The Role of Information Incompleteness in Defending Against Stealth Attacks

TL;DR

This work analyzes how incomplete admittance information affects information-theoretic stealth attacks against linearized state estimation in power systems within a Bayesian framework. By showing an equivalence between admittance incompleteness and perturbations in the state covariance, the authors derive sufficient conditions for regimes where stealth improves or destructiveness worsens, and they propose a convex optimization (P1) with a vertex-based solution (Theorem PDMax) plus a greedy algorithm to maximize stealth degradation. They further provide practical implementation via moving-target defense and validate the theory withIEEE test-system simulations, demonstrating conditions under which operator detectability and information leakage behave predictably. The results offer a principled approach to degrade attacker performance through controlled information incompleteness, improving defense and detection capabilities in smart grids.

Abstract

The effectiveness of Data Injections Attacks (DIAs) critically depends on the completeness of the system information accessible to adversaries. This relationship positions information incompleteness enhancement as a vital defense strategy for degrading DIA performance. In this paper, we focus on the information-theoretic stealth attacks, where the attacker encounters a fundamental tradeoff between the attack stealthiness and destructiveness. Specifically, we systematically characterize how incomplete admittance information impacts the dual objectives. In particular, we establish sufficient conditions for two distinct operational regimes: (i) stealthiness intensifies while destructive potential diminishes and (ii) destructiveness increases while stealth capability weakens. For scenarios beyond these regimes, we propose a maximal incompleteness strategy to optimally degrade stealth capability. To solve the associated optimization problem, the feasible region is reduced without excluding the optimal solution, and a heuristic algorithm is then introduced to effectively identify the near-optimal solutions within the reduced region. Numerical simulations are conducted on IEEE test systems to validate the findings.

Figures (5)

• Figure 1: Contributions of the paper.
• Figure 2: Performance of the attack in \ref{['Equ:A_bar']} on IEEE 30 Bus test system when $\textnormal{SNR}=30 \ \textnormal{dB}$ and $\rho=0.5$.
• Figure 3: Tradeoff change on IEEE 30 Bus test system when $\beta \in \left[-1, 1\right]$, $\textnormal{SNR}=30 \ \textnormal{dB}$, and $\rho=0.5$.
• Figure 4: Performance of Algorithm \ref{['Algo:greedy_1']} on IEEE 30 Bus test system when $\textnormal{SNR}=30 \ \textnormal{dB}$ and $\rho=0.5$ under different values of $\alpha$, in which the dashed lines denote the attack performance under the complete admittance information setting.
• Figure 5: Performance of Algorithm \ref{['Algo:greedy_1']} on IEEE 30 Bus test system when $\textnormal{SNR}=30 \ \textnormal{dB}$, $\rho=0.5$, and $\alpha = 1$ under different values of $k$, in which the dashed lines denote the attack performance under the complete admittance information setting.

Theorems & Definitions (25)

• Lemma 1
• proof
• Proposition 1
• Lemma 2
• Lemma 2
• proof
• Lemma 3
• proof
• Theorem 1
• proof