Improved Bounds for Coin Flipping, Leader Election, and Random Selection

Random selection is a fundamental task in fault-tolerant distributed computing where processors select a random outcome from some domain. Two special cases of this, leader election (where the processors designate a leader amongst themselves) and collective coin flipping (where the processors agree on a common random bit), have been especially widely studied. We study these problems in the full-information model, where processors communicate via a single broadcast channel, have access to private randomness, and face a computationally unbounded adversary that controls some of the processors. Despite decades of study, key gaps remain in our understanding of the trade-offs between round complexity, communication per player in each round, and adversarial resilience. We make progress by proving new lower bounds for coin flipping protocols and both new upper and lower bounds for leader election and random selection protocols.