Byzantine Broadcast in Point-to-Point Networks using Local Linear Coding

TL;DR

This paper introduces NAB, an algorithm for Byzantine Broadcast in synchronous point-to-point networks, achieving a significant fraction of the network's capacity despite Byzantine faults, with proven bounds and optimality conditions.

Contribution

The paper presents NAB, the first Byzantine Broadcast algorithm that guarantees a constant fraction of network capacity in arbitrary point-to-point networks with Byzantine faults.

Findings

NAB achieves at least 1/3 of the capacity in general networks.

NAB achieves at least 1/2 of the capacity under additional network conditions.

The paper establishes an upper bound on Byzantine broadcast capacity.

Abstract

The goal of Byzantine Broadcast (BB) is to allow a set of fault-free nodes to agree on information that a source node wants to broadcast to them, in the presence of Byzantine faulty nodes. We consider design of efficient algorithms for BB in {\em synchronous} point-to-point networks, where the rate of transmission over each communication link is limited by its "link capacity". The throughput of a particular BB algorithm is defined as the average number of bits that can be reliably broadcast to all fault-free nodes per unit time using the algorithm without violating the link capacity constraints. The {\em capacity} of BB in a given network is then defined as the supremum of all achievable BB throughputs in the given network, over all possible BB algorithms. We develop NAB -- a Network-Aware Byzantine broadcast algorithm -- for arbitrary point-to-point networks consisting of $n$ nodes, wherein the number of faulty nodes is at most $f$, $f<n/3$, and the network connectivity is at least $2f+1$. We also prove an upper bound on the capacity of Byzantine broadcast, and conclude that NAB can achieve throughput at least 1/3 of the capacity. When the network satisfies an additional condition, NAB can achieve throughput at least 1/2 of the capacity. To the best of our knowledge, NAB is the first algorithm that can achieve a constant fraction of capacity of Byzantine Broadcast (BB) in arbitrary point-to-point networks.