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Chaotic Masking Protocol for Secure Communication and Attack Detection in Remote Estimation of Cyber-Physical Systems

Tao Chen, Andreu Cecilia, Daniele Astolfi, Lei Wang, Zhitao Liu, Hongye Su

TL;DR

This paper tackles privacy and reliability challenges in remote CPS estimation by introducing a chaotic masking protocol that hides sensor measurements with a chaotic signal while simultaneously estimating both the plant state and the chaotic state at the receiver. The masking is designed so no extra secure synchronization channel is required, and the de-masking succeeds in steady state via an extended observer. The authors establish stability conditions through LMIs and discuss robustness against eavesdropping, replay, and stealthy data-injection attacks, supported by simulations on aerospace and chaotic-masking benchmarks. The approach enhances privacy and attack detection in remote estimation, offering a practical, synchronization-free solution for secure CPS communications.

Abstract

In remote estimation of cyber-physical systems (CPSs), sensor measurements transmitted through network may be attacked by adversaries, leading to leakage risk of privacy (e.g., the system state), and/or failure of the remote estimator. To deal with this problem, a chaotic masking protocol is proposed in this paper to secure the sensor measurements transmission. In detail, at the plant side, a chaotic dynamic system is deployed to encode the sensor measurement, and at the estimator side, an estimator estimates both states of the physical plant and the chaotic system. With this protocol, no additional secure communication links is needed for synchronization, and the masking effect can be perfectly removed when the estimator is in steady state. Furthermore, this masking protocol can deal with multiple types of attacks, i.e., eavesdropping attack, replay attack, and stealthy false data injection attack.

Chaotic Masking Protocol for Secure Communication and Attack Detection in Remote Estimation of Cyber-Physical Systems

TL;DR

This paper tackles privacy and reliability challenges in remote CPS estimation by introducing a chaotic masking protocol that hides sensor measurements with a chaotic signal while simultaneously estimating both the plant state and the chaotic state at the receiver. The masking is designed so no extra secure synchronization channel is required, and the de-masking succeeds in steady state via an extended observer. The authors establish stability conditions through LMIs and discuss robustness against eavesdropping, replay, and stealthy data-injection attacks, supported by simulations on aerospace and chaotic-masking benchmarks. The approach enhances privacy and attack detection in remote estimation, offering a practical, synchronization-free solution for secure CPS communications.

Abstract

In remote estimation of cyber-physical systems (CPSs), sensor measurements transmitted through network may be attacked by adversaries, leading to leakage risk of privacy (e.g., the system state), and/or failure of the remote estimator. To deal with this problem, a chaotic masking protocol is proposed in this paper to secure the sensor measurements transmission. In detail, at the plant side, a chaotic dynamic system is deployed to encode the sensor measurement, and at the estimator side, an estimator estimates both states of the physical plant and the chaotic system. With this protocol, no additional secure communication links is needed for synchronization, and the masking effect can be perfectly removed when the estimator is in steady state. Furthermore, this masking protocol can deal with multiple types of attacks, i.e., eavesdropping attack, replay attack, and stealthy false data injection attack.
Paper Structure (18 sections, 6 theorems, 57 equations, 7 figures)

This paper contains 18 sections, 6 theorems, 57 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Remote Estimator
  4. System Protection with Chaotic Masking
  5. Masking Approach
  6. De-masking Approach
  7. Sufficient Conditions for the Existence of ${\bf{P}}$ and ${\bf{N}}$
  8. Defense of Eavesdropping Attack
  9. Eavesdropping Attack
  10. Eavesdropping Error Caused by Chaotic Masking
  11. Defense of Replay Attack
  12. Replay Attack
  13. Invalidating the Replay Attack Strategy
  14. Defense of Stealthy Data Injection Attack
  15. Stealthy Data Injection Attack
  16. ...and 3 more sections

Key Result

Proposition 1

For all $x\in \mathbb{R}^{n_x}$ and $\xi \in \Xi$, suppose that there exist a symmetric positive definite matrix ${\bf{P}}\in \mathbb{R}^{(n_x+n_\xi)\times (n_x+n_\xi)}$, and ${\bf{N}}\in \mathbb{R}^{(n_x+n_\xi)\times n_y}$ satisfying Then, the equilibrium point $\tilde{\textbf{x}}=0$ of system eq.extended_system3 is exponentially stable.

Figures (7)

  • Figure 1: Representation of the set $\Xi$ and $\bm\bar{\Xi}$ in ${\mathbb R}^2$.
  • Figure 2: R$\ddot{o}$ssler prototype-4 system from Eq. \ref{['eq.rossler']} for $a = b = 0.5$ with initial condition $\xi(0) = [0.1, 0.3,0]^\top$ .
  • Figure 3: Distance to unobservability
  • Figure 4: Simulation results without attack. (a)-(c) The chaotic signal and their corresponding estimations. (d) The norm of estimation error of the physical plant.
  • Figure 5: The eavesdropping error with and without masking protocol.
  • ...and 2 more figures

Theorems & Definitions (7)

  • Proposition 1
  • Definition 1
  • Lemma 1
  • Lemma 2
  • Proposition 2
  • Proposition 3
  • Proposition 4