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The authors give, for the first time, a precise mathematical analysis of the connectivity and security properties of sensor networks that make use of the random pre-distribution of keys. They also show how to set the parameters - pool and key ring size - in such a way that the network is not only connected with high probability via secure links but also provably resilient, in the following sense: they formally show that any adversary that captures sensors at random with the aim of compromising a constant fraction of the secure links must capture at least a constant fraction of the nodes of the network.
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