SecureArithmetic.jl

SecureArithmetic.jl is a Julia package for performing cryptographically secure arithmetic operations using fully homomorphic encryption. It currently provides a backend for OpenFHE-secured computations using OpenFHE.jl, and an unencrypted backend for fast verification of a computation pipeline.

Getting started

Prerequisites

If you have not yet installed Julia, please follow the instructions for your operating system. SecureArithmetic.jl works with Julia v1.10 and later on Linux, macOS and Windows platforms.

Installation

Since SecureArithmetic.jl is a registered Julia package, you can install it by executing the following commands in the Julia REPL: julia julia> import Pkg; Pkg.add("SecureArithmetic") If you plan on running the examples in the examples directory, you also need to install OpenFHE.jl: julia julia> import Pkg; Pkg.add("OpenFHE")

Usage

The easiest way to get started is to run one of the examples from the examples directory by includeing them in Julia, e.g., ```julia julia> using SecureArithmetic

julia> include(joinpath(pkgdir(SecureArithmetic), "examples", "simplerealnumbers.jl"))

Creating OpenFHE context... CKKS scheme is using ring dimension 16384

================================================================================ Creating unencrypted context...

================================================================================ simplerealnumbers with an OpenFHE context Input x1: [0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0, 5.0] Input x2: [5.0, 4.0, 3.0, 2.0, 1.0, 0.75, 0.5, 0.25]

Results of homomorphic computations: x1 = [0.24999999999993638, 0.500000000000056, 0.7500000000000366, 0.9999999999999498, 2.0000000000000333, 3.0000000000000675, 3.9999999999999902, 4.99999999999997] x1 + x2 = [5.2499999999999485, 4.499999999999966, 3.7500000000000533, 3.0000000000000466, 3.000000000000019, 3.7499999999999836, 4.499999999999986, 5.249999999999975] x1 - x2 = [-4.749999999999893, -3.4999999999999805, -2.249999999999964, -0.9999999999998668, 0.9999999999999534, 2.249999999999984, 3.5000000000000973, 4.749999999999956] 4 * x1 = [1.0000000000004539, 1.9999999999998535, 3.000000000000176, 4.000000000000274, 7.999999999998697, 12.000000000000373, 15.999999999998332, 20.00000000000011] x1 * x2 = [1.2500000000002318, 2.000000000000054, 2.2499999999994893, 1.9999999999998272, 2.000000000000205, 2.25000000000003, 1.9999999999997906, 1.2499999999996558] x1 shifted circularly by -1 = [0.4999999999998632, 0.749999999999976, 0.9999999999999369, 1.9999999999999858, 2.9999999999998677, 4.000000000000045, 5.000000000000059, 0.25000000000002087] x1 shifted circularly by 2 = [3.9999999999999973, 4.99999999999995, 0.2499999999999567, 0.49999999999996825, 0.7500000000000793, 0.9999999999998956, 2.00000000000004, 2.999999999999985]

================================================================================ simplerealnumbers with an Unencrypted context Input x1: [0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0, 5.0] Input x2: [5.0, 4.0, 3.0, 2.0, 1.0, 0.75, 0.5, 0.25]

Results of homomorphic computations: x1 = [0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0, 5.0] x1 + x2 = [5.25, 4.5, 3.75, 3.0, 3.0, 3.75, 4.5, 5.25] x1 - x2 = [-4.75, -3.5, -2.25, -1.0, 1.0, 2.25, 3.5, 4.75] 4 * x1 = [1.0, 2.0, 3.0, 4.0, 8.0, 12.0, 16.0, 20.0] x1 * x2 = [1.25, 2.0, 2.25, 2.0, 2.0, 2.25, 2.0, 1.25] x1 shifted circularly by -1 = [0.5, 0.75, 1.0, 2.0, 3.0, 4.0, 5.0, 0.25] x1 shifted circularly by 2 = [4.0, 5.0, 0.25, 0.5, 0.75, 1.0, 2.0, 3.0] ```

Memory issues

OpenFHE is a memory-optimized C++ library, but these optimizations can cause memory issues when transitioning to Julia.

In OpenFHE, large objects like Ciphertext, Plaintext, and CryptoContext are managed using std::shared_ptr. These objects are not freed until all associated std::shared_ptrs are destroyed. Since the Julia objects that hold a reference to these shared pointers are relatively small, Julia's garbage collector does not always free them automatically, as they are not considered a high priority for garbage collection. This is because Julia's garbage collector primarily focuses on "young" objects during its incremental collections, leaving some std::shared_ptrs in memory even when they are no longer in use. This may result in a significant increase in memory consumption over time, as a single Ciphertext object can occupy over 60 MB. Consequently, complex operations may lead to gigabytes of memory being occupied without being freed until the Julia session is terminated. One possible solution is to manually trigger Julia's garbage collector to perform a full collection, which will also clean up these "small" objects: julia GC.gc()

Additionally, OpenFHE optimizes memory usage in C++ by storing evaluation keys and CryptoContexts in static objects. These objects, being quite large, remain in memory until the Julia REPL is closed. To release them while the REPL is still running, you can execute the following function: julia release_context_memory() Note that this will invalidate all currently existing contexts, even those which are still in use. Thus you should only call these functions once you are done with a given FHE setup and want to start a new one. For more details, please refer to the documentation for release_context_memory.

Therefore, for a full cleanup of all OpenFHE-occupied memory, first ensure that all variables holding references to OpenFHE objects are out of scope and then execute julia release_context_memory() GC.gc() By running these commands at appropriate points in your code, you can prevent excessive memory usage and ensure efficient memory management when using SecureArithmetic.jl.

Multithreading

SecureArray internally stores encrypted data across multiple ciphertexts. Since most operations with secure arrays - such as addition, multiplication, or bootstrapping - are performed for each ciphertext individually, they can be parallelized across different threads. By default, parallelization is disabled - you can enable it with enable_multithreading: julia enable_multithreading() To disable it, use disable_multithreading: julia disable_multithreading() When multithreading is enabled, for loops iterating over ciphertexts in SecureArray use Threads.@threads to distribute work across Threads.nthreads() threads. However, if Julia runs with only one thread (Threads.nthreads() == 1), Threads.@threads is not applied for efficiency.

Since multithreading works by splitting for loops over ciphertexts in SecureArray, it is only effective if there are at least two ciphertexts.

Please be aware that mixing Julia's multithreading with OpenFHE's builtin OpenMP-based multithreading might cause troubles. Thus if in doubt, set the environment variable OMP_NUM_THREADS=1 to avoid potential issues.

Referencing

If you use SecureArithmetic.jl in your own research, please cite this repository as follows: bibtex @misc{schlottkelakemper2024securearithmetic, title={{S}ecure{A}rithmetic.jl: {S}ecure arithmetic operations in {J}ulia using fully homomorphic encryption}, author={Schlottke-Lakemper, Michael}, year={2024}, howpublished={\url{https://github.com/hpsc-lab/SecureArithmetic.jl}}, doi={10.5281/zenodo.10544790} }

Authors

SecureArithmetic.jl was initiated by Michael Schlottke-Lakemper (University of Augsburg, Germany). Together with Arseniy Kholod (University of Augsburg, Germany), he is its principal maintainer.

License and contributing

SecureArithmetic.jl is available under the MIT license (see LICENSE.md). Contributions by the community are very welcome! For larger proposed changes, feel free to reach out via an issue first.