  Sparse stealth attack constructions that minimize the mutual information
between the state variables and the observations are proposed. The attack
construction is formulated as the design of a multivariate Gaussian
distribution that aims to minimize the mutual information while limiting the
Kullback-Leibler divergence between the distribution of the observations under
attack and the distribution of the observations without attack. The sparsity
constraint is incorporated as a support constraint of the attack distribution.
Two heuristic greedy algorithms for the attack construction are proposed. The
first algorithm assumes that the attack vector consists of independent entries,
and therefore, requires no communication between different attacked locations.
The second algorithm considers correlation between the attack vector entries
which results in better attack performance at the expense of coordination
between different locations. We numerically evaluate the performance of the
proposed attack constructions on IEEE test systems and show that it is feasible
to construct stealth attacks that generate significant disruption with a low
number of compromised sensors.
