Evaluation of the probability of a successful attack in blockchain network

A probabilistic model, describing the beginning of active periods for an attacker and a miner as a random values with binomial distribution, is presented. Creating a false information block is meant by a successful attack. Estimates for the probability of intruder's successful attack under different conditions are obtained. Results of calculation confirm that attacker's probability of a successful attack decreases with the increase of positive difference between the attacker's and miner's session durations as well as with the growth of the number of active miners. Also, the probability of a successful attack increases with the growth of the positive difference between the expected start time of the miner's session and the start time of the attacker's session.