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 87
to Bob in the second time slot will do that to Alice in the fourth one.
5. Enemies E 1 and E 2 are located near enough to R 1 and R 2 , respectively, so that, if
both relays forward x,
5.1 in the second time slot, E 1 hears a 1 h a1 x from R 1 plus the interference a 2 h a2 h R2,E1 x
from R 2 , where h R2,E1 is the channel gain between R 2 and E 1 .
5.2 In the same manner, E 2 hears a 2 h a2 x from R 2 plus the interference a 1 h a1 h R1,E2 x
from R 1 , where h R1,E2 is the channel gain between R 1 and E 2 .
5.3 In the fourth time slot, E 1 hears a 1 h 1b x from R 1 plus the interference a 2 h 2b h R2,E1 x
from R 2 .
R 1 .
5.4 At the same time, E 2 hears a 2 h 2b x from R 2 plus the interference a 1 h 1b h R1,E2 x from
These assumptions are realistic and will hold except in an unlikely situation where
either the relays or the eavesdroppers are only few wavelengths away from the transmitter
or the receiver. Now, we would like to evaluate the security of each strategy.
Strategy 1 of Section 6.5 is totally unsafe since, when only one route is taken, there is
no interference from another route according to 5.1-5.4, therefore, the enemy E i closest
to the chosen route receives clear signal a i h ai x and a i h ib x and can derive ∑ i∈F a ih ai h ib x
as well as the whole key.
Strategy 2 is more secure since there is some interference according to 5.1-5.4. Even
when both enemies help each other, it is not easy to derive ∑ i∈F a ih ai h ib x if the interference
is strong and they do not know a 1 h R1,E2 and a 2 h R2,E1 . (Of course, if they do know
a 1 h R1,E2 and a 2 h R2,E1 , they simply have to solve a system of two linear equations.) An
interference cancellation scheme can be applied, but they still have some disadvantages
as compared with Alice and Bob. They may recover some, but not the whole key.
Strategy 3 with the forwarding probability of, let us say 0.5, is even more secure
since it is now impossible for each enemy to know whether it receives the desired signal
plus interference or merely the interference, especially if the interference is strong and
the enemies do not know a 1 h R1,E2 and a 2 h R2,E1 . With some rational guesses, they may