Protocols for Secure Communication in Wireless Sensor Networks

4.4. Multiple Hash Chains for Key Agreement 119
Probability of link key compromise
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
1 10 100 1000
Number of hash chains
Figure 4.6: Probability of key compromise depending on the number of hash chains, for different
sizes of adversaries. Note the logarithmic scale of the horizontal axis
4.4.4 Comparison with Random Key Pre-Distribution
Both the key agreement scheme based on multiple hash chains and the qcomposite
random key predistribution scheme provide a probabilistic level of
resilience. In both cases, it is measured by the fraction of a set of link keys that
can be expected to be compromised.
The hash chain scheme provides full connectivity, i.e. every node is able to
establish a link key with any other node. In contrast, the q-composite scheme
provides only partial connectivity. However, the latter allows the connectivity
to be set arbitrarily close to one if a reduced level of resilience is accepted.
The resilience of the hash chain scheme depends on the number t of chains
being used, and the size j of the attacker. The resilience of the q-composite
scheme depends on the size of the attacker n, the connectivity pc, and the parameter
q.
In terms of computational complexity, the hash chain scheme requires a
certain overhead since a number of hash computations have to be made by each
node before the link key can be derived.
We are going to compare the resilience of both schemes by an example. We
assume the same key ring size in both cases and ignore the storage overhead
for indices, which are roughly the same size in both cases and small compared
to the key size.
j=1
j=2
j=10
j=20