A mathematical introduction to cryptographic primitives in blockchain technology.

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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

**(Fill in the blank.)** A cryptographic key that is generated for each execution of a key-establishment process is ______.

(Fill in the blank.) A cryptographic key that is generated for each execution of a key-establishment process is ______.

**(Fill in the blank.)** In the blockchain, each block header, H, is uniquely defined by ________.


(Fill in the blank.) In the blockchain, each block header, H, is uniquely defined by ________.

Which attack aims at finding a different public key $R$ that hashes to the same address as a given $Q$ does?
$$
H=\text{RIPEMD160(SHA256(Q))}=\text{RIPEMD160(SHA256(R))}
$$

Which attack aims at finding a different public key <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi></mrow><annotation encoding="application/x-tex">R</annotation></semantics></math>R that hashes to the same address as a given <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Q</mi></mrow><annotation encoding="application/x-tex">Q</annotation></semantics></math>Q does?
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>H</mi><mo>=</mo><mtext>RIPEMD160(SHA256(Q))</mtext><mo>=</mo><mtext>RIPEMD160(SHA256(R))</mtext></mrow><annotation encoding="application/x-tex">H=\text{RIPEMD160(SHA256(Q))}=\text{RIPEMD160(SHA256(R))}
</annotation></semantics></math>H=RIPEMD160(SHA256(Q))=RIPEMD160(SHA256(R))

**(Fill in the blank.)** Bitcoin’s public keys are protected by ________.

(Fill in the blank.) Bitcoin’s public keys are protected by ________.

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: Bitcoin Under Broken Crypto Primitives