About this Course
4.6
48 ratings
7 reviews
Specialization
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100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Beginner Level

Beginner Level

Hours to complete

Approx. 12 hours to complete

Suggested: This is Course 2 in a 4-course specialization. Estimated workload: 15-hours per week....
Available languages

English

Subtitles: English
Specialization
100% online

100% online

Start instantly and learn at your own schedule.
Flexible deadlines

Flexible deadlines

Reset deadlines in accordance to your schedule.
Beginner Level

Beginner Level

Hours to complete

Approx. 12 hours to complete

Suggested: This is Course 2 in a 4-course specialization. Estimated workload: 15-hours per week....
Available languages

English

Subtitles: English

Syllabus - What you will learn from this course

Week
1
Hours to complete
3 hours to complete

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....
Reading
5 videos (Total 60 min), 10 readings, 2 quizzes
Video5 videos
Divisibility, Primes, GCD14m
Modular Arithmetic15m
Multiplicative Inverses12m
Extended Euclidean Algorithm13m
Reading10 readings
Course Introduction10m
Lecture Slides - Divisibility, Primes, GCD10m
Video - Adam Spencer: Why I fell in love with monster prime numbers15m
L16: Additional Reference Material10m
Lecture Slides - Modular Arithmetic10m
L17: Additional Reference Material10m
Lecture Slides - Multiplicative Inverses10m
L18: Additional Reference Material10m
Lecture Slides - Extended Euclidean Algorithm10m
L19: Additional Reference Material10m
Quiz2 practice exercises
Practice Assessment - Integer Foundation18m
Graded Assessment - Integer Foundation16m
Week
2
Hours to complete
3 hours to complete

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....
Reading
4 videos (Total 51 min), 9 readings, 2 quizzes
Video4 videos
Euler's Totient Theorem16m
Eulers Totient Function12m
Discrete Logarithms15m
Reading9 readings
Lecture Slides - Square-and-Multiply10m
Video - Modular exponentiation made easy10m
L20: Additional Reference Material10m
Lecture Slide - Euler's Totient Theorem10m
L21: Additional Reference Material10m
Lecture Slide - Eulers Totient Function10m
L22: Additional Reference Material10m
Lecture Slide - Discrete Logarithms10m
L23: Additional Reference Material10m
Quiz2 practice exercises
Practice Assessment - Modular Exponentiation12m
Graded Assessment - Modular Exponentiation20m
Week
3
Hours to complete
3 hours to complete

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....
Reading
3 videos (Total 25 min), 5 readings, 2 quizzes
Video3 videos
Moduli Restrictions, CRT-to-Integer Conversions10m
CRT Capabilities and Limitations8m
Reading5 readings
Lecture Slide - CRT Concepts, Integer-to-CRT Conversions30m
L24: Additional Reference Material10m
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30m
Lecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30m
Video - How they found the World's Biggest Prime Number - Numberphile12m
Quiz2 practice exercises
Practice Assessment - Chinese Remainder Theorem12m
Graded Assessment - Chinese Remainder Theorem20m
Week
4
Hours to complete
3 hours to complete

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....
Reading
3 videos (Total 36 min), 8 readings, 3 quizzes
Video3 videos
Fermat's Primality9m
Miller-Rabin13m
Reading8 readings
Lecture Slide - Trial Division10m
L27: Additional Reference Material10m
Lecture Slide - Fermat's Primality10m
L28: Additional Reference Material10m
Lecture Slide - Miller-Rabin10m
Video - James Lyne: Cryptography and the power of randomness10m
L29: Additional Reference Material10m
The Science of Encryption10m
Quiz3 practice exercises
Practice Assessment - Primality Testing12m
Graded Assessment - Primality Testing20m
Course Project8m

Instructors

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William Bahn

Lecturer
Computer Science
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Richard White

Assistant Research Professor
Computer Science
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Sang-Yoon Chang

Assistant Professor
Computer Science

About 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....

About the Introduction to Applied Cryptography Specialization

Cryptography is an essential component of cybersecurity. The need to protect sensitive information and ensure the integrity of industrial control processes has placed a premium on cybersecurity skills in today’s information technology market. Demand for cybersecurity jobs is expected to rise 6 million globally by 2019, with a projected shortfall of 1.5 million, according to Symantec, the world’s largest security software vendor. According to Forbes, the cybersecurity market is expected to grow from $75 billion in 2015 to $170 billion by 2020. In this specialization, students will learn basic security issues in computer communications, classical cryptographic algorithms, symmetric-key cryptography, public-key cryptography, authentication, and digital signatures. These topics should prove useful to those who are new to cybersecurity, and those with some experience....
Introduction to Applied Cryptography

Frequently Asked Questions

  • Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

  • When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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