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#### 100% online

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#### Approx. 16 hours to complete

Suggested: 4 weeks, 2-5 hours/week...

#### English

Subtitles: English, Greek

### Skills you will gain

Number TheoryCryptographyModular Exponentiation

#### 100% online

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

#### Approx. 16 hours to complete

Suggested: 4 weeks, 2-5 hours/week...

#### English

Subtitles: English, Greek

### Syllabus - What you will learn from this course

Week
1
4 hours to complete

## Modular Arithmetic

10 videos (Total 90 min), 4 readings, 13 quizzes
10 videos
Problems6m
Divisibility Tests5m
Division by 212m
Binary System11m
Modular Arithmetic12m
Applications7m
Modular Subtraction and Division11m
Python Code for Remainders5m
Slides1m
Slides1m
Slides1m
12 practice exercises
Divisibility15m
Remainders10m
Division by 45m
Four Numbers10m
Division by 10110m
Properties of Divisibility10m
Divisibility Tests8m
Division by 24m
Binary System8m
Modular Arithmetic8m
Remainders of Large Numbers10m
Modular Division10m
Week
2
4 hours to complete

## Euclid's Algorithm

7 videos (Total 78 min), 4 readings, 7 quizzes
7 videos
Least Common Multiple8m
Diophantine Equations: Examples5m
Diophantine Equations: Theorem15m
Modular Division12m
Greatest Common Divisor: Code15m
Extended Euclid's Algorithm: Code10m
Slides1m
Slides10m
7 practice exercises
Greatest Common Divisor10m
Tile a Rectangle with Squares20m
Least Common Multiple10m
Least Common Multiple: Code15m
Diophantine Equations15m
Diophantine Equations: Code20m
Modular Division: Code20m
Week
3
4 hours to complete

## Building Blocks for Cryptography

14 videos (Total 91 min), 4 readings, 6 quizzes
14 videos
Existence of Prime Factorization2m
Euclid's Lemma4m
Unique Factorization9m
Implications of Unique Factorization10m
Remainders7m
Chinese Remainder Theorem7m
Many Modules5m
Fast Modular Exponentiation10m
Fermat's Little Theorem7m
Euler's Totient Function6m
Euler's Theorem4m
Slides10m
Slides10m
Fast Modular Exponentiation7m
Slides10m
5 practice exercises
Integer Factorization20m
Remainders8m
Chinese Remainder Theorem: Code15m
Fast Modular Exponentiation: Code20m
Modular Exponentiation8m
Week
4
5 hours to complete

## Cryptography

9 videos (Total 67 min), 4 readings, 2 quizzes
9 videos
RSA Cryptosystem14m
Simple Attacks5m
Small Difference5m
Insufficient Randomness7m
More Attacks and Conclusion5m
Many Time Pad Attack10m
Slides10m
Randomness Generation10m
Slides and External References10m
2 practice exercises
RSA Quiz: Code2h
RSA Quest - Quiz6m
4.6
28 Reviews

## 50%

started a new career after completing these courses

## 40%

got a tangible career benefit from this course

### Top reviews from Number Theory and Cryptography

By PWNov 22nd 2018

I was really impressed especially with the RSA portion of the course. It was really well explained, and the programming exercise was cleverly designed and implemented. Well done.

By LJan 2nd 2018

A good course for people who have no basic background in number theory , explicit clear explanation in RSA algorithm. Overall,a good introduction course.

## Instructors

### Alexander S. Kulikov

Visiting Professor
Department of Computer Science and Engineering

### Michael Levin

Lecturer
Computer Science

Associate Professor
Computer Science Department

## About University of California San Diego

UC San Diego is an academic powerhouse and economic engine, recognized as one of the top 10 public universities by U.S. News and World Report. Innovation is central to who we are and what we do. Here, students learn that knowledge isn't just acquired in the classroom—life is their laboratory....

## About National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communicamathematics, engineering, and more. Learn more on www.hse.ru...

## About the Introduction to Discrete Mathematics for Computer Science Specialization

Discrete Math is needed to see mathematical structures in the object you work with, and understand their properties. This ability is important for software engineers, data scientists, security and financial analysts (it is not a coincidence that math puzzles are often used for interviews). We cover the basic notions and results (combinatorics, graphs, probability, number theory) that are universally needed. To deliver techniques and ideas in discrete mathematics to the learner we extensively use interactive puzzles specially created for this specialization. To bring the learners experience closer to IT-applications we incorporate programming examples, problems and projects in our courses....

## 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.