An Analysis of Blockchain Consistency in Asynchronous Networks: Deriving a Neat Bound

Formal analyses of blockchain protocols have received much attention recently. Consistency results of Nakamoto's blockchain protocol are often expressed in a quantity $c$, which denotes the expected number of network delays before some block is mined. With $\mu$ (resp., $\nu$) denoting the fraction of computational power controlled by benign miners (resp., the adversary), where $\mu + \nu = 1$, we prove for the first time that to ensure the consistency property of Nakamoto's blockchain protocol in an asynchronous network, it suffices to have $c$ to be just slightly greater than $\frac{2\mu}{\ln (\mu/\nu)}$. Such a result is both neater and stronger than existing ones. In the proof, we formulate novel Markov chains which characterize the numbers of mined blocks in different rounds.