Secure Private and Adaptive Matrix Multiplication Beyond the Singleton Bound

TL;DR

This paper introduces SRPM3, a secure, adaptive matrix multiplication scheme that detects malicious workers using Freivalds' algorithm, ensuring privacy and robustness in distributed computations with flexible efficiency trade-offs.

Contribution

It presents a novel security framework for adaptive private matrix multiplication schemes, incorporating efficient malicious worker detection and identification.

Findings

SRPM3 effectively detects malicious workers with high probability.

The scheme tolerates an arbitrary number of malicious nodes.

Theoretical and simulation results validate the security and efficiency of SRPM3.

Abstract

We consider the problem of designing secure and private codes for distributed matrix-matrix multiplication. A master server owns two private matrices and hires worker nodes to help compute their product. The matrices should remain information-theoretically private from the workers. Some of the workers are malicious and return corrupted results to the master. We design a framework for security against malicious workers in private matrix-matrix multiplication. The main idea is a careful use of Freivalds' algorithm to detect erroneous matrix multiplications. Our main goal is to apply this security framework to schemes with adaptive rates. Adaptive schemes divide the workers into clusters and thus provide flexibility in trading decoding complexity for efficiency. Our new scheme, SRPM3, provides a computationally efficient security check per cluster that detects the presence of one or more malicious workers with high probability. An additional per worker check is used to identify the malicious nodes. SRPM3 can tolerate the presence of an arbitrary number of malicious workers. We provide theoretical guarantees on the complexity of the security checks and simulation results on both, the missed detection rate as well as on the time needed for the integrity check.