New submission: Secure numerical simulations using fully homomorphic encryption
Together with
Yuriy Polyakov from Duality Technologies Inc. we have submitted our paper "Secure numerical simulations using fully homomorphic encryption". Thank you very much, Yuriy, for the productive and enjoyable collaboration on this project! ? 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.
Abstract
Together with Erik Faulhaber, Sven Berger, Christian Wei?enfels und Gregor Gassner,?we have submitted our paper "Robust and efficient pre-processing techniques for particle-based methods including dynamic boundary generation".
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Abstract
Obtaining high-quality particle distributions for stable and accurate particle-based simulations poses significant challenges, especially for complex geometries. We introduce a preprocessing technique for 2D and 3D geometries, optimized for smoothed particle hydrodynamics (SPH) and other particle-based methods. Our pipeline begins with the generation of a resolution-adaptive point cloud near the geometry's surface employing a face-based neighborhood search. This point cloud forms the basis for a signed distance field, enabling efficient, localized computations near surface regions. To create an initial particle configuration, we apply a hierarchical winding number method for fast and accurate inside-outside segmentation. Particle positions are then relaxed using an SPH-inspired scheme, which also serves to pack boundary particles. This ensures full kernel support and promotes isotropic distributions while preserving the geometry interface. By leveraging the meshless nature of particle-based methods, our approach does not require connectivity information and is thus straightforward to integrate into existing particle-based frameworks. It is robust to imperfect input geometries and memory-efficient without compromising performance. Moreover, our experiments demonstrate that with increasingly higher resolution, the resulting particle distribution converges to the exact geometry.