Byzantine Reliable Broadcast with Low Communication and Time Complexity

TL;DR

The paper tackles Byzantine reliable broadcast in asynchronous networks with up to $t< n/3$ Byzantine nodes by introducing a mechanism that reduces the constant overhead of erasure-code based approaches. It presents two algorithms, $\\mathcal{A}_{bit}$ and $\\mathcal{A}_{sig}$, that use $(n,2t+1)$ erasure codes and Merkle proofs or threshold signatures to achieve lower communication costs and favorable time complexity, achieving $\\mathcal{L}(n)=2$ for the bit-based variant and $\\mathcal{L}(n)=\\frac{5}{2}$ for the threshold-signature variant while maintaining reliability. The paper also shows practical optimizations that can reduce overhead to $\\frac{3}{2}$ under partial synchrony and proves a lower bound of $\\frac{3}{2}$ for a broad class of algorithms, outlining a path to near-optimal performance in real-world deployments. Overall, the work advances bandwidth-efficient reliable broadcast with implications for fault-tolerant consensus and distributed data dissemination.

Abstract

Byzantine reliable broadcast is a fundamental problem in distributed computing, which has been studied extensively over the past decades. State-of-the-art algorithms are predominantly based on the approach to share encoded fragments of the broadcast message, yielding an asymptotically optimal communication complexity when the message size exceeds the network size, a condition frequently encountered in practice. However, algorithms following the standard coding approach incur an overhead factor of at least 3, which can already be a burden for bandwidth-constrained applications. Minimizing this overhead is an important objective with immediate benefits to protocols that use a reliable broadcast routine as a building block. This paper introduces a novel mechanism to lower the communication and computational complexity. Two algorithms are presented that employ this mechanism to reliably broadcast messages in an asynchronous network where less than a third of all nodes are Byzantine. The first algorithm reduces the overhead factor to 2 and has a time complexity of 3 if the sender is honest, whereas the second algorithm attains an optimal time complexity of 2 with the same overhead factor in the absence of equivocation. Moreover, an optimization for real-world implementations is proposed, reducing the overhead factor to 3/2 under normal operation. Lastly, a lower bound is proved that an overhead factor lower than 3/2 cannot be achieved for a relevant class of reliable broadcast algorithms.

Figures (1)

• Figure 1: Given an input of size 1 MiB, encoding and decoding times for erasure codes with parameters $(n, t+1)$ and $(n, 2t+1)$ are shown for different network sizes. The circles and bars mark the averages and the 5th and 95th percentiles, respectively, of the measured times over 1000 runs.

Theorems & Definitions (20)

• definition 1: Reliable broadcast
• lemma 1
• lemma 2
• lemma 3
• theorem 1
• theorem 2: Communication complexity
• theorem 3: Time complexity
• theorem 4: Space complexity
• lemma 4
• lemma 5