Information Theoretic Secrecy in Two-Way Channels / Aly Mahmoud Mohamed AbdelRahman ElGamal

Supervisor: Moustafa Youssef

Thesis (M.A.)—Nile University, Egypt, 2009 .

"Includes bibliographical references"

Contents:
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Overview of Related Work . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Contribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2. The One-Way Wire-Tap Channel . . . . . . . . . . . . . . . . . . . . . . 7
2.1 System Model and Notation . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Discrete Memoryless Wire-Tap Channel . . . . . . . . . . . . . 10
2.3 The Gaussian Wire-Tap Channel . . . . . . . . . . . . . . . . . . . 13
3. Achievable Secrecy Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 System Model and Notation . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Channel Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Discrete Memoryless Channels . . . . . . . . . . . . . . . . . . . . 18
3.4 The Gaussian Channel . . . . . . . . . . . . . . . . . . . . . . . . . 24
v
4. A Practical Setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1 System Model and Notation . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Analytical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2.1 One-Way Communication with Feedback . . . . . . . . . . . 32
4.2.2 Two-Way Communication with Randomized Scheduling . . 33
4.3 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . 38
5. Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . 43
Bibliography . . . . . . . . . . . . .

Abstract:
This thesis is concerned with the study of realizing reliable and secure twoway
communication in the presence of a passive eavesdropper (Eve). Our approach
achieves perfect information theoretic secrecy via a novel scheme that employs both
random binning and channel prefixing. The key idea is to let both users jointly optimize
the prefix channel distributions, such that their new channel conditions are
favorable compared to Eve’s channel. Random binning is then used to exploit the
secrecy advantage offered by the cascade channel. An achievable rate region for the
general discrete memoryless channel is provided, and a corollary for the modulo-two
channel is given. Next, a practical setting, where the nodes have half-duplex antennas,
is explored for the modulo-two and Gaussian channels. In the Gaussian setting,
the channel coefficients are based on a free space path loss model. In this setting, we
use a randomized scheduling and power allocation scheme, where we allow Alice and
Bob to send symbols at random time instants. While Alice will be able to determine
the symbols transmitted by Bob, Eve will suffer from ambiguity regarding the source
of any particular symbol. This desirable ambiguity is enhanced, in our approach, by
randomizing the transmit power level. Finally, we interpret our results in an experimental
setup using IEEE 802.15.4-enabled sensor boards, and show that a Wireless
Body Area Network (WBAN) is a natural application to our approach.

Text in English, abstracts in English.