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Malware attacks constitute a serious security risk that threatens to slow down the large-scale proliferation of wireless applications. As a first step toward thwarting this security threat, we seek to quantify the maximum damage inflicted on the system due to such outbreaks and identify the most vicious attacks. We represent the propagation of malware in a battery-constrained mobile wireless network by an epidemic model in which the worm can dynamically control the rate at which it kills the infected node and also the transmission ranges and/or the media scanning rates. At each moment of time, the worm at each node faces the following tradeoffs: 1) using larger transmission ranges and media scanning rates to accelerate its spread at the cost of exhausting the battery and thereby reducing the overall infection propagation rate in the long run; or 2) killing the node to inflict a large cost on the network, however at the expense of losing the chance of infecting more susceptible nodes at later times. We mathematically formulate the decision problems and utilize Pontryagin Maximum Principle from optimal control theory to quantify the damage that the malware can inflict on the network by deploying optimum decision rules. Next, we establish structural properties of the optimal strategy of the attacker over time. Specifically, we prove that it is optimal for the attacker to defer killing of the infective nodes in the propagation phase until reaching a certain time and then start the slaughter with maximum effort. We also show that in the optimal attack policy, the battery resources are used according to a decreasing function of time, i.e., most aggressively during the initial phase of the outbreak. Finally, our numerical investigations reveal a framework for identifying intelligent defense strategies that can limit the damage by appropriately selecting network parameters.
Date of Publication: Oct. 2012