Network Coding and Wireless Physical-layer ... - Jacobs University

Chapter 6: Wireless Physical-layer Secret-key Generation (WPSG) in Relay Networks:
Information Theoretic Limits, Key Extension, and Security Protocol 85
Alice
h a1 R 1
h 1b
R 2
Bob
1 2
h a2
h 2b
h an
R n
h nb
Figure 6.7: A fork-rake network
secure protocols from insecure ones, let us consider a simplified fork-rake network in
Fig. 6.7 as an example. Alice broadcasts a pilot packet x to all relays R 1 to R n within her
transmission range. Each relay R i receives h ai x, where h ai is the channel gain between
Alice and the relay and x is the pilot sequence. Using an amplify-and-forward scheme,
each relay R i chooses whether to forward a i h ai x, where a i is the amplification gain to
Bob, or not. Then, Bob receives ∑ i∈F a ih ai h ib x, where h ib is the channel gain between
the relay R i and Bob, whereas F is the index set of relays that choose to forward the pilot
packet. After that, assuming that the channel gain has not changed yet, Bob derives the
key and broadcasts x back such that every relay receives h ib x. However, only the relay R i
that has previously forwarded the packet to Bob will forward a i h ib x to Alice, who derives
the same key from ∑ i∈F a ih ai h ib x [76].
We assume that no enemy is allowed to be too close to Alice or Bob such that its
channel parameters are uncorrelated to theirs. (If there are some correlations, the key
encoding scheme discussed in the next chapter can be applied.) Now, we will show that
the protocol security depends on the forwarding strategies of the relays. Three strategies
are shown in an ascending security order [76].
1. Only one route is taken, i.e., only one relay forwards the packet. This is insecure
because an enemy only needs to be close enough to that relay R i to listen to a i h ai x sent
to Bob and a i h ib x sent to Alice. If it knows a i , it can derive a i h ai h ib x as well as the key
with ease.
2. m routes are taken. This is insecure if there are k enemies and k ≥ m because each
of m out of k enemies can do the same as the single enemy does in 1. After that, they
meet and derive ∑ i∈F a ih ai h ib x. The enemy gang has an additional difficulty, however,