Efficient Byzantine Reliable Broadcast with Low Communication and Time Complexity

Core Concepts

This paper introduces novel mechanisms to lower the communication and computational complexity of Byzantine reliable broadcast protocols in asynchronous networks with less than a third of Byzantine nodes. Two algorithms are presented that achieve an overhead factor of 2 and 3/2 respectively, while also optimizing the time complexity.

Abstract

The paper introduces two algorithms for Byzantine reliable broadcast in asynchronous networks with less than a third of Byzantine nodes: Algorithm A_bit: Reduces the overhead factor to 2 compared to the optimal communication complexity. Has a time complexity of 3 rounds if the sender is honest. Requires only collision-resistant hash functions. Algorithm A_sig: Achieves an optimal time complexity of 2 rounds if the sender is honest. Has an overhead factor of 3/2 under normal operation. Utilizes threshold signatures to ensure progress even with a Byzantine sender. The key ideas are: Using (n,2t+1)-erasure codes instead of (n,t+1) to reduce fragment size. Introducing a step where nodes with 2t+1 fragments send missing fragments to other nodes. Leveraging threshold signatures to enable faster progress without compromising communication complexity. The paper also provides a lower bound showing that an overhead factor lower than 3/2 cannot be achieved for a relevant class of reliable broadcast algorithms.

Stats

The encoding (decoding) time is lower by a factor of 2.2-2.4 (1.8-2.0) when using an (n,2t+1)-erasure code compared to an (n,t+1)-erasure code.

Quotes

"The core idea is quite simple: a (n,2t+1)-erasure code is used instead, reducing the fragment size to |m|/(2t+1) ≈3/2 |m|/n." "If a node with 2t+1 fragments manages to reconstruct the message, it disseminates fragments again but only to the t nodes from which no fragment was received."

Key Insights Distilled From

Byzantine Reliable Broadcast with Low Communication and Time Complexity

by Thomas Loche... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2404.08070.pdf

Deeper Inquiries

How can the proposed algorithms be extended to handle dynamic network environments with nodes joining and leaving the network

To handle dynamic network environments with nodes joining and leaving the network, the proposed algorithms can be extended by incorporating mechanisms for node management. When a new node joins the network, it can go through a verification process to ensure its authenticity and obtain the necessary keying material for participation. The existing nodes can update their data structures to include information about the new node. Similarly, when a node leaves the network, the remaining nodes can adjust their data structures accordingly by removing the departing node's information. By implementing protocols for node addition and removal, the algorithms can adapt to changes in the network topology while maintaining the reliability of message dissemination.

What are the implications of the lower bound on the overhead factor for the design of practical Byzantine reliable broadcast protocols

The lower bound on the overhead factor has significant implications for the design of practical Byzantine reliable broadcast protocols. It sets a theoretical limit on how efficiently information can be disseminated in the presence of Byzantine nodes while ensuring reliability and fault tolerance. Protocol designers must consider this lower bound when optimizing communication complexity and time complexity in real-world implementations. The bound serves as a benchmark for evaluating the efficiency of new protocols and can guide the development of more efficient and scalable Byzantine fault-tolerant systems. By understanding and respecting this lower bound, protocol designers can strive to achieve optimal performance while guaranteeing the necessary reliability and fault tolerance properties.

Can the techniques introduced in this paper be applied to improve the performance of other distributed protocols that rely on reliable broadcast as a building block

The techniques introduced in the paper can be applied to improve the performance of other distributed protocols that rely on reliable broadcast as a building block. By optimizing communication complexity and time complexity, these techniques can enhance the efficiency and scalability of various distributed systems. For protocols such as atomic broadcast, distributed key generation, secure data replication, and secret sharing that depend on reliable message dissemination, reducing the overhead factor and improving the overall efficiency can lead to better system performance. Implementing the novel mechanisms and algorithms proposed in the paper can help enhance the reliability and fault tolerance of distributed systems while minimizing communication and computational complexity.