Protocols for Secure Communication in Wireless Sensor Networks

6.4. Security Evaluation 183
Number of functional paths
1e+06
900000
800000
700000
600000
500000
400000
300000
200000
100000
0
0 200 400 600 800 1000 0.001
Number of compromised nodes
CANVAS approximation
CANVAS simulation
Absolute error
Relative error
Figure 6.12: Precision of approximation compared to simulation, N = 1000
by capturing k + kd/2 nodes, where d is the average node degree. Assuming
the partition has two approximately equally sized parts, there are about N/2
nodes in each of it. This leaves about 2 × N 2 /4 = N 2 /2 secure communication
paths in total, i.e. half of the total number of communication paths. However,
half of the secure paths are fully contained in one block of the partition, and
the other half in the other block. All paths between both blocks are compromised.
If important messages flow from one block to the other, they are prone
to manipulation.
6.4.2 Numerical Approximation
A node capture attack proceeds by successive compromise of nodes. Thus,
the status of a node can either be non-compromised or compromised. A configuration
defines for each node its status. Thus, it is a mapping C : N →
{legitimate,compromised}. For brevity, we write C(x) = {s ∈ N : C(s) = x},
where x ∈ {legitimate,compromised}.
An attack is a sequence of configurations C0,C1,...,Cn. The initial configuration
contains no compromised nodes, i.e. C0(compromised) = /0. All
subsequent configurations build monotonously on the previous one, such that
Ci(compromised) ⊂ Ci+1(compromised). The nodes whose status is newly set
to compromised in each step are chosen according to the different types of attacks,
which are described in Section 3.3.6. For example, in a random spread
100
10
1
0.1
0.01
Relative error