Complexity of Multi-Value Byzantine Agreement

TL;DR

This paper introduces an efficient Byzantine agreement algorithm that achieves linear per-bit complexity while guaranteeing correctness, surpassing previous quadratic bounds, and potentially approaching network capacity limits.

Contribution

The paper presents a novel Byzantine agreement algorithm with linear per-bit complexity using error detection and adaptive routing, improving over existing methods that allow errors.

Findings

Achieves linear complexity per bit in Byzantine agreement

Guarantees correctness even in worst-case scenarios

Potential to reach network capacity limits

Abstract

In this paper, we consider the problem of maximizing the throughput of Byzantine agreement, given that the sum capacity of all links in between nodes in the system is finite. We have proposed a highly efficient Byzantine agreement algorithm on values of length l>1 bits. This algorithm uses error detecting network codes to ensure that fault-free nodes will never disagree, and routing scheme that is adaptive to the result of error detection. Our algorithm has a bit complexity of n(n-1)l/(n-t), which leads to a linear cost (O(n)) per bit agreed upon, and overcomes the quadratic lower bound (Omega(n^2)) in the literature. Such linear per bit complexity has only been achieved in the literature by allowing a positive probability of error. Our algorithm achieves the linear per bit complexity while guaranteeing agreement is achieved correctly even in the worst case. We also conjecture that our algorithm can be used to achieve agreement throughput arbitrarily close to the agreement capacity of a network, when the sum capacity is given.