ADFGVX cipher

ADFGVX is the enhanced version of ADFGX, entering German military use in June 1918. The only difference from its predecessor: a sixth label, V, which lets the grid grow from 5×5 (25 cells) to 6×6 (36 cells).

This enlargement solves a real problem: ADFGX couldn’t cipher digits (0-9) directly — they had to be spelled out (eins, zwei, drei), lengthening messages and aiding analysis. ADFGVX embeds all ten digits in the grid next to the 26 letters.

Principle

Step 1 — 6×6 Polybius

The grid holds 36 cells (26 letters + 10 digits), shuffled by a secret key:

    A D F G V X
  A A B C D E F
  D G H I J K L
  F M N O P Q R
  G S T U V W X
  V Y Z 0 1 2 3
  X 4 5 6 7 8 9

Each plain character is replaced by the pair (row-label, col-label). For instance: C → AF, I → DF, E → AV, 7 → XV.

Step 2 — Columnar transposition

Identical to ADFGX: the intermediate text (ADFGVX pairs) is written into a rectangular grid under a keyword, then read column by column in the alphabetic order of the keyword letters.

Example (step 1 only)

Plaintext CIPHE with the grid above:

C → A F    I → D F    P → F G    H → D D    E → A V

Result: AFDFFGDDAV.

History

• March 1918: ADFGX enters service.
• June 1918: ADFGVX replaces ADFGX so digits can be transmitted directly.
• May–June 1918: Georges Painvin breaks the method (both variants) by exploiting formatted military headers and multiple same-length messages. The French army then reads parts of the German traffic during the 1918 offensives — a decisive edge.

Painvin worked sleeplessly for weeks to break the system; he emerged exhausted and fell seriously ill. His work is regarded as one of the founding acts of modern cryptanalysis.

Variants and descendants

• ADFGX — 5-label predecessor, no digits.
• Schlüsselzusatz 42 (SZ 42, Lorenz) — German strategic-level machine used in WWII, far more complex.
• JN-25 — WWII Japanese naval code, similar principle (super-enciphered codebook).

Weaknesses

Same as ADFGX, with the extra difficulty offered by the enlarged alphabet:

• Formatted messages with fixed headers → exploitable cribs.
• Multiple same-length messages → geometric constraints on the transposition.
• Statistics on symbol pairs once the transposition is undone.

In CipherChronicle

ADFGVX is the peak of WWI hand ciphers: a carefully layered double step, breakable only with intense human work and multiple ciphertexts. Its grids can stage the two-phase resolution and the historical dimension.