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

Permutations are going to be very important throughout this course, so let’s spend some time learning about their structure, and how we can work with them. Notation Two types of …

Modular arithmetic is a type of arithmetic for integers (whole numbers) which “wraps around” when we reach a certain number, called the modulus. Since the English alphabet has 26 letters, …

The key flaw in the Vigenère cipher was the repetition of the codeword. In our example above, where the plaintext BOTHER THE THEOREM was encrypted using the seven-letter codeword KASISKI …

Here are some examples of ciphertexts and the codewords which were used to create them. Use your Caesar wheel to decipher them back to plaintext English. Codeword: VIGENERECiphertext: XNAYSWLMWWJFSXSW Codeword: …

The Vigenère cipher works similarly to the shift cipher that we’ve already studied. However, it uses a codeword to change the shift as we work through the plaintext, making it …

Chris Hughes gives a short introduction to the Vigenère cipher. What do you think some of the strengths and weaknesses of using a codeword might be?

Suppose that we have a tool which gives us a measure of how “likely” it is that a given piece of text is written in English: let’s call this the …

We’ve seen that there are over 403 octillion ways of permuting the 26 letters of the English alphabet. That’s 403 followed by 24 zeros. Checking one permutation per second to …

Jess Hargreaves gives an introduction to substitution ciphers, and how they may be decrypted using frequency analysis. Did you find anything in this video particularly surprising?

Emilie Dufresne gives an introduction to the Caesar cipher. Have you heard about, or used, the Caesar cipher before? Let us know about your experiences in the comments below.

In our opening film, Chris Hughes introduces the course, and explains the difference between codes and ciphers. How this all works Each week will have a theme, and we’ll learn …

As we’ve seen, a shift cipher is a simple type of substitution cipher: a way of jumbling up the letters of our alphabet. In this part of the course we’ll …

In this activity we’ll show you how to create a Caesar wheel, which will make it really easy to work with shift ciphers. It’s worth taking the time to make …

The Caesar cipher is the simplest example of a substitution cipher, in which we replace one letter in our text with another letter, in order to confuse the reader by …