Lower Bounds for Distributed Coin-Flipping and Randomized Consensus

We examine a class of collective coin- ipping games that arises from randomized distributed algorithms with halting failures. In these games, a sequence of local coin ips is generated, which must be combined to form a single global coin ip. An adversary monitors the game and may attempt to bias its outcome by hiding the result of up to t local coin ips. We show that to guarantee at most constant bias, (t2) local coins are needed, even if (a) the local coins can have arbitrary distributions and ranges, (b) the adversary is required to decide immediately whether to hide or reveal each local coin, and (c) the game can detect which local coins have been hidden. If the adversary is permitted to control the outcome of the coin except for cases whose probability is polynomial in t, (t2=log2 t) local coins are needed. Combining this fact with an extended version of the well-known Fischer-Lynch-Paterson impossibility proof of deterministic consensus, we show that given an adaptive adversary, a...

• Type: Conference
• Year: 1997
• Where: STOC
• Authors: James Aspnes
• Keywords: Algorithms, Local Coin, Local Coin Ips, Single Global Coin, STOC 1997