The Doubled Key

The intercept

Western Front, winter 1939–40 — the quiet months the newspapers called the “Phoney War”. An Army station on the Westwall sends its routine weather report. This time nobody hands you the message’s starting position: the operator chose his own, and sent it disguised at the head of the message.

The day’s key sheet (shared by every station on the net)

Message header (sent ahead of the message): HRK WQPDIF

Ciphertext

CQPAA WTVGT CMBEJ WZZQP ROPHF HVDMQ NMYKX VFJAT

The procedure

This is how Army and Luftwaffe traffic was keyed between September 1938 and May 1940. The Enigma touch manual (§2.3) walks through the later, post-1940 version of the same idea. The difference is that before May 1940 the message key was encrypted twice.

1. Set up the machine from the key sheet with the setup modes: Modell, then Rotor for the reflector and rotor order, then Ring, then the plugboard.
2. The first three letters of the header, HRK, were sent in the clear. They’re the operator’s own choice of home position (Grundstellung) for this message. Leave setup mode and turn the rotors to HRK.
3. Type the next six letters, WQPDIF. This decrypts them back into the operator’s chosen message key. The key was always encrypted twice in a row, so a letter garbled in transit would show up as two halves that don’t match.
4. Turn the rotors to the recovered 3-letter message key (not HRK) and decrypt the ciphertext.

Hint

Click for a hint

Three rotors and ring settings written as numbers mean Modell I. The Enigma I labels its rotor positions with numbers too, so, as the manual puts it, you “convert the home position and decrypted message key back from letters to numerical rotor positions” (A = 01 … Z = 26, or read them off the plugboard sockets). HRK is 08 18 11.

Step 3 should give you two identical 3-letter halves. If they don’t match, a setting upstream is wrong. Check the ring settings first; they’re the easiest to enter in the wrong order.

That built-in repetition was also the procedure’s weak point. Every doubled key told an eavesdropper that letters 1 and 4, 2 and 5, and 3 and 6 of the enciphered indicator came from the same plaintext letter. It was dropped on 1 May 1940.

Solution

Click to reveal the solution

Recovered message key: NBW (14 02 23 on the Enigma I). At HRK, the six letters WQPDIF decode to NBWNBW, and both halves match.

Plaintext: WETTERBERIQTSAARBRUCKENNEBELSIQTGERINGXX. It reads “Wetterbericht Saarbrücken, Nebel, Sicht gering” (“Weather report, Saarbrücken: fog, visibility poor”). Turn the rotors to NBW and decrypt the ciphertext to get it. Three of the manual’s message-prep rules (§2.3) show up here:

• ü is written as u (Saarbrücken → SAARBRUCKEN).
• The pair ch is written as q (Bericht → BERIQT, Sicht → SIQT).
• The closing XX is padding to a multiple of five.

Why doubling the key was a mistake

Because the same message key was enciphered twice, the 1st and 4th letters of every indicator were linked by a fixed relationship that depended only on the day’s rotor order and positions. Given enough intercepts from one day, those relationships form permutations. The cycle structure of those permutations doesn’t change with the plugboard, which let Marian Rejewski’s team at the Polish Cipher Bureau recover daily settings. Rejewski had first reconstructed the rotor wiring in 1932–33, helped by German manuals and monthly keys that French intelligence passed to the Poles.

The version where every station also used the key sheet’s own Grundstellung was even weaker, and it ended on 15 September 1938. That change is why this 1940 message carries an operator-chosen HRK in the clear. The Kriegsmarine had already moved to a codebook-based indicator system in May 1937.