A mathematical introduction to cryptographic primitives in blockchain technology.

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cryptographic.tar.gz

ellipticCurves

Algorithms

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

**(Fill in the blank.)** Blockchain technologies such as Bitcoin and Ethereum are examples of ____________ architectures and systems.

(Fill in the blank.) Blockchain technologies such as Bitcoin and Ethereum are examples of ____________ architectures and systems.

**(Fill in the blank.)** In distributed systems, distribution refers to differences in ______.

(Fill in the blank.) In distributed systems, distribution refers to differences in ______.

A distributed system is a collection of independent computers that appears to its users as a single coherent system.

A distributed system is a model in which components located on networked computers communicate and coordinate their actions by passing messages.

A distributed system is a system in which computation and storage of information are distributed across independent components that communicate and coordinate their actions by passing messages.

What is the correct definition of distribution systems?

What is the correct definition of distribution systems?

**(Fill in the blank.)** In the CAP theorem, CAP stands for ________.

(Fill in the blank.) In the CAP theorem, CAP stands for ________.

**(Fill in the blank.)** “The computer of any user that joins a system acts as a node of the system” is the concept of ______.

(Fill in the blank.) “The computer of any user that joins a system acts as a node of the system” is the concept of ______.

Which failure is the simplest and most easily detectable in distributed systems?

Which failure is the simplest and most easily detectable in distributed systems?

What is an algorithm whose behavior is partly controlled by random events?

What is an algorithm whose behavior is partly controlled by random events?

**Termination:** Every correct process is eventually decided in finite time.

**Agreement:** All correct processes decide for the same value, i.e., no two correct processes decide differently.

**Validity:** If all correct processes started by proposing the same initial value
$v$ ∈ $V$, then any correct process in the decision state has chosen that value $v$.

**Liveness:** A consensus protocol guarantees liveness if all non-faulty processes participating in consensus eventually produce a value.

Which aren’t the correct conditions for the agreement or consensus problem?

Which aren’t the correct conditions for the agreement or consensus problem?

If process 0 is non-faulty, then any non-faulty process $i$ obtains the value $v$.

If processes $i$ and $j$ are non-faulty, then they both obtain the same value.

Allowing all the processes to agree upon an "incorrect" value if a failure occurs.

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

Quiz: Distributed Systems