ADFGVX cipher

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. These letters were chosen deliberately because they sound very different from each other when transmitted via Morse code. The intention was to reduce the possibility of operator error.

[edit] Operation of ADFGX

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:

i and j have been combined, to make the alphabet fit into a 5 × 5 grid.

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

A  T  T  A  C  K  A  T  O  N  C  E
AF AD AD AF GF DX AF AD DF FX GF XF

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 (here, "CARGO"):

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

Next, we alphabetize (or otherwise sort) the letters in the transposition key (changing CARGO to ACGOR), rearranging the columns beneath the letters along with the letters themselves:

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

Then it is read 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.

[edit] ADFGVX

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.

[edit] 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.

Painvin broke the ADFGX cipher in April 1918, a few weeks after the Germans launched their Spring Offensive. As a direct result, the French army discovered where Ludendorff intended to attack. The French concentrated their forces at that point and stopped the Spring Offensive.

The ADFGX and ADFGVX ciphers are now regarded as insecure for any purpose.

Note: the claim that Painvin's breaking of the ADFGX cipher stopped the German Spring Offensive of 1918, while frequently made,^[1] is disputed by some. In his 2002 review of Sophie de Lastours' book on this subject, La France gagne la guerre des codes secrets 1914-1918, in the Journal of Intelligence History, (Journal of Intelligence History: volume 2, Number 2, Winter 2002) Hilmar-Detlef Brückner states:

Regrettably, Sophie de Lastours subscribes to the traditional French view that the solving of a German ADFGVX-telegram by Painvin at the beginning of June 1918 was decisive for the Allied victory in the First World War because it gave timely warning of a forthcoming German offensive meant to reach Paris and to inflict a critical defeat on the Allies. However, it has been known for many years, that the German Gneisenau attack of 11 June was staged to induce the French High Command to rush in reserves from the area up north, where the Germans intended to attack later on. To achieve this, its aim had to be grossly exaggerated. This the German High Command did by spreading rumors that the attack was heading for Paris and beyond; disinformation proved effective then - and apparently still does. But the German offensive was not successful because the French had a sufficient number of reserves at hand to stop the assault and did not need to bring in additional reinforcements. Moreover, it is usually overlooked that the basic version of the ADFGVX cipher had been particularly created for the German spring offensive in 1918, meant to deal the Allies a devastating blow. It was hoped that the cipher ADFGX would protect German communications against Allied cryptographers during the assault and this is what it indeed did. Telegrams in ADFGX appeared for the first time on 5 March, the German attack started on 21 March. When Painvin presented his first solution of the code on 5 April, the German offensive had already petered out.

[edit] Other uses

Although the ADFGVX is moot technologically and cryptographically, if the cipher is taken as a predecessor for a mechanical cipher machine or a cipher implemented in software then it still remains useful. An ADFGVX style tableau has billions of variations if a 7x7 size is chosen. The resulting diagraphs can be fed into a software Enigma (that does not support enciphering numbers) analog increasing its cryptographical power. By choosing different tableaus it is possible to allow Enigma style traffic to continue to be transmitted, but making the traffic more difficult to break.

[edit] Notes

[edit] External links

• Implementation of ADFGVX in JavaScript

[edit] 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 0-89412-284-3