Imagine a wooden box about the size of a small suitcase. Open the lid and there is a keyboard, like a typewriter, and above it a second set of letters that light up one at a time.
You press a letter. A different letter lights up. Somebody writes that letter down.
That is the whole machine, from the outside. It was called Enigma, and versions of it were used by the German army, navy and air force to encipher very nearly everything they said to each other for the entire war.
The confidence in it was total, and it was not stupidity. By the standards of nineteen forty, the arithmetic said it could not be broken.
Inside the box are three rotating discs, called rotors, each wired so that a letter going in one side comes out somewhere else.
Here is the important part. Every time you press a key, the first rotor turns one position. So the wiring changes with every single letter. Press the letter A five times in a row and you get five different letters out.
That already destroys the oldest trick in codebreaking, which is counting how often each letter appears. In English, E is much the commonest letter, and in a simple cipher the commonest symbol is probably E. With Enigma there is nothing to count. The output is flat.
And there was more. The rotors could be taken out and put back in a different order. Each could be started at any of twenty-six positions. And on the front of the machine was a plugboard where pairs of letters were swapped by cables before and after the rotors, which multiplied everything again.
The number of possible settings, for the army machine, runs to somewhere around a hundred and fifty million million million. Written out, that is a one followed by twenty digits.
The settings were changed every day at midnight.
In nineteen thirty two, Poland had every reason to be worried about Germany, and the Polish Cipher Bureau did something nobody else had thought of doing.
Everywhere else in Europe, codebreaking was done by linguists. People who were good at languages, crosswords, anagrams. Poland decided that Enigma was not a language problem but a mathematics problem, and went to a university to recruit.
They ran a secret course for mathematics students at the University of Poznan, chose the best of them, and hired three: Marian Rejewski, Jerzy Rozycki and Henryk Zygalski. Rejewski was twenty-seven.
Rejewski was given the Enigma problem more or less on his own, in a locked room, and told to see what he could do.
He treated the machine as a system of equations. Over a period of weeks he worked out the internal wiring of the rotors, without ever having seen inside one, from the pattern of what went in and what came out. Mathematicians who have looked at that piece of work since tend to describe it in the same way, which is as one of the finest things ever done in the field.
Rejewski broke Enigma, but not by beating the arithmetic. Nobody ever beat the arithmetic. He beat the habits of the people using it.
Every message began with the sender choosing a three-letter key for that particular message, and then transmitting it twice at the start, so that the receiver could be sure of having got it right.
That doubling was intended to prevent mistakes. What it actually did was hand the codebreakers six letters, at the start of every message, that were known to be the same three letters twice over.
That is a crack, and once you have a crack you can put a lever in it. Over thousands of messages a day, the relationships between those repeated letters revealed the machine's settings.
The Poles built machines to do the searching, and called them bombes. Nobody is quite sure why. The most repeated explanation is that they made a ticking noise, and the second most repeated is that one of them was eating an ice cream dessert of that name when the idea arrived. Both may be true and neither is documented.
By nineteen thirty eight, Poland was reading a substantial part of German military traffic. Nobody else in Europe knew this. Britain and France had both largely concluded that Enigma was hopeless.
Then in late nineteen thirty eight the Germans added two extra rotors to the set, so that instead of three rotors in six possible orders there were five rotors to choose three from, in sixty possible orders.
That multiplied the work by ten overnight, and Poland could not afford ten times as many machines. They were, in the summer of nineteen thirty nine, about to lose the ability to read anything.
They were also about to be invaded, and they knew it.
So in July nineteen thirty nine, five weeks before the invasion, the Polish Cipher Bureau invited French and British representatives to a meeting in the Kabaty Woods outside Warsaw, and gave everything away.
The British party arrived expecting a polite exchange of theories. Instead the Poles told them the internal wiring of the rotors, explained seven years of method, demonstrated the bombes, and then produced two complete working reconstructions of the Enigma machine, built in Poland, and gave one to each country to take home.
One of the British officers present said afterwards that the party travelled back through Paris in a state of some emotion. Poland was invaded on the first of September. The three mathematicians escaped through Romania to France. Rejewski and Zygalski reached Britain later in the war. Rozycki never did: he drowned in nineteen forty two when the ship he was travelling on sank in the Mediterranean.
It is worth walking through it once, because the machine only makes sense with people attached to it.
A German unit had a printed sheet, changed monthly, giving that day's settings: which three rotors, in which order, at which starting positions, and which pairs of letters to connect on the plugboard. The sheet was printed in soluble ink on paper that could be destroyed in a hurry.
Two men worked the machine. One typed the message letter by letter. The second watched the lamps and wrote down whichever letter lit up, because the operator could not watch his own fingers and the lamps at the same time.
The resulting nonsense was then handed to a third man, who tapped it out in Morse code on a radio, into the open air, where anybody at all could hear it.
That is the thing to hold onto. None of this was stolen or intercepted in any dramatic sense. Every message was broadcast to the whole world on purpose, and the entire security of the German war effort rested on the belief that hearing it would do you no good.
It matters to say this plainly, because for a long time it was not said at all. Enigma was broken in Poland, by Poles, years before Britain got anywhere near it, and everything that happened at Bletchley Park afterwards started from a gift handed over in a wood five weeks before Poland was destroyed.
For decades after the war the story was told as though it began in England in nineteen thirty nine. Rejewski went home to Poland afterwards and worked as a clerk in a factory office. He was not able to talk about any of it until the nineteen seventies, and he died in nineteen eighty, having lived to see only the beginning of the record being corrected.
The machine itself was not a military secret in the sense of being invented for the army. Enigma began as a commercial product, advertised to banks and businesses in the nineteen twenties as a way of keeping their telegrams private. Anybody could buy one. The German military bought the idea and made it much stronger.
Here is something to think about tonight. The unbreakable part of Enigma was never broken. What was broken was a small, sensible, well-meant safety habit: sending the key twice so that nobody made a mistake. Can you think of a rule that makes something safer and less safe at the same time?