The security of blockchain systems depends on the distribution of mining power across participants. If sufficient mining power is controlled by one entity, they can force their own version of events. This may allow them to double spend coins, for example. For Proof of Work (PoW) blockchains, however, the distribution of mining power cannot be read directly from the blockchain and must instead be inferred from the number of blocks mined in a specific sample window. We introduce a framework to quantify this statistical uncertainty for the Nakamoto coefficient, which is a commonly-used measure of blockchain decentralization. We show that aggregating blocks over a day can lead to considerable uncertainty, with Bitcoin failing more than half the hypothesis tests ({\alpha} = 0.05) when using a daily granularity. For these reasons, we recommend that blocks are aggregated over a sample window of at least 7 days. Instead of reporting a single value, our approach produces a range of possible Nakamoto coefficient values that have statistical support at a particular significance level {\alpha}.

翻译：区块链系统的安全性取决于参与者之间的算力分布。若某个实体控制了足够多的算力，它就可能强制推行自身版本的事件记录——例如实施双花攻击。然而对于工作量证明区块链，其算力分布无法直接从链上读取，必须通过特定采样窗口内挖掘的区块数量进行推断。我们提出一个量化纳卡莫托系数统计不确定性的框架（该系数是衡量区块链去中心化程度的常用指标）。研究表明：以天为单位的区块聚合会导致显著的不确定性，当采用日粒度时，比特币在超过半数假设检验中失效（显著性水平α=0.05）。基于这些发现，我们建议区块聚合的采样窗口至少为7天。与传统报告单一数值的方法不同，我们的方法能够生成在特定显著性水平α下具有统计支持的纳卡莫托系数可能取值范围。