Information-Theoretic Attacks in the Smart Grid

Gaussian random attacks that jointly minimize the amount of information obtained by the operator from the grid and the probability of attack detection are presented. The construction of the attack is posed as an optimization problem with a utility function that captures two effects: firstly, minimizing the mutual information between the measurements and the state variables; secondly, minimizing the probability of attack detection via the Kullback-Leibler divergence between the distribution of the measurements with an attack and the distribution of the measurements without an attack. Additionally, a lower bound on the utility function achieved by the attacks constructed with imperfect knowledge of the second order statistics of the state variables is obtained. The performance of the attack construction using the sample covariance matrix of the state variables is numerically evaluated. The above results are tested in the IEEE 30-Bus test system.Comment: 2017 IEEE International Conference on Smart Grid Communications (SmartGridComm

Information-theoretic attacks in the smart grid

Gaussian random attacks that jointly minimize the amount of information obtained by the operator from the grid and the probability of attack detection are presented. The construction of the attack is posed as an optimization problem with a utility function that captures two effects: firstly, minimizing the mutual information between the measurements and the state variables; secondly, minimizing the probability of attack detection via the Kullback-Leibler (KL) divergence between the distribution of the measurements with an attack and the distribution of the measurements without an attack. Additionally, a lower bound on the utility function achieved by the attacks constructed with imperfect knowledge of the second order statistics of the state variables is obtained. The performance of the attack construction using the sample covariance matrix of the state variables is numerically evaluated. The above results are tested in the IEEE 30-Bus test system

Learning requirements for stealth attacks

The learning data requirements are analyzed for the construction of stealth attacks in state estimation. In particular, the training data set is used to compute a sample covariance matrix that results in a random matrix with a Wishart distribution. The ergodic attack performance is defined as the average attack performance obtained by taking the expectation with respect to the distribution of the training data set. The impact of the training data size on the ergodic attack performance is characterized by proposing an upper bound for the performance. Simulations on the IEEE 30-Bus test system show that the proposed bound is tight in practical settings.Comment: International Conference on Acoustics, Speech, and Signal Processing 201

Information Theoretic Data Injection Attacks with Sparsity Constraints

Information theoretic sparse attacks that minimize simultaneously the information obtained by the operator and the probability of detection are studied in a Bayesian state estimation setting. The attack construction is formulated as an optimization problem that aims to minimize the mutual information between the state variables and the observations while guaranteeing the stealth of the attack. Stealth is described in terms of the Kullback-Leibler (KL) divergence between the distributions of the observations under attack and without attack. To overcome the difficulty posed by the combinatorial nature of a sparse attack construction, the attack case in which only one sensor is compromised is analytically solved first. The insight generated in this case is then used to propose a greedy algorithm that constructs random sparse attacks. The performance of the proposed attack is evaluated in the IEEE 30 Bus Test Case.Comment: Submitted to SGC 202

Recovery of missing data in correlated smart grid datasets

We study the recovery of missing data from multiple smart grid datasets within a matrix completion framework. The datasets contain the electrical magnitudes required for monitoring and control of the electricity distribution system. Each dataset is described by a low rank matrix. Different datasets are correlated as a result of containing measurements of different physical magnitudes generated by the same distribution system. To assess the validity of matrix completion techniques in the recovery of missing data, we characterize the fundamental limits when two correlated datasets are jointly recovered. We then proceed to evaluate the performance of Singular Value Thresholding (SVT) and Bayesian SVT (BSVT) in this setting. We show that BSVT outperforms SVT by simulating the recovery for different correlated datasets. The performance of BSVT displays the tradeoff behaviour described by the fundamental limit, which suggests that BSVT exploits the correlation between the datasets in an efficient manner

Compressive Privacy for a Linear Dynamical System

We consider a linear dynamical system in which the state vector consists of both public and private states. One or more sensors make measurements of the state vector and sends information to a fusion center, which performs the final state estimation. To achieve an optimal tradeoff between the utility of estimating the public states and protection of the private states, the measurements at each time step are linearly compressed into a lower dimensional space. Under the centralized setting where all measurements are collected by a single sensor, we propose an optimization problem and an algorithm to find the best compression matrix. Under the decentralized setting where measurements are made separately at multiple sensors, each sensor optimizes its own local compression matrix. We propose methods to separate the overall optimization problem into multiple sub-problems that can be solved locally at each sensor. We consider the cases where there is no message exchange between the sensors; and where each sensor takes turns to transmit messages to the other sensors. Simulations and empirical experiments demonstrate the efficiency of our proposed approach in allowing the fusion center to estimate the public states with good accuracy while preventing it from estimating the private states accurately

Information Theoretic Data Injection Attacks with Sparsity Constraints

International audienceInformation theoretic sparse attacks that minimize simultaneously the information obtained by the operator and the probability of detection are studied in a Bayesian state estimation setting. The attack construction is formulated as an optimization problem that aims to minimize the mutual information between the state variables and the observations while guaranteeing the stealth of the attack. Stealth is described in terms of the Kullback-Leibler (KL) divergence between the distributions of the observations under attack and without attack. To overcome the difficulty posed by the combinatorial nature of a sparse attack construction, the attack case in which only one sensor is compromised is analytically solved first. The insight generated in this case is then used to propose a greedy algorithm that constructs random sparse attacks. The performance of the proposed attack is evaluated in the IEEE 30 Bus Test Case

Data-Injection Attacks

In this chapter we review some of the basic attack constructions that exploit a stochastic description of the state variables. We pose the state estimation problem in a Bayesian setting and cast the bad data detection procedure as a Bayesian hypothesis testing problem. This revised detection framework provides the benchmark for the attack detection problem that limits the achievable attack disruption. Indeed, the trade-off between the impact of the attack, in terms of disruption to the state estimator, and the probability of attack detection is analytically characterized within this Bayesian attack setting. We then generalize the attack construction by considering information-theoretic measures that place fundamental limits to a broad class of detection, estimation, and learning techniques. Because the attack constructions proposed in this chapter rely on the attacker having access to the statistical structure of the random process describing the state variables, we conclude by studying the impact of imperfect statistics on the attack performance. Specifically, we study the attack performance as a function of the size of the training data set that is available to the attacker to estimate the second-order statistics of the state variables.Comment: arXiv admin note: substantial text overlap with arXiv:1808.0418

Data-Injection Attacks

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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