Course Summary
Learn the mathematical foundations of cryptography and its applications in secure communication, digital signatures, and more.Key Learning Points
- Understand the basics of cryptography and its applications
- Learn mathematical concepts such as modular arithmetic and number theory
- Explore symmetric and asymmetric encryption methods
- Gain hands-on experience with programming assignments
- Apply cryptography in real-world scenarios
Related Topics for further study
Learning Outcomes
- Understand the mathematical foundations of cryptography
- Implement cryptographic algorithms in programming assignments
- Apply cryptography in real-world scenarios
Prerequisites or good to have knowledge before taking this course
- Basic understanding of algebra and computer programming
- Familiarity with number theory is helpful
Course Difficulty Level
IntermediateCourse Format
- Online self-paced
- Video lectures
- Programming assignments
Similar Courses
- Applied Cryptography
- Cryptography I
Related Education Paths
Notable People in This Field
- Security Technologist
- Cryptographer
Related Books
Description
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.
Outline
- 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
Summary of User Reviews
The Mathematical Foundations of Cryptography course on Coursera has received positive reviews from users. The course is well-structured and covers the topic comprehensively. Many users found the lectures engaging and the assignments challenging.Key Aspect Users Liked About This Course
The course is well-structured and covers the topic comprehensively.Pros from User Reviews
- Engaging lectures
- Challenging assignments
- In-depth coverage of mathematical foundations of cryptography
- Good balance between theory and practical applications
- Excellent instructor knowledge
Cons from User Reviews
- Some users found the course material too advanced
- Lack of hands-on coding exercises
- Not suitable for beginners without a strong mathematical background
- Some users experienced technical difficulties with the platform
- Limited interaction with other students and the instructor
William Bahn
4.6 Raiting
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