  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.
