Fault-Tolerant Distributed Computing in Full-Information Networks

Shafi Goldwasser, Elan Pavlov, Vinod Vaikuntanathan

Abstract: 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+epsi) faulty players (for any constant epsi > 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 tolerating t = O(n/((log n) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1.58</sup> )) faulty players. A compiler that converts any randomized protocol Pi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> designed to tolerate t fail-stop faults, where the source of randomness of Pi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> is an SV-source, into a protocol Pi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out</sub> that tolerates min(t, n/3) Byzantine faults. If the round-complexity of Pi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</sub> is r, that of Pi <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">out</sub> 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