• • •
Göttingen was turning out to be less rewarding than expected for Marian Rejewski. The course on actuarial problems was interesting enough, but he missed home. In particular, back in Poland, in Bydgoszcz, there was a girl he had known since he was quite small: Irena Lewandowska. Marian could get to Bydgoszcz easily from Poznań; it was only about an hour and a half away on the train. He could visit his mother regularly and check on the lottery shop that she ran and then he would also be able to see Irena. But Göttingen was too far away for that.
There were three other Polish students at Göttingen with whom Rejewski struck up acquaintanceships, but none of them was particularly close. There was also a current of anti-Semitism, which would culminate at Göttingen within a couple of years with the expulsion and emigration of the lifeblood of the faculty in what was called a ‘great purge’. Rejewski could not avoid getting caught up in this; it was the main political debate of the time. Everyone, it seemed, blamed the woes of Germany on Jewish influence, and the ‘Jewish problem’ was a theme which echoed in Poland as well. Göttingen seemed to be as much about toxic politics as imaginative mathematics. As for the mathematics, none of the other Polish students at Göttingen thought much of Marian Rejewski. So much for them as well. Marian Rejewski had better options than to spend his 1930 summer holidays in Göttingen.
Back home in Bydgoszcz, Marian Rejewski found a letter waiting for him from his old tutor Professor Krygowski at Poznań. He was being offering a post as teaching assistant at the university, but Rejewski would have to give up the second year of the Göttingen course. It wasn’t hard to make the decision: the railway timetable said it all. Rejewski took up his duties in September 1930, but before long he was wondering about that old cryptology course. Professor Krygowski explained that there was no plan to re-run the course, but two other ‘graduates’ had, apparently, been invited to work for the Biuro Szyfrów.
There were two ways of looking at this. Either it was a disappointment that Zygalski and Różycki had been taken on but Rejewski had not, or it was an opportunity: perhaps the only reason Rejewski hadn’t been asked was because he was away. So Rejewski decided to test whether the opportunity to join the Biuro Szyfrów was still there. He got in touch with Zygalski, who asked the boss. The boss was Gwido Langer, who came down to size up the candidate for himself. The candidate was unassuming and unmilitary, exactly what they needed. Rejewski was hired.
Down in the basement of the City Garrison Headquarters, next door to the Kaiser’s old palace, the three alumni of the Poznań University Mathematics Faculty were set to work. The palace was conveniently close for Rejewski’s day job, even if the basement was not the most elegant part of the complex. Here, the three cryptologists worked on problems of double transposition, the textbook challenges explained in General Givierge’s book.
There was also the code book of the German Navy to reconstruct. For some communications, the German Navy were still using old-fashioned codes in a four-letter format, but slowly Rejewski and his partners began to unravel its structure. It seemed to be alphabetical – lots of sentences began with groups like YOPY and YWIN – maybe those were questions, which typically in German begin with ‘W’ (wann, warum, wie, and so forth). Then one day there came a giveaway message comprising only six groups, beginning with YOPY, and the response which came back was clearly a four-digit number. It was a practice message. A question with an answer that every self-respecting German should know, probably a history question. The German-educated Poles could guess what this had to be: Wann wurde Friedrich der Grosse geboren? [When was Frederick the Great born?] Answer: 1712. They now had the first groups of the code and began to reconstitute the entire book.
• • •
Over the years, Gustave Bertrand had learned a lot about intelligence, a great deal about signals and radio and a fair bit about codes and ciphers. But he would be the first to admit that he was no match for machine ciphers. To squeeze the value out of Hans-Thilo Schmidt’s Enigma manuals he asked the experts. He went to talk to his old friends at the Section du Chiffre.
Bertrand recorded what the Section du Chiffre thought:
At the Section du Chiffre of the Army General Staff … the question ‘Cipher Machine’ was still at zero: anyhow, the old cryptologists … had decreed that this method was unassailable and that there was no capacity to deal with it. A fortiori, the young cryptanalysts relied on the advice of the older ones and all the texts enciphered in this way went straight into the waste-basket …3
The apparently priceless documents, which he had photographed in the bathroom, were not so much priceless as useless. Completely useless. The Engima problem was unsolvable without the actual machine. The manuals explained how the machine worked; how it was set up; how the information about settings was transmitted; how it was operated; how you send a message; and how you decrypt an enciphered signal. All that is fantastically good. But it was all useless if you don’t have the machine. Without knowing how the coding rotors are wired and without knowing the internal wiring, it was just not possible to apply this information.
So the solution to Enigma was to get a machine. It might just be possible that Schmidt could get hold of one and photograph its innards, but that would be too much to ask of him. There was, however, another possibility: to turn to France’s sniffy friends across the Channel.
John Hessell Tiltman was possibly the greatest cryptanalyst they had across the Channel. He was working at the Government Code & Cypher School (GC&CS), which had been glued together from the British Navy and Army code-breaking departments at the end of the Great War and put under the control of the Foreign Office, with MI6 sandwiched in between. Tiltman had joined in 1920 as a two-week secondee from the army to help out with a backlog of Russian decrypts and then stayed for the rest of his life. In 1932, he had been in Paris, asking the French to help with a perennial problem – that Britain’s precious navy might be under threat from the Soviets. Tiltman came with an incomplete set of materials on Soviet naval codes, which he hoped the French might be able to complement. Alas, the answer was no, but the potential for cooperation had been established. So it might be, a little later, that the British could help the French with a somewhat different problem of incompletely understood ciphers: the problem of the machine.
The British had sniffed around the Enigma machine before.4 Knowing what they did about signals intelligence, the idea of machine encryption was appealing. The military attaché in Berlin went to have a look and got hold of a prospectus for Enigma. At the World Postal Congress in Stockholm, the British brought home the daily bulletin for 7 August 1924, which included a report on a demonstration of the machine, with a nicely incomprehensible piece of cipher text and its solution. The machine was demonstrated in London to the Foreign Office. The manufacturers caught the scent of an order and took out British patent rights in October 1925. Then GC&CS got involved. An Enigma machine was purchased and delivered up to the boffins for a once-over.
The boffin was Mr Foss. In his report, Mr Foss coolly explained how you could decipher Enigma messages, even if you didn’t know how the machine had been set up. Sure, you needed to know the wiring of the rotors and you needed to have an inspired guess at the likely content of some of the message. (Mr Foss called the guesswork a ‘crib’: having endured years of translating Latin at school, he knew that schoolboys could make sense of gibberish if someone told you what at least some of it meant. At school, they called the cheat translation at the back of the book a ‘crib’.) Mr Foss concluded his analysis with a section, General Remarks. The Enigma had some weak points. But if you had to use it, he would suggest that you should have several rotors at your disposal, choosing three each time, and you should encipher and conceal the information which had to be sent to the recipient about the starting positions of the three rotors.
Like so many technical reports, Mr Foss’s study was put in a file. The British would not be buying the Enigma machine for their own secure communications. But now Captain Til
tman had made the diplomatic link between GC&CS and Captain Bertrand’s Section D, perhaps the boffinry might be extracted from its file and put to good use. The question was duly put, via the proper channels, which is to say MI6’s liaison officer in Paris.
Bertrand’s bathroom photographs were carefully evaluated at MI6. The photography was good, but MI6 independently came to the same conclusion as the Section du Chiffre. The documents were, unfortunately, useless. Useless, that is, unless you happened to have the German modified version of the Enigma. And in any case, on proper reflection, it would not be the done thing to get too close to the French. The photographs were carefully filed and carefully forgotten, and carefully worded expressions of lukewarm thanks were carefully passed back to the Deuxième Bureau. In sum, the British were a dead end.
Having now held the documents for nearly three weeks, despite the unenthusiastic reaction of his French and British peers, Gustave Bertrand was sure they had some value. There must be someone who could squeeze some information out of them. Bertrand had one option left. His boss agreed. Through the military attaché in the embassy in Warsaw, Bertrand requested a meeting with Lieutenant-Colonel Langer of the Polish Biuro Szyfrów. The precious photographs were packed and sent in the diplomatic bag and Bertrand took the long train journey through Germany to once again renew his acquaintanceship with his Polish friends.
Bertrand and Langer met on 8 December 1931.5 The photographs were greeted by Langer, and Stefan Mayer his boss, with stupefaction and delight. Mayer asked for forty-eight hours to make an evaluation, to see what could be done with them. Meanwhile, the impatient Bertrand had to kick his heels in his hotel, wander around the sights of the Citadel, the mediaeval quarter and the wide, elegant eighteenth-century district now known as the Old Town. Finally, at the appointed hour, Mayer and Langer saw Bertrand once again.
The documents from Verviers were the real deal. ‘Vous avez fait donner l’artillerie lourde’ [you brought out the big guns], said Langer to Bertrand.6 ‘The Schmidt documents were welcomed like manna in the desert, and all doors were immediately opened,’ said an overjoyed Bertrand.7 At last, he had found someone who understood these things and could put the information to proper use. Thanks to the bathroom photographs, the modifications made from the commercial machine were clearly apparent: in particular, it was evident that there had been an addition of a plugboard to the front of the Enigma machine, one which swapped over pairs of letters as the electric current entered and left the bank of three rotors. Alas, this precious material was not enough to fully solve the puzzle of Enigma, as Langer explained: the documents did not disclose the wirings inside the machine; how the rotors were wired; how the plugboard was connected to the contacts on the rotor housing; what the connections were in the ‘reflector’ which returned the electric current back through the rotors. If only – he continued – if only we had the monthly charts which informed operators of the settings …
So there was no immediate prospect of a breakthrough on the Enigma, but nevertheless the meeting between Bertrand and Langer was enormously significant in building a rapport between two teams with different and complementary areas of expertise. Not only were the Poles actually showing their technical abilities to be streets ahead of the French and British experts, but the tentative grafting of French-acquired material on to Polish stock was now showing buds which might, in time, bear fruit.
On his return to France, Bertrand was thrown straight into another meeting with Hans-Thilo Schmidt, once again in Verviers, the week before Christmas 1931.8 This time, Bertrand was trusted with the camera alone, and off to the bathroom he went while Rex and Asche, together with Bertrand’s superior, Major André Perruche, cover-name Alison, went off to sink a few glasses of wine. This time the photographs included a description of different types of Enigma machines in use since 1928 and a table of settings: just what the Poles had put on their Christmas list! And in the new year there were more meetings. The first was in May, which yielded more tables of Enigma settings, as well as numerous other secret military materials. Following the May meeting, Bertrand went again to Warsaw. As before, Langer was enthusiastic; as before, the materials provided were not quite enough. This time it was Maksymilian Ciężki who explained the problem. The settings tables alone did not give them what they needed to reconstitute the wirings. Ideally, they’d like the actual wiring diagrams. But failing that, maybe some examples of coded messages, together with their plain text equivalents?
It was beginning to feel like a thankless task, but Bertrand had faith in his Polish colleagues. At least they were making the effort. But to ask Hans-Thilo Schmidt for the wiring diagrams or messages requested by the Biuro Szyfrów would put him in the most extreme danger. Hans-Thilo Schmidt was proving himself France’s most valuable asset, not because of the Enigma documents, but because of the other things he was producing, such as a note on the mobilisation of the German Cipher Office; the manual cipher keys used by the German Army; an appreciation by the army about the use of tanks, motorisation and the transportation of armoured units; and a senior insider’s view of the situation in Germany as the Nazi Party grew into Germany’s most potent political force. There was more of this to come; to endanger the source by asking for specifics on a gamble for Enigma would be foolish in the extreme. All the same, Bertrand sensed that they were close to a breakthrough on Enigma. The head of the French intelligence service, Colonel Louis Rivet, intervened: leave it to Rex to decide. If Rex could coach Schmidt in the fine arts of tradecraft, perhaps the critical materials could be obtained without undue risk. This was an extraordinary responsibility to give to Rodolphe Lemoine, but his roguish past was entirely submerged in his new identity as Rex, the talented intelligence agent trusted at the highest levels.
On 2 August 1932, Rex met Hans-Thilo Schmidt at the Hotel Adlon, a stone’s throw from the Reichstag building in Berlin. The mesmeric charm of Rex – and the lure of cash – outbid the need for caution. Schmidt agreed to see what he could do. A fortnight later, Rex left Berlin having deposited a stash of papers for transmission to Paris in the diplomatic bag. These contained the Enigma settings for the forthcoming months of September and October and an all-important enciphered message, together with its plain text for comparison. For bonus, there were also technical notes on Enigma for the German Army and Air Force; a study on the German Officer Corps; and a twenty-page secret report on the potential build-up of Germany’s forces and resources. It was another incredible haul.
Bertrand once again sent the Enigma documents by diplomatic bag to Warsaw and once again went himself to the city, where the staff of Gwido Langer’s radio intelligence section were being concentrated. The need for an outpost at Poznań had passed – interception could be carried out where it was needed – but for cryptographic research and evaluation of intelligence, it was better that the personnel involved were located together and closely connected with the Second Department of the General Staff. The extra-mural personnel – Ciężki’s precious mathematicians – had all graduated by mid 1932 and were free of the ties to the University at Poznań, which had previously kept them at the town. So the Poznań team had come to Warsaw.
The move was made at the beginning of September 1932, a couple of weeks before Bertrand’s visit. For Marian Rejewski, the move was not so convenient. Irena was still in Bydgoszcz and the train journey to her from Warsaw was a lot longer than from Poznań. For the other two code-breakers, the change was a positive one. For them, Warsaw was a vibrant, exciting and attractive place. For Henryk Zygalski there may have been some wry enjoyment in the idea that the new offices assigned to the German Cryptographic Unit were located where Frederyk Chopin had spent part of his childhood: the elegant colonnaded Saxon Palace in the recently renamed Marshal Józef Piłsudski Square.
About the beginning of November 1932, Maksymilian Ciężki walked into the room where Marian Rejewski worked in the Saxon Palace.
‘Good morning.’
‘Good morning, Mr Captain.’
> ‘How are you finding it, Mr Rejewski?’
‘Most agreeable, thank you, Mr Captain.’
It was all very polite. In fact the new offices were nothing remarkable. Civilian supernumeraries attached to a special sub-section of a department whose function nobody knows are not going to be allocated the swankiest offices, particularly if they are working in intelligence, which is well known to be the lowest form of military life.
‘Could you come to my office, please, Mr Rejewski. There is something new I should like to discuss.’
‘Certainly, Mr Captain.’
Ciężki closed the door of his office. ‘Mr Rejewski, do you have any spare time, during the evenings?’
‘Yes, indeed, Mr Captain.’
‘Good, good,’ said Ciężki. ‘In that case, I would like you to come into the office in the evenings. I have something which might interest you. In fact it is something quite difficult: our best men have not got anywhere with it.’ There is nothing better calculated to stir up the ambition of a mathematician than to tell him that a problem is too difficult. Captain Ciężki had the full attention of Civilian Supernumerary Rejewski. ‘I need not mention, Mr Rejewski, that nobody else must know about this work, nor must they even know what you are working on.’
Actually, the one thing better calculated to stir up the ambition of a mathematician working on an impossible problem is to tell him that the work is also deadly secret. In a separate cubicle, away from his morning workplace, Marian Rejewski began to study the problem of Enigma after hours. Each component of the Enigma machine swapped around the letters of the alphabet. And that, as Marian Rejewski could see, was a problem in permutations.
Professor Krygowski had taught a module at Poznań on Group Theory, of which permutations is an amusing subcategory. With normal algebra, you can divide a number by two and then multiply it by two and you finish up with what you started with. If you tried that sort of thing with an egg, however, you would finish up not with a reconstituted egg but with an urgent need for a saucepan. Manipulating permutations contains the same idea: you have to treat permutations like eggs, since reversing an operation doesn’t put you back where you started. Rejewski had enjoyed permutations at Poznań and Captain Ciężki had just served up a nice problem in permutation algebra. Marian Rejewski was going to get to work on some equations and de-scramble the Enigma.
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