Recognizing the need for a deeper understanding of the interdependence between critical infrastructures, such as the power grid and the communication network, a number of models have been proposed and analyzed in the last few years. However, most of these proposed models are over simplified and fail to capture complex interdependencies that may exist between these critical infrastructures. The recently proposed Implicative Interdependency Model is able to capture these complex interdependencies involving conjunctive and disjunctive relationships to overcome most of these limitations. Due to the existing interdependencies between the power and communication networks, a failure involving a small set of power and/or communication network entities can trigger a cascading event, resulting in the failure of a much larger set of entities through the cascading failure process. This implies that an adversary with an intent of destroying a specific set of entities E′ (real targets), no longer needs to make an effort to destroy E′ directly, but instead identify a set of smaller entities E′ (pseudo targets), whose destruction eventually leads to the destruction of the real target set E′ due to the cascading failure process. A clever adversary will thus try to identify the smallest set of pseudo target entities E00, whose destruction eventually destroys E′. We refer to this problem as the Smallest Pseudo Target Set Identification Problem (SPTSIP). We divide the problem into four classes, and show that it is solvable in polynomial time for one class, and is NP-complete for others. We provide an approximation algorithm for the second class, and for the most general class, we provide an optimal solution using ILP, and a heuristic solution. We evaluate the efficacy of our heuristic using power and communication network data of Maricopa County, Arizona. The experiments show that our heuristic almost always produces near optimal results.