Information-Theoretic Data Injection Attacks on the Smart Grid

In this thesis, we use information-theoretic measures to quantify the caused disruption and the probability of detection of the data injection attacks. Specifically the attacker minimizes the mutual information between the state variables and the compromised measurements to minimize the amount of information acquired by the operator from the measurements about the state variables. Also the attacker minimizes the Kullback-Leibler divergence between the distribution of measurements with attack and without attack to minimize the probability of detection.
The stealth attacks achieve these two contradictive objectives by minimizing the equal sum of them, which is generalized to the weighted sum later. Closed-form expression for the optimal Gaussian attack is proposed for the stealth attacks and the generalized stealth attacks when the attacker prioritizes the probability of detection over the disruption. Additionally, a closed-form expression of the probability of detection is obtained. To inform the design guidelines for the corresponding weighting parameter, a concentration inequality upper bound is proposed for the probability of detection.
RMT tools are used to characterize the ergodic performance of the attacks when the attacker only gets access to a limited number of samples of the state variables. For the non-asymptotic scenario, an upper bound is proposed for the ergodic performance, for which a simple convex optimization needs to be solved to compute it. For the asymptotic case, a closed-form expression is provided for the ergodic performance of the attacks.