CAT and DOG: Improved Codes for Private Distributed Matrix Multiplication

2025-01-21

AI Summary

This paper addresses the challenges of high computational overhead, excessive worker-node requirements, and difficult privacy-efficiency trade-offs in private distributed matrix multiplication (PDMM/SDMM). We propose a novel polynomial coding framework based on outer-product partitioning (OPP). Our key innovation is the cyclic additive table (CAT), which introduces modular-additive degrees of freedom and breaks away from conventional polynomial interpolation paradigms. Based on CAT, we design three coding schemes: CATx, GASPrs, and DOGrs. CATx achieves the lowest worker count among all existing methods under low-privacy settings. GASPrs and DOGrs consistently outperform state-of-the-art (SOTA) approaches across multiple parameter configurations, offering superior communication-computation trade-offs while simultaneously ensuring strong privacy guarantees and efficient execution.

Technology Category

• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Privacy

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We present novel constructions of polynomial codes for private distributed matrix multiplication (PDMM/SDMM) using outer product partitioning (OPP). We extend the degree table framework from the literature to cyclic addition degree tables (CATs). By restricting the evaluation points to certain roots of unity, we enable modulo-addition in the degree table. This results in additional freedom when designing constructions. Based on CATs, we present an explicit construction, called CATx , that requires fewer workers than existing schemes in the low-privacy regime. Additionally, using regular degree tables, we present new families of schemes, called GASPrs and DOGrs , that outperform the state-of-the-art for a range of parameters.

Problem

• Private Distributed Matrix Multiplication
• Resource Optimization
• Computational Performance Enhancement

Innovation

• Polynomial Coding
• Privacy-preserving Distributed Matrix Multiplication
• Efficiency Enhancement