دانلود کتاب Some Fundamentals of Mathematics of Blockchain

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Preface
Contents
Chapter 1: Motivation for Mathematics of Blockchain
Chapter 2: Some Fundamentals of Mathematics of Blockchain
1 Preliminaries on Analysis
1.1 Basic Functions and Conventions
1.2 Hashing Function
1.3 Probability
1.4 Concatenation
1.5 Memoryless Property of Positive Continuous Random Variables
2 Block Modelling
2.1 Mathematics of Blockchain
2.2 Time for Mining Blocks
3 Merkle Tree
3.1 Complete Merkle Tree
3.2 Uncomplete Merkle Tree
4 Transaction Data
Chapter 3: Digital Signature
1 Preliminaries on Needed Algebra
1.1 Group
1.2 Field
1.3 Morphism
1.4 Characteristic
2 Elliptic Curves
2.1 Weierstrass Equation
2.2 Non-singularity
3 The Underlying Abelian Group
4 Elliptic Curve Digital Signature Algorithm (ECDSA) and Schnorr Signature
5 Back to the Blockchain
Chapter 4: Blockchain Contributors: The Network of Users
1 Preliminaries on Graph and Matrix Theories
1.1 Notations and Facts
1.2 Equivalence Between the Set of Graphs and the Set of Matrices
2 Bitcoin Network
3 Some Modeling for the Network of Users
3.1 Perron-Frobenius Theorem
3.2 Invariants of an Adjacency Matrix
3.3 Random Walk and Principal Invariants
3.4 Symmetric Group and Principal Invariants
3.5 First Hitting Times and Absorption Probability
3.6 A Quick Word on Diffusion and Propagation of Information
4 Diffusion Models on a Graph
4.1 ``S´´ Shapes
4.2 Bass Model
4.3 DeGroot Model
4.4 Diffusion on the Peer-to-Peer Network
Chapter 5: Halving and Cycles Theorem
1 Preliminaries on Modular Arithmetic
2 Bitcoin Halving
3 The Digit Pattern
4 The Cycles Theorem
4.1 Observation of Some Cycles
4.2 The Cycles Theorem
4.3 Binary Tree Representation of Halving
4.4 On an Algorithm for Predicting the Satoshi Digits
Chapter 6: On Improving the Merkle Trees: The n-Trees
1 Description of an n-Tree
2 Developments on an n-Tree Implementation
3 Empirical Comparison of Computation Times
4 A Mathematical Challenge for Finding the Right n
4.1 Problem Position
4.2 Partial Solution
5 A Full Solution to the Mathematical Challenge for Finding the Right n
5.1 The Cost Function
5.2 Considering the n-Tree Nodes in the Cost Function
5.3 Empirical Analysis
5.4 A Word on an Analytical Derivation of the Optimal Value
6 The Dynamic n-Tree
6.1 Principles
6.2 Static Tree: Authentication Path
6.3 Dynamic Tree: Authentication Path
Chapter 7: Entropy of Peer-to-Peer Network
1 Blockchain Network, Blockchain Transaction Network, and Peer-to-Peer Network
2 The Shannon Entropy and the Entropy Rate for the Peer-to-Peer Network
2.1 Shannon Entropy and Entropy Rate
2.2 Markov Traceability
2.3 Maximal Entropy Random Walk
3 Privacy and the Blockchain Transaction Graph
3.1 The Privacy Issue
3.2 A Privacy Violation Model
4 The Particles Model and the Entropy of Privacy
4.1 Entropy of Privacy
4.2 The Particles Model
4.3 Average Entropy
4.4 Privacy Entropy Rate
Chapter 8: Applications: Selection of Research Studies
1 Satoshi Nakamoto´s White Paper: On the Probability of a 51% Attack
2 On forecasting Bitcoin Price with Chainlets
3 On Valuing Bitcoin Price with Metcalfe´s Law
4 On Valuing Bitcoin Price from an Equilibrium Approach
5 Weights Contribution of a Crypto Portfolio through the Euler Allocation
6 On Tracing Knowledge Publicly: The MathCoin as an Example
Conclusion
References
Index