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

TL;DR

EVA-S3PC introduces a data-disguising based framework for efficient, verifiable secure three-party matrix computation, achieving high Float64 precision and substantially reduced communication relative to prior SMPC approaches. It defines five elementary protocols (S2PM, S3PM, S2PI, S2PHM, S3PHM) with formal security proofs in the semi-honest real-number setting and a Monte Carlo-based verification mechanism. The framework enables secure 3-party linear regression over vertically partitioned data with accuracy nearly identical to plaintext training, validated on standard datasets with favorable efficiency and communication metrics. These results suggest EVA-S3PC as a scalable, accurate solution for privacy-preserving collaborative modeling across domains such as finance and healthcare.

Abstract

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.

Figures (9)

• Figure 1: Secure Three-Party Cooperative Modeling Problem
• Figure 2: Framework of EVA-S3PC
• Figure 3: S3PLR Training and Prediction Based on Basic Secure Protocol Library
• Figure 4: Communication overhead (/KB) for classical SMPC frameworks in S2PM(a), S3PM(b), S2PI(c), and S3PHM(d) with matrix dimensions $N$ from 10 to 50 and numerical distribution $\delta$ in $[E-4, E+4]$ in $\mathbb{R}$. The HE method is excluded from S2PI due to lack of support for matrix inversion. As S2PHM involves two executions of S2PM, its communication overhead is similar and therefore not shown.
• Figure 5: Runtime allocation of different stage in S2PM (a) and S3PM (b), including preparation, online computation, verification, and communication costs, tested with parameters $N=10, 20, 30, 40, 50$.

Theorems & Definitions (16)

• Definition 1: Semi-honest adversaries model evans2018pragmatic
• Definition 2: Computational Indistinguishability goldreich2004foundations
• Definition 3: Privacy in Semi-honest 2-Party Computation lindell2017simulate
• Definition 4: Privacy in Semi-honest 3-party computation
• Definition 5: Security Model in field of real number
• Lemma 1
• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4