This course is part of the Introduction to Applied Cryptography Specialization

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Introduction to Applied Cryptography SpecializationUniversity of Colorado System

About this Course

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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.

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Course 2 of 4 in the

Introduction to Applied Cryptography Specialization

Beginner Level

Approx. 14 hours to complete

English

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Flexible deadlines

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Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 2 of 4 in the

Introduction to Applied Cryptography Specialization

Beginner Level

Approx. 14 hours to complete

English

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Instructors

Instructor rating

4.47/5 (61 Ratings)

Offered by

University of Colorado System

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Syllabus - What you will learn from this course

Week1

Week 1

4 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.

4 hours to complete

5 videos (Total 60 min), 10 readings, 2 quizzes

5 videos

Course Introduction3mDivisibility, Primes, GCD14mModular Arithmetic15mMultiplicative Inverses12mExtended Euclidean Algorithm13m

10 readings

Course Introduction10mLecture Slides - Divisibility, Primes, GCD10mVideo - Adam Spencer: Why I fell in love with monster prime numbers15mL16: Additional Reference Material10mLecture Slides - Modular Arithmetic10mL17: Additional Reference Material10mLecture Slides - Multiplicative Inverses10mL18: Additional Reference Material10mLecture Slides - Extended Euclidean Algorithm10mL19: Additional Reference Material10m

2 practice exercises

Practice Assessment - Integer Foundation30mGraded Assessment - Integer Foundation30m

Week2

Week 2

4 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.

4 hours to complete

4 videos (Total 51 min), 9 readings, 2 quizzes

4 videos

Square-and-Multiply7mEuler's Totient Theorem16mEulers Totient Function12mDiscrete Logarithms15m

9 readings

Lecture Slides - Square-and-Multiply10mVideo - Modular exponentiation made easy10mL20: Additional Reference Material10mLecture Slide - Euler's Totient Theorem10mL21: Additional Reference Material10mLecture Slide - Eulers Totient Function10mL22: Additional Reference Material10mLecture Slide - Discrete Logarithms10mL23: Additional Reference Material10m

2 practice exercises

Practice Assessment - Modular Exponentiation30mGraded Assessment - Modular Exponentiation30m

Week3

Week 3

3 hours to complete

Chinese Remainder Theorem

3 hours to complete

3 videos (Total 25 min), 5 readings, 2 quizzes

3 videos

CRT Concepts, Integer-to-CRT Conversions6mModuli Restrictions, CRT-to-Integer Conversions10mCRT Capabilities and Limitations8m

5 readings

Lecture Slide - CRT Concepts, Integer-to-CRT Conversions30mL24: Additional Reference Material10mLecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30mLecture Slide - Moduli Restrictions, CRT-to-Integer Conversions30mVideo - How they found the World's Biggest Prime Number - Numberphile12m

2 practice exercises

Practice Assessment - Chinese Remainder Theorem30mGraded Assessment - Chinese Remainder Theorem30m

Week4

Week 4

4 hours to complete

Primality Testing

4 hours to complete

3 videos (Total 36 min), 8 readings, 3 quizzes

3 videos

Trial Division13mFermat's Primality9mMiller-Rabin13m

8 readings

Lecture Slide - Trial Division10mL27: Additional Reference Material10mLecture Slide - Fermat's Primality10mL28: Additional Reference Material10mLecture Slide - Miller-Rabin10mVideo - James Lyne: Cryptography and the power of randomness10mL29: Additional Reference Material10mThe Science of Encryption10m

3 practice exercises

Practice Assessment - Primality Testing30mGraded Assessment - Primality Testing30mCourse Project30m

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TOP REVIEWS FROM MATHEMATICAL FOUNDATIONS FOR CRYPTOGRAPHY

by MJMay 28, 2020

It's actually more informative.... Really I improved myself in Foundation s of cryptography

by TLAug 18, 2018

Good course, but would like some more exercises to implement the mathematics learnt.

by ASMay 1, 2020

I enrolled for this course because Number Theory is my area of interest. This course has helped me to spend my time effectively during this lockdown period. Thank you Coursera.

by VTJul 28, 2020

The course content and the assignments were quite meticulously designed and delivered efficiently.

View all reviews

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.

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I subscribe to this Specialization?
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.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

More questions? Visit the Learner Help Center.

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Mathematical Foundations for Cryptography

About this Course

Instructors

William Bahn

Richard White

Sang-Yoon Chang

Offered by

University of Colorado System

Syllabus - What you will learn from this course

Integer Foundations

Modular Exponentiation

Chinese Remainder Theorem

Primality Testing

Reviews

TOP REVIEWS FROM MATHEMATICAL FOUNDATIONS FOR CRYPTOGRAPHY

About the Introduction to Applied Cryptography Specialization

Frequently Asked Questions

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Mathematical Foundations for Cryptography

About this Course

Instructors

William Bahn

Richard White

Sang-Yoon Chang

Offered by

University of Colorado System

Syllabus - What you will learn from this course

Integer Foundations

Modular Exponentiation

Chinese Remainder Theorem

Primality Testing

Reviews

TOP REVIEWS FROM MATHEMATICAL FOUNDATIONS FOR CRYPTOGRAPHY

About the Introduction to Applied Cryptography Specialization

Frequently Asked Questions

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