Intermittent Encryption Strategies for Anti-Eavesdropping Estimation

TL;DR

This paper proposes intermittent encryption strategies to enhance anti-eavesdropping in control systems, balancing security and resource efficiency, and analyzes their effectiveness for both stable and unstable systems.

Contribution

It introduces stochastic and deterministic intermittent encryption schemes, analyzes their impact on eavesdropper MSE, and designs an optimal encryption matrix for maximum security.

Findings

Eavesdropper MSE converges under stable systems with intermittent encryption.

An encryption matrix that maximizes steady-state MSE is developed.

Unbounded eavesdropper MSE achievable in unstable systems with appropriate encryption strategies.

Abstract

In this paper, an anti-eavesdropping estimation problem is investigated. A linear encryption scheme is utilized, which first linearly transforms innovation via an encryption matrix and then encrypts some components of the transformed innovation. To reduce the computation and energy resources consumed by the linear encryption scheme, both stochastic and deterministic intermittent strategies which perform the linear encryption scheme only at partial moments are developed. When the system is stable, it is shown that the mean squared error (MSE) of the eavesdropper converges under any stochastic or deterministic intermittent strategy. Also, an analytical encryption matrix that maximizes the steady-state of the MSE is designed. When the system is unstable, the eavesdropper's MSE can be unbounded with arbitrary positive encryption probabilities and decision functions if encryption matrices are chosen appropriately. Then, the relationship between the aforementioned encryption parameters and the eavesdropper's MSE is analyzed. Moreover, a single intermittent strategy which only encrypts one message is discussed. This strategy can be unavailable for stable systems, but can make the eavesdropper's MSE unbounded in unstable systems for the encrypted message satisfies a linear matrix inequality (LMI) condition. The effectiveness of the proposed methods is verified in the simulation.