Refined Bitcoin Security-Latency Under Network Delay

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 $\lambda\Delta$.