Back to Number Theory and Cryptography

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511 ratings

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110 reviews

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. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this short course, we will make the whole journey from the foundation to RSA in 4 weeks. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest!
As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Do you have technical problems? Write to us: coursera@hse.ru...

SS

Jul 31, 2020

I loved this course! It is unlike any I have taken before. All courses in this specialization have always included fun activities to make the taught content fun and understandable.

PW

Nov 21, 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.

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By Konstantin K

•Dec 19, 2017

Formulas, formulas... lack of examples - lack of understandings. Though topics of the course are very useful and interesting.

Last quest was fascinating. But in my case notebook stopped giving me any results and I managed to get only 1/4 of tasks.

By Doug D

•Dec 26, 2018

It serves as a table of contents of the material which makes it useful to seek out other lecturers on YouTube. I wouldn't recommend someone uses this course by itself.

By liang t

•Jan 2, 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.

By Steven W

•Dec 12, 2017

This is a really is a special course. It doesn't have any puzzles like the first few but, you get to go on a RSA quest, ala cicada 3301, and practice your new cryptography skills. At the end of your quest you gain ultimate knowledge.

By Pedro H

•Jun 17, 2018

Really nice introduction to discrete math and basic algorithms. The content is quite basic, but as mentioned in the syllabus is for beginners. Still, for those of you who are at that level is worth taking this specialization.

By Pete W

•Nov 22, 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 T K

•May 28, 2020

I cant think of any other best way of presenting cryptography to beginners. Everything presented in the course has some connection to cryptography, really enjoyed RSA quest.

By Gholamreza S T

•Oct 16, 2018

This course is not deep and rigorous enough to familiarize you with fundamentals of Number Theory. It just covers some theorems! No reference book is suggested, and worst of all accent of teachers makes it really hard to understand the material.

By Prasad K

•Mar 19, 2019

Concepts are poorly explained. It is very hard to follow the instructors. Need better quality courses.

By William H

•Apr 3, 2020

My first experience with cryptography. The coding assignments are enough to make me think and ensure that I understood the concepts.

By Ashish D S

•Jul 23, 2018

Excellent course, this course is more about numerical theory behind cryptography.

It has excellent assignments using Python.

By Jinqiang Z

•Dec 9, 2017

in a short 4 weeks, it explains the theory of RSA well and also the RSA itself.

By Tomasz L

•Sep 2, 2019

The final project is absolutely awesome!

By ANTHONY R

•Jul 2, 2018

This is worse course I’ve taken as far as getting certified as far as exams, quizzes. Bad external tools that don’t work. Bizarre instructions to complete exams. And graders who have no clue as to what the issues, looking at questions in forums. The Notebook function is sometimes cumbersome. And use of it as educational material was confusing.However if just auditing, this course is great. And material is covered with seriousness, and goes beyond summary treatments in other crypto classes on schemes based on number theoretic concepts.

By Nikita S

•Mar 25, 2021

Professional instructors explain all the number theory necessary for the implementation of the RSA cryptosystem. The course ends with a nice labwork where you implement RSA and conduct several attacks on incorrect implementations. Michael Levin is one of my favorite instructors. I have a feeling that this course was somewhat short, but maybe it is caused by the fact that it is a part of the five-course specialization.

By Amy G

•Apr 24, 2020

This course was fantastic. It was easy to follow for someone with no previous number theory or cryptography background. Writing RSA encryption and implementing attacks at the end was very rewarding, and I loved the course's Final Quest solving a series of puzzles to find the answer to the ultimate question of life, the universe and everything!

By Bhargav D

•Dec 27, 2018

It was indeed a great course. I already had the fundamentals of Cryptography and No. Theory but this course helped me brush up my fundamentals and the instructors kept things simple and concise and most importantly to the point at the same time. The puzzles, quizzes, and the quizzes in between the videos were awesome too.Thank You.

By UMAR T

•Mar 15, 2020

Excellent course by Vladimir Podolskii Associate Professor Computer Science,Michael Levin Lecturer Computer Science , and Alexander S. Kulikov Visiting Professor Department of Computer Science and Engineering by Univ. of Sand Diego California and National Research University for teaching learners about cryptography.

By Srinath S

•Aug 1, 2020

I loved this course! It is unlike any I have taken before. All courses in this specialization have always included fun activities to make the taught content fun and understandable.

By Michal B

•Mar 28, 2020

For me (as a number theory teacher) it was quite easy and fast, but I have enjoyed it and had fun!

By Greg M

•Apr 21, 2019

good material, good presentation, very good problem sets. thank you!

By Ruben G C

•Jun 4, 2019

Very funny and interesting course. Ideal to play with Python.

By Yordan S

•Jan 1, 2019

I really loved the final quiz. It was very interesting.

By Dmytro F

•Jan 30, 2018

Very good introductory course to number theory and RSA.

By Aditya D

•Oct 7, 2018

I really liked the structure of the topics

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