Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Codes and Game Theory for Key Agreement with Untrusted Participants

Nebojsa Milosavljevic

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2011-6
January 22, 2011

http://www.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-6.pdf

In this work we study the problem of confidential communication when different resources of randomness are available. We start with the relay channel where source observations are available at each terminal. We study the scenario where the transmitter (Alice) sends a private message to the destination (Bob), which is confidential to the relay (Eve). Alice and Bob also want to agree on a secret key that is protected from Eve. We propose an achievable scheme and show that if the channel is degraded or reversely degraded, the secret message-secret key sum rate is optimal. Then, we consider a scenario where three terminals, Alice, Bob and Charlie, observe memoryless correlated observations. Alice wants to agree with Bob on a key that is secured from Charlie. At the same time Alice wants to agree with Charlie on a key that is secured from Bob. We further assume that Alice has no knowledge on how the distributed sources are correlated, and that she is the one who constructs the codebooks for the key agreement. In order to construct the codebooks which would achieve a desired level of secrecy, Alice request some information from Bob and Charlie about their observations. Since Bob and Charlie act like eavesdroppers to each other, they may not be completely honest about what they observe. Therefore, their reports are based on some objective that is a function of the key rate and the amount of information they can learn about the other user’s key, called the leakage rate. We approach this problem from a game-theoretic point of view. For a class of Bob and Charlie’s objective functions that are linear in the key rate and the leakage rate, we characterize a Nash equilibrium. Then, we propose a strategy that Alice can apply in order to ensure that Bob and Charlie’s honest reporting is always a Nash equilibrium. Finally, for the binary erasure source distributions we extend this concept to the multiple terminal case.

Advisor: Kannan Ramchandran and Michael Gastpar


BibTeX citation:

@mastersthesis{Milosavljevic:EECS-2011-6,
    Author = {Milosavljevic, Nebojsa},
    Title = {Codes and Game Theory for Key Agreement with Untrusted Participants},
    School = {EECS Department, University of California, Berkeley},
    Year = {2011},
    Month = {Jan},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-6.html},
    Number = {UCB/EECS-2011-6},
    Abstract = {In this work we study the problem of confidential communication when different resources of randomness
are available.
We start with the relay channel where source observations are available at each terminal. We
study the scenario where the transmitter (Alice) sends a private message to the destination (Bob),
which is confidential to the relay (Eve). Alice and Bob also want to agree on a secret key that is
protected from Eve. We propose an achievable scheme and show that if the channel is degraded or
reversely degraded, the secret message-secret key sum rate is optimal.
Then, we consider a scenario where three terminals, Alice, Bob and Charlie, observe memoryless
correlated observations. Alice wants to agree with Bob on a key that is secured from Charlie. At
the same time Alice wants to agree with Charlie on a key that is secured from Bob. We further
assume that Alice has no knowledge on how the distributed sources are correlated, and that she is
the one who constructs the codebooks for the key agreement. In order to construct the codebooks
which would achieve a desired level of secrecy, Alice request some information from Bob and Charlie
about their observations. Since Bob and Charlie act like eavesdroppers to each other, they may
not be completely honest about what they observe. Therefore, their reports are based on some
objective that is a function of the key rate and the amount of information they can learn about the
other user’s key, called the leakage rate. We approach this problem from a game-theoretic point of
view. For a class of Bob and Charlie’s objective functions that are linear in the key rate and the
leakage rate, we characterize a Nash equilibrium. Then, we propose a strategy that Alice can apply
in order to ensure that Bob and Charlie’s honest reporting is always a Nash equilibrium. Finally,
for the binary erasure source distributions we extend this concept to the multiple terminal case.}
}

EndNote citation:

%0 Thesis
%A Milosavljevic, Nebojsa
%T Codes and Game Theory for Key Agreement with Untrusted Participants
%I EECS Department, University of California, Berkeley
%D 2011
%8 January 22
%@ UCB/EECS-2011-6
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2011/EECS-2011-6.html
%F Milosavljevic:EECS-2011-6