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

106
Chapter 7: Physical-layer Key Encoding for Wireless Physical-layer Secret-key
Generation (WPSG) with Unequal Security Protection (USP)
A
A
x 1 + w
w
x 2 + x 3 x 2 + 2x 3
B
x 1 + w
w
C
B
x 2 + x 3 x 2 + 2x 3
C
F
F
x 1 + w
x 1 + 2w
w
x 2 + x 3 2x 2 + 3x 3
x 2 + 2x 3
x 1 + 2w
G
x 1 + 2w
G
2x 2 + 3x 3 2x 2 + 3x 3
D
E
D
E
(a)
(b)
Figure 7.4: Secure network coding in a butterfly network with (a) Shannon security and
(b) weak security
7.6 Weakly Secure Network Coding in the Scalable
Security Framework
Bhattad and Narayanan explain the difference between Shannon security and weak security
in their work on weakly secure network coding [35]. They state that the source
information is Shannon secure if I(X; Y) = 0, where X = [x 1 , x 2 , ..., x r ] is the source
information and Y is the set of messages to which an eavesdropper can listen. In the case
of Shannon security, the eavesdropper has no information about the source at all. On the
other hand, the source information is weakly secure if I(x i ; Y) = 0, 1 ≤ i ≤ r.
The difference between two security concepts can be illustrated by secure network
coding in Fig. 7.4. The goal of secure network coding is to make sure that an eavesdropper
who has access to a limited number k of edges cannot decrypt the source information.
Figures 7.4 (a) and (b) are an example of secure network coding with k = 1. According
to the figures, the node F performs network coding by adding the symbol from the edge
BF to that from CF , yielding a symbol in F G. In Fig. 7.4 (a), the source symbol x 1 is
mixed with a random symbol w, whereas in Fig. 7.4 (b), two source symbols x 2 and x 3
are mixed together. Observe that, for both figures 7.4 (a) and (b), the eavesdropper who
has access only to a single edge cannot decrypt x 1 , x 2 , or x 3 .