University of Colorado Boulder - Mathematical Foundations for Cryptography
- Offered byCoursera
- Public/Government Institute
Mathematical Foundations for Cryptography at Coursera Overview
Duration | 14 hours |
Total fee | Free |
Mode of learning | Online |
Difficulty level | Beginner |
Official Website | Explore Free Course  |
Credential | Certificate |
- Overview
- Highlights
- Course Details
- Curriculum
Mathematical Foundations for Cryptography at Coursera Highlights
- This Course Plus the Full Specialization.
- Shareable Certificates.
- Graded Programming Assignments.
Mathematical Foundations for Cryptography at Coursera Course details
- Welcome to Course 2 of Introduction to Applied Cryptography. In this course, you will be introduced to basic mathematical principles and functions that form the foundation for cryptographic and cryptanalysis methods. These principles and functions will be helpful in understanding symmetric and asymmetric cryptographic methods examined in Course 3 and Course 4. These topics should prove especially useful to you if you are new to cybersecurity. It is recommended that you have a basic knowledge of computer science and basic math skills such as algebra and probability.
Mathematical Foundations for Cryptography at Coursera Curriculum
Integer Foundations
Course Introduction
Divisibility, Primes, GCD
Modular Arithmetic
Multiplicative Inverses
Extended Euclidean Algorithm
Course Introduction
Lecture Slides - Divisibility, Primes, GCD
Video - Adam Spencer: Why I fell in love with monster prime numbers
L16: Additional Reference Material
Lecture Slides - Modular Arithmetic
L17: Additional Reference Material
Lecture Slides - Multiplicative Inverses
L18: Additional Reference Material
Lecture Slides - Extended Euclidean Algorithm
L19: Additional Reference Material
Practice Assessment - Integer Foundation
Graded Assessment - Integer Foundation
Modular Exponentiation
Square-and-Multiply
Euler's Totient Theorem
Eulers Totient Function
Discrete Logarithms
Lecture Slides - Square-and-Multiply
Video - Modular exponentiation made easy
L20: Additional Reference Material
Lecture Slide - Euler's Totient Theorem
L21: Additional Reference Material
Lecture Slide - Eulers Totient Function
L22: Additional Reference Material
Lecture Slide - Discrete Logarithms
L23: Additional Reference Material
Practice Assessment - Modular Exponentiation
Graded Assessment - Modular Exponentiation
Chinese Remainder Theorem
CRT Concepts, Integer-to-CRT Conversions
Moduli Restrictions, CRT-to-Integer Conversions
CRT Capabilities and Limitations
Lecture Slide - CRT Concepts, Integer-to-CRT Conversions
L24: Additional Reference Material
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
Video - How they found the World's Biggest Prime Number - Numberphile
Practice Assessment - Chinese Remainder Theorem
Graded Assessment - Chinese Remainder Theorem
Primality Testing
Trial Division
Fermat's Primality
Miller-Rabin
Lecture Slide - Trial Division
L27: Additional Reference Material
Lecture Slide - Fermat's Primality
L28: Additional Reference Material
Lecture Slide - Miller-Rabin
Video - James Lyne: Cryptography and the power of randomness
L29: Additional Reference Material
The Science of Encryption
Practice Assessment - Primality Testing
Graded Assessment - Primality Testing
Course Project
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Student Forum
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