ENIGMA

The Enigma is an electromechanical cipher machine, patented by Arthur Scherbius in 1918 and adopted by the German military in the years before the Second World War. Tens of thousands were built. Every branch of the Wehrmacht trusted it, because the numbers seemed unanswerable: rotor choice, rotor positions and plugboard together give roughly 158,962,555,217,826,360,000 possible keys. The Germans concluded that nobody could try them all. They were right. That turned out not to matter.

Every key press sends one pulse of current through the machine:

1. THE ROTORS STEP FIRST. The right rotor advances every keystroke; at its notch it carries the middle rotor, which can drag the left one along (the famous double-step). The machine never enciphers twice the same way.
2. The current enters the PLUGBOARD. If the letter is steckered, it is swapped before it reaches the wheels.
3. It passes through the THREE ROTORS, right to left, each a scrambled alphabet turned to an ever-changing position.
4. The REFLECTOR (UKW) bounces it back through all three rotors again by a different path, then through the plugboard a second time, and a LAMP lights: that is the cipher letter.

The reflector makes the machine its own mirror: enciphering and deciphering are the same operation with the same settings. It also means a letter can never encipher to itself. That small honesty was the crack in the armour, and the codebreakers drove a truck through it.

Operators worked from monthly key sheets. The Tagesschlüssel (daily key) fixed the rotor order (Walzenlage), the ring settings (Ringstellung) and the plugboard pairs (Steckerverbindungen). For each message the operator then chose his own three-letter Spruchschlüssel, the message key. He picked a random start position, sent it in clear, and typed the message key at that position to encipher it. The receiver reversed the little dance.

You can replay that dance with the real message below: its indicator reads WXC KCH. Set the wheels to W X C, type KCH, and the lamps answer B L A: the start position for the message itself.

Not by trying every key. Marian Rejewski broke the machine with mathematics in Poland in 1932; in 1939 the Poles handed their work to the Allies, and at Bletchley Park Alan Turing and Gordon Welchman built the Bombe around a simple lever: the crib. A guessed scrap of plaintext, WETTERVORHERSAGE in a morning weather report, an eagerly predictable heading, and the one certainty that no letter is ever itself, let the Bombe discard keys by the million. Operators helped: lazy message keys, reused fillers, stereotyped endings. The machine was very good. The habits around it were not. By some estimates, reading Enigma shortened the war in Europe by years.

The lesson survives every technology: the cipher is only as strong as the person who is bored of using it.

What follows is a real Wehrmacht signal, sent on 7 July 1941 during Operation Barbarossa by the commander of the SS-Totenkopf Division to LVI Armeekorps, and broken again in modern times by Frode Weierud and Geoff Sullivan of the Crypto Simulation Group. Press EINSPIELEN and the machine takes the day's key, dials the message key, copies the ciphertext into MESSAGE IN (and to your clipboard), and the 1941 plaintext walks out below, eighty-five years later, letter for letter.

Reading the decrypt: X is the full stop, numbers are spelled out (EINS AQT DREI NULL = 1830), Q stands for CH (RIQTUNG = RICHTUNG), and place names are sent twice against garbling. The Kenngruppen (RFUGZ, FNJAU), which only named the key net, are omitted here.

In translation: Reconnaissance unit from Kurtinowa north-west of Sebez on the flight corridor in direction Dubrowki, Opotschka. Started to move at 18:30. Attack. Infantry Regiment 3 goes slowly but surely forwards. 17:06, I Battalion, Infantry Regiment 3 on the flight corridor starting 16 km east-west of Kamenec.

Message courtesy of Frode Weierud and Geoff Sullivan, cryptocellar.org. A situation report from a Tuesday, preserved by mathematics. Most Tuesdays get less.

Older still: this is the example from the German Army's own 1930 Enigma instruction manual, the most reproduced Enigma message in existence. It predates the war, uses the early reflector A and the older double-key indicator, and shows the machine at its most textbook. Press EINSPIELEN and read a drill exercise from 1930.

Reading it: same conventions as the wartime traffic. X is the stop, Q stands for CH (BEOBAQTET = BEOBACHTET, FEINDLIQE = FEINDLICHE), and numbers are spelled (DREI KM = 3 km). The doubled message-key group that opened the real transmission (PKPJXI) is omitted; we start at the message key A B L.

In translation: Enemy infantry column observed. Begins at the south exit of Baerwalde. Ends three kilometres east of Neustadt.