Random Selection with an Adversarial Majority

  • Ronen Gradwohl
  • Salil Vadhan
  • David Zuckerman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4117)

Abstract

We consider the problem of random selection, where p players follow a protocol to jointly select a random element of a universe of size n. However, some of the players may be adversarial and collude to force the output to lie in a small subset of the universe. We describe essentially the first protocols that solve this problem in the presence of a dishonest majority in the full-information model (where the adversary is computationally unbounded and all communication is via non-simultaneous broadcast). Our protocols are nearly optimal in several parameters, including the round complexity (as a function of n), the randomness complexity, the communication complexity, and the tradeoffs between the fraction of honest players, the probability that the output lies in a small subset of the universe, and the density of this subset.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ronen Gradwohl
    • 1
  • Salil Vadhan
    • 2
  • David Zuckerman
    • 3
  1. 1.Department of Computer Science and Applied MathWeizmann Institute of Science 
  2. 2.Division of Engineering & Applied SciencesHarvard University 
  3. 3.Department of Computer ScienceUniversity of Texas at Austin 

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