This paper delves into the fundamental trade-off between security, latency, and throughput in proof-of-work longest-chain-wins protocols, also known as the 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 closed-form finite-latency bound applicable to all delays and mining rates up to the ultimate fault tolerance. Notably, for most parameters relevant to Bitcoin and proof-of-work Ethereum, the gap between the upper and lower bounds is significantly narrower than the best gaps previously established in the literature. 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最长链协议（即Nakamoto共识）中安全性、延迟与吞吐量之间的基本权衡。我们推导出违反交易安全概率的新上界与下界，这些界限是诚实与恶意挖矿速率、区块传播延迟的上界、以及以时间和区块深度衡量的交易确认延迟的函数。研究结果首次给出了适用于所有延迟及挖矿速率直至最终容错极限的闭式有限延迟界限。值得注意的是，对于比特币和工作量证明以太坊的大多数相关参数，该上界与下界之间的差距显著窄于文献中先前建立的最佳差距。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，该权衡最终由期望的容错能力和区块大小增加时区块传播延迟的增长共同决定。