Worst case time requirement to cover a secure ad-hoc wireless network under full visibility

In this work our focus is on the cover time analysis of a secure ad-hoc wireless network, when the nodes are allowed to move within a compact space. We consider a secure wireless random network in 2-dimensional space, and a sequence X_n = {X₁, X₂,⋯X_n}, with n nodes distributed uniformly over a compact space C ⊂ R². We derive a strong law result for the cover time of the network and proved that for key pool of order of n log n and key ring of order of log n, the cover time of the network is of order of n^5/2/(log n)² almost surely.