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Breaking Enigma and the legacy of Alan Turing in Code Breaking, City University, London

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Edited by Christopher Douce, Friday, 18 May 2018, 09:08

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As soon as I received an email advertising a public lecture at City University by Processor David Stupples on 17 April about the life and legacy of Alan Turing, a couple of weeks after finishing reading Alan Hodge's biography, I knew I had to make the time to come along.  This blog is a summary of some aspects of the event, accompanied by a set of thoughts that the lecture inspired.  I should add that I'm neither a mathematician and nor a cryptographer, but the story of code breaking and the history of Bletchley Park (and how it came to be) is one that has and continues to fascinate me.

David Stupples is professor of systems and cryptography at City University.  His lecture is one of a series of lectures that are given at City, but this one coincides with the centenary of Alan's birth.  The lecture also celebrates the creation of the City University Centre for Cybersecurity Sciences (City University website).

David's lecture began at the end, beginning briefly with Alan Turing's death in 1954, before moving onto a number of subjects which relate to cryptography, the breaking of the enigma code, stories about daring plots to capture code books and then concluding by speaking briefly about Alan Turing's legacy.

Before I attempt to summarise (to the best of my abilities) some of the points that David spoke about during his lecture, he also mentioned an interesting connection between City University and the centre of wartime code breaking at Bletchley Park (website).  David mentioned a former faculty member, Arnold Lynch.  Apparently Arnold worked with electrical engineer Tommy Flowers (Wikipedia), helping to design a fast input device to the Colossus machines that were designed with help from the post office research station (Wikipedia) at Dollis Hill, London.  The work centred on the reading of paper tape loops using light as opposed to mechanics.  Colossus, Bletchley Park and Turing are intrinsically linked, but as far as I understand they are different stories.  They are linked through cryptography, which is a subject that David introduces.

Cryptography

What is cryptography?  In essence, it is study that is concerned with the hiding and writing of secret messages.  David began by introducing us all to the Caesar cipher (Wikipedia), a simple 'monoalphabetic substitution cipher'.  Simply put, you take one letter and replace it with another.  Such ciphers are easy to crack because you can eventually figure out which letter is which by looking at the structure of messages and also the frequency of individual letters.

A more sophisticated approach is to encode groups of letters (bigrams or trigrams) as a single code.  This method, we were told, dates back to Napoleonic times.  We were then introduced to the beginnings of the theory of Enigma codes through the Vigenère cipher (Wikipedia), which I had never heard of before.

David added an interesting aside, saying that this cipher was attacked by Lord Byron's daughter, Ada, Countess of Lovelace.  Ada is also known for her work with the Victorian computing pioneer, Charles Babbage, who proposed, designed and partially built different computing engines: the analytical engine and the difference engine.

Returning to the subject in hand, one approach to encrypt a message is to use a book of codes.  A character (or group of characters) are matched with an entry in a code book, which then have a precise meaning.  Using the technical phrases: there is ciphertext (the message that you can't read), and then the plaintext (the message that you can).

One of the biggest challenges is getting these code books to the people who need to read the messages, and this is one of the biggest challenges that need to be overcome.  David hinted at the mysterious but practical notion of asymmetric keys  (Wikipedia), mentioning their application of number theory.

The Enigma and Codebreaking

One of the most interesting parts of David's talk was his description of the different types of Enigma machine that were deployed; different parts of the German military used different variants.  An Enigma machine comprises of plug boards (which I understand to be a character substitution mechanism) along with a number of rotors, and a reflector which passes a signal back through each of the rotors.  These elements, in combination with each other, create cryptographic combinations in numbers that are quite literally astronomical and unimaginable.  Different machines would have slightly different configurations and different numbers of rotors.  The greater the numbers of rotors, the more 'secure' the code.

Another added complexity was that Enigma operators can also use code books.  Code books in combination with plug boards in combination with rotors which have all been used to encrypt messages in another language presents a problem that feel as if it should be impossible to solve.

So, how was it possible to break the Enigma, to recover plain text from cipher text? I have to confess when it came to following some of the detail, I became a little lost.  Understanding codes and ciphers, how they work and their weaknesses requires the application of an energetic amount of mental gymnastics.  Knowing the background and context behind the discoveries is a useful prerequisite to understanding the detail.

The first aspect lies with some work carried out by Polish cryptographers, whose work was invaluable (Bletchley Park has a permanent exhibit which acknowledges their essential contribution).  There was also, apparently, a spy involved, who managed to gather some essential intelligence (which was another part of the story I had not heard of).

The second aspect, the Polish cryptographers also worked on devices that helped to apply brute force to the decrypting of messages.  They created something called a Bombe (Wikipedia).  Their work inspired a new generation of devices (a reconstruction of which can be seen at Bletchley Park).

The third aspect (and there probably are more than just three aspects, of course) is the occurrence of human error.  Enigma operators would make mistakes (as would operators of TUNNY, too), which would convey clues as to how the machines operated and were configured.

Context

Towards the end of the talk, David connected work that was carried out in the second world war to the time of the cold war.  This was the first time I had heard anyone speak about this subject and the connections.  The audience were shown photographs of KL47 and KL7 devices (Wikipedia) that could be considered to be the successors of Enigma.  We were then treated to some spy stories, which reminded us all that keeping (and uncovering) secrets is as much a human challenge as it is a technical one.

Cryptography isn't a subject that is only applicable to the military (although I clearly sense that the military and military intelligence has been the main driver).  It isn't only about keeping secrets safe from spies.  Whenever you buy something over the internet, when the padlock symbol lights up on your internet browser, you make use of asymmetric keys.  (Incidentally, this mechanism was independently discovered by two different groups, but this is totally different story).  

Also, whenever you make a call on a digital mobile phone, encryption comes into play.  David mentioned the situation where cryptography is used from the point when you request money from a cash machine, and the resulting information about transaction is transmitted onwards to other banking machinery.

A really interesting point that I took a note of is that there is a constant battle between cryptographers (those wishing to keep secrets) and cryptanalysts (those who are wishing to break into codes and extract secrets).  This is a battle that is going to run and run, with both mathematics and computing being central tools for both sides.

Reflections

The biographies and Turing, the history of Bletchley Park, and the development of some of the most fundamental ideas within computer science are all intrinsically connected.  With any lecture on the subject, there is a difficult decision to make about what to focus on, what to touch upon and what to leave out.  It was great to hear of references to Turing's theory of computability and his connection with the ACE computer at the National Physical Laboratory, as well as his link to the development of the world's first stored-program computer at the University of Manchester.

The history of the code breaking and learning about the social, political and technological environment in which it took place is fascinating.  One thought that I did have was that perhaps Turing, as a man, might have featured more.  But, as mentioned, it's tough to separate out the different elements of a broader complex story.  Code breaking, Turing and computing are all connected.

All in all, a lively and informative talk that presented, for me, a new angle on some very interesting aspects of the code breaking story.  

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