Algorithmic analysis of blockchain efficiency with communication delay

Abstract

A blockchain is a distributed hierarchical data structure. Widely-used applications of blockchain include digital currencies such as Bitcoin and Ethereum. This paper proposes an algorithmic approach to analyze the efficiency of a blockchain as a function of the number of blocks and the average synchronization delay. The proposed algorithms consider a random network model that characterizes the growth of a tree of blocks by adhering to a standard protocol. The model is parametric on two probability distribution functions governing block production and communication delay. Both distributions determine the synchronization efficiency of the distributed copies of the blockchain among the so- called workers and, therefore, are key for capturing the overall stochastic growth. Moreover, the algorithms consider scenarios with a fixed or an unbounded number of workers in the network. The main result illustrates how the algorithms can be used to evaluate different types of blockchain designs, e.g., systems in which the average time of block production can match the average time of message broadcasting required for synchronization. In particular, this algorithmic approach provides insight into efficiency criteria for identifying conditions under which increasing block production has a negative impact on the stability of a blockchain. The model and algorithms are agnostic of the blockchain’s final use, and they serve as a formal framework for specifying and analyzing a variety of non-functional properties of current and future blockchains.