Information-theoretic stealth attacks are data injection attacks that minimize the amount of information acquired by the operator about the state variables, while simultaneously limiting the Kullback-Leibler divergence between the distribution of the measurements under attack and the distribution under normal operation with the aim of controling the probability of attack detection. For Gaussian distributed state variables, attack
construction requires knowledge of the second order statistics
of the state variables, which is estimated from a finite number
of past realizations using a sample covariance matrix. Within
this framework, the attack performance is studied for the attack
construction with the sample covariance matrix. This results
in an analysis of the amount of data required to learn the
covariance matrix of the state variables used on the attack
construction. The ergodic attack performance is characterized
using asymptotic random matrix theory tools, and the variance
of the attack performance is bounded. The ergodic performance
and the variance bounds are assessed with simulations on IEEE
test systems
