Secure Two-Party Matrix Multiplication from Lattices and Its Application to Encrypted Control

TL;DR

This paper introduces a lattice-based secure two-party matrix multiplication protocol that preserves privacy and is applicable to encrypted control systems, reducing online computation and maintaining control precision.

Contribution

It presents a novel secure matrix multiplication protocol based on lattices, suitable for encrypted control, with proven security and practical efficiency improvements.

Findings

Lower online computational complexity for clients.

Maintains privacy of inputs, outputs, and parameters.

Ensures sufficient control input precision despite approximation.

Abstract

In this study, we propose a two-party computation protocol for approximate matrix multiplication of fixed-point numbers. The proposed protocol is provably secure under standard lattice-based cryptographic assumptions and enables matrix multiplication at a desired approximation level within a single round of communication. We demonstrate the feasibility of the protocol by applying it to the secure implementation of a linear control law. Our evaluation reveals that the client achieves lower online computational complexity compared to the original controller computation, while ensuring the privacy of controller inputs, outputs, and parameters. Furthermore, a numerical example confirms that the proposed method maintains sufficient precision of control inputs even in the presence of approximation and quantization errors.