In December 1932 a twenty seven year old mathematician sat in a room in Warsaw with a pile of intercepted German radio traffic, a set of stolen operating manuals, and no machine. By the end of the month Marian Rejewski had worked out the internal wiring of the Enigma’s rotors without ever having seen one.
Bletchley Park did not exist. Alan Turing was twenty and had not yet written his paper on computable numbers.
Why It Was Poland
Geography, mostly. Poland had been reconstituted in 1918 between Germany and the Soviet Union, and its intelligence service had no illusions about how long that arrangement might last. German army radio traffic went from unreadable to critical the moment it started using a machine cipher in the late 1920s, and the Polish Cipher Bureau, the Biuro Szyfrów, reacted in a way that was genuinely novel.
Instead of hiring more linguists, they hired mathematicians. In 1929 they ran a secret cryptology course at Poznań University, chosen because students from that region had grown up under German administration and spoke the language. Three of them were eventually brought to Warsaw: Rejewski, Jerzy Różycki and Henryk Zygalski.
Recruiting mathematicians to break ciphers seems obvious now. At the time, in Britain and France, codebreaking was still largely the business of classicists and crossword enthusiasts, and the assumption was that a cipher was a puzzle of language.
The Permutations, and the Guess
Rejewski’s attack has two parts, and it is worth separating them because only one of them is mathematics.
The mathematics used the German operating procedure against itself. An operator chose a three letter message key and, to guard against garbling, enciphered it twice at the start of the transmission, producing six letters. That meant that in every message the first and fourth letters were the same plaintext letter encrypted at two different machine positions, and so were the second and fifth, and the third and sixth.
Collect a day’s traffic and you can build three permutations of the alphabet, each of which is the product of the two transpositions. Rejewski then applied a result about the cycle structure of such products, and the crucial feature is that the pattern of cycle lengths depends only on the rotor positions, not on the plugboard settings. The plugboard was where the Germans believed their security lay: it swapped letters in pairs before and after the rotors and contributed astronomically to the number of possible settings. Rejewski’s method looked straight past it.
That reduced the problem to the rotors, and the rotors had known wiring once you could write out the equations. But the equations had one unknown Rejewski could not derive: the order in which the keyboard’s letters were connected to the entry ring of the first rotor.
On the commercial Enigma this connection followed the German keyboard layout, QWERTZU. Rejewski tried it, got nonsense, and then made a guess that is the single luckiest moment in the history of cryptanalysis. He assumed that whoever designed the military version had done the laziest possible thing and wired the entry ring in plain alphabetical order, A to B to C.
They had. The equations collapsed and the wiring came out.
What the French Supplied, and What They Did Not
Rejewski did not do this from traffic alone, and the honest version of the story includes Hans Thilo Schmidt, a clerk in the German cipher office who sold documents to French intelligence for money. His handler, Gustave Bertrand, passed the material to Warsaw: operating manuals, and the daily keys for September and October 1932.
This mattered enormously and it is often used to diminish Rejewski, which gets it backwards. The French had the same documents and their own cryptographers, and so did the British. Neither made any progress with them. Two months of keys plus a manual is not a solution: it tells you how the machine is operated, not how it is wired, and the keys are useless the moment the month ends.
The Poles turned that material into a reconstruction of the machine, then into a working replica, and then into a routine daily decryption service. By the mid 1930s they were reading a large fraction of German army and air force traffic as a matter of ordinary business.
The Machines Before the Bombe
Reading Enigma daily meant finding the day’s settings quickly, and the Poles built devices to do it:
- The cyclometer (around 1934), which let them compile a catalogue of the cycle patterns for all 105,456 rotor positions. Preparing the catalogue took over a year. With it in hand, the day’s settings could be found in about fifteen minutes
- Zygalski sheets (1938), perforated sheets stacked on a light table so that holes lining up indicated a possible setting. Twenty six sheets per rotor order, punched by hand
- The bomba kryptologiczna (1938), six electromechanical machines that automated the search. The name is Polish for bomb, and where it came from is disputed to this day, including a claim about an ice cream dessert the team was eating
Then the Germans made things harder. On 15 September 1938 they changed the indicator procedure, which destroyed the value of the cyclometer catalogue overnight. On 15 December 1938 they introduced two extra rotors, taking the possible rotor orders from six to sixty and multiplying the sheet work by ten. In January 1939 they increased the number of plugboard connections.
The mathematics still worked. The resources did not. Poland could not build sixty sets of Zygalski sheets and enough bomby in the time available, and it was becoming clear what the time available was.
Pyry, 25 July 1939
Five weeks before the invasion, Polish intelligence invited its French and British counterparts to a forest site at Pyry, south of Warsaw. From Britain came Alastair Denniston, the head of the Government Code and Cypher School, and Dilly Knox, its most formidable cryptanalyst. From France came Bertrand and Henri Braquenié.
The Poles told them everything. The permutation method, the cyclometer, the sheets, the bomba, the reconstruction of the wiring. And they gave each delegation a Polish built Enigma replica to take home.
Knox’s reaction is the detail everyone remembers, because he had been stuck for months on precisely the problem Rejewski had guessed his way past. Accounts describe him as initially furious, muttering the sequence QWERTZU, deflated at how simple the answer had been. He recovered his manners on the way home and later sent a note of thanks in Polish along with a gift for the team.
Six weeks later Poland was invaded from both sides. The Cipher Bureau destroyed its equipment and its staff escaped through Romania to France.
Why Bletchley Still Needed Turing
Here is the part that makes this a story about two achievements rather than a theft.
Every Polish method depended on the doubled message key, the procedure that encrypted the three letter setting twice. On 1 May 1940 the Germans abolished it. At that moment the entire Polish apparatus, the sheets and the bomby and the cycle theory, became worthless.
Turing had already anticipated this. The British Bombe he designed with Gordon Welchman did not exploit any particular indicator procedure. It worked from a crib, a guess at a fragment of plaintext, and searched for the settings that would not produce a logical contradiction, using Welchman’s diagonal board to make the plugboard deductions propagate. It was an attack on the machine rather than on a habit of its operators, which is why it survived every procedural change the Germans made for the rest of the war.
So the fair accounting is this. The Poles proved Enigma was breakable, reconstructed it, and handed over seven years of work at the moment they could no longer continue. Bletchley built something that did not depend on the German mistake the Poles had relied on, and then did it at industrial scale. Neither achievement substitutes for the other, and the British effort would have started years behind without Pyry.
What Happened to Them
Rejewski and Zygalski worked on German ciphers in France, at Bertrand’s station near Paris and then at Cadix in the unoccupied zone. Różycki drowned in January 1942 when the ship carrying him back from Algiers sank.
Rejewski and Zygalski reached Britain in 1943 after being imprisoned in Spain on the way. They were put in a Polish signals unit at Boxmoor and set to work on low grade German hand ciphers. Nobody told them that work on Enigma was continuing forty kilometres away on a scale they could not have imagined, and they never found out during the war.
Rejewski went home in 1946, worked as a clerk in a factory, and said nothing for twenty years. The secret held until Bertrand published in 1973 and Winterbotham’s book followed in 1974. Rejewski wrote his own account, mathematically precise and entirely without bitterness, and died in 1980.
Reading Turing’s Side of It
Turing’s own analysis of the machine survives in the manuscript known at Bletchley as the Prof’s Book, which sets out the structure of Enigma and the statistical and logical methods used against it in his own words and his own handwriting, corrections included.
Our remastered edition of Turing’s treatise on the Enigma reproduces that document, and it is the clearest way to see exactly where the British attack differed from the Polish one. There is more on the document itself in our post on what the treatise actually says.
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