Number Theory and Cryptography
- Offered byCoursera
- Public/Government Institute
Number Theory and Cryptography at Coursera Overview
Duration | 19 hours |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Beginner |
Official Website | Explore Free Course  |
Credential | Certificate |
- Overview
- Highlights
- Course Details
- Curriculum
Number Theory and Cryptography at Coursera Highlights
- Shareable Certificate Earn a Certificate upon completion
- 100% online Start instantly and learn at your own schedule.
- Course 4 of 5 in the Introduction to Discrete Mathematics for Computer Science Specialization
- Flexible deadlines Reset deadlines in accordance to your schedule.
- Beginner Level
- Approx. 19 hours to complete
- English Subtitles: Arabic, French, Portuguese (European), Greek, Italian, Vietnamese, German, Russian, English, Spanish
Number Theory and Cryptography at Coursera Course details
- 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!
- As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
- Do you have technical problems? Write to us: coursera@hse.ru
Number Theory and Cryptography at Coursera Curriculum
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
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