ADFGX cipher

The ADFGX cipher entered service with the German army in March 1918, just before the spring offensive on the Western Front. It combines a labeled Polybius and a columnar transposition — one of the first real modern cryptographic superpositions. It was broken by French Lieutenant Georges Painvin in April–June 1918, in a feat considered decisive for the Allied victory.

Principle

Step 1 — Labeled Polybius

A 5×5 grid holds the alphabet (I/J merged), shuffled by a secret key. Rows and columns are labeled with five letters chosen for their highly distinct Morse codes: A, D, F, G, X.

    A D F G X
  A A B C D E
  D F G H I K
  F L M N O P
  G Q R S T U
  X V W X Y Z

Each plaintext letter is replaced by the pair (row-label, col-label). For instance: C → AF, I → DG, E → AX.

Step 2 — Columnar transposition

The text obtained (twice as long, only A/D/F/G/X) is then written into a rectangular grid under a keyword, and read column by column in the alphabetic order of the keyword letters.

This double step significantly complicates analysis: after Polybius you only have five symbols instead of 26; after transposition, no local statistic survives.

Example (step 1 only)

Plaintext CIPHE with the grid above:

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

Step 1 result: AFDGFXDFAX.

The transposition step depends on an additional keyword (say KEY) and makes the final ciphertext non-trivial to track by hand — hence the method’s historical effectiveness.

Why five letters?

A, D, F, G, X were picked by Fritz Nebel because their Morse codes are:

A = ·−     D = −··     F = ··−·     G = −−·     X = −··−

The five symbols are very different from one another: low risk of confusion at reception, even under poor conditions. This is the first cipher jointly designed for its transmission channel.

Variants

• ADFGVX — 1918 extension to six labels, covering digits 0-9.
• Bazeries — another Polybius + transposition superposition.
• Nihilist — similar idea among Russian revolutionaries (Polybius + addition).

Weaknesses

Painvin broke ADFGX through two facts:

• Some intercepted messages shared identical opening structure (formatted military headers).
• Transposition leaves geometric constraints exploitable when multiple same-length ciphertexts are available.

Once the transposition is reversed, the Polybius step yields to frequency analysis of the ADFGX pairs.

In CipherChronicle

ADFGX is a strong historical cipher: it introduces the idea of layered methods and offers genuine resistance to naive analysis. Grids built on it can ask the player to unwind both layers in order.