Mathematical Foundations for Cryptography (Coursera)

Mathematical Foundations for Cryptography (Coursera)

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.

Class Deals by MOOC List - Click here and see Coursera's Active Discounts, Deals, and Promo Codes.

Course 2 of 4 in the Introduction to Applied Cryptography Specialization

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.

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.

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.

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.

Go to Class
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Related Courses

TCP/IP and Advanced Topics (Coursera) Coursera
University of Colorado System

TCP/IP and Advanced Topics (Coursera)

In this course, we give an in-depth study of the TCP/IP protocols. We examine the details of how IP enables communications across a collection of networks. We pay particular attention to the hierarchical structure of IP addresses and explain their role in ensuring scalability of the Internet. The role of address prefixes and the uses of masks are explained in details. We review in details about TCP three-way handshake, flow control, and congestion control. Furthermore, we provide an introduction to some advanced topics, including Multicast, SDN and security

Jul 6th 2026
5-12 Weeks
Discrete Mathematics (Coursera) Coursera
Shanghai Jiao Tong University

Discrete Mathematics (Coursera)

Discrete mathematics forms the mathematical foundation of computer and information science. It is also a fascinating subject in itself. Learners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Perhaps more importantly, they will reach a certain level of mathematical maturity - being able to understand formal statements and their proofs; coming up with rigorous proofs themselves; and coming up with interesting results.

Jul 6th 2026
5-12 Weeks
Introduction to Cybersecurity for Business (Coursera) Coursera
University of Colorado System

Introduction to Cybersecurity for Business (Coursera)

The world runs computers. From small to large businesses, from the CEO down to level 1 support staff, everyone uses computers. This course is designed to give you a practical perspective on computer security. This course approaches computer security in a way that anyone can understand. Ever wonder how your bank website is secure when you connect to it? Wonder how other business owners secure their network? Wonder how large data breaches happen? This is practical computer security. It will help you answer the question – what should I focus on?

Jul 6th 2026
5-12 Weeks
Calculus: Single Variable Part 3 - Integration (Coursera) Coursera
University of Pennsylvania

Calculus: Single Variable Part 3 - Integration (Coursera)

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences.

Jul 6th 2026
4 Weeks
Software Design Threats and Mitigations (Coursera) Coursera
University of Colorado System

Software Design Threats and Mitigations (Coursera)

The design step in developing software has some unique characteristics. First of all, it’s the only step where drawing pictures of things is the norm. Why is that? What do pictures do that other representations cannot do? Pictures have varying levels of detail; pictures have context. Pictures…paint a picture. Why are these things important? In this course, too, we begin looking at other disciplines (building architecture is a favorite one) for lessons on design.

Jul 6th 2026
5-12 Weeks
Linear Regression and Modeling (Coursera) Coursera
Duke University

Linear Regression and Modeling (Coursera)

This course introduces simple and multiple linear regression models. These models allow you to assess the relationship between variables in a data set and a continuous response variable. Is there a relationship between the physical attractiveness of a professor and their student evaluation scores? Can we predict the test score for a child based on certain characteristics of his or her mother? In this course, you will learn the fundamental theory behind linear regression and, through data examples, learn to fit, examine, and utilize regression models to examine relationships between multiple variables, using the free statistical software R and RStudio.

Jul 6th 2026
4 Weeks
Cybersecurity and the Internet of Things (Coursera) Coursera
University System of Georgia

Cybersecurity and the Internet of Things (Coursera)

Welcome to “Cybersecurity and the Internet of Things”! This course is for you if you are curious about the most recent trends and activities in the internet capabilities and concerns about programmed devices. There are complexities and areas of necessary awareness when the industrial sector becomes connected to your home.

Jul 6th 2026
4 Weeks
Number Theory and Cryptography (Coursera) Coursera
University of California, San Diego,Higher School of Economics - HSE University

Number Theory and Cryptography (Coursera)

We all learn numbers from the childhood. Some of us like to count, others hate it, but any person uses numbers everyday to buy things, pay for services, estimated time and necessary resources. People have been wondering about numbers’ properties for thousands of years. And for thousands of years it was more or less just a game that was only interesting for pure mathematicians. Famous 20th century mathematician G.H. Hardy once said “The Theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the word nowadays.

Jul 6th 2026
4 Weeks
Fibonacci Numbers and the Golden Ratio (Coursera) Coursera
The Hong Kong University of Science and Technology - HKUST

Fibonacci Numbers and the Golden Ratio (Coursera)

Learn the mathematics behind the Fibonacci numbers, the golden ratio, and how they are related. These topics are not usually taught in a typical math curriculum, yet contain many fascinating results that are still accessible to an advanced high school student. The course culminates in an explanation of why the Fibonacci numbers appear unexpectedly in nature, such as the number of spirals in the head of a sunflower.

Jul 6th 2026
3 Weeks