Learning-Augmented Perfectly Secure Collaborative Matrix Multiplication

2026-01-14

AI Summary

This work addresses information-theoretically secure multi-party matrix multiplication under local storage constraints and in the presence of semi-honest colluding adversaries. By encoding submatrices using sparse masking polynomials and integrating coefficient alignment with Beaver triples, the proposed protocol achieves perfect security. It further introduces, for the first time, a learning-augmented low-rank approximation mechanism grounded in tensor decomposition, which significantly enhances computational efficiency for large-scale matrix operations while preserving both optimal recovery thresholds and perfect privacy. Theoretical analysis confirms that any coalition of adversaries below the prescribed threshold gains only uniformly random shares, revealing no information about the inputs. Experimental results demonstrate up to an 80% improvement in computation speed for high-dimensional matrices compared to existing approaches.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

This paper presents a perfectly secure matrix multiplication (PSMM) protocol for multiparty computation (MPC) of $\mathrm{A}^{\top}\mathrm{B}$ over finite fields. The proposed scheme guarantees correctness and information-theoretic privacy against threshold-bounded, semi-honest colluding agents, under explicit local storage constraints. Our scheme encodes submatrices as evaluations of sparse masking polynomials and combines coefficient alignment with Beaver-style randomness to ensure perfect secrecy. We demonstrate that any colluding set of parties below the security threshold observes uniformly random shares, and that the recovery threshold is optimal, matching existing information-theoretic limits. Building on this framework, we introduce a learning-augmented extension that integrates tensor-decomposition-based local block multiplication, capturing both classical and learned low-rank methods. We demonstrate that the proposed learning-based PSMM preserves privacy and recovery guarantees for MPC, while providing scalable computational efficiency gains (up to $80\%$) as the matrix dimensions grow.

Problem

• secure matrix multiplication
• multiparty computation
• information-theoretic privacy
• learning-augmented computation
• perfect secrecy

Innovation

• learning-augmented
• perfectly secure matrix multiplication
• multiparty computation
• tensor decomposition
• information-theoretic privacy