TR06-026 Authors: Ronen Gradwohl, Salil Vadhan, David Zuckerman

Publication: 28th February 2006 18:39

Downloads: 2825

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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 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.