Many blockchain platform are subject to maximal value extraction (MEV), and users on the platform are losing money while sending transactions because the transaction order can be manipulated to extract value from them. Consensus protocols have been augmented with different notion of fair ordering in order to counter the problem. Out of all practical protocols, the most efficient BFT consensus requires $O(nTL + n^2T)$ communication complexity, where $n$ is number node, $T$ is number of transactions and $L$ is average transaction size. In this work, we propose a new system of BFT fair ordering protocols, Travelers, that substantially reduce the communication complexity. The proposed system of protocols satisfy a new notion of fair ordering, called probabilistic fair ordering, which is an extension to some existing notions of fairness. The new notion allows a small probability of error $\epsilon$, that adversary can insert some transactions at any location in a block, but for the remaining $1-\epsilon$ the a modified version of ordering linearizability holds. Our mechanism neither require a dissemination network nor direct submissions to all consensus nodes. The key innovation comes from a routing protocol, that is both flexible and efficient. We construct a protocol with $O(c\log({n})TL + n^2)$ communication complexity with $\epsilon = 1/n^c$ for some system parameter $c\ge 1$.

翻译：许多区块链平台存在最大可提取价值（MEV）问题，用户发送交易时因交易顺序可能被操纵以提取价值而蒙受损失。为应对该问题，共识协议引入了多种公平排序概念。在所有实用协议中，最高效的BFT共识需达到$O(nTL + n^2T)$的通信复杂度，其中$n$为节点数，$T$为交易数，$L$为平均交易大小。本文提出一种新型BFT公平排序协议系统Travelers，显著降低了通信复杂度。该系统满足一种称为概率公平排序的新公平概念，该概念是对现有公平性概念的扩展。新概念允许较小错误概率$\epsilon$，即攻击者可在区块任意位置插入若干交易，但剩余$1-\epsilon$比例中，修正版本的有序线性化性质得以保持。我们的机制既不需要扩散网络，也不要求向所有共识节点直接提交交易。关键创新在于一种兼具灵活性与高效性的路由协议。通过选取系统参数$c\ge 1$，我们构建了通信复杂度为$O(c\log({n})TL + n^2)$的协议，此时$\epsilon = 1/n^c$。