Comparison of Block Expectation Time for Various Consensus Algorithms

Context. We consider security properties of decentralized blockchain-based consensus protocols. The object of research is block confirmation time for users to get assurance that their transaction will not be reverted.

Objective. The goal of the paper is to analyze double-spend attacks on the different blockchain-based systems and compare resulting probabilities of attacker's success.

Method. We presented two models for two types of attacks on the Ouroboros protocol (for the general and covert adversaries). The models allow calculating the exact number of slots needed to achieve the required level of security. It was shown that the Ouroboros protocol allows achieving the required security level with significantly shorter confirmation period in comparison with Bitcoin. We estimated minimal number of confirmation blocks and compare estimation time for Bitcoin, GHOST and Ouroboros protocols. As a measure of comparison, we considered transaction confirmation time for which the probability of a double-spend attack is less than 0.1%. We use different standard probability distribution and different properties of Markov chains and Random Walks to get comparison of estimated security properties of Bitcoin blockchain against three different models of Bitcoin double spend attack. The splitting attack based on the model where resources of honest participants are divided to compete different chains is applied to Bitcoin and GHOST consensus protocols. Properties of Markov chains and Random Walks are also applied to obtain security estimations for the Ouroboros protocol.

Results. We developed methods to get specific numbers for average block confirmation time for Ouroboros protocol. We compared minimal number of confirmation blocks needed to ensure a high security for considered protocols: Bitcoin, GHOST and Ouroboros.

Conclusions. The obtained results allow determination of security bounds for the Bitcoin, GHOST and Ouroboros consensus protocols. Users of the practically deployed blockchain systems may get specific parameters for a given assurance level.