Protocols for Secure Communication in Wireless Sensor Networks

110 Chapter 4. Key Establishment
Alice
0 1 2 3 4 5 6
h
Bob
Figure 4.3: Two nodes using a hash chain to agree on a key
4.3 Key Agreement Based on Hash Chains
In this section, we describe how to use hash chains as a means for key agreement
between two parties. We exploit the fact that element q of a hash chain
can be derived from element p if and only if p ≤ q.
4.3.1 Hash Chains
Let h be a one-way hash function that is publicly known. A hash chain is a
sequence
σ = (zω)
for 0 ≤ ω < T where T ∈ IN is the length of the hash chain. z0 is the seed of the
hash chain. For all ω ≥ 1, the element σ[ω] = zω is obtained by applying the
hash function h to the previous element of the sequence, i.e.
zω = h(zω−1) = h ω (z0) .
We refer to the elements of a hash chain as (hash) chain values. The position
of a chain value zω is that value’s index ω in the hash chain. Whenever we refer
to a chain value, we implicitly assume that its index is also available.
Assuming that one element zu of the hash chain is known, it is easy to compute
all following elements zu+v,v > 0 in the chain. However, the one-way
property of h forbids it to compute any elements of the chain preceding the
known value. In particular, it is not possible to reconstruct the seed z0 of a hash
chain unless z0 is already known.
4.3.2 Single-Chain Key Agreement
Key distribution The key distribution center (KDC) generates a hash chain σ
of length T . For each node X, the KDC selects randomly (and uniformly) a
position ωX on the hash chain (0 < ωX < T ). The index ωX and its associated
chain value σ[ωX] is distributed to the respective node. We assume that Alice
and Bob receive the chain values σ[ωA] and σ[ωB], respectively.