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

Chapter 6: Wireless Physical-layer Secret-key Generation (WPSG) in Relay Networks:
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Information Theoretic Limits, Key Extension, and Security Protocol
6.4 Investigation of the Key Generation Rate
In a direct communication, if the transmitter and the receiver have not moved, no new key
can be generated since the channel is static. Therefore, the key generation rate depends
heavily on the movements of transmitter and receiver. Assuming that channel parameters
are sampled once every sampling time t s , the average key generation rate becomes
where
I k (it s ) = I
(ĥa (it s ); ĥa ′(it s)
R k = lim
n→∞
∑ n−1
i=0 I k(it s )
, (6.4)
nt s
∣ ĥa((i − 1)t s ), ĥa ′((i − 1)t s), ..., ĥa(0), ĥa ′(0) )
. (6.5)
The mutual information in (6.5) depends on how far the transmitter and the receiver
can travel within t s . It is therefore related to the velocity and the mobility model if the
value is to be obtained by simulation [76].
Note that, when the key is generated according to the one-relay model in Fig. 6.5, the
key generation rate is improved by the relay movement, which causes variation in channel
parameters even when both transmitter and receiver are static. This compensates for the
key loss due to the altered distribution shown in Fig. 6.6.
6.5 Security Protocol
Wireless communication between two nodes in a multi-path, multi-hop network does not
require that the forward transmission path and the reverse one are the same. However, if
our wireless physical-layer security scheme is used, they at least have to make sure that
they use the same channels for secret-key generation. Some protocols are discussed in this
section to achieve that purpose.
In an arbitrary network having some routers between Alice and Bob, we need a secure
protocol for the transmission of pilot symbols for the key generation. To differentiate