Biblio
Gaussian random attacks that jointly minimize the amount of information obtained by the operator from the grid and the probability of attack detection are presented. The construction of the attack is posed as an optimization problem with a utility function that captures two effects: firstly, minimizing the mutual information between the measurements and the state variables; secondly, minimizing the probability of attack detection via the Kullback-Leibler (KL) divergence between the distribution of the measurements with an attack and the distribution of the measurements without an attack. Additionally, a lower bound on the utility function achieved by the attacks constructed with imperfect knowledge of the second order statistics of the state variables is obtained. The performance of the attack construction using the sample covariance matrix of the state variables is numerically evaluated. The above results are tested in the IEEE 30-Bus test system.
A technique of finding a set of sequential circuit nodes in which Trojan Circuits (TC) may be implanted is suggested. The technique is based on applying the precise (not heuristic) random estimations of internal node observability and controllability. Getting the estimations we at the same time derive and compactly represent all sequential circuit full states (depending on input and state variables) in which of that TC may be switched on. It means we obtain precise description of TC switch on area for the corresponding internal node v. The estimations are computed with applying a State Transition Graph (STG) description, if we suppose that TC may be inserted out of the working area (out of the specification) of the sequential circuit. Reduced Ordered Binary Decision Diagrams (ROBDDs) for the combinational part and its fragments are applied for getting the estimations by means of operations on ROBDDs. Techniques of masking TCs are proposed. Masking sub-circuits overhead is appreciated.