  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 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.
