This paper investigates the stochastic behavior of an n-node blockchain which is continuously monitored and faces non-stop cyber attacks from multiple hackers. The blockchain will start being re-set once hacking is detected, forfeiting previous efforts of all hackers. It is assumed the re-setting process takes a random amount of time. Multiple independent hackers will keep attempting to hack into the blockchain until one of them succeeds. For arbitrary distributions of the hacking times, detecting times, and re-setting times, we derive the instantaneous functional probability, the limiting functional probability, and the mean functional time of the blockchain. Moreover, we establish that these quantities are increasing functions of the number of nodes, formalizing the intuition that the more nodes a blockchain has the more secure it is.

翻译：本文研究了持续受到监控并面临多个黑客不间断网络攻击的n节点区块链的随机行为。一旦检测到黑客入侵，区块链将开始重置，并清零所有黑客此前的攻击成果。假设重置过程耗时随机。多个独立黑客将持续尝试入侵区块链，直至其中一人成功。针对任意分布的入侵时间、检测时间和重置时间，我们推导了区块链的瞬时功能概率、极限功能概率及平均功能时间。此外，我们证明这些量是节点数的递增函数，形式化地证实了节点越多区块链越安全的直觉。