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Secure Index Coding

Mojahedian, Mohammad Mahdi | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 50985 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Aref, Mohammad Reza
  7. Abstract:
  8. Reliable and secure communication requires low error probability and low information leakage, respectively. But there are different metrics for error probability and information leakage. Two important reliability metrics are ϵ or zero probability of error. An ϵ-error criterion requires the (average or maximal) error probability to vanish as the blocklength increases, while a zero-error criterion, demands the error to be exactly zero for every given bloklength. Three important security metrics are weak, strong, or perfect secrecy. A weak notion of secrecy requires the percentage of the message that is leaked to vanish as the code blocklength increases, while a strong notion of secrecy requires the total amount of leaked information (not its percentage) to vanish as the blocklength increases. Perfect secrecy requires absolutely zero leakage of information, for every given blocklength. These reliability and security metrics lead to different notions of capacity which could be quite different. For instance, zero-error capacity, which was originally introduced by Shannon,could be zero in a point-to-point channel, while the ϵ-error could be non-zero for the same channel. One can then ask “how capacity behaves under different reliability and security metrics?”. In this thesis, we address this issue. To this end, we investigate the index coding problem in the presence of an eavesdropper. Messages are to be sent from one transmitter to a number of legitimate receivers who have side information about the messages, and share a set of secret keys with the transmitter. To do this, the transmitter communicates to the legitimate receivers the public code C which is also heard by the eavesdropper. We assume perfect secrecy, meaning that the eavesdropper should not be able to retrieve any information about the message set from the public communication. We study the minimum key lengths for zero-error and perfectly secure index coding problem.Moreover, we consider a relaxation of the perfect secrecy and zero-error constraints to weak secrecy and asymptotically vanishing probability of error, and provide a secure version of the result, obtained by Langberg and Effros, on the equivalence of zero-error and ϵ-error regions in the conventional index coding problem. In addition, we consider a secure network coding problem (a generalized version of secure index coding) in which some secret keys are shared among legitimate nodes, and there exists an eavesdropper which is able to hear a subset of links. We show the equivalency of secure network coding under weak and strong secrecy conditions. For linear network coding, we show a stronger result: equivalency of “perfect secrecy and zero-error constraints” to “weak secrecy and ϵ-error constraints”. Finally, we consider a secure communication scenario consisting of a transmitter and a legitimate receiver which are communicating through an arbitrary network at the presence of an eavesdropper. We study the question of how to enhance secrecy at the cost of decreasing the message length. We give an answer to this question by introducing and utilizing a new correlation metric for measuring secrecy. We show that secrecy can be amplified by an exponential factor at the cost of reducing the message length
  9. Keywords:
  10. Security ; Zero-Error Communications ; Index Coding ; Correlation Metric ; Wire-line Network ; Secrecy Enhancement ; Zero-Error Communications ; Index Coding ; Correlation Metric ; Wire-line Network ; Secrecy Enhancement

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