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

摘要

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 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 capacity of BB in a given network is then defined as the supre-mum of all achievable BB throughputs in the given network, over all possible BB algorithms. We develop NAB-a Network-Aware BB algorithm-for tolerating f faults in arbitrary point-to-point networks consisting of n ≥ 3f + 1 nodes and having ≥ 2f + 1 directed node disjoint paths from each node i to each node j. We also prove an upper bound on the capacity of BB, 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 general point-to-point networks.