The Mathematics of Cryptography with Dr James Grime
From Caesar to Enigma, and beyond
4.91 (195 reviews)
1,778
students
8.5 hours
content
Apr 2022
last update
$74.99
regular price
What you will learn
Understand the methods of classical cryptography such as monoalphabetic ciphers, polyalphabetic ciphers and transposition ciphers.
Understand the mathematics of modular arithmetic.
Understand and apply the methods of classical cryptanalysis such as the Kasiski Test and Friedman Test.
Understand the Enigma Machine and the method used to break Enigma in World War II.
Understand the mathematics of RSA internet encryption.
Why take this course?
Cryptography is the science of secrets and secret messages. In this course we will learn more about the mathematics behind codes and code breaking.
The course will start with easy ciphers and how they were broken, before moving to more sophisticated ciphers including the famous World War II Enigma machine and modern internet encryption.
The course contains over 6 hours of lectures, with an additional 2 hours of exercises and solution videos.
Topics covered in the course include:
Monoalphabetic ciphers;
Modular arithmetic;
Polyalphabetic ciphers;
The Enigma Machine; and
Public Key Cryptography.
During this course we will introduce many important mathematical concepts including modular arithmetic, sets, functions, probability, statistics, combinatorics and number theory.
Ciphers and techniques in the course include:
Substitution ciphers;
Transposition ciphers;
Commuting ciphers;
Frequency analysis;
The Vigenere cipher;
The Kasiski test;
Index of Coincidence;
The Friedman test;
Diffie-Hellman;
Elliptic curve cryptography;
RSA internet encryption; and
Digital signatures.
Finally, we will end the course with a brief look at the future of cryptography.
The course is intended to be self-contained and comes with a set of notes that you can complete as we go through the course.
The course comes with many exercises after each section, with solutions, that allow you to test what you have learnt.
Cryptography touches on a broad range of topics and is one of the most fascinating applications of maths. By the end of this short course, we will have introduced several fundamental ideas in mathematics, and even answer whether there such a thing as an unbreakable code.
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Reviews
Eliot
October 2, 2023
I really enjoyed this course. The maths was gentle and explained very clearly. Having the notes mostly done was a real luxury. Thanks for putting this together, I am inspired to study this topic in more depth.
Leszek
September 1, 2023
Dr. Grime provides understandable and useful explanations of the math behind public key cryptography.
Lydia
June 21, 2023
I really liked the varied exercises and how it was split into good sized chunks. It was very unique and I spent my time wisely doing this course!
Marco
June 20, 2023
Excellent course!!!! I'm an IT professional looking to fill the gaps that I have on security, and this course looked quite nice. I like mathematics so I considered that this could help me to understand some aspects that of cryptography. And guess what!!?? Yes, I'm quite happy for having taken this nice and fancy course. The instructor has a really nice way to explain, he has a nice accent that can be understood easily (at least for me that I'm not a native English speaker), the examples are easy to understand, I had to watch some videos twice though. Of course I don't think this is the way that cryptography is applied in real life strictly speaking, but the course gives a very reasonable idea of how cryptography is implemented.
Sergey
May 29, 2023
Very engaging instructor, gives a good perspective of how we got from the simple Caesar cypher to more advanced techniques via the continuous leverage of modulo arithmetic.
Perry
May 23, 2023
So far it’s very well explained. In addition, the instructor (I’m sorry, I forgot his name) is obviously extremely enthusiastic about what he’s teaching which makes the course that much more enjoyable.
Jediah
April 23, 2023
I love how Dr Grime starts with simple mono/polyalphabetic ciphers and shows you the maths behind the simple forms of encrypting/decrypting the ciphers; then based on this simple forms of ciphers he introduces some of the theories that underpin advanced forms of cryptography (which you don't get to, until later).
I ended up needing to use a lot of external resources too (like Khans) to reinforce some of the learnings - and it was really hard to read Dr. Grime's writing [I can't tell you how many times, in reviewing the video, I thought he wrote 2 instead of Q].
This is also not the first time I've gone through this subject matter in some detail, but I learn new things every time which helps me understand some of the more obscure ideas I missed on the previous passes; and I'm sure I will be going through it again in the future.
Overall, it was an excellent resource - so much so that I purchased a personal company on Udemy (originally took it on a business subscription) - so that I could reference the course in the future.
Suryanarayanan
December 14, 2022
Great starting point. Clear and concise. Reasonable course duration. Lots of problems discussed and solutions provided.
Francis
October 23, 2022
Really enjoying the course. Very clear explanation of all concepts. Excellent practice exercises to work through.
anonymous
September 28, 2022
If it was about reading, there is no need to have a professor. Just send the PDF, I can read it by myself.
Bryan
August 27, 2022
This was a wonderful course. There are great exercises reinforcing the superb lectures. I learned the answers to so many questions I've been curious about for the last 30 years.
It might be just me, but I had some trouble with watching the video while filling in the notes.
Finding where to write in the notes took me longer when the space was small or at the beginning or end of a line. It would have been easier if each location was underlined, especially since I printed the normal-size pdf which is formatted differently than those in the onscreen large format. I had to pause the videos quite regularly to keep up because of having to search for where to write.
Mauro
August 6, 2022
this course is accurate and deep. many exemples and exercices help me in understanding arguments.
five stars
Vincent
July 3, 2022
I enjoyed following this cryptography course. For those wondering, I'd say it is more geared towards the mathematically-inclined than programmers. The lectures and explanations are clear, the content is interesting and the pacing is good, more like a traditional in-person course. Lectures consist of going through the provided notes, and filling in the blanks. Exercises are pen-and-paper style math problems. It is a minimalist approach to teaching; I think there could have been some more real-life videos of using Enigma, some screen-sharing of a browser when explaining RSA, etc to make it more compelling. Having seen Numberphile's videos on Enigma, you should not expect the same level of "entertainment" out of it. Finally, you get a nice free Number Theory and Modular Arithmetic primer included. Thanks Dr Grime for the nice content!
Nicola
April 12, 2022
This course is an absolute perfect match for me! Really simple and fluid to follow and understand, and the exercises are interesting and leave you with additional knowledge.
Thanks Dr. Grime, this is an amazing job for a course!
Rose
April 3, 2022
This course offers the mathematics of code and code-breaking, and suitable for students and general public, even if your background is not in STEM. If you love puzzles and comfortable with numbers, this course is good for you. Dr. Grime is a well-known science communicator with years of experience presenting to academics and general audience, so you will have engaging experience and be inspired with new knowledge. You will not feel bored, a lot of pop-culture reference and cheesy jokes in the lessons to keep you entertained. There is a handbook with blank spaces to be filled as you go through the lesson. I find it as a clever way to engage with the lesson without too much distraction of note-taking. The instructor will guide you through the courses with the basics each code system. The maths level required is around high-school level, mainly about modular arithmetics and probability. Some parts of the lesson could be quite confusing if you're not familiar with the concepts, but you can always pause and replay the videos. I am very satisfied with this course and recommend it to anyone who is interested in applied maths. I hope Dr. Grime would have other interesting courses in the future.
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4309482
udemy ID
9/20/2021
course created date
6/3/2022
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