Byzantine Broadcast Under a Selective Broadcast Model for Single-hop Wireless Networks

TL;DR

This paper introduces a new selective broadcast model for single-hop wireless networks, analyzing Byzantine fault-tolerant broadcast, and provides algorithms and bounds for its efficiency and complexity.

Contribution

It proposes a novel selective broadcast model that combines features of reliable and point-to-point channels, along with algorithms and bounds for Byzantine broadcast.

Findings

Order-optimal multi-valued Byzantine broadcast algorithm in bit complexity.

Efficient Byzantine broadcast algorithm in message complexity.

Lower bounds on bit and message complexities for the model.

Abstract

This paper explores an old problem, {\em Byzantine fault-tolerant Broadcast} (BB), under a new model, {\em selective broadcast model}. The new model "interpolates" between the two traditional models in the literature. In particular, it allows fault-free nodes to exploit the benefits of a broadcast channel (a feature from reliable broadcast model) and allows faulty nodes to send mismatching messages to different neighbors (a feature from point-to-point model) simultaneously. The {\em selective broadcast} model is motivated by the potential for {\em directional} transmissions on a wireless channel. We provide a collection of results for a single-hop wireless network under the new model. First, we present an algorithm for {\em Multi-Valued} BB that is order-optimal in bit complexity. Then, we provide an algorithm that is designed to achieve BB efficiently in terms of message complexity. Third, we determine some lower bounds on both bit and message complexities of BB problems in the {\em selective broadcast model}. Finally, we present a conjecture on an "exact" lower bound on the bit complexity of BB under the {\em selective broadcast} model.