Simple closed-form upper and lower bounds are developed for the security of the Nakamoto consensus as a function of the confirmation depth, the honest and adversarial block mining rates, and an upper bound on the block propagation delay. The bounds are exponential in the confirmation depth and apply regardless of the adversary's attack strategy. The gap between the upper and lower bounds is small for Bitcoin's parameters. For example, assuming an average block interval of 10 minutes, a network delay bound of ten seconds, and 10% adversarial mining power, the widely used 6-block confirmation rule yields a safety violation between 0.11% and 0.35% probability.

翻译：简单的封闭式上下界限是为了中本共识的安全而开发的,这取决于确认深度、诚实和对立的区块开采率以及块块传播延迟的上限。界限在确认深度中是指数性的,不管对手的攻击策略如何,都适用。对于Bitcoin的参数来说,上下界限之间的距离很小。例如,假设平均区块间隔为10分钟,网络延缓10秒,对立的采矿力为10%,广泛使用的6个区块确认规则就会产生0.11%至0.35%的安全侵犯概率。