Development of a Linear-Scaling Consensus Mechanism of the Distributed Data Ledger Technology

Abstract

The paper highlights the problem of scalability and security of distributed ledger systems. For this purpose, a reliable system consensus method is proposed, aimed for the linearly scalable consensus mechanism application. An appropriate consensus protocol was developed. Mathematical models are proposed to analyze the scalability and security of blockchain protocols created based on the sharding process. Approximate calculations of the failure probabilities of one shard were determined, and as a result, for each blockchain chain by probability estimates based on hypergeometric and binomial distributions. Based on tail inequalities, the fundamental problem of determining the failure probability for a given sharding protocol is less than a predetermined threshold is investigated. Given the network failure probability threshold, a procedure is proposed for calculating the average period during which the network can fail. Thus, to achieve a given level of security (in terms of the period to failure), an approach was developed allowing determining the minimum shard size that should be formed using blockchain protocols based on the segmentation process. A numerical experiment and a comparative analysis of the obtained estimates were carried out to show the mathematical models’ effectiveness.