In a blockchain, the longest chain, which has the greatest proof-of-work effort spent in it, represents the majority decision. To change the transaction data of a block, an attacker has to control more computing power than other honest nodes. This situation can happen if the attacker can hack into the systems of honest nodes. To analyze the probability of such event, we propose a probability model for analysis of attacks on blockchain. The model is based on the structure of a peer-to-peer network. We assume the state of each honest node follows a two-state (hacked or normal) Markov chains. A hacked node is assumed to be controlled by the attacker and its computing power belongs to the attacker. On the other hand, the computing power of a normal node belongs to the honest longest chain. We apply the model to study the probability of the majority decision is controlled by the attacker and the duration of such event. In addition, we analyze the magnitude of the loss for such event.
Hsieh, Ming-hua; Chung, Ming-Tao; and Chi, Yan-Ping, "A Probability Model for Analysis of Attacks on Blockchain" (2016). ICEB 2016 Proceedings. 41.