This paper delves into the fundamental trade-off between security, latency, and throughput in proof-of-work (PoW) longest-chain-fork-choice protocols, also known as the PoW Nakamoto consensus. New upper and lower bounds on the probability of violating transaction safety are derived as a function of honest and adversarial mining rates, an upper bound on block propagation delays, and transaction confirmation latency, both in time and in block depth. The results include a first non-trivial closed-form finite-latency bound applicable to all delays and mining rates up to the ultimate fault tolerance. Notably, the gap between the upper and lower bounds is narrower than the best gaps previously established for a wide range of parameters relevant to Bitcoin and its derivatives such as Litecoin and Dogecoin, as well as for Ethereum Classic. Furthermore, the paper reveals a fundamental trade-off between transaction throughput and confirmation latency, ultimately determined by the desired fault tolerance and the growth of block propagation delay as block size increases.

翻译：本文深入探讨了工作量证明（PoW）最长链分叉选择协议（即PoW中本共识）中安全性、延迟与吞吐量之间的基本权衡关系。研究推导了交易安全性被破坏概率的新上界与下界，该概率是诚实与恶意挖矿速率、区块传播延迟上界以及交易确认延迟（包括时间延迟与区块深度）的函数。所得结果包含首个非平凡的闭式有限延迟界，该界适用于所有延迟情况以及直至最终容错极限的全部挖矿速率。值得注意的是，对于比特币及其衍生币（如莱特币、狗狗币）以及以太坊经典等系统所涉及的大部分参数范围，本文给出的上下界间隙较以往最佳结果更为紧凑。此外，本文揭示了交易吞吐量与确认延迟之间的根本性权衡关系，该关系最终由期望的容错能力以及区块大小增加时区块传播延迟的增长特性所决定。