Course: The Mathematics of Cryptography: From Ancient Rome to a Quantum Future

We have seen that quantum computers have the power to break RSA, hence in a world with quantum computers our use of this cryptographic method is certainly taken away. However, …

Quantum computers threaten current cryptographic techniques, but may hold the key to complete – provable – security. In this video, Hamid introduces the concept of quantum cryptography. What do you …

Using the mathematical insights of permutations, Rejewski invented a device called a cyclometer that enabled him to infer the daily settings from listening in to the encrypted messages. Rejewski’s cyclometer …

By thinking of the Enigma machine as a sequence of permutations, and applying the theory we have already met, we will now take the first steps to see how the …

How does cycle structure change when we perform different operations on permutations? More importantly, when doesn’t it change? Cycle structure of inverse permutations Hopefully you tried out the exercises at …

In Week 1 we met the idea of permutations, and saw one way of representing them – the Cauchy two-line notation. We also saw how to compose two permutations together, …

Before we can understand how Enigma was broken, we need to appreciate the details of how messages were sent in practice. Before 15 Sept 1938 the operator set the machine …

The difficulty in reading Enigma-encrypted messages came not just from the machine itself but mainly from the manifold different ways of setting the machine up. Without knowing the daily settings, …

This step will show you how to build a simplified Enigma machine using only a Pringles tube. The wiring in the model is accurate – that is the genuine wiring …

The Enigma machine was used extensively by the German military to encrypt its communications throughout the Second World War (and for a few years beforehand); however it was broken by …

In this video, Emilie explains how Rejewski was able to deduce the cycle structure of the permutation of the “double Enigma machine”, and how this dramatically reduced the number of …

Watch this video to hear Emilie explain how the double-encryption of the message indicators was a weakness that could be exploited by mathematicians. Is there anything that strikes you as …

In this video, Chris shows how to make a simplified version of the Enigma machine. Written instructions, along with the pictures you’ll need to print off, are provided in the …

In this video, Chris Hughes gives an introduction to the Enigma machine. Have you heard about Enigma before? Use the comments below to tell us what you’ve heard about how …

How does knowledge of the codeword length help us to break the Vigenère cipher? Recap: we’ve see that the distances between occurrences of the most common trigram are very likely …