Title: Secure logistic regression training based on fully homomorphic encryption

Authors: Shiwen Wei; Zhili Chen; Xin Chen; Benchang Dong; Yizheng Ren; Jie Fu

Addresses: Software Engineering Institute, East China Normal University, Shanghai, China ' Software Engineering Institute, East China Normal University, Shanghai, China ' Software Engineering Institute, East China Normal University, Shanghai, China ' Software Engineering Institute, East China Normal University, Shanghai, China ' Software Engineering Institute, East China Normal University, Shanghai, China ' Computer Science Department, Stevens Institute of Technology, Hoboken, NJ, USA

Abstract: With the advancement of AI, many fields increasingly rely on AI to process data, which raises concerns about privacy breaches. Homomorphic encryption allows computations on encrypted data, offering strong privacy protection. This paper proposes a secure logistic regression model based on the CKKS, achieving an optimal trade-off between computational efficiency and model performance. We improve training efficiency and convergence speed by approximating the Sigmoid activation function with a first-order polynomial and incorporating a momentum-based stochastic gradient descent algorithm. Experimental results show that our secure model strikes an excellent balance between model performance and computational efficiency. Compared to previous studies, our model achieves shorter training times per iteration and consistently outperforms prior work on multiple datasets. Even on the most challenging dataset, the accuracy of our model is only 0.73% lower than that of previous methods. Furthermore, we validate the outstanding performance of the model on large-scale datasets containing real-world data.

Keywords: CKKS homomorphic encryption; privacy-preserving computation; machine learning; logistic regression.

DOI: 10.1504/IJICS.2025.150024

International Journal of Information and Computer Security, 2025 Vol.28 No.4, pp.424 - 444

Received: 15 Nov 2024
Accepted: 14 Jun 2025
Published online: 21 Nov 2025 *

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