Team for Research in
Ubiquitous Secure Technology

Citation
Amin Aminzadeh Gohari, Venkatachalam Anantharam. "Information-Theoretic Key Agreement of Multiple Terminals - Part I: Source Model". Submitted to ``IEEE Transactions on Information Theory", 2008, 2008; This is the first part of a two part paper. The first part is on Source Model while the second part is on Channel Model.

Abstract
This is the first part of a two-part paper on information-theoretically secure secret key agreement. In this part, we study the secrecy problem under the widely studied source model. In the source model the terminals wishing to generate a secret key, as well as the eavesdropper, receive the respective coordinates of a block of independent and identically distributed copies of jointly distributed random variables, after which the terminals are allowed interactive authenticated public communication, at the end of which each terminal should be able to generate the key. We derive a new upper bound on the secrecy capacity that strictly improves the currently best upper bound, due to Renner and Wolf. Further, while the Renner-Wolf bound is defined only in the case of two terminals, the new upper bound applies to the general multi-terminal case. The technique used for deriving our bound is to find certain properties of functions of joint probability distributions which will imply that they dominate the secrecy capacity, and then prove the bound by a verification argument. We also define a problem of communication for omniscience by a neutral observer and establish the equivalence between this new problem and the problem of secret key agreement. This generalizes an earlier result of Csisz´ar and Narayan. Finally, we prove a new lower bound on the secrecy capacity in the general multi-terminal case that in the two terminal case is strictly better than what is essentially the currently best known lower bound, namely the maximum of the two one-way secrecy capacities.

Electronic downloads

• HTML

  Amin Aminzadeh Gohari, Venkatachalam Anantharam. <a
  href="http://www.truststc.org/pubs/408.html"
  >Information-Theoretic Key Agreement of Multiple
  Terminals - Part I: Source Model</a>,
  <i>Submitted to ``IEEE Transactions on Information
  Theory", 2008</i>,  2008; This is the first part
  of a two part paper. The first part is on Source Model while
  the second part is on Channel Model.

• Plain text

  Amin Aminzadeh Gohari, Venkatachalam Anantharam.
  "Information-Theoretic Key Agreement of Multiple
  Terminals - Part I: Source Model". <i>Submitted
  to ``IEEE Transactions on Information Theory",
  2008</i>,  2008; This is the first part of a two part
  paper. The first part is on Source Model while the second
  part is on Channel Model.

• BibTeX

  @article{GohariAnantharam08_InformationTheoreticKeyAgreementOfMultipleTerminals,
      author = {Amin Aminzadeh Gohari and Venkatachalam Anantharam},
      title = {Information-Theoretic Key Agreement of Multiple
                Terminals - Part I: Source Model},
      journal = {Submitted to ``IEEE Transactions on Information
                Theory", 2008},
      year = {2008},
      note = {This is the first part of a two part paper. The
                first part is on Source Model while the second
                part is on Channel Model.},
      abstract = {This is the first part of a two-part paper on
                information-theoretically secure secret key
                agreement. In this part, we study the secrecy
                problem under the widely studied source model. In
                the source model the terminals wishing to generate
                a secret key, as well as the eavesdropper, receive
                the respective coordinates of a block of
                independent and identically distributed copies of
                jointly distributed random variables, after which
                the terminals are allowed interactive
                authenticated public communication, at the end of
                which each terminal should be able to generate the
                key. We derive a new upper bound on the secrecy
                capacity that strictly improves the currently best
                upper bound, due to Renner and Wolf. Further,
                while the Renner-Wolf bound is defined only in the
                case of two terminals, the new upper bound applies
                to the general multi-terminal case. The technique
                used for deriving our bound is to find certain
                properties of functions of joint probability
                distributions which will imply that they dominate
                the secrecy capacity, and then prove the bound by
                a verification argument. We also define a problem
                of communication for omniscience by a neutral
                observer and establish the equivalence between
                this new problem and the problem of secret key
                agreement. This generalizes an earlier result of
                Csisz´ar and Narayan. Finally, we prove a new
                lower bound on the secrecy capacity in the general
                multi-terminal case that in the two terminal case
                is strictly better than what is essentially the
                currently best known lower bound, namely the
                maximum of the two one-way secrecy capacities.},
      URL = {http://www.truststc.org/pubs/408.html}
  }
  

Posted by Amin Aminzadeh Gohari on 10 Jun 2008.
For additional information, see the Publications FAQ or contact webmaster at www truststc org.