Protocols for Secure Communication in Wireless Sensor Networks

100 Chapter 4. Key Establishment
• S = |K | denotes the size of the key pool.
• m is a global parameter and denotes the key ring size, which is the same
for all nodes.
• A (pseudo-) random number sequence generator Ψ g where g acts as a
seed.
Ψ takes four parameters: a node identifier, a lower bound on the output,
an upper bound on the output, and the number of elements in the generated
sequence. Ψ may generate “real” random numbers or pseudo-random numbers.
In any case, we assume that Ψ is “stable”, i.e. for the same input, it will
produce the same output in a given context (which is determined by g). The
produced numbers are integers within the given (inclusive) bounds. If the numbers
are generated pseudo-randomly, the node identifier is used as part of the
seed. This enables other parties to reproduce the same sequence of numbers.
As an additional constraint, Ψ will produce any number at most once.
Based on these elements, we define a key selection function F, which returns
for a given node ID a set of keys:
F(IDu) = 〈K [v1],...,K [vm]〉
where Ψ g (IDu,1,S,m) = 〈v1,...,vm〉 for a given g.
4.2.2 Pre-Distribution Phase
The initial phase of a key pre-distribution scheme is performed in a secure
environment, assuming that the adversary does not have access to the nodes
during this phase, e.g. before deployment. The key distribution center (KDC)
is responsible for performing this initial phase. The KDC computes for each
node u the key ring F(IDu) and loads the selected keys onto the node.
There are two parameters in this scheme that can be varied and that are
important regarding the security properties of the scheme: the size S of the key
pool and the size m of key rings. There is a trade-off between connectivity and
attack resilience. The larger the key pool is, the more resilient the scheme will
be against an attacker, since the probability that a captured node contains the
root keys required to derive a certain link key is lower. However, connectivity
suffers since the intersection of the key rings of two nodes trying to establish
a link key tends to be smaller. Larger key rings, on the other hand, increase
connectivity as the intersection of two key rings contains more elements. But
an attacker also learns more root keys when capturing a single node, thereby
increasing his chance to compromise a link key.