ADFGVX

What the sixth symbol buys

Adding V takes the grid from twenty-five cells to thirty-six. That holds all twenty-six letters plus the digits 0 to 9, so the shared cell of ADFGX disappears, I and J are separate letters again, and the shared-cell control goes with it. Nothing else changes: look the character up, write its row and column as two of the six symbols, then transpose the whole stream under a keyword.

Why digits mattered in the field

Army traffic is full of numbers. Map references, times, unit designations, quantities of ammunition. In ADFGX each one had to be spelled out, so a time like 1200 went as EINSZWEINULLNULL: sixteen letters and thirty-two symbols, against the four characters and eight symbols the six by six square needs.

Length was one cost. The other was that spelled-out numbers are stereotyped. The same words in the same shapes recur across message after message, which gives a cryptanalyst a crib: a stretch of probable plaintext to slide along the ciphertext until it fits. Putting the digits in the square shortened the traffic and removed a family of predictable phrases at once.

The grid above

NA1C3H8TB2OME5WRPD4F6G7I9J0KLQSUVXYZ read six characters to a row, with PRIVACY as the transposition key. ATTACK AT 1200AM encrypts to DGDDDAGDDGAFADDFDADVDVFAADVX, the digits carried through as characters in their own right, and that string is the one the reference example prints. Anything outside those thirty-six cells, spaces and punctuation included, is dropped before the square is consulted.

June 1918

V joined the alphabet on 1 June 1918, on the Western and Eastern fronts at once. The listening post on the Eiffel Tower took down a message that same day, sent from Remaugies north of Compiègne. Georges Painvin, who had been reading ADFGX since early April, worked on it for something like twenty-six hours and broke it on 2 June. In France it is still called the radiogram of victory: “Rush munitions. Even by day if not seen.”

Ammunition moving forward on that scale marked where the German blow was coming. Foch put reserves behind Compiègne, and the attack that opened on 9 June between Montdidier and Noyon was broken by a French counterattack two days later. How much of that the decrypt is responsible for has been argued over ever since.

Related

ADFGX is the five-symbol original, and the page for it covers the Morse reasoning behind the letter choice. Polybius square is the coordinate lookup with no transposition on top. Nihilist takes the same coordinates and adds a keyword to them instead of shuffling them.