Refinement of estimates of the success probability of a double-spend attack on the Blockchain System, Based on the Independent Players Model

Abstract

Blockchain technology is being studied in many innovative applications, such as: cryptocurrencies, smart contracts, communication systems, healthcare, Internet of Things, financial systems, software development, electronic voting and many others. Using a transparent and fully distributed peer-to-peer blockchain architecture, applications benefit from a data-only model, in which “transactions” are accepted into the blockchain ledger and, if the system is functioning properly, cannot be modified or deleted. The transparency of blockchain systems makes it possible to store publicly available and irrefutable records. A peer-to-peer blockchain system provides verifiable ledger maintenance without centralized management, which solves the problems of a single point of failure and a single point of trust. The article deals with the issue of the security of application of accounting systems built on decentralized principles using blockchain technology. Particular attention is paid to the problem of the possibility of double spending in such accounting systems. The article exemplifies the reorganization of records in blockchain ledgers, performed by successfully carrying out a 51% attack on consensus algorithms based on proof of work. Given refinement of analytical expressions of 51% attack probability obtained in the works of S. Nakamoto and M. Rosenfeld using a more general model, namely, the model of independent players, where the probability of block formation by attackers and an honest network are independent events. The results of comparing of the success probability of a double-spending attack on the blockchain systems calculated according to different models are presented.