CONTENT RATING: PG-13 (themes: sex)

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Enigma was one of the most advanced mechanical ciphers of its time. In this first episode, we look back at the history of cryptology to see the ashes from which this cryptographic titan rose. Below you will find data, audio credits, further reading, and a transcript of the podcast.

Did you like this podcast miniseries? Would you have changed anything? Want something different? More of the same? This Festival of Social Science event was supported by the ESRC and they’d love to know your views on it, so if you have a moment, please fill in this quick survey to let them know your thoughts.

Audio credits

Scott Holmes – Business Gateway
Kai Engel – Downfall [Satin]
Kai Engel – Dark Alleys [Satin]
Kai Engel – Contention [Satin]
Kai Engel – Snowmen [Cold]
Lee Rosevere – Healing

Credits, sources, and more

Bletchley Park (2019). Podcast. Available at <https://www.bletchleypark.org.uk>

Corera, G. (2014). “Poland’s overlooked Engima codebreakers”, BBC News (Warsaw), 5^th July 2014. Last accessed 10^th July 2019. Available at: < https://www.bbc.co.uk/news/magazine-28167071>

Dziewanowski, M.K. (1994). “Polish Intelligence During World War II: The Case of Barbarossa”, East European Quarterly, 28(3), 381-391.

Helm, S. (2015). If This Is A Woman. Inside Ravensbrück: Hitler’s Concentration Camp for Women. London: Little, Brown Book Group.

Kozaczuk, W. (1984). ENIGMA: How the German Machine Cipher Was Broken, and How It Was Read by the Allies in World War Two. London: Arms and Armour Press.

Kuhl, A. (2007). “Rejewski’s Catalog”, Cryptologia, 31(4), 326-331.

Lelwic, J. (2005). “Marian Rejewski – the man from Bydgoszcz who helped the allies win the war”. In: J.S. Ciechanowski, J. Garbowski, E. Maresch, H. Piechocka-Lipka, H. Sowińska, and J. Sylwestrzak (Eds.), Rejewski: Living with the Enigma Secret (pp. 45-66). Bydgoszcz: Bydgoszcz City Council.

Milner-Barry, S. (1993). “Hut 6: Early days”. In: F. H. Hinsley and A. Stripp (Eds.), Codebreakers: The Inside Story of Bletchley Park (pp. 89-99). Oxford: Oxford University Press.

Mollin, R.A. (2005). Codes: The Guide to Secrecy from Ancient to Modern Times. Boca Raton: Taylor & Francis Group.

Oleksiak, W. (2014). “The Hacker Who Saved Thirty Million Lives”, Culture.pl. Last accessed 10^th July 2019. Available at: <https://culture.pl/en/article/the-hacker-who-saved-thirty-million-lives>

Rejewski, M.  (1981). “How Polish Mathematicians Deciphered the Enigma”, Annals of the History of Computing, 3(3), 213-234.

Schmidt, U. (2005). “‘The Scars of Ravensbrück’: Medical Experiments and British War Crimes Policy, 1945-150”, German History, 23(1), 20-49).

Sebag-Montefiore, H. (2000). Enigma: The Battle for the Code.

Singh, S. (1999) The Code Book. New York: Doubleday.

Sowińska, H. (2005). “Life’s Enigma”. In: J.S. Ciechanowski, J. Garbowski, E. Maresch, H. Piechocka-Lipka, H. Sowińska, and J. Sylwestrzak (Eds.), Rejewski: Living with the Enigma Secret (pp. 21-44). Bydgoszcz: Bydgoszcz City Council.

Stripp, A. (1993). “The Engima Machine: Its mechanism and use”. In: F. H. Hinsley and A. Stripp (Eds.), Codebreakers: The Inside Story of Bletchley Park (pp. 83-88). Oxford: Oxford University Press. 

Turing, D. (2015). Prof: Alan Turing Decoded. Gloucestershire: The History Press.

Turing, D. (2018a). “Finally remembered: the Polish codebreaker key to Bletchley Park cracking Enigma”, iNews: The Essential Daily Briefing. Last accessed 11^th July 2019. Available at: <https://inews.co.uk/news/uk/bletchley-park-alan-turing-dermot-henryk-zygalski-chichester-polish-codebreaker/>

Turing, D. (2018b). X, Y & Z: The Real Story of How Enigma Was Broken. Gloucestershire: The History Press.

Winston, G. (2016). “Polish codebreakers cracked Enigma in 1932, before Alan Turing”, War History Online, 30^th May 2016. Last accessed 11^th July 2019. Available at: <https://www.warhistoryonline.com/guest-bloggers/wheatcroft-collection-m4-105mm-tank-engine.html>

Woytak, R.A. (1982). “A conversation with Marian Rejewski”, Cryptologia, 6(1), 50-60.

Transcript

These Enigma episodes have been supported by the Economic and Social Research Council, or ESRC, as part of their annual Festival of Social Science. This Festival celebrates the amazing research and advancements of our best and brightest scientists, and this year, almost five hundred events are happening all over the country from Saturday the 02^nd to Saturday the 09^th of November, 2019. You can check out the official hashtag #ESRCFestival on Twitter, and you might even find that some of the events are in the news.

Case S01E14 – Enigma, part 2 of 3.

In the last episode we looked at steganography – hiding the message in some crafty way in clothes or music or digital content. And we looked at cryptography – hiding the meaning in some crafty way through transposition or substitution. And then we had a long look at just one way in which substitution ciphers can be mechanised. That method is Enigma, and for most countries, for years, its almost impenetrable complexity utterly defeated all attempts at cryptanalysis.

It would take painful, costly decades, before the right minds were in the right places at the right times to painstakingly unpick each inch of Enigma, and so now, our story turns back to the eerie twilight years following World War I. Old tensions continue to simmer across Europe, but added to this, the poison of newly wrought enmities begins, inexorably, to cast an ever darkening shadow over the coming years.

Welcome

Welcome to en clair, an archive of forensic linguistics, literary detection, and language mysteries. You can find case notes about this episode, including credits, acknowledgements, and links to further reading at the blog. The web address is given at the end of this episode. And, if you get a moment, leave us a rating wherever you get your podcasts from.

The Bureau of Ciphers

Enigma manifested itself as such a danger during World War I, that, even in 1926, eight years after the First World War had officially ended, British, American, and French cryptanalysts were still trying to crack the cipher, and with virtually no success whatsoever. With the passing years, however, the Allies began to feel that they had little to fear from Germany. The country was, in their view, depleted, exhausted, crushed, and the urgency with which they had first approached the challenge of deciphering German communications began to fade. With it, both the number and calibre of Allied cryptanalysts also fell (Singh, 1999: 143). The problem now was increasingly seen as purely academic – interesting, but not urgent. At least, not in the UK, the US, or France.

In Poland, however, the climate was very different. The country had only just regained its sovereignty in 1918 with the end of the First World War, but whilst almost everyone else had turned to recovering and rebuilding, Poland found itself engaged in a series of bitter skirmishes with the Soviet Union. The Polish-Soviet war fomented for two long years before finally grinding to a hostile stop in March of 1921, though it’s worth noting that many of the deep schisms and factions that this created in surrounding countries still exist to this day.

In short, though World War I had ended, and though even the smaller, more personal Polish-Soviet war had juddered to a wrathful ceasefire, it was far from peacetime in Poland. The threat of further invasion loomed on the western border with Germany, and the eastern border with communist Russia. Poland was caught in the vice of two malevolent storms, one full of the fire of a newly galvanising Germany, and the other breathing all the ice of implacable hostility. And both countries were keen to expand their territories.

At its simplest, Poland was desperately vulnerable. Not for them, the sense of ease and willingness to believe that all was now well with the world. Instead, the Poles established Biuro Szyfrów (or the Bureau of Ciphers) (Singh, 1999: 143), because, as Singh notes:

If necessity is the mother of invention, then perhaps adversity is the mother of cryptanalysis. (Singh 1999: 144)

During the Polish-Soviet War, the Biuro had intercepted and deciphered more than 100 messages, cementing the importance of its place in Polish military intelligence (Oleksiak, 2014), and seven years later, it was not only still hard at work, but evolving.

Remember that one way to attack a cipher is through frequency analysis. Those frequencies are, of course, derived from the message, or in other words, from language, and for many that naturally suggests linguists as the obvious experts to hire. However, the method of frequency analysis is pure mathematics. And in May of 1926, the then-chief of the Biuro, Major F. Pokorny was given permission to seek out not linguists but skilled mathematicians to try to break the mechanical cipher, Enigma (Turing, 2018b: 44).

Just a radio

A couple of years pass by. Then, one Saturday afternoon, something intriguing happens. One of those tiny happenstances that can change the fate of worlds. Sometime between the end of 1927 and the start of 1928 a parcel arrives in Warsaw, in Poland. It has come from Germany, and its label claims that it contains radio equipment (Rejewski, 1981: 213). And then, as the parcel is making its inoffensive way to customs, a German embassy official gets in touch. The parcel has been sent to the wrong address by mistake. It must be returned. No, not just returned. Returned before it is even processed through customs.

Such peremptory, almost panicky insistence from such a personage is rather marked and it arouses the suspicions of sleepy weekend customs officers. What well-paid embassy official wastes their Saturday chasing a parcel? A parcel containing some pieces of radio or other? Why would such an unremarkable parcel need to be stopped before it had been checked by customs? Silence, or a much more casual, careless approach here would probably have aroused less interest, but instead, aghast at the error, perhaps even fearing possible extreme reprisals, the embassy official had made things infinitely worse, and the customs workers, suspecting some plot, inform the Biuro Szyfrów.

Biuro employees open the parcel and carefully consider its contents (Sebag-Montefiore, 2000: 21). And you will not be surprised to know that, of course, it did not contain radio equipment. Instead, it was a commercial version of the Enigma cipher machine (Rejewski, 1981: 213). Try to hang onto the fact that this is a commercial version, because this detail becomes crucial just a little later on.

Somewhat perplexed by the frankly extraordinary boon that had landed in their laps, the Biuro contacted two engineers from the Polish radio company, Wytwόrnia Radiotechnicza AVA, or just AVA from now on, since they come back up several more times (Kozaczuk, 1984: 25). These AVA engineers, Ludomir Danilewicz and Atoni Palluth, examine the machine over what remains of the weekend. Then, with excruciating care, the Biuro repacks it back into its parcel, and obligingly return it to the German embassy. There have never been any indications that the Germans were aware that the parcel had been opened, but more on that in a second (Sebag-Montefiore, 2000: 21).

Sending the device back might seem like a terrible decision, but remember that intelligence is a delicate game of cat and mouse and cheese. It is not enough to merely know things about your enemy. It is also vital to know what they know, and to know what they know about what you know. If the Germans thought the Poles ignorant of the parcel’s contents and significance, their confidence in Enigma would remain high. If, however, they felt like Enigma had been substantially compromised, they might change it all overnight, and that would put the Poles, and indeed any other Allies who had made any progress, right back to square one in their codebreaking efforts.

If there is one crucial principle that accompanies codebreaking, it is absolute secrecy. Secrecy not just about any failures, but also, and especially, about any success that one may have had. Likewise, if there is a crucial codemaking principle, it is absolute secrecy about knowing when one’s code has been cracked. This too might sound bizarre, but if you know that the enemy has cracked your code, and they think that you’re ignorant of their success, they are much more likely to trust the communications from you that they then intercept and decipher. So much the better, because now you can feed them trustworthy-seeming messages whilst also working on a brand new cipher. Better still, if they don’t learn about this new cipher, with luck, they will continue to focus all their attention on the old one, blinded by the idea that they have found all that there is to find. And for precisely the same reasons, the Germans may have known very well that their Enigma had been opened and inspected by the Poles, but better to seem more ignorant that they really were. In essence, as we will see so many times in this series, the cryptology of war is a gigantic, high-stakes, life-and-death game of poker that is so secretive, no one is ever really sure of all the people who are even playing.

So, back to this Saturday morning parcel from Germany. To maintain the charade of ignorance and to stop the Germancryptographers from taking defensive steps, it was vital for the Poles to seem entirely unsuspicious about the German embassy’s sudden fascination with mere radio equipment, to ensure that the parcel looked as though it had never been opened, and to send it straight back, bright and early, on Monday morning. And the Germans too may have played the same game, pretending to find the parcel exactly as untouched as the Poles were suggesting.

Whatever the case, for the Polish, the clue was enough. If Enigma machines were being moved around, something was clearly afoot. And sure enough, only a few months later, on 15th July 1928, Polish signals intelligence, or SIGINT – specifically, radio telegraphers, began to pick up the first German messages encrypted using Enigma. Biuro cryptanalysts were immediately ordered to decipher them (Rejewski, 1981: 213). Antoni Palluth, one of the radio engineers from AVA who had studied the commercial Enigma machine, and Captain Maksymilian Ciężki (head of the German section of the Biuro) both attempted to break the cipher, along with Leonard Danilewicz and Wiktor Michałowksi (Turing, 2018b: 42-3). But their best efforts were entirely unsuccessful. This, as it turned out, was because the military version of Enigma was wired differently to the commercial version. After some time spent fruitlessly trying to make any progress, at last, the attempts were abandoned.

But this was not defeat. Remember that Poland stood between the simmering threat of Germany and the freezing menace of Russia. They knew, as well, that Germany was moving its Enigma machines around. And now they had started to intercept Enigma-encrypted messages over the airwaves. Though the messages could not be read, one layer of meaning was clear. Secret coordination and organisation was underway. These are the hallmarks of large-scale military operations. As yet, these first signs were mere distant seismic shivers, but they told a dark story. Across the miles, the gears of war were slowly beginning to grind up to speed again. And Poland would be first to face the onslaught. It didn’t matter, then, that they couldn’t yet crack Enigma. They had to keep trying, and time was rapidly running out.

Marian Rejewski

Marian Rejewski was born on the 16th of August 1905 in German-controlled Bromberg (now Bydgoszcz). He was the youngest of seven children (Turing, 2018b), and after completing secondary school, he began studying mathematics at Uniwersytet Poznański (Poznań University) (Singh, 1999: 149).

In early 1929, a quiet, bespectacled, 23-year-old Rejewski was writing up his master’s dissertation, when he was approached by a younger mathematics student holding a sheet of paper (Woytak, 1982:50). This page came from the Biuro, and contained a list of twenty German-speaking mathematicians from the University. Rejewski’s name was amongst those on the list, and he and the others were invited to meet with Professor Zdzisław Krygowski, the director of the Mathematics Institute at Poznań University. Rejewski was close to graduating and pondering his next steps, and so, perhaps curious, perhaps seeking a future for himself, perhaps merely out of politeness, he agreed to go (Woytak, 1982: 50).

The purpose of the meeting was to invite the students on the list to take part in a cryptography course. The course began on Tuesday the 15th of January 1929 at an off-campus military facility (Turing, 2018b: 45). The students were assembled in a large mathematics seminar room and they were addressed by three men: Major Franciszek Pokorny, then head of the Polish section of the Biuro, Captain Maksymilian Ciężki, head of the German section of the Biuro, and Antoni Palluth, the civilian employee and engineer who was interested in short-wave radio and who had inspected the commercial Enigma that had been mistakenly posted to Warsaw. Pokorny explained that the students had been invited to take part in a course in Poznań about cryptography, which was to take place once or twice per week, for a couple of hours each time, at a military facility (Woytak, 1982: 51). Indeed, the course was not at all a secret, nor even secretive, other than that it was also doubling as a selection process (Turing 2018b: 45).

Rejewski soon realised that the first lecture by Pokorny and the second lecture by Ciężki were almost entirely based on a French cryptography book by General Marcel Givierge (Woytak, 1982: 51). For reasons we can only guess at,Rejewksi did not attend the third lecture. Instead, he graduated with a master’s degree in mathematics on the 01st of March 1929, moved to Göttingen in Germany, and began a course in actuarial statistics. Cryptography, at least then, did not seem to hold any magic for him. Instead, he had determined that he would become… an insurance mathematician (ibid.).

How differently our lives can turn out compared to the plans we had for ourselves in our early twenties.

Alan Turing

As Rejewski’s life, education, and experience was taking shape across the sea in Poland and Germany, in the UK, another as-yet-unknown star equally unaware of what he would yet do or become was also in the ascendant.

Alan Mathison Turing.

Born in Britain on the 21st of June, 1912 (Turing, 2015: 25), at the age of fourteen, Turing began his first term at Sherborne School in Dorset. There was no public transport available on his first day, as it happened to be on the same day as the General Strike, so Turing cycled there from Southampton, a distance of about 100km (Singh, 1999: 166). As someone who has once cycled 40km on a very nice road bike, on excellent roads, and in suitable clothing, I cannot remotely wonder at the fact that this feat was later reported in a local newspaper. But this gives a small idea of who and what Turing was.

Generally known at Sherborne as shy and socially awkward, Turing was often criticised in his school reports for untidiness, neglecting elementary mathematics in favour of advanced algebra, conducting chemistry experiments, and for doing equations during his religious education lessons (Turing, 2015: 49). He was also rather a loner, and made only one close friend in his early years: Christopher Morcom, a boy from the year above (Singh, 1999: 166; Turing, 2015: 54).

Both boys were passionate about science, and the experiments Turing had initially conducted in isolation he now did with his friend. Sadly, Christopher Morcom had tuberculosis. This flared up on the 06th February 1930 (Turing, 2015: 56), and he passed away just five days later. Turing requested a photograph of his friend from Morcom’s mother, which she sent to him. His thank you letter to her read, “He is on my table now, encouraging me to work hard.”

Morcom’s death cemented Turing’s solitary nature, and his desire to solve problems through working on them alone. Perhaps, like so many of us, he was afraid of forming any further deep bonds because they, too, might one day be broken (ibid.). In other ways, however, Morcom’s death seems not to have changed Turing. His school reports still criticised him for a lack of discipline and an inability to focus on conventional topics dictated by the syllabus. Instead, he preferred to follow his nose and ask his own questions (Turing, 2015: 58) – an inclination that would later serve him, and his country, very well indeed.

Changing paths

A few months after Morcom’s death, during the summer of 1930, as Turing was coming to terms with his loss, Rejewski left Germany and went to visit his home in Bydgoszcz back in Poland. Whilst there, he received a letter from his older supervisor, Professor Krygowski, offering him a teaching assistantship at Poznań University. Perhaps uninspired with Göttingen or wishing to be back in his home country or maybe simply in need of paid work, Rejewski opted to quit the statistics course, move back to Poznań, and become a teaching assistant (ibid.).

Upon his return, Rejewski asked what had become of the cryptography course he had briefly attended, and he discovered that, far from it petering out into nothing, the Biuro had set up an office close to the university in Poznań, on Ulica Świętego Marcina (St. Martin’s Street). In addition, two of his fellow students on the course – Henryk Zygalski from near Poznań, and Jerzy Różycki from Wyszkόw, both aged just twenty-one – had been selected to work there (Turing, 2018b: 60).

Rejewski expressed an interest in working there himself, and found himself being visited by then-Lieutenant Colonel Gwido Langer. This interview, or appraisal, or whatever one might call it, seems to have been successful, since the Biurosubsequently agreed to take him on (Woytak, 1982: 52). Colonel Władysław Kozaczuk notes:

If one were to hazard a characterisation of the little team, its strength might be said to have stemmed from the diversity of the men’s personalities. Marian Rejewski’s penetrating mind and skill in formulating questions and advancing far-reaching hypotheses from scarce information were supported by the precision, energy, and perseverance of Henryk Zygalski, who was from Poznań (such qualities being ascribed in Poland to inhabitants of this region), and Jerzy Rόżycki, born in the Ukraine and educated in Russian and Polish schools, contributed elements of vivid imagination and intuition. (Kozaczuk, 1984: 9)

Suddenly finding oneself employed by the Bureau of Ciphers might sound glamorous and exciting, but, as is so often the case, the reality was rather different. Rejewski, Zygalski, and Różycki found themselves working in the basement of the City Garrison Headquarters (Turing, 2018b: 63).

However, this branch office in Poznań had only ever been intended as a temporary measure, and in 1931, as soon as Zygalski and Różycki had graduated, it closed down. Instead, all three mathematicians were invited to move to Warsaw to continue working for the Biuro. Once more, Rejewski had a decision to make: should he remain in Poznań as a teaching assistant for his old professor? Or should he move to Warsaw to work as a cryptanalyst for the military?

Rejewski chose cryptanalysis.

Meanwhile, back in Britain, Turing’s school reports continued uncomplimentary, but at the same time, he was far from failing in his school career. Christopher Morcom’s parents created a prize for science in their son’s memory, and Turing won this twice: once in 1930, around the same time that Rejewski started working for the Biuro, and then again in 1931, just as the Biuro’s branch office closed and the three Polish mathematicians relocated to Warsaw (Turing, 2015: 60).

Indeed, Turing maintained a close relationship with Christopher’s parents, especially his mother, and visited them frequently. As his school career began to come to its natural conclusion, in December of 1930, Turing earned a scholarship to study mathematics at King’s College in Cambridge University. While the traditional college for mathematics at Cambridge at the time was Trinity, they had filled all of their scholarship places. Any candidates who were considered a “near miss” (Turing, 2015: 65) were invited to King’s instead. As it happened, though, by this point, King’s had cultivated a reputation of outstanding academic excellence. Unsurprisingly, then, Turing accepted the scholarship, and began his studies in the autumn of 1931.

Turing fitted in well in this college. Dermot Turing argues that this was partly “because homosexuality was part of the establishment, almost suffused into the stonework” (2015: 68; see also Singh, 1999: 169). Despite fitting in so well, or perhaps even because of it, and because of the many distractions that this new life at university may have provided, Turing’s first-year exam results were disappointing. He received only a 2nd class grade, and he wrote to his mother that he could “hardly look anyone in the face after it” (Turing, 2015: 71).

Possibly galvanised or having sufficiently found his feet, Turing’s grades began to improve significantly, and at the age of just twenty-two, he was chosen for a fellowship at King’s (Turing, 2015: 81).

Hans Thilo-Schmidt

For a while, we’re going to leave the sleepy, academic trials and tribulations of Turing in Cambridge and Rejewski in Warsaw, and we’re going to turn our gaze to the simmering pressure cooker of Berlin, in Germany. To its ordinary citizens, and those invisible casualties of war, whose injuries are not of the body, but of the ego. Of their pride.

In June of 1931, a German walked into the French Embassy in Berlin. He looked suspicious, and uncertain. Paranoid, even. The purpose of this visit, he told the embassy official, was that he wanted to establish an appropriate contact in the French Government. The Deuxième Bureau perhaps. That is, the equivalent of the British agency, MI5.

Well, to identify an appropriate contact in the Deuxième Bureau, first he must explain a little more. What was his purpose? He had something to sell. Oh? What was he selling? Secret documents. Really. And what secret documents might these be? Secret documents from the German Defence Ministry Cipher Office (Sebag-Montefiore, 2000: 15). Was the Deuxième Bureau interested? He could prove his worth. For a price.

You can imagine their surprise, and interest, and also their suspicion. Who was this man? What was his motive? Was he a particularly stupid spy? Or an extraordinarily cunning one, playing a game far too elaborate for them to deduce? Were they in danger? Were the French Government about to be duped? Who had sent him? Or had he simply walked in off the street, of his own volition?

The man was Hans-Thilo Schmidt.

He would later be given the cryptonym – that is, the codename – Asché. Schmidt was born in Berlin in 1888 to an upper-middle-class family. His father was a university history professor, and his mother a baroness from a Prussian family who lost her title when she married (Singh, 1999: 144; see also Sebag-Montefiore, 2000: 15). The Schmidts were not wealthy in money, though they were certainly not poor either. Rather, they were wealthy in other powerful currencies – connections and consequence. From his earliest years, then, Schmidt’s sense of his self, his entitlements, his proper position in society, the achievements that should naturally accrue to him, is likely to have been strongly shaped.

Aged twenty-eight, Schmidt married Charlotte Speer, the daughter of a prosperous milliner – that is, a hat-maker. Schmidt’s new mother-in-law ran a shop selling umbrellas, walking sticks, and, inevitably, hats, to the smart, fashionable Germans of Berlin, and the profits from this shop went towards purchasing a house with some land in the rural area of Ketschendorf. One can’t help but read between the lines of some of the historical accounts of this period and get the sense that Schmidt’s family were handing his care over to his new wife and her family, perhaps in the hopes that they might make something of him, or at least, keep him out of trouble.

Schmidt had a sister, Martha, and a brother, Rudolf. As war arrived, Schmidt and Rudolf enlisted in the German Army and both fought in the First World War, but when the war ended in 1918, Schmidt was not considered worthy enough to retain (Singh, 1999: 144), and he was sent home, unemployed. Such a circumstance could wound even the toughest of us. Fighting for one’s country, putting one’s life on the line, feels like a course of action worthy of at least some recognition, and then to be found somehow inadequate or unnecessary could well canker in the soul of the most loyal patriot, but Schmidt might not have stewed over his rejection quite so bitterly had he not found such a stark contrast between his fate and his brother’s. Rudolf was not merely retained by the army, he was quickly promoted, and eventually took up the position of Chief of Staff of the Signal Corps.

In fact, in one of those extraordinarily unpredictable twists of fate, Rudolf would be the official who approved the Army’s use of Enigma. And his little brother Schmidt would- but I’m getting ahead of myself.

Schmidt returned home to his wife, Charlotte, and their two children, daughter Giselle and son Hans-Thilo, named after himself, hoping that they could rely upon his wife Charlotte’s family business to support them. But with the end of the war came the crushing depression and then the hyperinflation which made it impossible to succeed, especially in a line of retail for items that one could, and indeed, for a time, must necessarily live without (Sebag-Montefiore, 2000:15-16). The business folded, the shop closed, and Schmidt and his family were left with nothing (Singh, 1999: 144).

Schmidt had little left to lose, and doubtless even more aggrieved at having to beg for favours, he went to his older brother for help. Rudolf had been the head of the Chiffrierstelle – that is, the Enigma command centre – from 1925 to 1928, and he was able to arrange a job for Schmidt with his successor to the role, Major Oschmann (Sebag-Montefiore, 2000: 18; Singh, 1999: 144-5). The Chiffrierstelle was based in Berlin, and it was responsible for creating and using ciphers and codes. Because of Rudolf’s authority and recommendation, Schmidt was immediately entrusted with the highest levels of confidence, including being given a key to the safe that held the ciphers and codes.

I can only wonder here how I would feel if MI5 were to get in touch with me today and ask me to join their cipher and code department as one of their most trusted employees who had the metaphorical keys to the metaphorical vault of all their best work. Aside from the inevitable excited panic attack – and I’m not sure how much I’m kidding about that – I would be unbearably, wildly thrilled. Probably I wouldn’t be able to shut up about it, which is why it’s almost certainly never going to happen. Of course, this was the Nazi regime, which might have taken some of the glow off of it, but instead of finding himself dropped into the very lap of success and greatness, it seems that Schmidt found only woes and shortcomings. To him, this was a job. It was better than no job, but it was hardly better than being entirely unemployed. Indeed, in some ways, it was worse than being unemployed. He had to leave his family behind in Bavaria and live alone and isolated in an expensive capital city on a salary that could not support him in the style that he felt was appropriate, never mind sending back money to his wife and children (Sebag-Montefiore, 2000: 17-18).

Remember, this was the son of a one-time baroness and a professor. He had grown up in a nice house with a number of servants and he had never known real want. Or, indeed, exertion. His parents were respected and consequential. His brother had become a figure of real importance in the German Army, who commanded respect and held a great deal of power. Where was his success? His admiration? His power?Schmidt resented his brother’s status. He resented this paltry job that he’d had to beg for and that, in his view, paid barely enough. He resented his rejection from the German Army (Singh, 1999: 145). And he resented living a contracted, lesser, poorer life than the one he felt he should have. That everyone else seemed to have.

Indeed, based on the various histories and descriptions, Schmidt appears to have been almost a caricature of weakness, self-pity, and lack of discipline. Over time there have been many questions about his initial motivations for betraying the Nazis. If we take a dim view of him, then it’s easy to believe that this was all about personal gain, vanity, glory, revenge, stupidity, and worse. If we want to give him the utmost benefit of the doubt, then he may well have been morally opposed to the brutal Nazi regime.

But the bald fact of the matter was that Schmidt had debts of money, and excesses of appetite. Indeed, his inability to resist temptation became almost infamous. He engaged in a brazen string of extra-marital affairs with maids hired by his wife, to the extent that his children began having to check at doors in order to avoid walking into scenes of him in flagrante delicto. (And yes, his version of poverty still involved having maids about the place – I wish I were that poor.) His wife’s reaction was to hire ever-less-attractive maids, and Schmidt’s response to his children’s questions on the matter was to explain to them that he simply loved women so very much. If that wasn’t grotesque enough, his sister, Martha, not only regularly covered for his betrayals, but even arranged a girlfriend in Berlin for him that would, in her view, look after him properly.

And just remember, he did not simply work in the Chiffrierstelle, he was one of the most trusted employees. Anyone who works in security and intel will recognise what I’m pointing out here. Schmidt was not simply a good candidate for being compromised and then exploited. He was platinum standard. Weak. Vain. Needy. Easily seduced by flesh or finances. And in a position of extraordinary trust.

In the end, however, it didn’t even require someone to convince him that selling state secrets was his best new life decision. He went right on ahead and came to that conclusion himself. As I’ve said, as part of his role, Schmidt had access to the safe, and in that safe, the manuals for Enigma were kept. How long it took him to go from morosely pondering his debts to speculating how much those manuals were worth, I couldn’t say, but at some point, he recognised that this was information that someone would pay for. And pay well (Sebag-Montefiore, 2000: 18).

Codename: Asché

But back to the French Embassy, and indeed, embassies in general. Usually, a well-run embassy will have in place procedures for dealing with such a scenario. Schmidt would be known in some circles as a walk-in. During peacetime or wartime, for as long as there have been humans, there have been other humans willing to hand over information – that is, intelligence – in return for money, protection, escape, favour, revenge, and more. Prior to embassies, finding the right person and not getting caught in the process was rather awkward. Tell the wrong official or general or confidante, and you could find yourself in a dungeon – or worse, on a chopping block. But when the notion of governments in general and diplomacy in particular started to formalise, countries began to allow the creation of embassies on their own soil. And these missions – that is, the people from those other states and country – created on foreign soil little singularities of secrecy and intrigue.

Embassies and their missions are protected, diplomatically. And I mean really protected. The international legislative frameworks and agreements around embassies are extraordinary, yes, but it’s not just that. Or, one might say, that’s really only the formality of the matter. Embassies are protected by almost sacred depths of convention and tradition,they are steeped in the history, and they are thoroughly well-guarded by the fatal examples of the past. Spying on embassies is considered extraordinarily poor form, and secretly infiltrating one is such a breach of diplomatic trust that it can set back relations between countries by decades, causing untold harm to cooperation, trade, and intelligence sharing. We all know that it happens, of course, and some countries are worse than others for it, but getting caught is unpardonable. Meanwhile, open attacks on and invasions of embassies are deemed to be outright acts of war, no different than if the host nation had literally invaded that other country’s home soil. But there’s more. Embassy officials and diplomats are continually sending and receiving streams of extremely sensitive information both about their homelands, and about their hosts. Diplomacy relies very heavily on not ruffling feathers by, for instance, accidentally revealing that you have assessed the current president to be an idiot, personally vain, very vulnerable to flattery, and so on. These are essential details for the homeland in knowing how to handle such a person, but they’re going to cause a lot of unnecessary problems if such words find their way into the public sphere. So just like military operations, embassies as extensions of their domestic governments also need to ensure that their communications are extremely confidential, usually through the use of encrypted and encoded communications. And, given that their role is to keep their own governments up to date with what is happening with the host nation’s government, their connections to higher authorities back home are automatically privileged. They don’t mess around chatting to the concierge. Their intelligence gets straight to the people in charge. And, since good diplomacy can also involve nice meals, fancy hotels, pleasing gifts, and impressive social entertainments, the pockets of the wealthier embassies can be very deep indeed.

All of this creates the perfect conditions for the would-be defector. The walk-in knows that the embassy is worth approaching, that it’s almost certainly safe to be in, and that the people in charge can pay, pass on the intelligence, and even protect their new source. As a result, embassies do not merely expect walk-ins. During wars in particular, they are actively prepared for them. And many will have thoroughly clear clandestine service protocols – essentially a step-by-step walk-in handler guide. Firstly, the walk-in must be vetted for their worth and, quite frankly, for their mental health. Assuming that they do not seem to be suffering from genuine delusions or personality disorders, and that they seem to have something to tell, then the quality of their intelligence needs to be assessed. For instance, a factory worker who can only tell with confidence one small fact about one weapon that they work on every day is useful, but not critical. One wouldn’t want to wake up all the heads of all the European intelligence agencies for such a walk-in. Probably not even the head of the embassy’s home agency even.

By contrast, a trusted employee from the Chiffrierstelle with access to the most sensitive information about the enemy’s communications encryption machine? If such a claim can be verified, then this is certainly worth waking up the boss, and paying for. Handsomely. In such scenarios, if the person is assessed as mentally fit, sincere in their intent, and in possession of high quality intel, then there is usually a call or other transmission to other more senior figures with the authority to act. That transmission might contain a codephrase, let’s say Red Rose, that indicates a walk-in of a certain calibre and importance. In the background, the machinery begins to silently work. More calls and communications flit back and forth between embassy and various agencies. Background checks are swiftly carried out. Assessments are made. Histories and records and traces are picked over. A profile is quickly created suggesting likely motives, credibility, weaknesses, and so forth. All of this is crucial information since, after all, the embassy is dealing with a person who cannot be trusted and who is willing to betray sensitive information for money. If they will do that once to one country, they can do that again to another country. Going into a negotiation or even just an interview with such a person without being properly informed about them beforehand is not wise. After all, what if this person isn’t really an innocent walk-in, but is in fact an extraordinarily cool, calm German spy playing an exquisite game of double-cross. They walk in pretending to sell information, and perhaps they even hand over some high-quality intelligence, but their intention may well be to infiltrate the very spy networks arrayed against the Germans. To learn names, identities, procedures, gaps in intelligence, how much they value certain information, and more. If espionage and secret selling is anything, it is a never-ending layer cake of possible deceit.

With all of this in mind, the official who has greeted Schmidt is doing a lot of quick thinking, wondering quite what sort of person he is, and endeavouring to judge whether these grand claims of having access to the very heart of Enigma are in fact the first manoeuvres of a counterintelligence strike, or the ramblings of a mentally unstable individual in need of medical attention.

Schmidt, it seems, had envisioned a degree of scepticism ahead of schedule, or he knew enough of the workings of embassies and wartime espionage, or he was simply desperate to start selling secrets as fast as possible. No sooner was he asked to provide some proof of his access to this information than he produced some of the very documents in question and later, he details in a letter his access to the coding manuals for Enigma. Surely this would be of interest to the Deuxième Bureau? He could meet them? What about Belgium? What about Holland? He is so keen that he suggests times, and places, but also, unsurprisingly, he is wary and does not want to meet on German soil. What were they worth? Would the Deuxième Bureau pay? Did they want to buy copies of these documents?

And the answer, it seems, was yes.

Codename: Rex

In early November 1931, just as a 23-year old Alan Turing was starting a scholarship at King’s college in Cambridge, and 26-year-old mathematician Marian Rejewski was moving to Warsaw to become a full-time cryptanalyst, 43-year-old Schmidt was meeting with an agent from the French Secret Service with the intention of selling him secret documents from the very heart of the German Enigma office.

The rendezvous place? The Grand Hotel in Verviers, Belgium, on the border with Germany.

The French Secret Service agent? Rudolf Stallman, also known as Rodolphe Lemoine, codenamed Rex.

And Schmidt’s newly minted codename? Asché. Later, he would also be known as Source D, but we’ll stick with his surname for now.

Unsurprisingly, Rex’s first interest was to better understand the motivations behind his new asset. Why, he wanted to know, was Schmidt taking such a dangerous step? Schmidt’s answer was that he was in dire financial difficulty, and that he owed no loyalty to his country given that Germany – that is,the German Army – had not shown loyalty to him. Seemingly satisfied that Schmidt could be worked with, Rex asked him to bring some documents to the next meeting. He wanted to see them upfront so that they could negotiate their monetary value (Sebag-Montefiore, 2000: 19). Schmidt was keen and prompt. Just a few days later, on Sunday the 08th of November 1931, the same two men met again in the same location for the same purpose. But this time, Rex was accompanied by 34-year-old Captain Gustave Bertrand, a French military intelligence agent (Sebag-Montefiore, 2000: 19). If the Deuxième Bureau were to properly evaluate the worth of the documents, then they must have expert eyes assess them, and Schmidt’s haul did not disappoint.

Captain Bertrand was astounded at what he had managed to bring: two manuals that explained in detail how to operate the military version of Enigma currently in use by the Germans (ibid.). Rex and Bertrand conferred, and in the end, Schmidt was offered 10,000 marks if he would allow them to photograph these two top-secret manuals. They couldn’t be taken away, of course, since they would be very quickly missed. This was long before the advent of photocopiers, and with such confidential documents, the number of copies would be kept to a strict minimum anyway. Similarly, their whereabouts would also be thoroughly accounted for at all times. Schmidt must get them back to the safe before anyone raised the alarm, and so photographing the manuals was the only option.

But what is 10,000 marks worth? Were they offering him treasure or trash? Well, it’s actually really difficult to get an accurate estimate because throughout the wars the currency changed a few times. For a while it was the mark, then from 1925 to 1948 it was the Reichsmark, then after 1948 it was the Deutschmark, and added into this, the chaos of the post-war depression and hyperinflation all meant that for years, the value of the currency fluctuated wildly. Throw into the mix some patchy record keeping and in total, it’s difficult to get close to a realistic figure. Extremely tentatively, based on a lot of head-scratching and searching, this offer may have been worth something like 50,000 Deutschmarks in today’s money, or around £5,000 today, which translates to around $6,000. But it could just as easily have been worth ten times that, and judging by subsequent events, my estimates are on the low side.

Whatever the actual value of the offer, it would seem that Schmidt not only snapped it up, he was eager for more of the same. From the perspective of the Deuxième Bureau, however, this apparent bargain proved to be deeply anticlimactic. The problem was, neither Rex nor Captain Bertrand were active cryptographers or cryptanalysts, and so they had not realised that the documents would enable them to encipher messages using Enigma, but not to decipher them. In other words, the manuals would enable the Allies to create a replica of the military version of the Enigma machine and to use it – but they still could not crack the German ciphers without knowing how the machine was initially set up. Remember what I said all the way back in the first and second episodes. Knowing the method is useless unless you also have the key, or in the case of Enigma, both the daily key and the message key (Sebag-Montefiore, 2000: 20). And Enigma has some insanely high number of potential starting configurations, so guessing is out of the question.

Stymied, Rex and Captain Bertrand sought second opinions from British cryptanalysts, who confirmed that the documents were useless for decrypting German messages (ibid.). This substantially reduced the value of the documents in the opinion of the French. Now it was less an extraordinary scoop, more just another annoying piece of the puzzle. So, the French turned to the Biuro Szyfrów in Poland.

Priceless

From 1921, a formal agreement between France and Poland – the Franco-Polish Military Convention – had been in place, and this committed both parties to keeping lines of communication open (Turing, 2018b: 51). As we already know very well by now, Poland’s Biuro Szyfrów already had its own history with the Enigma machine dating back to before the war, and they had had access to a commercial version of the machine. The documents that Rex and Bertrand had obtained from Schmidt were duly sent across to Poland in a diplomatic bag (Turing, 2018b: 66), though one might suspect that the French believed that they were merely passing on a task that would prove as impossible for the Poles to crack as it had been for the French and the British.

Unsurprisingly, the Poles reiterated the same message. Schmidt’s documents were useful in revealing that the Germans had adapted the commercial version of Enigma for military use, but those manuals could not be used to crack the Enigma cipher. Not without additional information, anyway. However, the Poles had another angle to try. The then-head of the Biuro Szyfrów, 37-year-old Major Gwido Langer, requested that Captain Bertrand approach Schmidt once more, but this time ask him to procure documents that detailed the settings of the Enigma machine – that is, the monthly books containing the daily keys – that were currently being used by the Germans (Sebag-Montefiore, 2000: 22). Schmidt’s day in the sun was not yet over.

Schmidt met with Rex and Captain Bertrand several more times, took many more marks from them, and handed over ever more documents. In turn, over the course of the five months from May to September of 1932, those confidential papers found their way to the Biuro Szyfrów in Poland, and of those, some contained details of the military Enigma settings– the daily keys (Sebag-Montefiore, 2000: 23; Turing, 2018b: 67). But Schmidt was himself becoming a serious problem.As with so many of his life choices, it seems, Schmidt appeared unable to stop himself from gradually poisoning the very well that he had committed to digging. Rather than discretely enjoying his sudden, lucrative income, he was instead brazenly advertising his newfound wealth. He embarked upon an extravagantly lavish lifestyle, and travelled to Switzerland and Czechoslovakia for extended holidays with his wife (Sebag-Montefiore, 2000: 27). Even to the untrained eye, such a sudden, prolific expenditure in a country strangled by a severe economic depression was extraordinary. To try to get some sort of control over the situation, Schmidt’s handlers put an end to him smuggling top-secret documents over the borders. It was a needlessly risky option for someone of his status and employment anyway, but all the more foolhardy when the documents he had provided by that point had proven less than fruitful in helping to crack Enigma. Instead, they instructed him to use steganography – specifically, to write letters in invisible ink – and through this, to provide the French with information about the plans of the German military (Sebag-Montefiore, 2000: 23).

First principles

As Schmidt was turning his access to secrets into steady supply of ready cash in Verviers, and as Turing was receiving his disappointing first year results in Cambridge, by the 01st of September 1932, the three young Polish mathematicians, Rejewski, Zygalski, and Różycki, were all settling into the Biuro Szyfrów in Warsaw. No sooner were they in their new offices that they were assigned a new task: solve a German naval cipher (Woytak, 1982: 52). Although it took some time, as they were relatively new to the job, they did eventually manage to crack the cipher.

A year later, between late October and early November in 1932, Rejewski was approached by Captain Maksymilian Ciężki. If you have an extraordinary memory, you might remember that he was the head of the German section of the Biuro Szyfrów. Captain Ciężki asked Rejewski if he would be willing to work afternoons on a different cipher (Woytak, 1982: 52-3). But he would be working alone, and he would not be permitted to inform his colleagues what he was doing (Sebag-Montefiore, 2000: 33).

This cipher turned out to be Enigma.

Rejewski accepted, and began to pit his formidable intellect against the ultimate mechanical cipher. But, as you may remember from the second episode in this miniseries, Enigma is not a single process. There are three scramblers, one reflector, a plugboard with multiple switched letters, the ever-changing daily keys, and the individual message keys. The complex, multi-layered Enigma cipher simply could not be cracked by one perfectly aimed silver bullet. Instead, each step in the process must be dismantled inch by painstaking inch in a perfect reversal of the encipherment.

This was a challenge that had utterly defeated the British, the French, and all other nations that had tried their hand at it. So, could this young Polish mathematician make progress where all others had floundered and failed?

Military machines

The Biuro Szyfrów handed those manuals to Rejewski in the hopes that these would allow him to break new ground with Enigma (Sebag-Montefiore, 2000: 37). But as the French had realised, and the British had confirmed, Rejewski quickly concluded that for his purposes, the manuals were…

…not so much priceless as useless. Completely useless. The Enigma problem was unsolvable without the actual machine. The manuals explained how the machine worked; how it was set up; how the information about the settings was transmitted; how it was operated; how you send a message; and how you decrypt an enciphered signal. All of 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. (Turing, 2018b: 64)

Instead, if Rejewski wanted to decipher Enigma, what he really needed was a replica of the military Enigma machine. Not a theoretical description or an exploded diagram or an operation booklet. An actual physical copy. And so this is where he began (ibid.).

You might also remember that one of Rejewski’s talents was his ability to extrapolate and theorise on the basis of extremely sparse data, and that talent now became critical. In a feat of mathematical deduction far beyond the capabilities of my brain, Rejewksi developed an algebraic formula which hypothetically enabled him to calculate the wiring inside the right-hand entry scrambler – but only if he knew the settings of the military machine that the Germans had used. At this point, Captain Maksymilian Ciężki (head of the German section of the Biuro) handed Rejewski the codebooks detailing the daily keys for September and October of 1932. Schmidt, doubtless keen to maintain his lifestyle, had sold these to the French in August 1932 (ibid.).

At this point, it was deep into the winter of 1932. The September codebook was already out of date, and the October one would very soon follow suit, but at this stage, this didn’t entirely matter. Rejewski could go back to codes sent during the days listed in the codebooks and work on those as test cases. He soon discovered, however, that his formula was somehow not supplying him with the right answer. Were this me, my confidence in my mathematical prowess is so low I would have automatically assumed that my maths was entirely at fault, but Rejewski knew better, and thank goodness too. The problem, he discovered, was that he had assumed that an element of the wiring in the military version was the same as in the commercial version. And of course, it wasn’t. Once this was corrected, in an extraordinary step forward, the importance of which cannot be overstated, he was able to use his formula to calculate the wirings inside all three scramblers (Sebag-Montefiore, 2000: 38).

By the end of 1932, the machine was effectively solved (Woytak, 1982: 54). That is, Rejewski knew not only how to operate it from the manuals, but how to build it from the information he had managed to extract and extrapolate. And as you should recall, what he needed more than anything was a physical machine. As soon as Rejewski informed his superiors of his success, the Biuro began to build replicas of the military version of the Enigma machine in conjunction with AVA, the Polish radio company who you may remember from the awkward customs incident in the third part of this miniseries. Replicating the Enigma machine simply would not have been possible without Rejewski’s formula (Sebag-Montefiore, 2000: 40).

Keys and codebooks

As October passed, and the last of the codebooks in Rejewski’s possession effectively expired, he now faced the exact reverse of the problem he’d had before. Two months ago, he’d had the keys for September and October, supplied by Schmidt, but no replica of the military Enigma machine. Now he had his replica, but no access to the daily keys (Woytak, 1982: 55).

In fact, duplicity upon duplicity, Schmidt was still meeting with Rex throughout this time, and at each meeting he was in actually handing over more codebooks listing the daily keys for subsequent months (Singh, 1999: 156). But Major Langer, the overall head of the Biuro Szyfrów, and Captain Maksymilian Ciężki (head of the German section of the Biuro) specifically opted not to share them with Rejewski. Their rationale? They did not want Rejewski to become dependent on the codebooks. If the Germans tightened up security or if Schmidt was caught, their ability to acquire new codebooks would be lost, so it was crucial to be able to operate on a more parsimonious intelligence diet, as it were (Singh, 1999: 157; Woytak, 1982: 55).

Rejewski’s next task, then, was to find a way to identify the daily keys without the codebooks. The Poles by this point had quickly determined that the Germans were using a doubly-encrypted message key in the first six letters of every message. Rejewski later wrote:

The fact that the first six letters of each message formed its three-letter key, twice enciphered, was obvious, and I will not dwell on the matter. (Rejewski, 1981: 217)

Obvious to him, perhaps, but I guess we’ll just have to take his word for it.

The Germans had opted to encrypt the message-key twice to ensure that there was no risk of having to re-send the message itself if the message key was somehow garbled or received incorrectly. Re-sending messages is a grave risk to security, because it produces the same content using yet more of the encryption pattern, and such an extremity was generally avoided by the Germans. Ironically, however, twice-encrypting the message key, though it was only three letters twice over, was simply making the exact same mistake on a much smaller scale (Turing, 2015: 121).

…this precaution [of twice-encrypting the message key] opened a tiny chink in Enigma’s armour, a chink wide enough to insert the point of a crowbar and prise it wide open. (Turing, 2015: 121)

Sure enough, Rejewski noted the following patterns: the first and fourth letters of every message key, while different to each other when enciphered, ultimately represented the same plaintext letter, repeated twice. This holds too for the second and fifth letter, and the third and sixth. Thus all of the relationships between these pairs of letters (the 1st and 4th, 2nd and 5th, and 3rd and 6th) are determined by the initial settings of Enigma (Rejewski, 1981: 217). If this starts to feel increasingly complicated as I proceed, just relax and let is wash over you. The point, as I’m sure you’ve thoroughly gathered by now, is that Enigma was an absolute mental carpet bomb, and no matter how simply this is explained, it’s going to be hard to keep up with the details.

Anyway, with each successive message, Rejewski would summarise the relationships between these letters by writing them out in table form. The top row of the table would list the first letter of every encrypted message, and the bottom row listed the corresponding fourth letter of every encrypted message. With a sufficiently large enough sample of messages for that day, he was effectively able to create a fully complete “alphabet of relationships” (Singh, 1999: 151; see also Rejewski, 1981: 217) for the 1st and 4th letter. It would look something like this (taken from Singh, 1999: 151):

1st letter:​A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
4th letter:​F Q H P L W O G B M V R X U Y C Z I T N J E A S D K

He would then repeat this exercise for the 2nd and 5th, and the 3rd and 6th, and then he would look for characteristic structure in these tables (Rejewski, 1981: 217). One example of this structure was chains of letters (Singh, 1999: 152). For example, the letter A on the top row might correspond with the letter F on the bottom row. Then we look for F on the top row, and find that its corresponding letter on the bottom row is W. Then we look at W on the top row and discover that we’ve gone back to A. This represents a complete chain or circle of letters with exactly three links: AFW. The number of links in each chain of letters was different – it could be three or seven or nine – and the chains themselves would change on a daily basis. Sometimes the number of links between chains on a given day would be mostly very low, and on other days they would be very high. Intuitively, we can infer that the links between letter chains must be determined by some aspect of the daily key, and, as we already know, this key changes every twenty-four hours at midnight (Singh, 1999: 151-2).

Rejewski determined that the number of links in the chain of letters reflected just the scrambler settings (that is, their position in the machine, and the letter they were oriented to, to start with) and that these chains had nothing to do with the plugboard cablings. This massively reduced the scope of possible settings from ten quadrillion to just 105,456. While this was still an enormous job, it was by no means impossible. Over the course of a year, all 105,456 settings of the replica Enigma machine were scrutinised by a team at the Biuro, and they generated a massive catalogue which listed the chain lengths generated by each and every scrambler setting of the machine.

What Rejewski effectively had now was a primitive form of database (Singh, 1999: 154). When messages began to arrive on any given day, he would begin by figuring out the chains of letters in that day’s message key. Once he knew the number of links, he could look them up in his database, and BINGO. He had the appropriate scrambler settings for that day. He was helped by the fact that the German cryptographers were not particularly good at choosing message keys at random:

It is well known that a human being gifted with consciousness and memory does not have the ability to imitate chance in a faultless manner. Among other things, it is the task of the cryptologist to uncover and suitable make use of these deviations from chance. (Rejewski, 1981: 219)

In the beginning, the German cryptographers would often choose message keys that were simply a repetition of the same three letters, such as AAA or BBB (Rejewski, 1981: 218; Woytak, 1982: 56). When they were no longer allowed to do this, they would deliberately avoid repeating letters, but this also constitutes a pattern. They would also just choose letters next to each other on the keyboard, or diagonal to each other (Woytak, 1982: 56). Whenever yet another particular combination of letters were banned, the Poles would inevitably find some new sort of structure in the German’s choice of message keys. As Rejewksi put it:

Whenever there is arbitrariness, there is also a certain regularity. There’s no avoiding it. (Woytak, 1982: 56)

Approximately five or six people were employed for the exclusive purpose of deciphering the message keys. Rejewksilater invented the cyclometer, a machine that mechanically cycled through the possible permutations each day, a process which took only fifteen minutes (Oleksiak, 2014).

The first crack

While the Poles were now able to determine the message keys and the scrambler settings, they still were missing one aspect of the daily keys: the plugboard cablings. And this Rejewksi solved through the simple process of elimination. He now had the military version of the Enigma machine and was able to deduce both the positions and orientations of the scramblers from the doubly-encrypted message key (Singh, 1999: 154). From there, he would take an intercepted enciphered message and type it into the machine. The majority of the output would be meaningless without the plugboard cablings, but persistence tended to pay off: after a while, words or phrases would appear that were slightly garbled/misspelt but nonetheless recognisable. This was especially true for the names of places and vessels. These effectively provided a hook for Rejewksi to latch onto: if he managed to figure out what the word or phrase was meant to be, he could also figure out which letters in that phrase had been swapped, and which had not. With enough recognisable words and phrases to analyse, the plugboard cablings could be worked out (Singh, 1999: 154).

Thus, Rejewski was now able to put together all of the pieces of the puzzle: the machine, its scrambler settings, the plugboard cablings, and the message keys. And as a result, the Biuro Szyfrów was able to read every intercepted message sent by the Germans.

Indeed, the Germans did not introduce any changes to their method of encryption for the next few years, and the team at the Biuro Szyfrów were able to work on developing their methods of decryption. For this purpose, Rejewksi was reunited with his colleagues Zygalski and Różycki (Rejewski, 1981: 223). Różycki developed what they referred to ask the “clock method” (ibid.) which enabled them to determine which of the scramblers was on the right-hand-side of the machine on any given day. And, without going into endless detail, the interesting thing about this method was that it relied not on pure mathematics for once, but upon the frequency of letters within the German language (Rejewski, 1981: 224).

More machines

As the Poles quietly worked away deciphering intercepted Enigma messages, outside of their Biuro Szyfrów, the world continued to turn. In Germany, in 1933, a largely unknown figure by the name of Adolf Hitler became first Chancellor, and then Führer. His first six years in power were widely lauded as an outright success as his leadership led to a rapid economic recovery, lifting the country out of the depression that had been strangling it. With his rise to power, the abridged version of his autobiography and manifesto, Mein Kempf, quickly became a bestseller.

Also in Germany during this time, Hans-Thilo Schmidt risked his life on at least six separate occasions between 1933 and 1936 to smuggle documents to the French military intelligence agent, Gustave Bertrand. Doubtless much of this was motivated by money, but perhaps some of Schmidt’s zeal was also driven by his brother, Rudolf Schmidt, being promoted to general on 1st October 1936. Meanwhile, the French agent Bertrand duly passed copies of Schmidt’s documents onto the Biuro Szyfrów in Poland. Indeed, Bertrand maintained an interest in the progress being made by the Poles, and even travelled to Warsaw several times, but in a classic intelligence manoeuvre that likely later raised several eyebrows, the head of the Biuro Szyfrów, Major Gwido Langer offered him little information. For many years, in fact, the French were under the impression that the Poles had been no more successful in cracking Enigma than either the British or the French (Sebag-Montefiore, 2000: 31).

Over the sea in England, meanwhile, Turing was eyebrow-deep in the mathematical debates around logic, and in particular, the notion of undecidability. Bear with me here because, though it’s complex, it’s also interesting. And it’s relevant. Logician Kurt Gödel had argued that there were some mathematical questions which could not be answered through logical proof (Turing, 2015: 85). This notion proved particularly controversial. At the time, maths as a discipline was widely assumed to be infallible. That is, there was nothing it could not solve. To state that there existed, out there, in the universe, these terrifying undecidable questions flew directly into the face of this very comforting notions of disciplinary supremacy, and almost in a fervour, mathematicians began to try to identify these so-called undecidable questions, so that they could “put them safely to one side” (Singh, 1999: 168).

Turing was keenly interested in mathematical logic, as well as machines and computing. In May of 1936, just weeks before his twenty-fourth birthday, Turing submitted a paper on the topic entitled On Computable Numbers to the Proceedings of the London Mathematical Society. In this paper, he reformulated Gödel’s problem by describing a hypothetical series of machines that could be designed to perform specific mathematical operations, such as dividing, multiplying, squaring, or factoring. He referred to these as Turing machines. He then outlined another hypothetical machine, one which could be programmed to combine all of the functions of the series of Turing machines. This he referred to as a universal Turing machine, and argued that it would be capable of answering any question that could be answered through logic. But, this did not solve the problem of identifying the undecidable questions: as Turing himself pointed out in his paper, there are some problems which simply cannot be solved by machines (Turing, 2015: 87).

Regardless, in addressing this new, terrifying debate in mathematics, what Turing had essentially done with his paper was provide “a blueprint for the modern programmable computer” (Singh, 1999: 169). Yes, the technology did not exist yet to turn his hypothetical devices into reality, but his paper was well received by mathematicians, and we are alive now in a time of computers because of his work.

Whilst his paper was working its steady way through the review process, Turing had been invited to spend a year in the US at Princeton’s Institute for Advanced Study, and he embarked on this journey on 23rd of September 1936. Three weeks later, on the 12th of November, his paper was read by the reviewers of the Proceedings of the London Mathematical Society, and they chose to publish it in two parts on the 30th of November and the 23rd of December 1936. Not quite a year later, in the autumn of 1937, still in the US, Turing began to take considerable interest in cryptanalysis, owing to the increasingly likely possibility of war with Germany, and sure enough, in March 1938 Germany annexed Austria. However, Europe at large made little real response to this militarily aggressive manoeuvre. Similarly, Turing was preoccupied with writing a thesis for his PhD on the topic of ordinal logics and relative computing. His thesis was approved on 17th May 1938 (Turing, 2015: 107), and the following month, the Department of Mathematics at Princeton awarded him his PhD. Turing had now been in the US for almost two years, far longer than his intended one-year visit, and though he was offered a position there, he decided instead to return to Cambridge at the end of June, 1938 (Turing, 2015: 102).

Back in Poland, the French Secret Service had a new plan, and suggested to the Poles that they should effectively pretend to have cracked Enigma. This, they hoped, would trigger the Germans to switch to a cipher that would potentially be less secure (ibid.). The head of the Biuro Szyfrów, Major Gwido Langer was horrified, primarily because, as you know, the Biuro had not only cracked Enigma, they had done so five years ago and had been reading all the German Enigma messages they could intercept for the past half-decade (Sebag-Montefiore, 2000: 33). A change in cipher was exactly what they did not want. Indeed, internally, at the start of 1938, the head of the Polish intelligence department, Colonel Stefan Mayer, requested statistics representing how many of the intercepted German messages had successfully been deciphered by the Poles within a period of two weeks. The number was 75% (Rejewksi, 1981: 225), but Rejewski later argued that they were perfectly capable of deciphering a far higher percentage, up to as much as 90%. The problem? They simply lacked the number of personnel required. Even a 75% success rate is extraordinary, however, given that many of the intercepted transmissions were heavily garbled by interference.

Perhaps prompted a little in the direction of preventing the French from starting such a story themselves, the Poles began to share the content of decrypted messages with the Allies, but they would not elaborate on their methods of decryption. Essentially, they were afraid of counterintelligence (Oleksiak, 2014). Whilst they were passing on decrypted messages, they were a valuable and useful ally, and worth protecting by their more powerful neighbours, but if France or Britain could have the method for themselves, they would not have hesitated to immediately get access to it by any number of more or less honourable means. With their method would go their advantage, and so, keeping their means and practises secret was, in its own way, an act of self-preservation.

But this five golden years of secret success, and the thin veneer of safety it was buying for the Poles, was about to go up in flames.

Bombes and cards

On the 15th of September 1938, the Germans introduced changes to their methods of decryption. Perhaps they had caught wind of the possible infiltration of their code. Perhaps this was simply akin to the wisdom of changing one’s password at regular intervals – that is, more a method of prevention than a deliberate attempt to cure any known problem. Or perhaps it was a bit of both. Whatever the case, the net result was still the same. Previously, German cryptographers were setting their machines to a pre-specified initial position using the day key in the monthly codebooks, and then, at the very start of the message, they were twice enciphering the message key, and thereafter, switching the settings to match that message key for the rest of the message. But now, instead of using the monthly codebooks and daily key settings, they were told that they should select their own initial position (Rejewksi, 1981: 226; Sebag-Montefiore, 2000: 41). This three-letter initial position was sent to the message recipient unenciphered, followed by the twice-enciphered message key. In a single stroke, Rejewski’s letter chain method and all its accompanying databases and mechanical systems were rendered entirely useless (Singh, 1999: 156), and the understaffed, underfunded Polish Biuro Szyfrów was left scrambling to pick up the pieces and begin anew.

Within weeks Rejewksi came up with the idea to create an adapted version of the military Enigma machine which would be used to mechanise the process of decipherment of the message key. The engineers from the radio station, AVA,managed to create six of these devices by November 1938 (Rejewski, 1981: 227). Their purpose was to work in parallel,and by doing so, they drastically shortened the usual exhaustive search process: passing through all 17,576 possible scrambler orientations – a job that could take up to two hours – until they found a match.

The units were referred to as bomby kryptologiczne (or cryptologic bombes) although nobody, including Rejewksi himself, can seem to remember why (Sebag-Montefiore, 2000: 41). One story (Kozaczuk 1984) suggests that they were irreverently christened with this name by Rόżycki (p. 298). Another claims that they were named after a type of ice cream that was popular at the time, a bombe glacé in the shape of a hemisphere (Sebag-Montefiore, 2000: 41; Singh, 1999: 156). Still others have suggested that it was because of the sinister ticking noise they made whilst operating (Singh, 1999: 156; see also Oleksiak, 2014). In short, it seems that the real provenance of the names has quietly fallen out of living memory, and far into the depths of myth and muse.

Whatever the case, the Biuro did not rest here. Around the same time that the bombes were being built, Zygalski created a manual method using perforated sheets of card. This might seem technologically a step backward, especially as the bombes did not take as long to manufacture as the perforated sheets, but card does not randomly malfunction or require much in the way of regular maintenance to function effectively. Zygalski’s method was effectively a catalogue which made use of the relationships between pairs of letters in the twice-encrypted message key (Rejewksi, 1981: 227; Sebag-Montefiore, 2000: 42). Specifically, the mathematicians were focussing on so-called “females” (Sebag-Montefiore, 2000: 42) – instances when “the same letter appeared in both versions of the enciphered triplet in the same place” (Turing, 2015: 122). When this happened, they were able to work backwards to figure out which settings of the machine could possibly allow a plaintext letter to be enciphered twice as the same letter (Turing, 2015: 122; see also Oleksiak, 2014). Again, remember what I said about how easy this stuff is to follow. Entire advanced courses are taught about Enigma alone and you’re trying to absorb it in a podcast episode, so if you’re losing the finer details, don’t worry. I’ve literally researched and fact-checked and scripted and narrated this and only on the fourth or fifth reading have I sometimes finally worked stuff out.

Anyway, the sheets had a full alphabet along the top and down both sides, creating a 26×26 matrix which in turn represented all 676 potential positions of the right-hand and middle scramblers. Small holes were cut into the sheets at each point where the right-hand and middle scramblers could potentially create a “female” (Turing, 2015: 123).

Once a set was completed, the relevant sheets for a particular day’s message key were stacked on top of one another atop a table with a light shining through the surface. Any places in which the light shone through the perforations in all of the cards indicated which settings could have produced that “female”. Those were then checked manually by the team (Sebag-Montefiore, 2000: 43). But there was a catch. Creating these sheets involved making around 150,000 perforations in pieces of card with a razor blade, and they already lacked resources and manpower.

Three months later, they had only managed to make two sets of sheets for each of the six possible scrambler positions, leaving them heavily reliant on the bombes, and then another devastating blow destroyed all the Biuro’s latest efforts. On the 15th December 1938, the Germans began to introduce yet more changes to the way they used Enigma (Rejewksi, 1981: 227; Sebag-Montefiore, 2000: 43).

Quietly, in absolute secrecy, Germany was preparing for all-out war.

End of part 2 of 3.

Outro

This episode of en clair was researched and fact-checked by Rebecca Jagodziński. And it was scripted, narrated, and produced by me, Dr Claire Hardaker. And it was supported by the Economic and Social Research Council as part of their Festival of Social Science. However, this work wouldn’t exist in its current form without the prior effort of many others. You can find acknowledgements and references for those people at the blog. Also there you can find data, links, articles, pictures, older cases, and more besides.

The address for the blog is wp.lancs.ac.uk/enclair. And you can follow the podcast on Twitter at _enclair. If you like, you can follow Rebecca on Twitter at RjJagodzinski, and you can follow me on Twitter at DrClaireH.