Extrapolation to calculate the probability of a double spending attack

Abstract

One of the important aspects of the efficiency of modern distributed networks built using blockchain technologies is the study of the security of consensus protocols. In particular, the most common cryptocurrencies and blockchain systems with probabilistic consensus protocols are subjects to so-called double-spending attack. The basis of such an attack is the use of the attacker's computing capabilities to form alternative blockchains. If the generated sequence is longer than the public chain of blocks, the attacker can present it as the proof of work and thus disrupt the correct functioning of the network. In this article we explore the probability of a successful double-spending attack, derive formulas for evaluating the corresponding events, consisting of the formation by the attacker of an alternative sequence of blocks. These formulas are extremely cumbersome and difficult to calculate. The paper proposes simplified analytical expressions to quickly assess the probability of a successful doublespending attack. For this we use the extrapolation of intermediate calculations using the Lagrange interpolation formulas, as well as binomial approximation. The simulation results show that the use of simplified expressions allows us to provide acceptable accuracy of calculations.