  In this paper, we study the problem of secure routing in a multihop wireless
ad-hoc network in the presence of randomly distributed eavesdroppers.
Specifically, the locations of the eavesdroppers are modeled as a homogeneous
Poisson point process (PPP) and the source-destination pair is assisted by
intermediate relays using the decode-and-forward (DF) strategy. We analytically
characterize the physical layer security performance of any chosen multihop
path using the end-to-end secure connection probability (SCP) for both
colluding and non-colluding eavesdroppers. To facilitate finding an efficient
solution to secure routing, we derive accurate approximations of the SCP. Based
on the SCP approximations, we study the secure routing problem which is defined
as finding the multihop path having the highest SCP. A revised Bellman-Ford
algorithm is adopted to find the optimal path in a distributed manner.
Simulation results demonstrate that the proposed secure routing scheme achieves
nearly the same performance as exhaustive search.
