Springer, 2023. — 155 p. — ISBN: 978-3-031-31322-6.
This book provides a foundation for the mathematics of blockchain. It is inspired by a general analysis and synthesis of the current knowledge of blockchain technology and starts by laying a foundation for the mathematics of blockchain. The aim is for research in the area of blockchain to lead their study from the construction highlighted in this book.
First, the basis of a blockchain is set: block, transaction contents, block header, Merkle tree, nonce, Proof-of-Work. Connections with elliptic curves and cryptographic signatures are made.
Second, the book ties this with a Graph and Matrix Theories approach and models the peer-to-peer relationship through the Bitcoin Network.
Third, is proposed further modeling, notably around halving, optimal storing, or diffusion of information, which are consequences of the mathematical foundation. The notion of Entropy of Privacy and the Particles model are introduced.
Finally, the mathematical statements therein are proven and essential reminders can be found before each section, so the content can be accessible from a graduate level.
First of all, what is a blockchain? It is a chain of distinct and consecutive blocks, a technology of data storage, and information transmission without a third party that controls the entire process. It is a distributed database, such that information is sent by users, and internal contents are reviewed regularly in the form of the ledge (public for Bitcoin or Ethereum), thus enhancing a chronological chain (a timing chain). The whole set is cryptographically secured.
Traditionally, a blockchain is sharing the data it contains, which is the reason why it usually is referred to as a “public ledge.” Contrary to the common data-storing technology, blockchain builders have their copy of the content: the mechanism can ensure a unanimous agreement on the correct content of the blockchain, which ensures the conformity of the data copies. Thus, any kind of cheat (such as double-spending in the context of Bitcoin) is avoided. This allows a large amount of people, or entities, to agree on a consensus, thus making an incarnating immutable truth. To properly understand how important the concept of blockchain is, we propose five applications of the blockchain technology below (except Bitcoin which we will see in detail later).
Motivation for Mathematics of Blockchain.
Some Fundamentals of Mathematics of Blockchain.
Digital Signature.
Blockchain Contributors: The Network of Users.
Halving and Cycles Theorem.
On Improving the Merkle Trees: The n-Trees.
Entropy of Peer-to-Peer Network.
Applications: Selection of Research Studies.