The Enigma Cipher Machine

Messages Anyone Can Hear

Radio let units talk without laying wires, but radio waves go everywhere and the other side listens too. A message has to be enciphered before it is sent and deciphered when it arrives.

Codebooks worked by hand are slow and error-prone, and a captured book gives everything away. In the 1920s machines took over: with every letter the wiring inside changes, so the same letter comes out differently this time and the next. The Enigma I went into service with the German Army in 1930, later with the Air Force too; more than twenty thousand were built.

Press a Key, a Lamp Lights

The Enigma prints nothing. The operator presses a key, a letter lights up on the lamp board, and a second person writes it down. When the message is done it goes out by radio in Morse.

As the key goes down the right-hand rotor moves on one step, and only then does the circuit close. So press A five times and five different lamps light, and none of them is A.

The Path of the Current

A 4.5 V battery drives it. From the key the current goes through the plugboard into the entry wheel, through the right, middle and left rotors, and into the reflector. The reflector sends it back by another contact, back through the three rotors, the entry wheel and the plugboard, and it lights a lamp.

Each rotor has 26 contacts on each face and 26 wires inside that join them in a scrambled order. Turn a rotor one step and the whole path changes.

The path: key → plugboard → entry wheel → right → middle → left → reflector → left → middle → right → entry wheel → plugboard → lamp

Rotors That Count Like an Odometer

The right rotor steps once for every key. Each rotor’s ring has a notch: as the right rotor passes its notch it takes the middle rotor one step, and as the middle rotor passes its own it takes the left one. Rotors I to V turn over at Q, E, V, J and Z.

There is one difference from an odometer. When the middle rotor reaches its notch, the next key steps it again together with the left rotor: the double step. With rotors I, II, III the windows go ADU, ADV, AEW, BFX, and the middle rotor stays on E for only one key. So the three rotors come round after 26 × 25 × 26 = 16,900 keys, not 17,576.

The Army’s Enigma I had figures 01–26 on its rings; the figure in a window stands for the letters A–Z

The Plugboard

Fold down the wooden flap at the front and there is the plugboard. Each twin cable plugs into the sockets of two letters and swaps them: once before the current enters the rotors, once after it leaves. In the war ten cables were the rule, so twenty letters were swapped in pairs and six stayed as they were.

The plugboard does not change from key to key, but it hides the rotors’ wiring behind one more unknown. Each socket has a thick hole and a thin one, so a plug only goes in one way round.

The Same Settings Decipher

The reflector joins its contacts in pairs. So at any one position, if A becomes B, B becomes A. The receiver sets the same rotors, rings, start positions and plugs as the sender and types the cipher in, and the lamps spell out the message. Enciphering and deciphering are one machine and one action.

The same reason makes a weakness: the current cannot come back to the contact it came in by, so no letter is ever enciphered as itself. It looks harmless. It became a tool in the codebreakers’ hands.

How Many Settings

The day’s key says which three of the five rotors go in and in what order, 60 ways; the start positions, 26 × 26 × 26 = 17,576; and how the ten cables go in, 150,738,274,937,250 ways. Multiplied, that is about 1.59 × 10²⁰.

Count the rings too and only the middle and right ones change when a turnover comes, another factor of 676: about 1.07 × 10²³, roughly a 77-bit key. The left ring only renames the start position and adds nothing new. The figures quoted in different places differ because they count different things. And the count assumes the other side knows how the rotors are wired, which it did.

60 × 17,576 × 150,738,274,937,250 × 676 ≈ 1.07 × 10²³

Taken Apart

On top is the rotor cover, with three small windows that show the rotors’ positions and three slots the knurled thumbwheels stand through. Under it, from left to right: the reflector, the left, middle and right rotors, and the entry wheel; at the right, the box for the 4.5 V battery.

In the middle are the lamp board and its 26 bulbs, in front of them the 26 keys, and behind the folded-down flap the plugboard and its cables. Around it all is the oak case with its hinged lid, which holds spare bulbs, spare cables and a green filter.

One Rotor, Cut Open

Inside a rotor’s bakelite core run 26 wires. One face carries 26 spring-loaded brass pins, the other 26 flat brass plates, and each wire joins a pin on one side to a plate on the other in a scrambled order. Each of the five rotors is wired differently.

The ring turns against the core: that is the ring setting. It changes which letter in the window goes with which wiring position, and when the notch comes round. The wire picked out in the section is the one the current takes now.

How It Was Broken

From 1932, three mathematicians of the Polish Cipher Bureau, Marian Rejewski, Jerzy Różycki and Henryk Zygalski, worked on the Enigma. Rejewski used the theory of permutations, together with operating instructions and several months of keys that French intelligence had obtained from a German informant, Hans-Thilo Schmidt, to work out how the rotors were wired; Poland then built copies of the machine. They invented the cyclometer and Zygalski’s perforated sheets, and in 1938 a machine called the bomba to find each day’s settings.

In December 1938 the Germans added rotors IV and V, and the rotor orders went from 6 to 60. In July 1939, at Pyry near Warsaw, the Poles gave everything they had, copies of the machine included, to the French and the British. At Bletchley Park in England, Alan Turing designed the British bombe and Gordon Welchman added the diagonal board; the first arrived in March 1940, and by the end of the war there were more than two hundred, run mostly by women.

A bombe works from a crib: a stretch of plain text the codebreakers could guess, from a weather report or a fixed opening. Slide the crib along the cipher, and any place where a letter would meet itself is ruled out, because the Enigma never enciphers a letter as itself. The places left go to the bombe, which runs through rotor orders and start positions at speed and throws out plugboard guesses that contradict themselves.

Slide the guessed text along the cipher: in red, a letter meets itself, so that place is ruled out

What It Changed

In Britain the intelligence from broken messages was called Ultra. It helped convoys in the Atlantic route round the U-boats, and it gave German dispositions in North Africa and before and after the Normandy landings. The work was kept secret for nearly thirty years after the war and came out in the 1970s, and so did the Polish part in it.

How much Ultra changed the war is something historians estimate differently. Harry Hinsley, the official historian of British wartime intelligence, argued that without it the Normandy landings might have waited until 1946 and the war would have lasted much longer; others think the effect was smaller. Questions of what would have happened cannot be tested. What is clearer: the bombes turned codebreaking into an industry, and the Enigma taught later designers that the machine will become known to the other side sooner or later, so the secret has to lie in the key alone.