Learning requirements for stealth attacks

TL;DR

This paper analyzes the data requirements for constructing stealth attacks in state estimation, focusing on how training data size affects attack performance and providing bounds validated by simulations.

Contribution

It introduces a theoretical framework linking training data size to attack performance using Wishart distribution analysis and proposes a tight upper bound validated through simulations.

Findings

The ergodic attack performance increases with training data size.

A tight upper bound for attack performance is derived.

Simulations confirm the bound's accuracy in practical scenarios.

Abstract

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.