Название: Some Fundamentals of Mathematics of Blockchain
Автор: Julien Riposo
Издательство: Springer
Год: 2023
Страниц: 155
Язык: английский
Формат: pdf (true), epub (true)
Размер: 20.7 MB

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, it is proposed further modelling, 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 literally is a chain of distinct and consecutive blocks, a technology of data storage, and information transmission without a third party which controls the entire process. It is a distributed database, such that information is sent by users, and internal contents are reviewed on a regular basis under the form of ledge (public for the Bitcoin or Ethereum), thus enhancing a chronological chain (a time 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 own copy of the content: the mechanism can assure a unanimous agreement of the correct content of the blockchain, which insures the conformity of the data copies. Thus, any kind of cheat (as double-spending in the context of Bitcoin) is avoided. This allows to a large amount of people, or entities, to agree on a consensus, thus made as 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).

Contents: