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Back to Number Theory and Cryptography

Number Theory and Cryptography, University of California San Diego

93 ratings
21 reviews

About this Course

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....

Top reviews


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 L

Jan 02, 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.

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21 Reviews

By Gautham A Nagendran

Dec 09, 2018

Amazing course, learnt a lot. The assignments were a bit difficult [ and time consuming ] but they helped me gain a better understanding of the concepts.

By Pete Wills

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 Gholamreza Sabery Tabrizy

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 Aditya Dutta

Oct 07, 2018

I really liked the structure of the topics

By Ramesh

Sep 23, 2018

Right amount off details with very simple and intuitive explanation.

By Ashish Dattatray Sarode

Jul 23, 2018

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

It has excellent assignments using Python.

By HaotianWang

Jul 19, 2018



Jul 02, 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 Samuel Ramos Sosa

Jun 18, 2018

very confusing explanations. had to look up everything elsewhere.

By Pedro Manuel Herrero Vidal

Jun 18, 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.