Information Theoretic Data Injection Attacks with Sparsity Constraints

TL;DR

This paper introduces a novel information-theoretic approach to designing sparse data injection attacks that minimize information gain and detection probability in Bayesian state estimation, with analytical and algorithmic solutions demonstrated on a power system test case.

Contribution

It formulates a new optimization framework for stealthy sparse attacks using mutual information and KL divergence, providing analytical solutions and a greedy algorithm for practical attack construction.

Findings

Analytical solution for single-sensor attack case.

Greedy algorithm effectively constructs sparse attacks.

Successful attack performance demonstrated on IEEE 30 Bus Test Case.

Abstract

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.