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.