EVA-S3PC: Efficient, verifiable, accurate secure matrix multiplication protocol assembly and its application in regression

Efficient multi-party secure matrix multiplication (SMM) is crucial for privacy-preserving machine learning (PPML), but existing mixed-protocol frameworks often face challenges in balancing security, efficiency, and accuracy. This paper presents an efficient, verifiable and accurate secure three-party computing (EVA-S3PC) framework that addresses these challenges by proposing elementary two-party and three-party matrix operations based on data obfuscation techniques. Our approach includes basic protocols for secure matrix multiplication, inversion, and hybrid multiplication, ensuring computational security and result verifiability. EVA-S3PC leverages Monte Carlo methods for robust anomaly detection, achieving a negligible error rate with a verification overhead that drops below 10 % for large-scale tasks. Experimental results demonstrate that EVA-S3PC achieves up to 14 significant decimal digits of precision in Float64 calculations, while reducing communication overhead by up to $54.8\%$ compared to state-of-the-art methods. Furthermore, regression models trained using EVA-S3PC on vertically partitioned data achieve accuracy nearly identical to plaintext training. The framework’s practical application in secure three-party linear regression illustrates its potential in distributed PPML scenarios, offering a scalable, efficient, and precise solution for secure collaborative modeling across various domains such as healthcare and finance.