INTERACTIVE COURSE

Intermediate

115 Lessons

23h

Certificate of Completion

AI Explanations

AI Explanations

11 Playgrounds

10 Quizzes

106 Illustrations

Takeaway Skills

Familiarity with the basics of number theory, abstract algebra, and computing an algorithm’s time complexity

Working knowledge of the fundamentals of cryptography algorithms and principles

An understanding of the RSA cryptosystem and elliptic curve-based cryptography

Familiarity with the major types of attacks against different cryptosystems

Working knowledge of concepts of blockchain in general as well as from the perspective of Bitcoin

An understanding of the limitations of the cryptographic technique in the post-quantum computation era

Familiarity with the types of attacks against blockchain technology after the advent of fully-capable quantum computers, and their remedies

Course Overview

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 ...

Course Content

1

Introduction

2

Preliminaries

IntroductionNumber TheoryEuler’s Totient Function 𝜑(n)Modular ArithmeticGroupsGroups: Elementary PropertiesSubgroupsCyclic GroupsThe Group of UnitsRingsFieldsFinite FieldsComputational ComplexityAsymptotic Order of GrowthClasses of Time ComplexityEfficiency of AlgorithmsQuiz: Preliminaries

3

Cryptographic Primitives

IntroductionCryptography BasicsA Basic CryptosystemSymmetric vs. Asymmetric CryptographyPublic-Key CryptographyThe Basic Functionality of a Public-Key CryptosystemThe Diffie-Hellman Key ExchangeThe Discrete Logarithm ProblemHash FunctionsThe Security of Hash Functions and the Birthday AttackReal Hash FunctionsReal Hash Functions: Structural WeaknessMerkle TreesQuiz: Cryptographic Primitives

4

Elliptic Curve Cryptography

IntroductionWeierstrass EquationsElliptic CurvesGroup LawElliptic Curves Over Finite FieldsAddition of PointsGroup StructureThe Elliptic Curve Discrete Logarithm ProblemAttacking the ECDLPCryptographically Secure Elliptic CurvesAdditional Security RequirementsRecommended Elliptic Curves by StandardsThe Elliptic Curve secp256k1The Elliptic Curve Digital Signature AlgorithmAttacks on ECDSAQuiz: Elliptic Curves Cryptography

5

Information Security in Software Systems

The CIA TriadAttacks Against Distributed SystemsProof-of-WorkQuiz: Information Security in Software Systems

6

Distributed Systems

18 Lessons

7

Introduction to Blockchain Technology

18 Lessons

8

Bitcoin

8 Lessons

9

Introduction to Quantum Computing

5 Lessons

10

Bitcoin Under Broken Crypto Primitives

5 Lessons

11

Post-Quantum Blockchains

6 Lessons

12

In Closing

2 Lessons

COURSE AUTHOR

How You'll Learn

You don’t get better at swimming by watching others. Coding is no different. Practice as you learn with live code environments inside your browser.

Videos are holding you back. Educative‘s interactive, text-based lessons accelerate learning — no setup, downloads, or alt-tabbing required.

Learn faster and smarter with adaptive AI tools embedded in every Educative course.

Built-in assessments let you test your skills. Completion certificates let you show them off.