This week, our team published the paper "Secure numerical simulations using fully homomorphic encryption" in Computer Physics Communications. It brings together two fields not often combined: scientific computing and cryptography. In the work, we show how numerical simulations can be performed without ever revealing the underlying data, by using fully homomorphic encryption (FHE). This approach makes it possible to protect highly sensitive information - such as patient data or financial records - even when computations are carried out on untrusted cloud systems. To the best of our knowledge, this is the first time that homomorphic encryption methods have been applied in the context of scientific computing.

While the publication primarily addresses fundamental research questions, the results highlight an important direction for the future: combining high-performance scientific computing with modern cryptography to enable novel, privacy-preserving applications. Beyond its scientific contribution, the work also reflects on our lab’s commitment to open science. All source code and data required to reproduce the results are openly available in a citable repository.

👏 We would like to congratulate first author Arseniy Kholod, who accomplished this work already at the Bachelor level, and thank Yuriy Polyakov and Duality Technologies for their excellent collaboration, which made this paper possible.

Abstract

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.