In cryptography, the ADFGVX cipher was a field cipher used by the German Army during World War I. ADFGVX was in fact an extension of an earlier cipher called ADFGX. Invented by Colonel Fritz Nebel and introduced in March 1918, the cipher was a fractionating transposition cipher which combined a modified Polybius square with a single columnar transposition. The cipher is named after the six possible letters used in the ciphertext: A, D, F, G, V and X.

 Contents

Suppose we need to send the plaintext message, "Attack at once". First, a secret mixed alphabet is filled into a 5 × 5 Polybius square, like so:

A D F G X
A b t a l p
D d h o z k
F q f v s n
G g j c u x
X m r e w y

i and j have been combined, to make the alphabet fit in a 5 × 5 grid. The labels of the columns and rows were chosen simply as characters which were difficult to confuse in the Morse code, to minimise errors in transmission.

Using this square, the message is converted to fractionated form:

```A  T  T  A  C  K  A  T  O  N  C  E
```

Next, the fractionated message is subject to a transposition similar to (but not quite the same as) the standard columnar. We write out the message in rows under a transposition key:

```C A R G O
_________
A F A D A
D A F G F
D X A F A
D D F F X
G F X F X
```

Then read it is off in columns, in keyword order, yielding the ciphertext:

```FAXDF ADDDG DGFFF AFAXX AFAFX
```

In practice, the transposition keys were about two dozen characters long. Both the transposition keys and fractionation keys were changed daily.

In June 1918, an additional letter, V, was added to the cipher. This expanded the grid to 6 × 6, allowing 36 characters to be used. This allowed the full alphabet (instead of combining I and J), plus the digits from 0 to 9. This mainly had the effect of considerably shortening messages which contained a large number of figures.

### Cryptanalysis

ADFGVX was cryptanalysed by French Army Lieutenant Georges Painvin. The work was exceptionally difficult by the standards of classical cryptography, and Painvin became physically ill during it. His method of solution relied on finding messages with stereotyped beginnings, which would fractionate the same, then form similar patterns in the positions in the ciphertext that had corresponded to column headings in the transposition table. (Considerable statistical analysis was required after this step had been reached — all done by hand.)

This meant it was only effective during times of very high traffic — but, fortunately for the cryptanalysts, that was also when the most important messages were sent.

## References

• Friedman, William F. Military Cryptanalysis, Part IV: Transposition and Fractionating Systems. Laguna Hills, CA: Aegean Park Press, 1992.
• General Solution of the ADFGVX Cipher System, J. Rives Childs, Aegean Park Press, ISBN 0894122843

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