Course Summary
Learn Number Theory and Cryptography concepts, including prime numbers, modular arithmetic, and RSA encryption, and apply them in real-world scenarios such as online security and data encryption.Key Learning Points
- Understand the fundamental concepts of number theory and cryptography
- Learn about prime numbers and modular arithmetic
- Apply these concepts in real-world scenarios such as online security and data encryption
Job Positions & Salaries of people who have taken this course might have
- USA: $92,000
- India: ₹8,00,000
- Spain: €37,000
- USA: $92,000
- India: ₹8,00,000
- Spain: €37,000
- USA: $75,000
- India: ₹6,00,000
- Spain: €30,000
- USA: $92,000
- India: ₹8,00,000
- Spain: €37,000
- USA: $75,000
- India: ₹6,00,000
- Spain: €30,000
- USA: $85,000
- India: ₹7,50,000
- Spain: €32,000
Related Topics for further study
Learning Outcomes
- Understand the principles of number theory and cryptography
- Learn how to apply number theory and cryptography concepts in real-world scenarios
- Gain knowledge on prime numbers and modular arithmetic
Prerequisites or good to have knowledge before taking this course
- Basic knowledge of algebra
- Familiarity with programming concepts
Course Difficulty Level
IntermediateCourse Format
- Online
- Self-paced
Similar Courses
- Applied Cryptography
- Introduction to Cryptography
Notable People in This Field
- Bruce Schneier
- Whitfield Diffie
Related Books
Description
We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about numbers’ properties for thousands of years. And for thousands of years it was more or less just a game that was only interesting for pure mathematicians. Famous 20th century mathematician G.H. Hardy once said “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the word nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this short course, we will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest!
Outline
- Modular Arithmetic
- Numbers
- Divisibility
- Remainders
- Problems
- Divisibility Tests
- Division by 2
- Binary System
- Modular Arithmetic
- Applications
- Modular Subtraction and Division
- Rules on the academic integrity in the course
- Python Code for Remainders
- Slides
- Slides
- Slides
- Divisibility
- Puzzle: Take the last rock
- Division by 101
- Remainders
- Division by 4
- Four Numbers
- Properties of Divisibility
- Divisibility Tests
- Division by 2
- Binary System
- Modular Arithmetic
- Remainders of Large Numbers
- Modular Division
- Euclid's Algorithm
- Greatest Common Divisor
- Euclid’s Algorithm
- Extended Euclid’s Algorithm
- Least Common Multiple
- Diophantine Equations: Examples
- Diophantine Equations: Theorem
- Modular Division
- Greatest Common Divisor: Code
- Extended Euclid's Algorithm: Code
- Slides
- Slides
- Greatest Common Divisor
- Tile a Rectangle with Squares
- Least Common Multiple
- Least Common Multiple: Code
- Diophantine Equations
- Diophantine Equations: Code
- Modular Division: Code
- Building Blocks for Cryptography
- Introduction
- Prime Numbers
- Integers as Products of Primes
- Existence of Prime Factorization
- Euclid's Lemma
- Unique Factorization
- Implications of Unique Factorization
- Remainders
- Chinese Remainder Theorem
- Many Modules
- Fast Modular Exponentiation
- Fermat's Little Theorem
- Euler's Totient Function
- Euler's Theorem
- Slides
- Slides
- Fast Modular Exponentiation
- Slides
- Integer Factorization
- Puzzle: Arrange Apples
- Remainders
- Chinese Remainder Theorem: Code
- Fast Modular Exponentiation: Code
- Modular Exponentiation
- Cryptography
- Cryptography
- One-time Pad
- Many Messages
- RSA Cryptosystem
- Simple Attacks
- Small Difference
- Insufficient Randomness
- Hastad's Broadcast Attack
- More Attacks and Conclusion
- Many Time Pad Attack
- Slides
- Randomness Generation
- Slides and External References
- RSA Quiz: Code
- RSA Quest - Quiz
Summary of User Reviews
Discover the world of number theory and cryptography in this Coursera course. Users have praised the course for its comprehensive content and engaging lectures. Overall, the course has received positive reviews from learners.Key Aspect Users Liked About This Course
Many users found the content to be comprehensive and engaging.Pros from User Reviews
- In-depth coverage of number theory and cryptography concepts
- Engaging lectures from knowledgeable instructors
- Challenging problem sets to reinforce learning
- Access to additional resources for further study
- Flexible pacing allows learners to work at their own speed
Cons from User Reviews
- Some users found the course material to be too advanced for beginners
- Limited interaction with instructors and other learners
- Occasional technical issues with the online platform
- Some users felt the assessments were too difficult
- Course may not be suitable for those looking for a more generalized math course
Alexander S. Kulikov
4.5 Raiting
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