Mathematical modelling of bitcoin and ethereum

Abstract

Blockchain technology provides a decentralized ledger that enables secure, transparent, and immutable information sharing. It serves as a platform for exchanging cryptographic coins with economic value or data over the internet without requiring a central authority, achieving consensus through a peer-to-peer network. This thesis presents mathematical models for Bitcoin and Ethereum (version 1.0 and 2.0), two of the most prominent blockchain platforms, to analyze and represent their core mechanisms. The models define transactions, blocks storing these transactions, and the consensus algorithms that synchronize blocks across the blockchain network, through the use of sets, tables, diagrams and algorithms. Additionally, a Finite State Machine (FSM) representation is provided to illustrate Ethereum’s transaction based state machine behavior. Use of cryptography in both Bitcoin and Ethereum, specifically Elliptic Curve Cryptography (ECC) for transaction validation has also been explored. By providing a mathematically structured representation of these systems, this thesis could help researchers and engineers gain a deeper understanding of blockchain mechanisms, analyze their security and efficiency, and explore potential optimizations. The simplified approach also makes the topic more accessible to those without a computer science background, encouraging interdisciplinary research and collaboration in blockchain development.