About this course: 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.
Who is this class for: Learners with CS experience or education looking to: ○ Enhance/refresh critical skills; ○ Seeking to expand their opportunities. Learners undecided about pursuing a bachelor’s degree: ○ Seeking professional credit that may be applied towards a bachelor’s degree.
Created by: University of Colorado System
Taught by: William Bahn, Lecturer
Computer Science
Taught by: Richard White, Assistant Research Professor
Computer Science
Taught by: Sang-Yoon Chang, Assistant Professor
Computer Science
| Basic Info | Course 2 of 4 in the Introduction to Applied Cryptography Specialization |
| Level | Beginner |
| Commitment | This is Course 2 in a 4-course specialization. Estimated workload: 15-hours per week. |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
Syllabus
WEEK 1
Integer Foundations
Building upon the foundation of cryptography, this module focuses on the mathematical foundation including the use of prime numbers, modular arithmetic, understanding multiplicative inverses, and extending the Euclidean Algorithm. After completing this module you will be able to understand some of the fundamental math requirement used in cryptographic algorithms. You will also have a working knowledge of some of their applications.
5 videos, 10 readings, 1 practice quiz
- Video: Course Introduction
- Reading: Course Introduction
- Video: Divisibility, Primes, GCD
- Reading: Lecture Slides - Divisibility, Primes, GCD
- Reading: Video - Adam Spencer: Why I fell in love with monster prime numbers
- Reading: L16: Additional Reference Material
- Video: Modular Arithmetic
- Reading: Lecture Slides - Modular Arithmetic
- Reading: L17: Additional Reference Material
- Video: Multiplicative Inverses
- Reading: Lecture Slides - Multiplicative Inverses
- Reading: L18: Additional Reference Material
- Video: Extended Euclidean Algorithm
- Reading: Lecture Slides - Extended Euclidean Algorithm
- Reading: L19: Additional Reference Material
- Practice Quiz: Practice Assessment - Integer Foundation
- Discussion Prompt: What do you think?
Graded: Graded Assessment - Integer Foundation
WEEK 2
Modular Exponentiation
A more in-depth understanding of modular exponentiation is crucial to understanding cryptographic mathematics. In this module, we will cover the square-and-multiply method, Eulier's Totient Theorem and Function, and demonstrate the use of discrete logarithms. After completing this module you will be able to understand some of the fundamental math requirement for cryptographic algorithms. You will also have a working knowledge of some of their applications.
4 videos, 9 readings, 1 practice quiz
- Video: Square-and-Multiply
- Reading: Lecture Slides - Square-and-Multiply
- Reading: Video - Modular exponentiation made easy
- Reading: L20: Additional Reference Material
- Video: Euler's Totient Theorem
- Reading: Lecture Slide - Euler's Totient Theorem
- Reading: L21: Additional Reference Material
- Video: Eulers Totient Function
- Reading: Lecture Slide - Eulers Totient Function
- Reading: L22: Additional Reference Material
- Video: Discrete Logarithms
- Reading: Lecture Slide - Discrete Logarithms
- Reading: L23: Additional Reference Material
- Practice Quiz: Practice Assessment - Modular Exponentiation
- Discussion Prompt: What do you think?
Graded: Graded Assessment - Modular Exponentiation
WEEK 3
Chinese Remainder Theorem
The modules builds upon the prior mathematical foundations to explore the conversion of integers and Chinese Remainder Theorem expression, as well as the capabilities and limitation of these expressions. After completing this module, you will be able to understand the concepts of Chinese Remainder Theorem and its usage in cryptography.
3 videos, 5 readings, 1 practice quiz
- Video: CRT Concepts, Integer-to-CRT Conversions
- Reading: Lecture Slide - CRT Concepts, Integer-to-CRT Conversions
- Reading: L24: Additional Reference Material
- Video: Moduli Restrictions, CRT-to-Integer Conversions
- Reading: Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
- Video: CRT Capabilities and Limitations
- Reading: Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions
- Reading: Video - How they found the World's Biggest Prime Number - Numberphile
- Practice Quiz: Practice Assessment - Chinese Remainder Theorem
- Discussion Prompt: What do you think?
Graded: Graded Assessment - Chinese Remainder Theorem
WEEK 4
Primality Testing
Finally we will close out this course with a module on Trial Division, Fermat Theorem, and the Miller-Rabin Algorithm. After completing this module, you will understand how to test for an equality or set of equalities that hold true for prime values, then check whether or not they hold for a number that we want to test for primality.
3 videos, 8 readings, 1 practice quiz
- Video: Trial Division
- Reading: Lecture Slide - Trial Division
- Reading: L27: Additional Reference Material
- Video: Fermat's Primality
- Reading: Lecture Slide - Fermat's Primality
- Reading: L28: Additional Reference Material
- Video: Miller-Rabin
- Reading: Lecture Slide - Miller-Rabin
- Reading: Video - James Lyne: Cryptography and the power of randomness
- Reading: L29: Additional Reference Material
- Practice Quiz: Practice Assessment - Primality Testing
- Discussion Prompt: What do you think?
- Reading: The Science of Encryption
Graded: Graded Assessment - Primality Testing
Graded: Course Project
FAQs
How It Works
Coursework
Each course is like an interactive textbook, featuring pre-recorded videos, quizzes and projects.
Help from Your Peers
Connect with thousands of other learners and debate ideas, discuss course material, and get help mastering concepts.
Certificates
Earn official recognition for your work, and share your success with friends, colleagues, and employers.
Creators
University of Colorado System
The University of Colorado is a recognized leader in higher education on the national and global stage. We collaborate to meet the diverse needs of our students and communities. We promote innovation, encourage discovery and support the extension of knowledge in ways unique to the state of Colorado and beyond.
Pricing
| Purchase Course | Audit | |
|---|---|---|
| Access to course materials | Available | Available |
| Access to graded materials | Available | Not available |
| Receive a final grade | Available | Not available |
| Earn a shareable Course Certificate | Available | Not available |
Coursera provides universal access to the world’s best education, partnering with top universities and organizations to offer courses online.
© 2017 Coursera Inc. All rights reserved.
