Protocols for Secure Communication in Wireless Sensor Networks

200 Chapter 6. Integrity-Preserving Communications
cluded in the process of shortcut assignment. By adding some tolerance to
the number of hops the token travels between assignments, the assignment can
be balanced such that all nodes will eventually serve as shortcuts to the same
number of other nodes.
There are two major problems with this approach. First, the number of messages
that have to travel through the network is very big. A ring can be easily
constructed based on a spanning tree, for example using an Echo algorithm,
which however leads to a rather inefficient ring structure. For n nodes in the
network, such a spanning tree contains n − 1 edges and therefore the corresponding
ring contains approximately 2n edges. In the optimal case, the ring
has n − 1 edges, but such a ring is hard to construct. Since each token has to
travel along each edge once, in total between roughly n 2 and 2n 2 messages have
to be transmitted. A related problem is the fact that each node has to process
at least n messages in total. The second problem is the distribution of shortcut
nodes. With the described approach, an even distribution of shortcut nodes
cannot be guaranteed.
A more efficient assignment of shorcut nodes, which also provides an even
shortcut node distribution, is based on a controlled selection process. Each
node X partitions the network in nS geographical regions and sends a request to
the center of each of these regions. The regions have to be constructed in a way
such that with one shortcut node in each region, full coverage is provided. By
construction, this approach provides an even distribution of the shortcut nodes.
Its scalability is also improved compared to the token ring approach. Each node
sends nS request messages, receives the same amount of responses, and each
message travels about L hops (average path length in the network). Thus, in
total 2nnSL messages are sent.
6.5.3 Long-Range Interleavings
In very large networks, it may be impossible to achieve full coverage with a
limited number nS of shortcuts and a given δ as a message may not be able to
reach the δ-neighbourhood of its destination with a single shortcut. However,
there might be another node, which is already part of the message path, that has
a shortcut in the δ area of the target, or at least closer to it than the previous one.
Thus, while a message travels on its path to its destination, additional shortcuts
can be used to span the complete distance to the δ-region of the destination.
This idea is depicted in Figure 6.22. Here, two additional shortcuts are being
used in order to get the message closer to the target G. The authentication links
“monitor” each other: The link between B and E ensures that the message is