Simulating a simplified version of a splitting attack on the blockchain based on the Proof-of-Stake consensus protocol

The splitting attack is one of the most important attacks on the blockchain, first of all for Proof-of-Work and Proof-of-Stake consensus protocols. Currently, there are no explicit analytical formulas for evaluating its success probability, which causes some distrust in blockchain technologies. In this paper, for a simplified (but still not simple) model of a splitting attack, the recurrent formulas allowing the evaluation of the exact values of the probability that an attacker will be able to build a branch of a given length are obtained. The correctness of these formulas is verified through numerical examples using the Monte Carlo method by constructing estimates with a specified confidence level and relative error. Keywords: blockchain, Proof-of-Stake, splitting attack, stakeholder, timeslot, slotleader, recursive formulas, Monte Carlo method.