The Blockchain Trilemma Described by a Formula

Abstract

The blockchain trilemma was first introduced in a 2017 blog post written by Vitalik Buterin, one of the cofounders of Ethereum. This trilemma claims that it is impossible to simultaneously achieve the three properties of decentralization, scalability, and security in a blockchain. While extensive analysis of blockchain performance has been conducted, the claim has been empirically accepted as true. However, no one has formulated this trilemma mathematically. In this paper, we present a formula that explicitly expresses the trilemma for Proof of Work blockchains. Furthermore, based on our mathematical representation of the trilemma, we illustrate the two categories of approaches for improving blockchain performance under the constraints of the trilemma.