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 machine learning, statistics, and image to remains challenge. The computational complexity some operations can significantly increase time. In this paper, we focus on the analysis two state-of-the-art HE matrix multiplication algorithms with best time space complexities. We show how their performance depends libraries execution context, considering standard Cheon–Kim–Kim–Song (CKKS) scheme fixed-point numbers based Microsoft SEAL PALISADE libraries. that Windows OS library Linux are options. general, PALISADE-Linux outperforms PALISADE-Windows, SEAL-Linux, SEAL-Windows by 1.28, 1.59, 1.67 times average different sizes, respectively. derive high-precision extrapolation formulas estimate larger matrices.