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Lower Bounds for Distributed Coin-Flipping and Randomized Consensus James Aspnes
 

Summary: Lower Bounds for Distributed Coin-Flipping and Randomized Consensus
James Aspnes
Abstract
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 re-
sult of up to t local coin ips. We show that to guaran-
tee at most constant bias, (t2) local coins are needed,
even if (a) the local coins can have arbitrary distribu-
tions and ranges, (b) the adversary is required to de-
cide 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 prob-
ability 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

  

Source: Aspnes, James - Department of Computer Science, Yale University

 

Collections: Computer Technologies and Information Sciences