Refined Bitcoin Security-Latency Under Network Delay

TL;DR

This paper improves security-latency bounds for Nakamoto consensus by analyzing the adversarial and honest chain race in three phases, providing tighter bounds for small network delay parameters.

Contribution

It introduces a refined analysis of the adversarial chain growth using phase-based modeling with random walks, resulting in improved security-latency bounds.

Findings

Tighter upper and lower bounds for block security after k-deep in the chain.

Probability distribution of adversarial chain growth modeled under similar network delay assumptions.

Enhanced understanding of the security-latency trade-offs in Nakamoto consensus.

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 $\lambda\Delta$.