Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben

2023 | Buch

Motivation for Mathematics of Blockchain Kapitel lesen Erstes Kapitel lesen

Some Fundamentals of Mathematics of Blockchain

verfasst von: Julien Riposo

Verlag: Springer Nature Switzerland

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Motivation for Mathematics of Blockchain
Abstract
Blockchain is a technology that increasingly attracts the attention of industrials and academics. However, to the best of the author's knowledge, the mathematical characteristics of blockchain have not sufficiently been covered. This is the purpose of the book.
Julien Riposo
Chapter 2. Some Fundamentals of Mathematics of Blockchain
Abstract
This section is introductory. We set the very first mathematics needed for any blockchain modeling, by considering a blockchain itself. The other parts of this chapter are depending on the contents of this section. The reader is supposed to be familiar with the basic mathematics, including probability and the used algebra, as well as the notions of bit, bytes, and hexadecimal in computer science. We re-introduce these notions first of all, for the convenience of the reader.
Julien Riposo
Chapter 3. Digital Signature
Abstract
The Digital Signature Algorithm is a particular asymmetric process, which is applied to the blockchain environment, to sign a transaction. Thus, this section is the straight continuation of the previous one, and explains the mechanism for digital signatures. In particular, the aim is to outline the purpose of unlocking an output for transacting.
Julien Riposo
Chapter 4. Blockchain Contributors: The Network of Users
Abstract
In this chapter, we focus on the communication between users and nodes through the Network of Users. Each user has connections with some others, and this allows exchange of information. A particular type of information concerns transaction, thus exchange of cash, or transaction lists between all the miners. These exchanges of information can be modeled by means of Graph and Matrix Theories. Papers [26, 27] are giving applications of the below theorization.
Julien Riposo
Chapter 5. Halving and Cycles Theorem
Abstract
This chapter is studying a pattern that has been identified in the Bitcoin halving process. As spurious as it might appear, the division by 2 of the block reward actually reveals some interesting characteristics in terms of available bitcoins. Collecting the 21 million bitcoins might appear to be impossible due to the protocol imposing the irreducible value of bitcoin, i.e., the Satoshi precision. The question of a change in the protocol through a soft fork might appear legitimate in order to allow the obtention of all the bitcoins. The reason is that minting new bitcoins is going to be less and less likely; this possibly could imply an inflation effect, thus motivating crypto-exchanges to possess more bitcoins than allowed by the current protocol.
Julien Riposo
Chapter 6. On Improving the Merkle Trees: The n-Trees
Abstract
In the context of Bitcoin Simplified Payment Verification (SPV) and Solvency, there are tree configurations where the path to the root is shorter than the one given by the usual binary tree, for the same computational memory – which is an essential strength. The n-trees have such properties, for n ≥ 2 (binary trees are for n = 2). We show that, for some values of number of transactions N ≥ 3, the system could be much faster, plus gain computational power, memory, and significantly reduce the computational time.
Julien Riposo
Chapter 7. Entropy of Peer-to-Peer NetworkPeer-to-peer network
Abstract
A strong flow of information 24/7 occurs between the agents of the peer-to-peer network. This intensive activity is a mark of perpetual evolution. One famous quantitative metric of evolution is entropy. We are going to synthesize three representative graphs of information flow. Entropy could be defined in the three of them, but by the equivalence of their information flow representation, one network might be more appropriate depending on the goal. One direct application of entropy is the increase of privacy of users: the Particles Model is explained and closes this chapter.
Julien Riposo
Chapter 8. Applications: Selection of Research Studies
Abstract
Many studies have been developed around the blockchain, and it is obviously impossible to deal with all of them. In this final section, we would like to highlight key blockchain research topics through the viewpoint of the developed theory above. The selected articles bore the attention of the author, but are far from exhaustively reflecting the overall research, and the below could specifically be seen as examples whose underlying blockchain theory, the one developed previously in this book, is general, and can gather a priori distinct blockchain topics.
Julien Riposo
Backmatter
Metadaten
Titel
Some Fundamentals of Mathematics of Blockchain
verfasst von
Julien Riposo
Copyright-Jahr
2023
Electronic ISBN
978-3-031-31323-3
Print ISBN
978-3-031-31322-6
DOI
https://doi.org/10.1007/978-3-031-31323-3

Premium Partner

    Bildnachweise