Protocols for Secure Communication in Wireless Sensor Networks

4.3. Key Agreement Based on Hash Chains 111
Algorithm 1 Determine common key
Global values:
h: a one-way hash function
Input:
X: ID of the local entity executing the algorithm
Y : ID of the peer entity
ωX,HX: local hash chain information
Output:
The common chain key K
1: send(ωX)
2: ωY := receive()
3: if ωX < ωY then
4: K := h ωY −ωX (HX)
5: else
6: K := HX
7: end if
8: return K
Key agreement Alice and Bob agree on a common value using the hash chain
in the following way. First, they exchange their chain indices. Then, they select
the chain value that is “lower” in the chain, i.e. the one with the bigger position
index, as their common value. The agreed-upon value K will either be σ[ωA] or
σ[ωB]:
K = σ[max(ωA,ωB)]
The node whose value is “higher” (i.e., closer to the seed) in the chain performs
a number of applications of the hash function to eventually arrive at the
other node’s value. This number is determined by the difference between both
position indices. This procedure is described as Algorithm 1.
Example 2 (Key agreement based on a hash chain). Consider the situation in
Figure 4.3 where a hash chain of length seven is shown (only indices, no key
values are visible). Alice’s value ωA = 2 is “higher” in the hash chain than
Bob’s value ωB = 4. Therefore, the agree-upon common value will be σ[ωB].
Alice performs two hash computations to obtain Bob’s chain value from σ[ωA].
Note that Bob cannot construct Alice’s value σ[ωA] on his own and also does
not learn that value during the protocol’s execution.
4.3.3 Chain Key Resilience
Let’s assume that there is an adversary Eve who tries to sneak on Alice and
Bob’s communication, i.e. carry out an attack on the confidentiality of their