Protocols for Secure Communication in Wireless Sensor Networks

108 Chapter 4. Key Establishment
pκ and p q κ denote the probability with which a communication link between a
pair of nodes are subject to eavesdropping or manipulation by an adversary who
has captured x nodes. It has to be noted that this probability is independent of
the number of nodes that are present in the network.
For illustration, Figure 4.2 shows graphs of equations 4.3 and 4.4 for different
connectivities.
The difference between the basic scheme and the q = 1 composite scheme
stems from the fact that in the basic scheme only one root key is used to determine
a link key while in the composite scheme, all shared root keys between
a pair of nodes are used for deriving the link key. This makes the composite
scheme more resilient against an attacker who needs to obtain more key material
to compromise a link key.
As pointed out in [39], the composite schemes are more resilient than the
basic scheme for small-scale attacks. However, the composite schemes for
q > 1 tend to reveal more information than the basic scheme to an attacker as
he captures more nodes. Hence, at some point, this advantage turns into an
disadvantage.