  We investigate the instantaneous and limiting behavior of an n-node
blockchain which is under continuous monitoring of the IT department of a
company but faces non-stop cyber attacks from a single hacker. The blockchain
is functional as far as no data stored on it has been changed, deleted, or
locked. Once the IT department detects the attack from the hacker, it will
immediately re-set the blockchain, rendering all previous efforts of the hacker
in vain. The hacker will not stop until the blockchain is dysfunctional. For
arbitrary distributions of the hacking times and detecting times, we derive the
limiting functional probability, instantaneous functional probability, and mean
functional time of the blockchain. We also show that all these quantities are
increasing functions of the number of nodes, substantiating the intuition that
the more nodes a blockchain has, the harder it is for a hacker to succeed in a
cyber attack.
