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Perfectly-Secure Key Distribution for Dynamic Conferences

  • Carlo Blundo
  • Alfredo De Santis
  • Amir Herzberg
  • Shay Kutten
  • Ugo Vaccaro
  • Moti Yung
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 740)

Abstract

A key distribution scheme for dynamic conferences is a method by which initially an (off-line) trusted server distributes private individual pieces of information to a set of users. Later any group of users of a given size (a dynamic conference) is able to compute a common secure key. In this paper we study the theory and applications of such perfectly secure systems. In this setting, any group of t users can compute a common key by each user computing using only his private piece of information and the identities of the other t − 1 group users. Keys are secure against coalitions of up to k users, that is, even if k users pool together their pieces they cannot compute anything about a key of any t-size conference comprised of other users.

First we consider a non-interactive model where users compute the common key without any interaction. We prove a lower bound on the size of the user’s piece of information of\( \left( {\begin{array}{*{20}c} {k + t - 1} \\ {t - 1} \\ \end{array} } \right) \) times the size of the common key. We then establish the optimality of this bound, by describing and analyzing a scheme which exactly meets this limitation (the construction extends the one in [2]). Then, we consider the model where interaction is allowed in the common key computation phase, and show a gap between the models by exhibiting an interactive scheme in which the user’s information is only k + t − 1 times the size of the common key. We further show various applications and useful modifications of our basic scheme. Finally, we present its adaptation to network topologies with neighborhood constraints.

Keywords

Symmetric Polynomial Communication Graph Neighborhood Constraint Dynamic Conference Cryp Tology 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Carlo Blundo
    • 1
  • Alfredo De Santis
    • 1
  • Amir Herzberg
    • 2
  • Shay Kutten
    • 2
  • Ugo Vaccaro
    • 1
  • Moti Yung
    • 2
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoBaronissi (SA)Italy
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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