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We investigate the instantaneous and limiting behavior of an n-nodeblockchain which is under continuous monitoring of the IT department of acompany but faces non-stop cyber attacks from a single hacker. The blockchainis functional as far as no data stored on it has been changed, deleted, orlocked. Once the IT department detects the attack from the hacker, it willimmediately re-set the blockchain, rendering all previous efforts of the hackerin vain. The hacker will not stop until the blockchain is dysfunctional. Forarbitrary distributions of the hacking times and detecting times, we derive thelimiting functional probability, instantaneous functional probability, and meanfunctional time of the blockchain. We also show that all these quantities areincreasing functions of the number of nodes, substantiating the intuition thatthe more nodes a blockchain has, the harder it is for a hacker to succeed in acyber attack.

Instantaneous and limiting behavior of an n-node blockchain under cyber attacks from a single hacker