A Comparative Study of Secure Outsourced Matrix Multiplication Based on Homomorphic Encryption

Homomorphic encryption (HE) is a promising solution for handling sensitive data in semi-trusted third-party computing environments, as it enables processing of encrypted data. However, applying sophisticated techniques such as machine learning, statistics, and image processing to encrypted data remains a challenge. The computational complexity of some encrypted operations can significantly increase processing time. In this paper, we focus on the analysis of two state-of-the-art HE matrix multiplication algorithms with the best time and space complexities. We show how their performance depends on the libraries and the execution context, considering the standard Cheon–Kim–Kim–Song (CKKS) HE scheme with fixed-point numbers based on the Microsoft SEAL and PALISADE libraries. We show that Windows OS for the SEAL library and Linux OS for the PALISADE library are the best options. In general, PALISADE-Linux outperforms PALISADE-Windows, SEAL-Linux, and SEAL-Windows by 1.28, 1.59, and 1.67 times on average for different matrix sizes, respectively. We derive high-precision extrapolation formulas to estimate the processing time of HE multiplication of larger matrices.