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 μ (resp., ν) denoting the fraction of computational power controlled by benign miners (resp., the adversary), where μ+ν =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 2μ/(ln(μ/ν)). 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.