A mathematical introduction to cryptographic primitives in blockchain technology.

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cryptographic.tar.gz

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Blockchain-based distributed public ledgers can securely store our data without the need for a centralized controlling authority. Blockchain technology uses intriguing mathematical and cryptographical concepts, which are usually misunderstood. 

This course presents a comprehensive overview of the basic concepts of blockchain while providing deep insights into its background in mathematics and cryptography. Next, you’ll learn about the critical cryptographical vulnerabilities and attacks against blockchain technology and how to encounter them. Finally, the course describes possible attacks against blockchains by a fully-capable quantum computer and the possible remedies.

By the end of this course, you’ll have a deep understanding of blockchain technology and its mechanisms, particularly the mathematics and cryptography involved in blockchain security.

Cryptographic Primitives in Blockchain Technology

## Introduction

Any blockchain relies on cryptographic primitives, which are based on mathematical concepts, namely on number-theoretic and algebraic structures. In order to understand the cryptographic concepts in the following chapters, we give a profound introduction to two mathematical fields: **number theory** and **algebra**.

### Chapter structure

# Introduction

Any blockchain relies on cryptographic primitives, which are based on mathematical concepts, namely on number-theoretic and algebraic structures. In order to understand the cryptographic concepts in the following chapters, we give a profound introduction to two mathematical fields: **number theory** and **algebra**.

## Chapter structure

Let's have a look at what we’ll cover in the section preliminaries.

Introduction

Preliminaries

Cryptographic Primitives

Elliptic Curve Cryptography

Information Security in Software Systems

Distributed Systems

Introduction to Blockchain Technology

Bitcoin

Introduction to Quantum Computing

Bitcoin Under Broken Crypto Primitives

Post-Quantum Blockchains

In Closing

Introduction

Introduction

Chapter structure