Advances in Cryptology - CRYPTO 2006

Volume 4117 of the series Lecture Notes in Computer Science pp 409-426

Random Selection with an Adversarial Majority

  • Ronen GradwohlAffiliated withDepartment of Computer Science and Applied Math, Weizmann Institute of Science
  • , Salil VadhanAffiliated withDivision of Engineering & Applied Sciences, Harvard University
  • , David ZuckermanAffiliated withDepartment of Computer Science, University of Texas at Austin


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.