EVA-S3PC: Efficient, Verifiable, Accurate Secure Matrix Multiplication Protocol Assembly and Its Application in Regression

Efficient multi-party secure matrix multiplication is crucial for privacy-preserving machine learning, 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 with elementary 2-party and 3-party matrix operations based on data obfuscation techniques. We propose basic protocols for secure matrix multiplication, inversion, and hybrid multiplication, ensuring privacy and result verifiability. 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 art methods. Furthermore, 3-party regression models trained using EVA-S3PC on vertically partitioned data achieve accuracy nearly identical to plaintext training, which illustrates its potential in scalable, efficient, and accurate solution for secure collaborative modeling across domains.