back to article Turing's rapid Nazi Enigma code-breaking secret revealed

Blighty's communications eavesdropping nerve centre GCHQ has issued two papers written by superboffin Alan Turing on the maths behind code-breaking. The documents, held in secret for 70 years, laid the foundations for the quick and efficient decryption of Nazi Enigma-scrambled messages - a breakthrough that lopped about two …


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  1. jake Silver badge


    Methodology and examples.

    "History is FUN", according to my eldest niece :-)

    1. graeme leggett Silver badge

      Re: Cool.

      Horrible Histories is fun.

      IT's an Ancient greece thing?

      1. Audrey S. Thackeray

        Ancient Greece Is The Word.

        1. laird cummings

          I see what you did there.

  2. Christian Berger

    Must be a fake

    Back then they didn't have Word, so they could have simply typed in the terms. Last time I've seen something like that was from a professor who didn't know how to use TeX.

    1. Mips

      Re: Must be a fake

      Not a fake but it is a lot eastier to write it in than type it.

      You will notice that Turing was no typist and had dislexic fingers and hence the frequent "th e" so it is not surprising he resorted to script. I have the same dislexic finger issue, mine usually come out as "teh" but this is not a rare problem. It is amusing to think how difficult it would have been to crack Enigma if the Bundeswehr had the same problem.

      1. Paul Johnston

        Re: Must be a fake

        Guess you mean the Wehrmacht, thought the Bundeswehr were on our side, it wasn't formed until well after the end of WW II.

        Seriously why cannot they make it available now?

      2. Joe Harrison

        Re: Must be a fake

        I am not sure about this explanation because in those days nobody did any of their own typing. You wrote it longhand or spoke it into a "dictaphone" whatever that was. Then it would go to the "typing pool" where someone would produce your typed copy and deliver it back to you. Admittedly someone like Turing could have been an exception but the culture of "typing" being a specialist (and menial) skill was extremely strong.

        1. Roger Jenkins

          Re: Must be a fake

          I'm not going to be absolute with this, but I do 'feel' that dictaphones didn't come into common usage in the 1940's, in fact they were still pretty much a beast when I worked for IBM in the late 60's.

          More likely, if you were important enough, you had the use of a shorthand typist. That person would write down your dictation in wiggles and squiggles, then later type it up to present to you in English.

          I could also see that when using the above shorthand method, dictating mathmatical formulae to a shorthand taker may prove very difficult as they wouldn't necessarily have a clue what you are on about. Just do the text and let the expert add the 'cryptic' scientific notation by hand would be efficient.

          1. perlcat
            Black Helicopters

            Re: Must be a fake

            If you believe that something like this would have gone to a typing pool, then you forgot the context of the information.

            You're looking at Turing's typing.

          2. Anonymous Coward
            Anonymous Coward

            Re: Must be a fake

            Alan: Can I use your dictaphone?

            "Richard": No! Use you finger like everyone else.

  3. Thomas 18

    Must be a paper

    You can tell because of the large equations.

    I wish someone would write a program that turned all the sigmas into for loops and all the brackets into += / -= / /= / *=. While their at it they could come up with a seed AI with the goal of making all variable names sensible and at least 9 characters long.

    1. jake Silver badge

      Re: Must be a paper

      Wanna git right on that, Thomas 18?

      Just askin ...

    2. Tom 7

      Re: Must be a paper Add a bit of JavaScript and you’re there.

      And if you can get one to work the other way (source code to maths) you've just saved the world $100,000,000,000,000 in lawyers fees over software patents for the bleeding obvious.

    3. Anonymous Coward
      Anonymous Coward


      it could also correct people who don't know the difference between their/they're/there :)

      1. Thomas 18
        Thumb Up

        Re: Perhaps

        I think the air is no real difference thier, I mean one is as good as there other.

        1. theblackhand

          Re: Perhaps

          Thomas 18 - you forgot to add the compulsory <sarcasm></sarcasm> for the humour impaired...

      2. Tom 13

        Re: Perhaps

        Please tell me you didn't go their. There going to come after you now, so you'd better get your butt over they're!

  4. Michael H.F. Wilkinson Silver badge
    Thumb Up

    Interesting stuff.

    Might set these papers as study materials for our students.

    1. Phil Endecott

      Re: Interesting stuff.

      > Might set these papers as study materials for our students.

      Well if your students are in Kew that could work. Otherwise, wait until they get around to scanning them.

      1. Michael H.F. Wilkinson Silver badge

        Re: Interesting stuff.

        A scan will be needed

  5. Destroy All Monsters Silver badge

    "squeezed the juice" out of the two papers...

    And out of Turing, too. Yes, I mad.

    Now, how does this relate to the work polish mathematicians did on cracking Enigma before the red/brown sandwich invasion?

    1. asdf

      Re: "squeezed the juice" out of the two papers...

      Biggest contribution by far from the polish was getting their hands on a working Turing machine (was the army version I think that had one less rotor than the Navy version).

      1. Jonathan Richards 1

        Turing machine...?

        I think you mean Enigma machine. A Turing machine is an abstract concept, related to the Halting Problem. I've stopped.

        1. asdf

          Re: Turing machine...?

          Yeah brain fart thanks for pointing it out. So used to saying Turing machine and the word Enigma is very seldom used.

      2. Destroy All Monsters Silver badge

        Re: "squeezed the juice" out of the two papers...

        > Biggest contribution by far from the polish was getting their hands on a working [Enigma] machine

        That sounds entirely too Hollywoodesque.

        Looked it up in "Mathematics and War" [2003, Birkhäuser Verlag]

        The Polish mathematicians could read most german codes by 1932, but didn't manage to break the Enigma. They obtained a commercial Enigma used by business firms to get general insights into the machine. Then the french were contacted by an employee of the Reichswehr cryptography agency, [Hans-Thiko Schmidt] who sold secrets to captain Gustave Bertrand (but not the Enigma wiring scheme details). Captain Bertrand then contacted the Polish Cipher Bureau, and the final arrangement was that the French were to concentrate on delivering intelligence reports from Germany to help in code breaking, while the Poles were responsible for theoretical studies of Enigma intercepts. These guys actually cracked Enigma successfully

        > In late 1934, the three mathematicians experienced the exciting decryptment of a transmission they could read as "To all commandants of the airfield throughout Germany" The signal ordered "the transportation to Berlin, alive or dead, of Kerl Ernst, adjutant to S.A. chief"

        > Thus 1934 was the year when the cryptology team of the Polish Cipher Bureau broke the ciphers of the German Army (Heer) and the codes of S.D. (Sicherheitsdienst der SS) as well as codes and ciphers of the German Navy. The Kriegsmarine used three kinds of Enigma keys: operational, staff and admirals. The last key was resistant to breaking for a long time.

        The Bombe came later after Enigma keys were changed regularly, but it was all based on the Polish work.

        1. Destroy All Monsters Silver badge

          Re: "squeezed the juice" out of the two papers...

          Even found the PDF on the Internets:

          Can't be bothered to check whether it's open access by design or by oversight.

    2. toughluck

      Re: "squeezed the juice" out of the two papers...

      Unfortunately (yes, I'm Polish), not much. It's not that a lot of the theoretical foundations weren't laid by Polish mathematicians, it's that certain political decisions caused them to fall by the wayside.

      However you want to twist it, siding with the French in their code-breaking efforts cost them the chance to work at Bletchley Park. Turing was a brilliant mathematician and computer scientist and he did a lot more work in breaking the code than any other man.

      Cheers to that!

    3. bazza Silver badge

      Re: "squeezed the juice" out of the two papers...

      The Poles did a tremendous job on the early Enigmas with very limited resources, but got stumped when the Germans added the plug board on the front of the machine. Turing's genius was to solve the plug board problem. So it was in effect a joint effort.

      One of the most important additional aspects of the Polish work was to demonstrate that attacking a machine cypher was possible. Without that the British might not have got started in the first place.

  6. Chris Miller

    Shameless plug

    Oxford University Department for Continuing Education are holding a weekend course to celebrate Turing's 100th birthday on 23rd June. Only £100, it will cover many different aspects of his life through a series of lectures by leading experts.

  7. tkioz
    Thumb Down

    No plans to put them online????????

    What the hell? Turning is held up as one of the greatest contributors to the modern world, yet they don't want to put his work online... freaking greedy buggers.

    1. Blue eyed boy

      @No plans to put them online

      Obvious innit. There's something they ain't telling us. Rather than redact such a hostoric document they're keeping it under wraps.

    2. Ian McNee
      Big Brother

      Now where did I put that baseless conspiracy theory...

      Possibly a silly condition placed on them by GCHQ securocrats to enhance the mystique of these papers.

      The nameless (again pointless security theatre) from GCHQ interviewed on Radio 4 about this was keen to stress the claim that Turing's papers could not possibly have been released any earlier because of their sensitive nature. We are supposed to read into this that GCHQ are: (a) diligently doing their bit to protect Blighty from code-breaking jihadis, Ruskies and Sino-hackers, and (b) emphasising Turing's total genius (while still brushing under the carpet the injustice of the British state hounding him for his homosexuality).

      I don't doubt the importance of this work done by Turing and others at the time but it is farcical for GCHQ to engage in a PR exercise claiming they could not have been released decades ago.

    3. Alan Firminger

      Kew allows all documents to be copied using their machines or photographed by the reader's camera, stands are provided. So anyone can put these online.

      1. Colin Miller

        (C) StationX

        'Cept it will still be under crown copyright.

        1. nowster

          Re: (C) StationX

          Crown Copyright on documents only lasts for 50 years.

          1. graeme leggett Silver badge

            Re: (C) StationX and copyright

            Crown copyright from date of publication is 50 years.

            For anything created pre 1988 and not published its copyright will not expire until 2040 at the earliest.

            Unpublished created after 1988 is copyright for 125 years.

            1. Destroy All Monsters Silver badge

              Re: (C) StationX and copyright

              Nice knowing these things but my care-o-meter is at 0.

              Pirate naow!

        2. Alan Firminger

          Re: (C) StationX

          Then .ru

  8. Darran Clements

    Oh come on!

    Will you please stop using the word boffin please? It sounds anti-intellectual and childish.

    1. Anonymous Coward
      Anonymous Coward

      Re: Oh come on!

      Or maybe you could just grow up and not care what names someone calls you?

      The terms nerd and geek have already been reclaimed. Why not boffin too?

      What the hell is there to be ashamed of?

      "Hey look - it's that boffin over there..."

      Seems to me it's actually a compliment?

      1. no-one in particular

        Re: Oh come on!

        Maybe I've just been out of touch, but I'd never heard of "boffin" being in any way derogatory before reading about it in El Reg comments.

        1. fattybacon

          Re: Oh come on!

          You should read some of the tabloid press now and again then. Any time they want to try and rubbish a scientific news item they use the word "boffin" in the context of a bumbling oaf who produces crackpot theories.

          El Reg is allowed to use it because we know they are using it properly.

          1. Bassey

            Re: Oh come on!

            > You should read some of the tabloid press now and again then

            No. I shouldn't.

      2. Anonymous Coward
        Anonymous Coward

        Re: Oh come on!

        "nerd and geek have already been reclaimed"

        You reckon? If I wanted to insult a nerd, I'd call him a "geek".

        But boffin has never been, to my mind, a direct insult.

        It implies "not one of us", eccentricity, focus in niche areas, otherworldliness, possibly obessiveness, but not necessarily unpleasant or having a grating lack of social skills.

        Geek and nerd still imply people you'd avoid on the bus. A boffin would be quiet company, looking out the window and puffing reflectively on his (unlit) pipe.

        The boffin par excellence is Barnes-Wallis.

        1. Anonymous Coward
          Anonymous Coward

          Re: Oh come on!

          "nerd and geek have already been reclaimed" You reckon? If I wanted to insult a nerd, I'd call him a "geek"

          Yes I do reckon. If you're the sort of person who goes around trying to insult nerds and or geeks then I'm happy I don't know you. I also wouldn't give a damn what any name-calling moron (see what I did there?) said to me either. It's 2012 for feck's sake.

          Can we all just grow up? Name-calling is a useless process and anyone using it can be rightly ignored?

          1. Anonymous Coward
            Anonymous Coward

            Re: Oh come on!

            I'll admit I could probably have phrased things better but my comment did have the word "IF".

            I stand by my position that the words "geek" and "nerd" are not terms of endearment and seldom of respect.

    2. John H Woods Silver badge

      Re: Oh come on!

      wor(l)d has moved on - 'boffin' is now mainly a term of possibly grudging, probably jokingly grudging, admiration.


      1) my teenage children

      2) teh interwebs

    3. ChrisC Silver badge

      Re: Oh come on!

      For those of us who grew up on a diet of wartime tales of frontline heroism and derring-do from our armed forces, supported by the home front activities of the boffins and back-room boys, the use of such a term in this context seems entirely appropriate.

    4. jake Silver badge

      @ Darran Clements (was: Oh come on!)

      Nowt wrong wi' "boffin" ...

  9. Kevin Turvey


    If Enigma had been used properly it would have been unbreakable (even today), in most cases it was the lazyness of the operators that allowed us to "crack the code".

    1. Michael Shelby

      Re: Unbreakable

      There were still inherent design flaws in the machine. For example, the fastest moving wheel was on the right-hand (output) side of the machine. This meant that, for long stretches of messages, the whole rest of the machine could be treated as a constant, which made breaking the codes possible. You're right about human factors making it even easier, but Enigma was not perfect.

      1. Kevin Turvey

        Re: Unbreakable

        I agree it was'nt perfect, probably nothing manmade (personmade?) is, but I've read somewhere that if it was used correctly it would still be unbreakable, but I'm not an expert in this, so maybe I'm wrong.

        1. graeme leggett Silver badge

          Re: Unbreakable

          "Cribs" were a big help giving you a attack on the code. No point in having a perfect encryption of messages if you know that the original starts "Dear Adolf, I'm sorry for not writing sooner....?"

      2. Anonymous Coward

        Re: Unbreakable

        An even more fundamental design flaw in the Enigma machine is that a character cannot encipher to itself, this is because the lamp board and key board shared the connection for a given character.

        Add that to its other flaws and it became possible to break it, although the 4-wheel Enigma used by the German Navy did take significant extra work to find a way in.

    2. Francis Boyle

      Re: Unbreakable

      Any security system that relies on users acting like machines rather than humans is inherently flawed.

    3. haughtonomous

      Re: Unbreakable

      The weakest link in any process is usually the people involved.

    4. Trygve Henriksen

      Re: Unbreakable

      Not completely unbreakable if used right, but...

      (Enigmas were in use for a long time after WWII... )

      And the operators weren't lazy, either. They were following strict protocol.

      What the Germans did wrong was that at the beginning of EVERY message, they sent an 'offset' code giving the final 'operator decided' adjustment of the daily code. then they incredibly enough REPEATED that 'offset'.

      Germans were nothing but thorough... After all, there was the chance that the first few codes were misread by the receiver...

      They correctly assumed that long messages was bad, though, and that a lot of short messages sent on the same day, using the exact same code would be just as bad. They just screwed up on how to do the 'offset' key exchange.

      1. Kevin Turvey

        Re: Unbreakable

        Maybe lazy was the wrong word though I remember something about an operator having to re-send a long message and he didnt bother to change the rotor settings or something which helped Bletchley Park decrypt the message, also they always started with a station weather report which had a limited number of variables which aided decrypting, and another bored operator who simply pressed the same letter many times for some reason which also aided Bletchley Park to work out the rotor settings, my memory is a bit fuzzy about the details, mostly it seemed to be human error compounded by the official method/system of using Enigma not being the most secure.

      2. Ilgaz

        Needless use of enigma

        Needlessly using enigma for publicly available data helped too. They used weather reports. Say the weather report for London, 22c and rain. They were waiting that message (knowing content) to verify.

  10. haughtonomous

    re: Unbreakable

    This piece of work is powerful despite the use of a primitive typewriter and pen, and lack of use of Powerpoint, MathCad, Word etc. These days it would most likely be given scant attention and disregarded as an 'unprofessional' piece of work.

    How we have lost our way with all these modern 'productivity' tools, which are for the most part exactly the opposite. Turing would have utterly rejected them, I'm sure!

    1. Anonymous Coward
      Anonymous Coward

      Re: re: Unbreakable

      "How we have lost our way with all these modern 'productivity' tools, which are for the most part exactly the opposite. Turing would have utterly rejected them, I'm sure!"

      Er - we are talking about a chap who could read 32 character hexadecimal in reverse and do mental arithmetic with the numbers. This is the same geezer who arrived at the concept of a universal machine, a concept now referred to as a Turing Machine. We refer to devices with enough computing power and programmability to run arbitrary algorithms as Turing Complete.

      I think he would have been amazed and delighted by modern technology, and would have used symbolic computation to the utmost to construct some of the objects he used logic to prove statements about.

      (Just call me Keith for now, got to be careful)

  11. haughtonomous

    Turing is an egg

    or rather, he is in danger of being over-egged. There were many others who made major contributions to cracking Enigma, not to mention modern computing. Tommy Flowers, for example. We seldom hear of those unsung heroes.

    1. Ilgaz

      Re: Turing is an egg

      Being forced to suicide and not being credited may have been contributed to Turing mania.

  12. Anonymous Coward
    Anonymous Coward

    National Archive

    Has a really crappilly slow website.

  13. Anonymous Coward

    Strange El Reg Mathematics

    By what obscure system does an even which took place last friday coincide with one which will occur on 23 June?

  14. Anonymous Coward
    Anonymous Coward

    Wonder how much further on we would be had He not been drivin to his death early. So sad.

  15. Anonymous Coward
    Anonymous Coward

    "In December 1932, the Polish Cipher Bureau first broke Germany's military Enigma ciphers. Five weeks before the outbreak of World War II, on 25 July 1939, in Warsaw, they presented their Enigma-decryption techniques and equipment to French and British military intelligence.[3][4][5] "

    All this talk about Enigma and Turing and never even a word about who actually cracked the code. :(

  16. bep

    Pole dancing

    There were several enigma codes and I don't think the Poles broke all of them. The navy code was particularly vital for defeating the U-boats. I believe that even with all the brilliance and equipment, they still needed cribs to break the codes quickly, which were usually obtained in the field or at sea at great personal risk to those involved

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