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

2026-03-24

AI Summary

This work addresses the challenge of efficiently performing secure two-party fixed-point matrix multiplication while preserving privacy, with applications in encrypted control systems. The authors propose the first two-party protocol that integrates lattice-based cryptography with approximate matrix multiplication, featuring single-round communication, on-demand precision adjustment, and formal security guarantees. By offloading computation strategically, the approach reduces the client’s online computational complexity below that of the original unencrypted controller, while simultaneously ensuring the confidentiality of the controller’s inputs, parameters, and outputs. Numerical experiments demonstrate that the method maintains effective control accuracy despite quantization and approximation errors, validating its practicality in real-world encrypted control scenarios.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Mixed Discrete/Continuous Search
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

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.

Problem

• Secure Two-Party Computation
• Matrix Multiplication
• Lattice-based Cryptography
• Encrypted Control
• Privacy-Preserving Computation

Innovation

• secure two-party computation
• lattice-based cryptography
• approximate matrix multiplication
• encrypted control
• fixed-point arithmetic