The Problem of Double Costs in Blockchain Systems

The paper investigates the probability of one of the most famous attacks - double spending attacks on the blockchain system, which are based on consensus mechanisms based on the proof of the work done using hash functions. Unlike previously known works describing the analytical expression for the probability of success of a double-spend attack, this paper proposes a model of independent players that is different from existing models. In our opinion, this model more adequately describes the processes that occur during the formation of a chain of blocks, but leads to other quantitative results. An expression is given that characterizes the probability of an attacker conducting a successful double-spend attack on a blockchain system depending on the number of confirmations used, as well as the hashrate by an honest network and the attacker. Quantitative results are presented, as well as a comparison of the results obtained with the most famous works in this area. Based on the results obtained, recommendations are given for determining the “safe” number of confirmations for successfully resisting a double spending attack on the blockchain system.