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On Different Information Theoretic Security Measures in Communication Network

Kavian, Masoud | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52883 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza; Mirmohseni, Mahtab
  7. Abstract:
  8. Reliable and secure communication requires low error probability and low information leakage, respectively. In this thesis we study different security parameters in communication networks. Three important security metrics are noted by weak, strong, and perfect secrecy. A weak condition on secrecy requires the percentage of the message leaked to the adversary vanish as the code length increases, while a strong condition on secrecy requires the total amount of leaked information (not its percentage) vanish as length increases. Perfect secrecy requires absoloutely zero leakage of information for every given block length. An intriguing question is to determine the secrecy rate under secrecy metric in communication networks. Therefore Mojahedian et. al. have proved the equivalency between the weak and strong secrecy metrics in wire-line networks in the secrecy rate point of view. Here, we are interested in studying the equivalency between the weak and strong secrecy condition under a stronger metric, i.e., the Renyi mutual information Also, we focus on another problem to find equivalency between the strong and perfect secrecy metrics. We answer these questions using the output statistics of random binning (OSRB) and exact common information tools. To make the connection between secrecy rate in weak and strong metrics, we generalize the OSRB theorem for Renyi mutual information for (1<α<2) and then we show that negligible decrease of message rate makes the equivalency between the weak and strong metrics. Our proof works for any communication network with different topologies and noise distributions. In our major contribution, we prove the equivalency between strong and perfect secrecy condition in general wire-line networks. For this purpose, at first we consider two basic structures, i.e, and we call them cascade and parallel structure channels and we employ the coupling method. Since we need to induce the independent distribution over network, in addition to the coupling method, we have to make the coordination between all nodes by sharing common randomness. Thus, we utilize the exact common information to determine the amount of shared randomness for making this coordination in parallel structure. Finally we extend this proof to provide perfect secrecy in general networks.
  9. Keywords:
  10. Output Statistics of Random Binning (OSRB) ; Perfect Security ; Weak Security ; Strong Secrecy ; Exact Common Information ; Renyi Mutual Information

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