How the Enigma Was Beaten: Rotors, Hunches and the Bombe

Three small letters, a typewriter-like keyboard and a panel of waiting lamps: the host presses the keys one after another, a different lamp lights up each time, and the encrypted form of the word Veritasium emerges. When the rotors are reset and the same text is typed again, the word comes back in the clear; if a single setting is off by one notch, only gibberish remains. That small demonstration condenses the whole argument of the video into one scene: what made the Enigma fearsome was not the tangle of wires but the fact that those wires rearranged themselves with every keystroke, which is why the Allies' work started from scratch every midnight.

The first surprise is in the machine's birth certificate: Enigma was no Nazi invention but the commercial product of a 1918 patent by German engineer Arthur Scherbius . Scherbius wanted to protect banks' and businesses' correspondence, and his typewriter-like boxes were off-the-shelf goods anyone could buy. Poland, Britain and Russia all acquired such devices; as Sir Dermot Turing recounts in the video, the manufacturer went door to door looking for a market. The German army bought the same off-the-shelf product, secretly altered its insides, and kept those alterations to itself.

From commercial typewriter to military secret

The trick that sets the machine apart from earlier ciphers shows up in a single key: the host presses L once and the panel lights Y ; pressing the same key again lights H instead. In fixed-rule systems like the Caesar cipher a letter always becomes the same letter; in Enigma the rule changes with every press. That is why classic frequency analysis , counting the most common letter and matching tables, fails here. The narrator stresses this difference because the entire codebreaking story revolves around this moving target.

Opening the box reveals the source of the trick: three rotors side by side, each with a metal contact per letter of the alphabet on both faces and a maze of cross-wired connections inside. Pressing a key sends current from the first rotor to the second and then the third, changing letters at every crossing; a component called the reflector then sends the current back along a completely different path, and the panel shows which letter lights. The critical detail is that the rightmost rotor advances one notch with every keystroke, and once it completes a full turn a pawl drops and steps the middle rotor forward. As Wikipedia's Enigma entry explains, this stepped motion forces every letter through a different electrical path.

The operator's setup choices form the first layer of the arithmetic: the order in which the three rotors are slotted in (three factorial, six arrangements) and the three-letter start position shown in the window (26 cubed). Their product exceeds a hundred thousand even for the commercial model. The German army added two more layers: the ring setting , which shifts the relation between the visible letter and the internal wiring, and the plugboard between keyboard and rotors. In the video's example the letter Q is wired to R ; a letter with no cable passes through unchanged. By the late 1930s typical use meant six cables, worth on the order of a hundred billion possibilities on its own; the total key space reached a mind-bending seven times ten to the eighteenth.

The arithmetic of hundred trillions

Hidden inside that enormous number is an elegant subtlety: the machine is reciprocal , so if pressing E lights K under one setting, pressing K lights E . The receiver therefore needs no separate decryption procedure; typing the ciphertext into an identically set machine is enough. To keep the whole network on the same setting the Germans distributed daily key sheets , one page per day of the month; each morning the operator configured the machine from that day's sheet. Because the sheet changed at midnight, even a lucky break into one day's setting was worthless the next morning.

At this point the story moves to a quiet mansion in the English countryside, Bletchley Park . Conveniently placed between London, Oxford and Cambridge, the centre gathered chess players, puzzle enthusiasts and academics alongside hundreds of women from the Royal Navy; the roughly 150-strong starting team was to examine signals from listening stations and guess the day's setting. But an impassable wall stood in the way: the Nazis had changed the rotors' internal wiring too, and without that wiring no trial of settings meant anything. By the summer of 1939 the British had made essentially no progress.

The turning point in the video comes from years earlier, from an unexpected quarter: in 1931 an employee of the German cipher office sold Enigma secrets to French intelligence for cash, and manuals, sample messages and key sheets changed hands. The French, unsure what to do with the material, passed it to their Polish allies, whose mathematicians spotted a fatal weakness in the sheet procedure. Before each message the operator picked three letters (say GEX ) and encrypted them twice under the day's setting (say ASDEIW ); the receiver decrypted the first six letters and set the window to those three. Encrypting the same text twice created a mathematical link between the first and fourth letters, and that link was enough to pry the door open.

Poland's quiet triumph

The man who saw the link was the young mathematician Marian Rejewski , who applied the permutation theory he remembered from his undergraduate years; together with colleagues Jerzy Rozycki and Henryk Zygalski he reconstructed the military Enigma's wiring in late 1932 and 1933 without ever seeing or capturing a machine. As Wikipedia's Rejewski biography records, the team built tools like the cryptologic card catalog and the cryptologic bomb and began reading German military traffic by the mid-1930s. But in 1939 the Nazis added two new rotors, raising the choice from three to five (sixty orders, a tenfold jump), and raised the plugboard to ten cables, worth some 150 trillion combinations on its own and growing the total space fifteen-thousandfold past a hundred sextillion. With invasion looming, Poland summoned British and French intelligence in July 1939 and laid everything on the table; a month later the country was invaded, the codebreakers fled, and the Bomba device they had built to get into Enigma messages was left behind.

By the 1940s the Germans had realised the doubly-encrypted indicator was a mistake and switched procedure: the operator picked three letters (say VER ), sent them in the clear over the air, set the window to them, then passed a second trio (say ITA ) through the machine and set the window to that. But humans are terrible at randomness: girlfriends' names (the famous CIL case, source of the term cillies ) and city names (a window of BER made an indicator of LIN likely) recurred constantly. The British codebreaker John Herivel followed a subtler trail: across hundreds of messages the first letters were not spread evenly across the alphabet but clustered around one point, because operators rarely moved the rotors more than a notch or two from the sheet setting, and that clustering betrayed the day's setting. Using such clues the host genuinely solves a message prepared by his producer, finding the rotor order by trial and eliminating plug guesses until the sentence James is a legend appears after about an hour. This section of the video carries a one-sentence sponsorship by Incogni, a service that petitions data brokers to delete personal information.

For networks where human sloppiness was not enough, Turing looked for a different door and found it in the dullest messages of all: the daily weather reports arriving at the same hour every morning. A message from a station off Biscay could be guessed to contain the string WETTERVORHERSAGEBISKAYA ; the problem was finding where inside the ciphertext that string began. Here an unchanging flaw of the machine stepped in: in Enigma no letter can ever encrypt to itself, because the current cannot return along the same wire. Sliding the guessed text along the ciphertext until no letter coincides with itself is enough, and the surviving position yields the crib , the solid guess.

From loops to victory

Turing turned that guess into a logical test: imagine three Enigma clones set to rotor positions such as 6, 22 and 9; if R becomes Y in the first machine, Y becomes S in the second, and S becomes R again in the third, a perfect loop closes. With the wrong settings a loop almost never forms, so a machine could scan all settings and discard the ones that fail to loop. One loop alone returned hundreds of false hits, so Turing accumulated more loops in what was called the menu. The plugboard's 150 trillion possibilities fell to an elegant cancellation: each letter passes the plugboard, runs through the rotors and passes the same plugboard again, so two consecutive plugboards cancel out; a single R-Z guess was wired live into the circuit, and if wrong the current spread across many wires, displaying the impossibility. The device built with engineer Harold Keen was named the Bombe in honour of Poland's Bomba; the first prototype arrived in March 1940, ran thirty-six Enigmas in parallel and scanned every combination in about thirteen minutes. When its indicator drums stopped it offered the key of the day, but every stop needed manual checking because of false stops. Gordon Welchman 's diagonal board addition (if R is plugged to Y , the reverse holds too) eliminated more than ninety percent of false stops; a hundred stops shrank to four, and with the August 1940 revision sixteen Bombes were reading routinely by the end of 1941. According to TNMOC, the first Bombe, Victory , began work at Bletchley Park on 14 March 1940, and by war's end 211 Bombes were chasing the keys of three to five thousand messages a day.

The results were felt at the front: as GCHQ recounts, from the spring of 1940 Luftwaffe traffic was read regularly; the German air force fielded 2,600 aircraft for a four-to-one superiority, and the picture of Hugh Dowding 's fighter management and the Sea Lion preparations came into focus through Ultra intelligence. In North Africa decrypts exposing the German army's fuel shortages paved the way for Bernard Montgomery 's victory at El Alamein . When the German navy added a fourth rotor, Turing devised a new statistical method, worked with the navy on tricks like gardening , laying mines to force a report that would yield a guess, and keys were seized from sinking submarines. According to uboat.net's technical pages the navy used codebooks such as the Kurzsignalheft and Wetterkurzschluessel ; the Dolphin cipher was read with keys captured from the weather ships Muenchen and Lauenburg in June and July 1941, and cryptanalytic reading resumed from August 1941. The 1943 reversal in submarine losses, nearly a hundred American Bombes joining that year and the 1944 Normandy landings add up to historians' estimate that the war was shortened by up to two years. The host closes with two hooks: the entirely different machine Hitler used, with a key space stated in the video around ten to the hundred and seventieth, and an unsolved naval message waiting in the description.