University of Colorado System
Mathematical Foundations for Cryptography
University of Colorado System

Mathematical Foundations for Cryptography

This course is part of Introduction to Applied Cryptography Specialization

Taught in English

Some content may not be translated

William Bahn
Richard White
Sang-Yoon Chang

Instructors: William Bahn

17,801 already enrolled

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Course

Gain insight into a topic and learn the fundamentals

4.6

(317 reviews)

Beginner level
No prior experience required
14 hours (approximately)
Flexible schedule
Learn at your own pace

Details to know

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Assessments

9 quizzes

Course

Gain insight into a topic and learn the fundamentals

4.6

(317 reviews)

Beginner level
No prior experience required
14 hours (approximately)
Flexible schedule
Learn at your own pace

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This course is part of the Introduction to Applied Cryptography Specialization
When you enroll in this course, you'll also be enrolled in this Specialization.
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There are 4 modules in this course

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.

What's included

5 videos11 readings2 quizzes1 discussion prompt

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.

What's included

4 videos9 readings2 quizzes1 discussion prompt

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.

What's included

3 videos5 readings2 quizzes1 discussion prompt

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.

What's included

3 videos8 readings3 quizzes1 discussion prompt

Instructors

Instructor ratings
4.5 (61 ratings)
William Bahn
University of Colorado System
2 Courses27,560 learners

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