On Connectivity Thresholds in the Intersection of Random Key Graphs on Random Geometric Graphs
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چکیده
Abstract—In a random key graph (RKG) of n nodes each node is randomly assigned a key ring of Kn cryptographic keys from a pool of Pn keys. Two nodes can communicate directly if they have at least one common key in their key rings. We assume that the n nodes are distributed uniformly in [0, 1]. In addition to the common key requirement, we require two nodes to also be within rn of each other to be able to have a direct edge. Thus we have a random graph in which the RKG is superposed on the familiar random geometric graph (RGG). For such a random graph, we obtain tight bounds on the relation between Kn, Pn and rn for the graph to be asymptotically almost surely connected.
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تاریخ انتشار 2013