Refined Bitcoin Security-Latency Under Network Delay
Mustafa Doger, Sennur Ulukus
TL;DR
The paper addresses the problem of quantifying how secure a PoW blockchain is as a function of confirmation depth $k$ and network delay $Δ$, focusing on the security-latency trade-off in Nakamoto consensus. It introduces a three-phase approach that combines a $Δ$-delay adversarial strategy with a rigged model, and leverages Markov-chain steady-state analysis and random-walk arguments to bound the probability of double-spend across pre-mining, confirmation, and post-confirmation phases. The main contributions are new, tighter lower and upper bounds on safety violations for small $λΔ$, with explicit distributions for adversarial growth during each phase and improved accuracy demonstrated in Bitcoin and PoW-Ethereum settings. These results enhance practical understanding of how security degrades with latency and provide sharper guidance for selecting confirmation depths in delay-prone networks. The work also highlights open-form expressions as a direction for future refinement and potential further tightening of adversarial strategies.
Abstract
We study security-latency bounds for Nakamoto consensus, i.e., how secure a block is after it becomes $k$-deep in the chain. We improve the state-of-the-art bounds by analyzing the race between adversarial and honest chains in three different phases. We find the probability distribution of the growth of the adversarial chains under models similar to those in [Guo, Ren; AFT 2022] when a target block becomes $k$-deep in the chain. We analyze certain properties of this race to model each phase with random walks that provide tighter bounds than the existing results. Combining all three phases provides novel upper and lower bounds for blockchains with small $λΔ$.