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Defending against attack is the key successful factor for sensor network security. There are many approaches that can be used to detect and defend against attacks, yet few are focused onmodeling attack distribution. Knowing the distribution models of attacks can help system estimate the attack probability and thus defend against them effectively and efficiently. In this paper, we use probability theory to develop a basic uniform model, a basic gradient model, an intelligent uniform model and an intelligent gradient model of attack distribution in order to adapt to different application environments. These models allow systems to estimate the attack probability of each node under a given position and time. Applying these models in system security designs can improve system security performance and decrease the overheads in nearly every security area. Based on these models, we describe a novel probability secure routing algorithm that is effective to defend against attacks whether they are detected or not. Besides this application, we also introduce some other applications, such as secure routing that can save systems available energy and resources while still providing enough security, detecting attack, and key management.

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