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

Thus far we’ve looked at how mathematics helped break the Enigma machine before the Second World War started. In the lead-up to the War, security improvements were made to Enigma, …

Now we have seen an outline of the mathematics behind RSA, let’s do a worked example. Using the previous example, let’s say Alice’s public keys are (N=187) and (e=27). Let’s …

In order for the RSA algorithm to be useful, Alice must be able to decrypt any message received. We shall now see how she can calculate the decryption exponent making …

Many congratulations for staying with us to the end of the course. Who knows, you may well find yourself studying together with others who also took this course in the …

The security of the RSA system relies on the difficulty of factoring (N) – the product of two large primes. Since the RSA method is used to protect the majority …

The RSA public key cryptosystem uses the difficulty of factoring large numbers as the basis of its trapdoor function. Unlike Diffie-Hellman, this system can be used to securely send messages. …

When we met the Diffie-Hellman algorithm, we saw how it created a shared secret between Alice and Bob. But they had no control over what that secret was. The RSA …

Here is how to understand the mathematics behind the Diffie-Hellman key exchange protocol. Suppose that Alice and Bob wish to create a shared secret key. They will have no control …

A worked example of how the Diffie-Hellman key exchange works. Check the calculations as Chris talks you through the example. Did you manage to successfully follow all of the steps?

How can two people communicate with each other in complete secrecy, without ever having met first to share a codebook, and over an insecure channel with others listening in? In …

In all the previous examples of ciphers that we have seen, the key used for encryption and decryption must be kept secret. In the 1970s, however, it was realised that …

Welcome to our final week. In this video, Chris looks ahead to the topics of our final week. All the examples that we’ve seen of classical cryptography methods have been …

We hope you’ve enjoyed this short course looking through some mathematical aspects in the history of cryptography. If there’s anything you’d like to discuss further, or questions you’d like to …

Let us see how using the Q-box allows us to detect eavesdropping. Suppose that Alice and Bob are using a Q-box to share random strings, as we just described. An …

We’ve introduced the idea of a Q-box as an analogy for how a quantum protocol works. Let’s now see how a Q-box can be used by two people to share …