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Decentralized Stealth Attacks on Cyber-Physical Systems

Xiuzhen Ye, Inaki Esnaola, Samir M. Perlaza, Robert F. Harrison

TL;DR

The paper addresses the vulnerability of CPS to decentralized stealth data-injection attacks by formulating attacker actions as random Gaussian inputs that minimize the global mutual information $I(X^n;Y_A^m)$ while constraining the KL divergence $D(P_{Y_A^m}\|P_{Y^m})$. It introduces three normal-form potential games ${\cal G}_1,{\cal G}_2,{\cal G}_3$ with convex cost functions, proves the existence and uniqueness of Nash Equilibria, and provides best-response dynamics to reach them. The analysis includes both global and local information metrics, with explicit convexity proofs and closed-form best-response updates, along with numerical evaluations on IEEE test systems to demonstrate convergence and tradeoffs between disruption and detectability. The results show that decentralized game-theoretic attack constructions are feasible and predictable, enabling scalable analysis and highlighting practical risks to CPS security under limited attacker coordination. Overall, the work links information-theoretic disruption, stealth criteria, and game theory to characterize and achieve decentralized stealth attacks in CPS, offering insights for both attack design and defense planning.

Abstract

Decentralized stealth attack constructions that minimize the mutual information between the state variables and the measurements are proposed. The attack constructions are formulated as random Gaussian attacks targeting Cyber-physical systems that aims at minimizing the mutual information between the state variables and measurements while constraining the Kullback-Leibler divergence between the distribution of the measurements under attacks and the distribution of the measurements without attacks. The proposed information metrics adopted measure the disruption and attack detection both globally and locally. The decentralized attack constructions are formulated in a framework of normal games. The global and local information metrics yield games with global and local objectives in disruption and attack detection. We have proven the games are potential games and the convexity of the potential functions followed by the uniqueness and the achievability of the Nash Equilibrium, accordingly. We proposed a best response dynamics to achieve the Nash Equilibrium of the games. We numerically evaluate the performance of the proposed decentralized stealth random attacks on IEEE test systems and show it is feasible to exploit game theoretic techniques in decentralized attack constructions.

Decentralized Stealth Attacks on Cyber-Physical Systems

TL;DR

The paper addresses the vulnerability of CPS to decentralized stealth data-injection attacks by formulating attacker actions as random Gaussian inputs that minimize the global mutual information while constraining the KL divergence . It introduces three normal-form potential games with convex cost functions, proves the existence and uniqueness of Nash Equilibria, and provides best-response dynamics to reach them. The analysis includes both global and local information metrics, with explicit convexity proofs and closed-form best-response updates, along with numerical evaluations on IEEE test systems to demonstrate convergence and tradeoffs between disruption and detectability. The results show that decentralized game-theoretic attack constructions are feasible and predictable, enabling scalable analysis and highlighting practical risks to CPS security under limited attacker coordination. Overall, the work links information-theoretic disruption, stealth criteria, and game theory to characterize and achieve decentralized stealth attacks in CPS, offering insights for both attack design and defense planning.

Abstract

Decentralized stealth attack constructions that minimize the mutual information between the state variables and the measurements are proposed. The attack constructions are formulated as random Gaussian attacks targeting Cyber-physical systems that aims at minimizing the mutual information between the state variables and measurements while constraining the Kullback-Leibler divergence between the distribution of the measurements under attacks and the distribution of the measurements without attacks. The proposed information metrics adopted measure the disruption and attack detection both globally and locally. The decentralized attack constructions are formulated in a framework of normal games. The global and local information metrics yield games with global and local objectives in disruption and attack detection. We have proven the games are potential games and the convexity of the potential functions followed by the uniqueness and the achievability of the Nash Equilibrium, accordingly. We proposed a best response dynamics to achieve the Nash Equilibrium of the games. We numerically evaluate the performance of the proposed decentralized stealth random attacks on IEEE test systems and show it is feasible to exploit game theoretic techniques in decentralized attack constructions.
Paper Structure (21 sections, 11 theorems, 45 equations, 6 figures, 3 algorithms)

This paper contains 21 sections, 11 theorems, 45 equations, 6 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Cyber-Physical Systems
  3. Observation Model
  4. Decentralized Data Injection Attacks
  5. Attack Detection
  6. Joint Detection
  7. Local Detection
  8. Information Theoretic Metrics
  9. Disruption Measure
  10. Detection Measure
  11. Game Formulation
  12. Convexity
  13. Best Responses
  14. Potential Games
  15. Existence and Achievability of Nash Equilibrium
  16. ...and 6 more sections

Key Result

Proposition 1

For all $i \in \{1,2,\ldots,m\}$, the random variables $X^n$ in Sigma_XX and $Y_{A_i}$ in ith_compromised satisfy where the matrix ${\bf H}$ is in eq:obs_noattack; the real $\sigma \in \mathds{R}_+$ is in EqZ; the matrix $\hbox{\boldmath$\Sigma$}_{X\!X}$ is in Sigma_XX; and the real $v_i$ is in distribution_A_i.

Figures (6)

  • Figure 1: The convergence in ${\cal G}_1$ in terms of the potential function $P_1$ on IEEE 9-bus test system with $\rho=0.9$, SNR = 30 dB. The red squares show the potential in the NEs.
  • Figure 2: The convergence in ${\cal G}_2$ in terms of the potential function $P_2$ on IEEE 9-bus test system with $\rho=0.9$, SNR = 30 dB. The red squares show the potential in the NEs.
  • Figure 3: The convergence in ${\cal G}_3$ in terms of the potential function $P_3$ on IEEE 9-bus test system with $\rho=0.9$, SNR = 30 dB. The red squares show the potential in the NEs.
  • Figure 4: The convergence in ${\cal G}_1$ in terms of tradeoff between mutual information and KL divergence on IEEE 9-bus test system with $\rho=0.9$, SNR = 30 dB.
  • Figure 5: The convergence in ${\cal G}_2$ in terms of tradeoff between mutual information and KL divergence on IEEE 9-bus test system with $\rho=0.9$, SNR = 30 dB.
  • ...and 1 more figures

Theorems & Definitions (26)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • ...and 16 more