in the
+article
+```bibtex
+@online{kholod2024secure,
+  title={{S}ecure numerical simulations using fully homomorphic encryption},
+  author={Kholod, Arseniy and Polyakov, Yuriy and Schlottke-Lakemper, Michael},
+  year={2023},
+  month={11},
+  doi={10.48550/arXiv.TODO},
+  eprint={TODO},
+  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
+```bibtex
+@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.TODO}
+}
+```
+
+
+## Abstract
+
+Data privacy is a significant concern in many environments today.
+This is particularly true if sensitive information, e.g.,  engineering, medical, or
+financial data, is to be processed on potentially insecure systems, as it is often the
+case in cloud computing. Fully homomorphic encryption (FHE) offers a potential solution
+to this problem, as it allows for secure computations on encrypted data. In this paper,
+we investigate the viability of using FHE for privacy-preserving numerical simulations of partial
+differential equations. We first give an overview of the CKKS scheme, a popular FHE
+method for computations with real numbers. This is followed by an introduction of our
+Julia packages OpenFHE.jl and SecureArithmetic.jl, which provide a Julia wrapper for the
+C++ library OpenFHE and offer a user-friendly interface for secure arithmetic
+operations. We then present a performance analysis of the CKKS scheme within OpenFHE,
+focusing on the error and efficiency of different FHE operations. Finally, we
+demonstrate the application of FHE to secure numerical simulations by implementing two
+finite difference schemes for the linear advection equation using the
+SecureArithmetic.jl package. Our results show that FHE can be used to perform
+cryptographically secure numerical simulations, but that the error and efficiency of FHE
+operations must be carefully considered when designing applications.
+
+
+## Numerical experiments
+
+The numerical experiments presented in the paper use
+[SecureArithmetic.jl](https://github.com/hpsc-lab/SecureArithmetic.jl).
+To reproduce the numerical experiments using SecureArithmetic.jl, you need to install
+[Julia](https://julialang.org/).
+
+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.
+
+
+## Authors
+
+- Arseniy Kholod (University of Augsburg, Germany)
+- [Yuriy Polyakov](https://ypolyakov.gitlab.io/) (Duality Technologies, Inc., United States)
+- [Michael Schlottke-Lakemper](https://lakemper.eu) (University of Augsburg, Germany)
+
+
+## License
+The contents of this repository are available under the [MIT license](LICENSE.md). If you reuse our
+code or data, please also cite us (see above).
+
+
+## Disclaimer
+
+Everything is provided as is and without warranty. Use at your own risk!