A mathematical introduction to cryptographic primitives in blockchain technology.

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cryptographic.tar.gz

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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

A branch of computing based on principles of quantum mechanics.

It’s solely used in computation to solve certain physics problems.

A branch of computing based on electromagnetism.

**(Fill in the blank.)** Instead of bits, Quantum computers use ________.

(Fill in the blank.) Instead of bits, Quantum computers use ________.

(Fill in the blank.) The ability of a quantum system to be in multiple states simultaneously is called ________.


(Fill in the blank.) The ability of a quantum system to be in multiple states simultaneously is called ________.

Which cryptography technique is secure from the impact of quantum Shor’s algorithm?

Which cryptography technique is secure from the impact of quantum Shor’s algorithm?

Given a qubit $|{\psi} \rangle = \alpha |0\rangle - \frac{\sqrt{3}}{2}\iota | 1 \rangle$

what is the value of $\alpha$?


Given a qubit <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">∣</mi><mi>ψ</mi><mo stretchy="false">⟩</mo><mo>=</mo><mi>α</mi><mi mathvariant="normal">∣</mi><mn>0</mn><mo stretchy="false">⟩</mo><mo>−</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac><mi>ι</mi><mi mathvariant="normal">∣</mi><mn>1</mn><mo stretchy="false">⟩</mo></mrow><annotation encoding="application/x-tex">|{\psi} \rangle = \alpha |0\rangle - \frac{\sqrt{3}}{2}\iota | 1 \rangle</annotation></semantics></math>∣ψ⟩=α∣0⟩−23<svg xmlns="http://www.w3.org/2000/svg" width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702
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c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54
c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10
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what is the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math>α?

**(True, False):** A quantum computer will outperform classical computers for every algorithm.

(True, False): A quantum computer will outperform classical computers for every algorithm.

Choose the correct option.

Choose the correct option.

Let's test what you have learned in this chapter.

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: Introduction to Quantum Computing