Analog Secure Distributed Matrix Multiplication over Complex Numbers

TL;DR

This paper introduces two secure distributed matrix multiplication schemes over complex numbers that balance security, accuracy, and efficiency, addressing practical limitations of finite field approaches.

Contribution

It proposes novel schemes for secure distributed matrix multiplication over complex numbers, accommodating collusion and straggling, with analysis of security and numerical accuracy.

Findings

Trade-off between security and numerical accuracy identified.

Schemes support colluding and straggling servers.

Security levels can be adjusted based on use case.

Abstract

This work considers the problem of distributing matrix multiplication over the real or complex numbers to helper servers, such that the information leakage to these servers is close to being information-theoretically secure. These servers are assumed to be honest-but-curious, i.e., they work according to the protocol, but try to deduce information about the data. The problem of secure distributed matrix multiplication (SDMM) has been considered in the context of matrix multiplication over finite fields, which is not always feasible in real world applications. We present two schemes, which allow for variable degree of security based on the use case and allow for colluding and straggling servers. We analyze the security and the numerical accuracy of the schemes and observe a trade-off between accuracy and security.