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

Symmetric encryption algorithms use the same key for both encryption and decryption.

Asymmetric-key encryption algorithms use two different but mathematically related keys.

What is the major difference between symmetric and asymmetric-key cryptosystems?

What is the major difference between symmetric and asymmetric-key cryptosystems?

**(Fill in the blank.)** Let $X$ and $Y$ be arbitrary sets. A function $\varphi: X \rightarrow Y$ is called a _____________ function if $\varphi(x)$ can be computed efficiently for every $x \in X$, and it’s practically infeasible to compute $\varphi^{-1}$ for almost all $y \in I m \varphi$.

(Fill in the blank.) Let <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math>X and <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math>Y be arbitrary sets. A function <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>φ</mi><mo>:</mo><mi>X</mi><mo>→</mo><mi>Y</mi></mrow><annotation encoding="application/x-tex">\varphi: X \rightarrow Y</annotation></semantics></math>φ:X→Y is called a _____________ function if <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>φ</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\varphi(x)</annotation></semantics></math>φ(x) can be computed efficiently for every <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>∈</mo><mi>X</mi></mrow><annotation encoding="application/x-tex">x \in X</annotation></semantics></math>x∈X, and it’s practically infeasible to compute <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>φ</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\varphi^{-1}</annotation></semantics></math>φ−1 for almost all <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi><mo>∈</mo><mi>I</mi><mi>m</mi><mi>φ</mi></mrow><annotation encoding="application/x-tex">y \in I m \varphi</annotation></semantics></math>y∈Imφ.

Transmitting keying information over public channels without compromising the security of the system.

Transmitting keying information over private channels without compromising the security of the system.

Transmitting keying information with a message over private channels without compromising the security of the system.

What is the primary purpose of the Diffie-Hellman key exchange?

What is the primary purpose of the Diffie-Hellman key exchange?

Which of the following is not one of the digital signature properties?

Which of the following is not one of the digital signature properties?

**(Fill in the blank.)** A hash-based cryptographic data structure that allows efficient database verifications in order to provide data integrity is known as a ___________.

(Fill in the blank.) A hash-based cryptographic data structure that allows efficient database verifications in order to provide data integrity is known as a ___________.

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: Cryptographic Primitives