Protocols for Secure Communication in Wireless Sensor Networks

182 Chapter 6. Integrity-Preserving Communications
1000 nodes with a communication range r = 100 have been used, the simulated
attack was a random spread attack. The figures show the absolute and relative
errors of the approximation compared to the simulation result.
For smaller numbers of compromised nodes, the approximation and the simulation
results match quite well. Both the absolute and relative errors increase
but are within acceptable limits – for x < N/4, the relative error remains below
0.1 in both cases. For higher x, the error increases slowly but remains below one
until x ≈ 3 4N. Beyond that threshold, the relative error increases rapidly. The
approximation overestimates the number of non-compromised paths, leading to
inaccurate results for high values of x. However, the absolute error remains in
the order of magnitude of the actual approximated values, so the approximation
is qualitatively still useful.
Number of functional paths
250000
200000
150000
100000
50000
0.0001
0
0 100 200 300 400 500 1e-05
Number of compromised nodes
CANVAS approximation
CANVAS simulation
Absolute error
Relative error
Figure 6.11: Precision of approximation compared to simulation, N = 500
To conclude, Equation 6.4 gives a good estimate of the number of functional
paths (or, equivalently, of the compromised paths) for smaller x assuming a random
spread attack. For other types of attacks we expect the approximation to be
much less accurate. For structured attacks, the impact of a compromised node
highly varies with its position relative to other compromised nodes. Especially
the partitioning attack achieves a big impact with only a small set of nodes.
Assuming a k-connected graph, in the worst case (from the network operator
point of view), the k nodes in the cut-off set and some of their neighbours are
captured. This leads to a partitioning of the network. This could be achieved
100
10
1
0.1
0.01
0.001
Relative error