Compressing Communication in Distributed Protocols

TL;DR

This paper introduces a method to compress communication in distributed selection protocols, reducing message size to polylogarithmic in the universe size while maintaining protocol properties and fault resilience.

Contribution

It provides a generic transformation that compresses messages in selection protocols to polylogarithmic size, applicable under Byzantine fault conditions.

Findings

Compressed messages of polylogarithmic size suffice for various protocols

The transformation preserves rounds, output distribution, and fault tolerance

Applicable to protocols with polynomially many rounds

Abstract

We show how to compress communication in selection protocols, where the goal is to agree on a sequence of random bits using only a broadcast channel. More specifically, we present a generic method for converting any selection protocol, into another selection protocol where each message is ``short'' while preserving the same number of rounds, the same output distribution, and the same resilience to error. Assuming that the output of the protocol lies in some universe of size $M$, in our resulting protocol each message consists of only $\mathsf{polylog}(M,n,d)$ many bits, where $n$ is the number of parties and $d$ is the number of rounds. Our transformation works in the presence of either static or adaptive Byzantine faults. As a corollary, we conclude that for any $\mathsf{poly}(n)$-round collective coin-flipping protocol, leader election protocol, or general selection protocols, messages of length $\mathsf{polylog}(n)$ suffice (in the presence of either static or adaptive Byzantine faults).