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

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Chapter 7: Physical-layer Key Encoding for Wireless Physical-layer Secret-key
Generation (WPSG) with Unequal Security Protection (USP)
c 4
N 4 − c 4
c 3 N 3 − c 3
c 2 N 2 − c 2
c 1 N 1 − c 1
It is weakly secure if
1
|F| n
Figure 7.3: An illustration of combinatorial weak security limit
< p g < 1. This p g should be determined by the application layer
who has a better idea about how weak the data security in each priority class should be
allowed to be.
In our scalable security framework, the guessing success probability is not the only
benchmark, since, for a given data priority i having N i data symbols, we are interested
in making sure that only up to a limited number c i of symbols are weakly secure with a
guessing success probability p g not exceeding a threshold p ti , whereas the other N i − c i
symbols are perfectly secure. Therefore, we propose in Definition 7.4 another benchmark
called the combinatorial weak security limit (CWSL) which provides the parameter c i for
each priority class. Prior to that, the concepts of a priority class, a priority classification
function, and an ordered scalable message are defined in Definitions 7.1-7.3, respectively.
A combinatorial weak security limit c i for each priority class i is illustrated in Fig. 7.3.
The smaller the i, the higher the priority and therefore the lower the proportion c i /N i of
weakly secure symbols. Note that c i symbols do not need to stick together at the front of
the data, but can be arbitrarily distributed.
Definition 7.1 Given a scalable message M= [m 1 , m 2 , ..., m ω ], a set of symbols with
priority class i, i > 0, is given by Q i = {q i1 , q i2 , ..., q iυi }, where each q ik , 1 ≤ k ≤ υ i , is a
distinct element in M. Each member in Q i is less important than any member in Q i−1
and may be useless without the recovery of some members in Q i−1 .
Definition 7.2 π(m j ) is a priority classification function of a scalable symbol m j belonging
to the scalable message M= [m 1 , m 2 , ..., m ω ] if and only if m j is of the priority class
π(m j ) ∈ Z + , 1 ≤ j ≤ ω.