The Mathematics of Cryptography with Dr James Grime

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.