Bitcoin Security-Latency Under Network Delay

We improve security-latency bounds of Nakamoto consensus by analyzing the race between adversarial and honest chains in three different phases: pre-mining, confirmation and post-confirmation. We find the probability distribution of the length of the adversarial chain and the rigged adversarial chain under jumper models during the confirmation interval. We analyze certain properties of this race to model pre-mining and post-confirmation phases with random walks that provide tighter bounds than existing results. Combining all three phases provides novel upper and lower bounds for blockchains with small $\lambda\Delta$.