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The emergence of Internet of Things (IoT) brings about new security challenges at the intersection of cyber and physical spaces. One prime example is the vulnerability of Face Recognition (FR) based access control in IoT systems. While previous research has shown that Deep Neural Network(DNN)-based FR systems (FRS) are potentially susceptible to imperceptible impersonation attacks, the potency of such attacks in a wide set of scenarios has not been thoroughly investigated. In this paper, we present the first systematic, wide-ranging measurement study of the exploitability of DNN-based FR systems using a large scale dataset. We find that arbitrary impersonation attacks, wherein an arbitrary attacker impersonates an arbitrary target, are hard if imperceptibility is an auxiliary goal. Specifically, we show that factors such as skin color, gender, and age, impact the ability to carry out an attack on a specific target victim, to different extents. We also study the feasibility of constructing universal attacks that are robust to different poses or views of the attacker's face. Our results show that finding a universal perturbation is a much harder problem from the attacker's perspective. Finally, we find that the perturbed images do not generalize well across different DNN models. This suggests security countermeasures that can dramatically reduce the exploitability of DNN-based FR systems.