LR-GD-RNS: Enhanced Privacy-Preserving Logistic Regression Algorithms for Secure Deployment in Untrusted Environments

The protection of data processing is emerging as an essential aspect of data analytics, machine learning, delegation of computation, Internet of Things, medical and financial analysis, smart cities, genomics, non-disclosure searching, among others. Often, they use sensitive information that cannot be protected by traditional cryptosystems. Homomorphic Encryption (HE) schemes and secure Multi-Party Computation (MPC) are considered suitable solutions for privacy protection. In this paper, we propose and analyze the performance of three homomorphic Logistic Regression (LR) models with Gradient Descent (GD) algorithms based on the Residue Number System (RNS). We compare their performance with four traditional non-homomorphic versions, one homomorphic algorithm based on RNS with Batch GD, and two state-of-the-art homomorphic algorithms. To validate our approach, we consider six public datasets of different medicine domains (diabetes, cancer, drugs, etc.) and genomics. We use a 5-fold cross-validation technique for a fair comparison in terms of the solution quality and training time. The results show that propose homomorphic solutions have similar accuracy with non-homomorphic algorithms, increased classification performance, and decreased training time compared with the state-of-the-art HE algorithms.