ADFGX Cipher
A German field cipher attacked through relationships among wartime messages
Painvin and other Allied analysts used repeated traffic, statistics and transposition analysis in 1918.
Why This Matters
ADFGX combined a coordinate substitution with columnar transposition. Its analysis during the 1918 offensives illustrates how related messages and operational procedures can assist an attack on a layered cipher. It does not establish that one analyst alone determined the war’s outcome.
As Germany prepared its 1918 Spring Offensive, Fritz Nebel designed the ADFGX cipher for front-line use. The letters A, D, F, G, X were specifically chosen because they sound very distinct in Morse code — reducing the risk of garbled transmissions misreading one letter as another.
Georges Painvin solved important ADFGX traffic in 1918 and then attacked its six-symbol extension, ADFGVX. Recovering particular keys required suitable intercepted material and sustained analysis; it was not a guaranteed solution to every message.
Step 1: keyed 5×5 square, keyword PRIVACY (I/J share a cell)
A D F G X
A P R I V A
D C Y B D E
F F G H K L
G M N O Q S
X T U W X Z
Coordinates are row, then column.
Each letter → pair from {A,D,F,G,X}
H → FF E → DX L → FX
Step 2: Columnar transposition with keyword
Write pairs in rows, read by column order
HELLO → FF DX FX FX GF
Column key: G E R M A N
F F D X F X
F X G F
Read A,E,G,M,N,R columns → F FX FF XF X DG
Final ciphertext: FFXFFXFXDG
Painvin used relationships among intercepted messages and hypotheses about their structure to recover keys. The work required suitable traffic, not a guaranteed attack from one short message. His own later account distinguishes particular recovered keys from a universal break of all ADFGX traffic.
| Concept from ADFGX Cipher | Modern Evolution |
|---|---|
| Polybius substitution → columnar transposition | AES combines substitution, row shifting, linear column mixing and round-key addition; the final round omits MixColumns |
| 5-letter output alphabet (A,D,F,G,X) | Compare a restricted output alphabet with the binary encodings used by digital systems |
| Field-usable design | Hardware cipher implementations optimize for speed and resource constraints |
| Exhibit | 20 of 172 |
| Era | WWI · March 1918 |
| Trust | Broken |
| Inventor | Fritz Nebel · German Army |
| Year | March 1918 |
| Key Type | Polybius key square + columnar key |
| Broken By | Georges Painvin and Allied analysts · 1918 |