This film shows original archive footage of the MI6 team at Whaddon Hall in WWII. No-one seems to know how or why this footage exists, it was strictly forbidden to film in Top Secret establishments, but here it is courtesy of our friends at Bletchley Park.
There are a lot, and I mean a LOT, of great maths and cryptography resources on YouTube. We have selected just a few for you here. Please do let us have your recommendations for more.
The Caesar shift cipher is where all training manuals start. It is easy to explain and use, and breaking it introduces the main ideas you need to crack any substitution cipher.
The affine shift cipher takes us a step beyond the Caesar shift, and into the world of mathematics. Here Youtube user Theoretically explains (theoretically) how you can crack this cipher even when you don’t know the key, assuming that you can work out some of the text.
The main weakness of a substitution cipher is that English text is far from random. The patters within it often help us to break the cipher. Here, Prof Surov Mukhopadhyay from the Department of Mathematics at IIT Kharagpur introduces us to the method of frequency analysis.
Paget takes us on from the simple Caesar shift to a random keyword substitution cipher.
The earliest practical and secure polyalphabetic cipher was the Vigenère system used by French diplomats from the mid XVIth Century. It took 300 hundred years for cryptanalysts to break it, and you can read about two methods to tackle it in the BOSS Cryptanalyst Handbook.
Charles Wheatstone was a Victorian pioneer of communications technology. His development of the Wheatstone bridge enabled the first commercial telegraph system, the forerunner of the modern internet. Recognising the need to secure this new, fast electrical communication system from the early hackers, Wheatstone invented the Playfair Cipher, named after his friend, Lord Playfair, who did a lot to promote it. Its security relies on the fact that instead of encrypting single letters it uses a table to look up the encryption of pairs of letters, messing with the frequency counts.
One way to disrupt frequency analysis is to use an anagramming cipher, rather than a substitution cipher. The text is just jumbled instead of replaced. Here, Asher Dupré introduces us to columnar transposition ciphers
Another way to disrupt frequency analysis is to use more than one cipher alphabet. The most famous polyalphabetic cipher by far is the Enigma cipher. It is notorious for two things: its difficulty and the fact that, despite that, it was broken repeatedly throughout the Second World War by the mathematicians and linguists at Bletchley Park.
Harry designed the first Pringle Can rotor encryption machine in 2005 to help BOSS agents crack a version of the notorious Russian Fialka cipher. We might publish more information about that case in a further training exercise later. For now we refer you to Franklin-Heath who have published full details of how to build a working Enigma machine for use in the field. It is no harder to make than a Caesar cipher wheel, though it is a lot harder to use. On the other hand it gives you pretty much the full power of the Enigma cipher for the cost of a tube of Pringles, which is also useful for field rations
In the early 1970s Whitfiled Diffie and Martin Hellman revolutionised the science of cryptography by inventing the first public key ciphers. These ingenious systems use different keys to encrypt and decrypt a message, allowing you to publish the encryption key for all the world to see, while keeping the decryption key safe. The idea underpins the security when you use a card machine or buy a book on Amazon, as well as diplomatic and military communications.
With so much riding on the difficulty of factorising large numbers it is no surprise that a lot of time is spent trying to do just that. The earliest method, the number sieve, is attributed to Erastothenes, a Greek mathematician who lived in the 3rd century BC.
They thought it would take 40 quadrillion years to factorise the large number “RSA-129”. It took just 17! Here Numberphile explains the problem.
While the RSA cipher together with the Rijndael cipher from the Advanced Encryption Standard provide ultimate security for current communications, they are not really practical for an agent in the field. They required computers to implement and these are a target for hackers and enemy agents. In the novel Cryptonomicon the author Neal Stephenson presented an alternative which uses just a deck of cards to provide an extremely high level of security in the field. The Solitaire Cipher was designed by cryptographer Bruce Schneier and here it is explained by the MathsGeeks.
Thomas Campbell takes us through the steps he took to crack the Solitaire cipher using Python for the last round of the competition in 2015. This is advanced cryptanalysis for experts, but as Thomas explains, he wasn’t an expert at the start of the Challenge! If you want to learn more, take a look at some of the videos below, and head over to the Training and Development section to pick up your handbook.
Many of the modern mathematical ciphers base their security on the prime factorisation problem: it is easy to multiply two large primes together, but much harder to find the two factors if all you know is the product. Quantum computers will change all that, making the RSA cipher obsolete. But it will also make possible new encryption techniques.
The Holy Grail of cryptography is the truly uncrackable cipher. It exists, and this video from the Khan Academy explains it and why it is both uncrackable and not more widely used.
If you need a laugh after hours spent staring at an impenetrable cipher then you could do worse than watch the Simpsons. Its writers are scientists, mathematicians and engineers, and the programme is full of Easter Eggs and surprises. Here Simon Singh spills some of the secrets.
The world’s second favourite Harry (sorry Harry, I think Potter might just about edge you) shows the world that embracing your inner maths nerd is a noble and admirable thing. If you like rap, poetry or maths then there is something here for you. If you like them all you will be in heaven!
The National Cipher Challenge Poet Laureate, Harry Baker.
If your tastes incline to the musical, rather than the poetical* then you might prefer Kyle D Evans take on life. Perhaps the most melodious of maths teachers.
* No-one is forcing you to choose, you are allowed to like both.
A fabulous introduction to the world of codes and ciphers featuring Simon Singh.