On Connectivity Thresholds in the Intersection of Random Key Graphs on Random Geometric Graphs

B. Santhana Krishnan; Ayalvadi Ganesh; D. Manjunath

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arXiv · 1301.6422

On Connectivity Thresholds in the Intersection of Random Key Graphs on Random Geometric Graphs

B. Santhana Krishnan·Ayalvadi Ganesh·D. Manjunath

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Abstract

In a random key graph (RKG) of $n$ nodes each node is randomly assigned a key ring of $K_n$ cryptographic keys from a pool of $P_n$ 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 $[0,1]^2.$ In addition to the common key requirement, we require two nodes to also be within $r_n$ 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 $K_n,$ $P_n$ and $r_n$ for the graph to be asymptotically almost surely connected.

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BibTeX RIS

B. Santhana Krishnan, Ayalvadi Ganesh, D. Manjunath. 2013-05-01. On Connectivity Thresholds in the Intersection of Random Key Graphs on Random Geometric Graphs. https://arxiv.org/abs/1301.6422

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