Fault-Tolerant Distributed Computing in Full-Information Networks

Shafi Goldwasser, Elan Pavlov, Vinod Vaikuntanathan
2006 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)  
In this paper, we use random-selection protocols in the full-information model to solve classical problems in distributed computing. Our main results are the following: • An O(log n)-round randomized Byzantine Agreement (BA) protocol in a synchronous full-information network tolerating t < n 3+ faulty players (for any constant > 0). As such, our protocol is asymptotically optimal in terms of fault-tolerance. • An O(1)-round randomized BA protocol in a synchronous full-information network
more » ... ing t = O( n (log n) 1.58 ) faulty players. • A compiler that converts any randomized protocol Π in designed to tolerate t fail-stop faults, where the source of randomness of Π in is an SV-source, into a protocol Π out that tolerates min(t, n 3 ) Byzantine faults. If the round-complexity of Π in is r, that of Π out is O(r log * n). Central to our results is the development of a new tool, "audited protocols". Informally "auditing" is a transformation that converts any protocol that assumes built-in broadcast channels into one that achieves a slightly weaker guarantee, without assuming broadcast channels. We regard this as a tool of independent interest, which could potentially find applications in the design of simple and modular randomized distributed algorithms. * Supported by NSF grants CNS-0430450 and CCF0514167. 1 The precise notion of a coin necessary to make the Rabin reduction go through is that of an ( , δ)common coin [13] . An ( , δ)-common coin is a coin with bias δ which all players agree on with probability . Thus, the protocols of [14, 27] construct an (1, δ)-common coin for some δ > 0. In other words, at the end of the coin-flipping protocol, all the players output the same semi-random bit with probability 1. In this work, we will construct an ( , δ)-common-coin protocol for some , δ > 0, without assuming broadcast channels. We then show, Main Theorem 1. For any constant > 0, there exists a BA protocol BA in a synchronous full-information network tolerating t < ( 1 3 − )n Byzantine faults, and runs for expected O( log n 2 ) rounds. Prior to our work, in the full information model, the best known BA protocol was due to Pavlov, and Vaikuntanathan [5] who construct an O(log n)-round protocol that tolerates t < ( 1 4 − )n faults, with quasi-polynomial communication complexity. Whereas the basic paradigm outlining the result of [5] was to use (in a complex fashion) the leader election protocol of Feige [14] , the basic building block outlining our new protocol is the random selection protocol of Russell and Zuckerman (RZ) [27] . Informally, we will use the committees defined by the RZ protocol as auditors for an execution of the RZ protocol itself. This is possible, since in the RZ protocol, the committees are defined in advance. This idea is not (at least directly) applicable to Feige's protocol since it constructs the committees on-the-fly.
doi:10.1109/focs.2006.30 dblp:conf/focs/GoldwasserPV06 fatcat:yfdtn3nmrbdbzdwow75ylapif4