Random Selection with an Adversarial Majority, Proceedings of the 2006 Annual International Cryptology Conference
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.
Ronen Gradwohl, Salil P. Vadhan, David Zuckerman
Gradwohl, Ronen, Salil P. Vadhan, and David Zuckerman. 2006. Random Selection with an Adversarial Majority. Proceedings of the 2006 Annual International Cryptology Conference. 26: 409-426.