Title: Stealth Attacks on the Smart Grid,
Abstract: Random attacks that jointly minimize the amount of information acquired by
the operator about the state of the grid and the probability of attack
detection are presented. The attacks minimize the information acquired by the
operator by minimizing the mutual information between the observations and the
state variables describing the grid. Simultaneously, the attacker aims to
minimize the probability of attack detection by minimizing the Kullback-Leibler
(KL) divergence between the distribution when the attack is present and the
distribution under normal operation. The resulting cost function is the
weighted sum of the mutual information and the KL divergence mentioned above.
The tradeoff between the probability of attack detection and the reduction of
mutual information is governed by the weighting parameter on the KL divergence
term in the cost function. The probability of attack detection is evaluated as
a function of the weighting parameter. A sufficient condition on the weighting
parameter is given for achieving an arbitrarily small probability of attack
detection. The attack performance is numerically assessed on the IEEE 30-Bus
and 118-Bus test systems.