The Enigma Machine: How Alan Turing Helped Break the Unbreakable Nazi Code

In 2001, none oth­er than Sir Mick Jag­ger bought the rights to a nov­el by Robert Har­ris called Enig­ma. The nov­el, a fic­tion­al­ized account of WWII British code­break­ers, then became a fea­ture film, writ­ten by Tom Stop­pard, pro­duced by Sir Mick, and star­ring Mr. Dougray Scott and Ms. Kate Winslett as der­ring-do Bletch­ley Park math­e­mati­cians and crypt­an­a­lysts employed in a race against time and the Nazis to break the fabled Enig­ma code before all hell breaks loose. It all sounds very dra­mat­ic (and I’ve heard the film is enter­tain­ing), but things didn’t hap­pen quite like that. Real­i­ty is nev­er so for­mu­la­ic or so good-look­ing. But the Enig­ma code was bro­ken, and the sto­ry of the code machine and its even­tu­al decryp­tion is fas­ci­nat­ing on its own terms. As Uni­ver­si­ty of Cam­bridge “Enig­ma Project Offi­cer” Dr. James Grime says–in the series of videos above and below–it’s a sto­ry of “how math­e­mati­cians can save lives.” Still with me?

Okay, so in the first video above, Dr. Grime gives us a thor­ough tour of the Enig­ma machine (Sir Mick owns one, by the way… but back to the his­to­ry…). Devel­oped by the Ger­mans, it’s a mar­velous encryp­tion method set into a small box that when opened resem­bles lit­tle more than a fan­cy WWII-era type­writer. Oh, but it’s clever, you see, because the Enig­ma machine (the one above belongs to sci­ence writer Simon Singh) trans­lates ordi­nary mes­sages into code through an inge­nious method by which no let­ter in the code ever repeats, mak­ing it almost impos­si­ble to decode in the ordi­nary ways. The machine was quite com­pli­cat­ed for its time; it works by send­ing the char­ac­ters typed by the keys through a series of circuits—first through three rotors like those on a com­bi­na­tion bike lock, but each with 26 places instead of ten.

Now at this point, the machine was noth­ing more than what was avail­able to any bank or busi­ness wish­ing to trans­mit trade secrets. But the Ger­man mil­i­tary machines had an extra lay­er of encod­ing: at the front of their machines was a “plug­board,” some­thing like a small switch­board. This allowed the cod­ing com­ing through the rotors to be rese­quenced for an extra lev­el of scram­bling. In the Ger­man mil­i­tary machines, the total num­ber of pos­si­ble com­bi­na­tions for mes­sage encryp­tions comes to a stag­ger­ing fig­ure in the quadrillions. (The exact num­ber? 158,962,555,217,826,360,000). There’s a lit­tle more to the machine than that, but Dr. Grime can explain it much bet­ter than I.

Of course, the Enig­ma Machine had to have a fatal flaw. Oth­er­wise, no nov­el, no movie, no dra­ma (and maybe no vic­to­ry?). What was it, you ask? Amaz­ing­ly, as you will learn above, the very thing that made the Enig­ma near­ly impos­si­ble to break, its abil­i­ty to encode mes­sages with­out ever repeat­ing a let­ter, also made the code deci­pher­able. But first, Alan Tur­ing had to step in. Sad­ly, Tur­ing is miss­ing from Enig­ma the film. (More sad­ly, he was dis­graced by the coun­try he served, which put him on tri­al for his sex­u­al­i­ty and humil­i­at­ed him to the point of sui­cide). But as Grime shows above, Tur­ing is one of the real heroes of the Enig­ma code sto­ry. Crypt­an­a­lysts ini­tial­ly dis­cov­ered that they could deci­pher ordi­nary words and phras­es (like “Heil Hitler”) in the Enig­ma mes­sages by match­ing them up with strings of ran­dom let­ters that nev­er repeat­ed.

But this was not enough. In order for the Enig­ma code to work for the Ger­mans, each operator—sender and receiver—had to have exact­ly the same set­tings on their rotors and plug­boards. (The mes­sages were trans­mit­ted over radio via Morse code). Each month had its own set­tings, print­ed on code sheets in sol­u­ble ink that eas­i­ly dis­solved in water. If the Allied code­break­ers deci­phered the set­tings, their decryp­tion would be use­less weeks lat­er. Fur­ther­more, the Ger­man navy had a more com­pli­cat­ed method of encod­ing than either the army or air force. The Pol­ish had devel­oped a machine called the Bombe, which could deci­pher army and air force codes, but not navy. What Tur­ing did, along with Gor­don Welch­man, was devel­op his own ver­sion of the Bombe machine, which allowed him to break any ver­sion of the Enig­ma code in under 20 min­utes since it bypassed most of the tedious guess­work and tri­al and error involved in ear­li­er by-hand meth­ods.

This is all very dra­mat­ic stuff, and we haven’t had one celebri­ty step in to dress it up. While I’m cer­tain that Enig­ma the film is a treat, I’m grate­ful to Dr. Grime for his engage­ment with the actu­al code­break­ing meth­ods and real per­son­al­i­ties involved.

A third video of extra footage and out­takes is avail­able here if you’re still hun­gry for more WWII code­break­ing secrets.

via Sci­ence Dump

Josh Jones is a writer and musi­cian. He recent­ly com­plet­ed a dis­ser­ta­tion on land, lit­er­a­ture, and labor.

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Comments (35)
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  • Patryk says:

    It was Poles who cracked Enig­ma, learn some his­to­ry here:

    “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.”

  • Seba says:

    As far as I know Pol­ish sci­en­tists cracked Enig­ma. :)

  • Ning says:

    Maybe actu­al­ly watch the videos ???
    He says the pol­ish cracked the army and air­force enig­ma machines — but not the naval ones.

  • Ning says:

    so if we are going to quote wikipedia — maybe use the right arti­cle

    “Alan Tur­ing, a Cam­bridge Uni­ver­si­ty math­e­mati­cian and logi­cian, pro­vid­ed much of the orig­i­nal think­ing that led to the design of the crypt­an­a­lyt­i­cal Bombe machines (an improve­ment of the Pol­ish Bom­ba), and the even­tu­al break­ing of naval Enig­ma.”

  • Piotr says:

    Właśnie, koledzy, obe­jrzyj­cie najpierw filmy :)

  • Chris says:

    I wrote a small book about the break­ing of the enig­ma code, if some­one wants to know more about this top­ic:

    (ebook, pdf and audio­book are free!)

  • Dee says:

    It was Poles who cracked Enig­ma!!! British liers!

  • f0ak says:

    Może najpierw przeczy­ta­j­cie artykuł, a nie robi­cie nasze­mu kra­jowi wstyd, potem się dzi­wicie, że resz­ta świa­ta ma nas za idiotów. Tutaj cytat:
    “The Pol­ish had devel­oped a machine called the Bombe, which could deci­pher army and air force codes, but not navy.”

  • Pawel says:

    Please don’t mind com­ments made by some, who had been brought here because of false infor­ma­tion post­ed on anoth­er web­site. Sad­ly they care not to read actu­al arti­cle, thus lack­ing basic knowl­edge and under­stand­ing.

  • robert says:

    To every­one who says that the Poles cracked the code.
    The Pol­ish did crack a type of the Engi­ma Code, but, it was at the start of the war. Even before that. The Ger­mans learned of them break­ing the code. So, they changed it. So in fact, both the British and the Pol­ish cracked the enig­ma code.

  • Jacob says:

    Dr. Miller at the NSA says the num­ber of com­bi­na­tions was much big­ger than the num­ber stat­ed in this arti­cle (3 X 10^114). Also, Mari­am Rejew­s­ki (Pol­ish math­e­mati­cian) broke the first ver­sions of enig­ma. Believe it or not, the Ger­mans kept chang­ing the machines to make it more dif­fi­cult to crack. Both the Poles and the Brits put some great efforts in crack­ing enig­ma. Unfor­tu­nate­ly, the Brits get most of the cred­it since the last bombes were made by them and they could crack all enig­ma codes.

  • Karenji Ramsuer says:

    I think every­one inter­est­ed in cryp­tol­ogy must see the “mind of code break­ers ” to under­stand in detail the impact of the ENIGMA machine

  • Raf says:

    Beau­ti­ful machine,

    As far as I know the Enig­ma machine is stronger than cur­rent Cred­it Card, because in Enig­ma machine occur more pos­si­bil­i­ty to encryp­tion than in CC.

    PS. Great arti­cle about Enig­ma, I was find­ing some arti­cle about this machine every­where, and I think that this arti­cle is one of the best!


  • Amanda Barr says:

    My grand­fa­ther, Alexan­der Barr, was also very involved in the work with enig­ma, I believe he was on the decod­ing team. Can any­one give me any details?

  • Mary T says:

    Won­der­ful videos about break­ing the Enig­ma code. Dr. Grime makes a com­pli­cat­ed sub­ject acces­si­ble and excit­ing.

  • David says:


  • Kaitain says:

    It’s a bit of tired trope to claim that “the Poles cracked Enig­ma”. They cracked an ear­li­er, much eas­i­er ver­sion of Enig­ma. The one used by the Kriegs­ma­rine dur­ing the war had a state space that was orders of mag­ni­tude larg­er. All the break­throughs at Bletch­ley Park were specif­i­cal­ly to address this vast­ly larg­er state space. This required both new com­put­ing machines and the inven­tion of inge­nious new heuris­tics for reduc­ing the size of the state space.

    The Pol­ish work was just the start­ing point for ULTRA. By their own admis­sion, the Poles did not have the resources to solve the lat­er incar­na­tions of Enig­ma.

  • David says:

    I under­stood that par­tial knowl­edge of the encryp­tion poten­tial result is used to find the machine set­tings for the day. Is this a deduc­tive or induc­tive process? Dr. Grime states that it is deduc­tive.

  • Jess says:

    The arti­cle states “its abil­i­ty to encode mes­sages with­out ever repeat­ing a let­ter”… this is a com­plete mis­un­der­stand­ing of the func­tion­al­i­ty.

    The machine was built in a way so that a let­ter could nev­er be encod­ed as itself. That was the flaw… it allowed crib­bing of com­mon words like Heil Hitler to rule out the impos­si­ble decryp­tions that had let­ters encod­ed as them­selves.

    Per­haps read a book before you write an arti­cle.

  • Jai says:

    Yes, but the Ger­man mil­i­tary invent­ed their own ver­sion of the enig­ma machine. Alan Tur­ing also devel­oped a machine that could deci­pher the code in under 20 min­utes, which helped the British enor­mous­ly when the Ger­mans changed the set­tings every­day towards the end of the war.

  • bonnie says:

    Thank you for these two fas­ci­nat­ing videos! Espe­cial­ly loved the cal­cu­la­tions as to how they derived the 159 quin­til­lion (or a lit­tle less) pos­si­ble com­bi­na­tions.

  • Sneha Anthony says:

    This infor­ma­tion real­ly helped my research project. It’s very inter­est­ing how Tur­ing con­tributed to the war. I think it’s amaz­ing idea and I’m glad I got to learn about it.

  • Sneha Anthony says:


  • Ian says:

    There is a dif­fer­ent between an “improve­ment” and a new inven­tion. What Tur­ing did was an improve­ment. The Pol­ish already made machines that can crack the Enig­ma code. What the navy uses is just a lit­tle dif­fer­ent from the army and air forces. It’s unfair to give Tur­ing too much cred­it because he got too much inspi­ra­tion from oth­ers.

  • wade says:


  • Samantha says:

    They did but the British made a much more advanced and quick­er way to break it.

  • john lee says:

    Inter­est­ing arti­cle. The Eng­lish did a great job at over­com­ing the Ger­man Enig­ma machine. The Pol­ish did a great job at over­com­ing the Ger­man Enig­ma machine too. Each coun­try did what they need­ed to do with­out regard to cred­it. The entire world dynam­ic was at stake dur­ing WWII. We can all hope his­to­ry does not repeat itself, but alas we have already for­got­ten the hor­rors of war. The mid­dle east is ablaze and every­one has their hands on the “fire” but­ton.
    Stay thristy my friends!


  • John says:

    The peo­ple at Bletch­ley Park recog­nise the fact that the Poles broke Enig­ma using math­e­mati­cians. They empha­sise the point that they showed the way for­ward to break­ing the Engi­ma and Lorentz codes. With­out the Poles, the British may have not had the head start they did.

    Don’t think it real­ly mat­ters who did what — the result is the same

    What is more inter­est­ing is what hap­pened to Rejew­s­ki — you would have thought the British might have made more use of him when he arrived in Eng­land — but he was giv­en some minor code break­ing role.

  • Mike Kinsman says:

    Watch the movie “The Imi­ta­tion Game”. It’s not tit­tled Enig­ma as sug­gest­ed in this arti­cle.

  • Mike Marks says:

    Why does the arti­cle say the movie is titled Enig­ma, when the real title of the movie ablut Enig­ma is The Imi­ta­tion Game. I watched it this week­end.

  • MemphisBelle says:

    Any­one out there admire the late Mered­ith Knox Gard­ner as much as I do? A cryp­to­log­i­cal hero like none oth­er.

  • Gustav Vogels says:

    A inter­est­ing arti­cle. I’m ger­man and I adore Alan Tur­ing and Gor­don Welch­man. For a peri­od of more than two years I con­struct­ed a Elec­tron­ic Tur­ing-Welch­man-Bombe. In a pre­sen­ta­tion on YOUTUBE with the title “Tur­ing Welch­man Bombe Elec­tron­ic Bombe” I explain step by step the whole decryp­tion pro­ce­dure. If you don’t speak ger­man, let YOUTUBE trans­late it and look at the sub­ti­tle.
    A lot of greet­ings from ger­many.
    Gus­tav Vogels

  • Ray says:

    Enig­ma (2001)
    The Imi­ta­tion Game (2014)

  • tyler shellabarger says:

    usa and britain are good allies,

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