Editing ADFGVX cipher (section)

== Cryptanalysis ==

ADFGVX was [[cryptanalysis|cryptanalysed]] by [[France|French]] Army [[Lieutenant]] [[Georges Painvin]], and the cipher was broken in early June 1918.<ref>{{cite book|last=Newton|first=David E.|title=Encyclopedia of Cryptography|year=1997|publisher=Instructional Horizons, Inc|location=Santa Barbara California|pages=6}}</ref> The work was exceptionally difficult by the standards of classical cryptography, and Painvin became physically ill during the process. His method of solution relied on finding messages with stereotyped beginnings, which would fractionate them and 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 that step had been reached, all done by hand.) It was thus effective only during times of very high traffic, but that was also when the most important messages were sent.

However, that was not the only trick that Painvin used to crack the ADFGX cipher.<ref name = "WWI_Codebreaking"/> He also used repeating sections of ciphertext to derive information about the likely length of the key that was being used. Where the key was an even number of letters in length he knew, by the way the message was enciphered, that each column consisted entirely of letter coordinates taken from the top of the Polybius Square or from the left of the Square, not a mixture of the two. Also, after substitution but before transposition, the columns would alternately consist entirely of "top" and "side" letters. One of the characteristics of frequency analysis of letters is that while the distributions of individual letters may vary widely from the norm, the [[law of averages]] dictates that groups of letters vary less. With the ADFGX cipher, each "side" letter or "top" letter is associated with five plaintext letters. In the example above, the "side" letter "D" is associated with the plaintext letters "d h o z k", and the "top" letter "D" is associated with the plaintext letters "t h f j r". Since the two groups of five letters have different cumulative frequency distributions, a frequency analysis of the "D" letter in columns consisting of "side" letters has a distinctively different result from those of the "D" letter in columns consisting of "top" letters. That trick allowed Painvin to guess which columns consisted of "side" letters and which columns consisted of "top" letters. He could then pair them up and perform a frequency analysis on the pairings to see if the pairings were only noise or corresponding to plaintext letters. Once he had the proper pairings, he could then use frequency analysis to figure out the actual plaintext letters. The result was still transposed, but to unscramble a simple transposition was all that he still had to do. Once he determined the transposition scheme for one message, he would then be able to crack any other message that was enciphered with the same transposition key.<ref name="WWI_Codebreaking"/>

Painvin broke the ADFGX cipher in April 1918, a few weeks after the Germans launched their [[German spring offensive|Spring Offensive]]. As a direct result, the French army discovered where [[Erich Ludendorff]] intended to attack. The French concentrated their forces at that point, which has been claimed to have stopped the Spring Offensive.

However, the claim that Painvin's breaking of the ADFGX cipher stopped the [[German spring offensive]] of 1918, while frequently made,<ref>"Painvin's manna had saved the French", wrote [[David Kahn (writer)|David Kahn]], in ''The Codebreakers - The Story of Secret Writing'', 1967, {{ISBN|978-0-684-83130-5}}, Chapter 9. Kahn also details the role that Painvin's decryption of German messages played in the French response to [[German spring offensive#Gneisenau|Operation Gneisenau]].</ref> is disputed by some. In his 2002 review of [[Sophie de Lastours]]' book on the subject, ''La France gagne la guerre des codes secrets 1914-1918'', in the [[Journal of Intelligence History]], ([https://web.archive.org/web/20060428005221/http://www.intelligence-history.org/jih/reviews-2-2.html ''Journal of Intelligence History'': volume 2, Number 2, Winter 2002)]  Hilmar-Detlef Brückner stated:

<blockquote>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.

Its aim had to be grossly exaggerated, which the German High Command did by spreading rumors that the attack was heading for Paris and beyond; the disinformation was effective and apparently still is. However, the German offensive was not successful because the French had enough reserves at hand to stop the assault and so did not need to bring in additional reinforcements.

Moreover, it is usually overlooked that the basic version of the ADFGVX cipher had been created especially 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, which happened.

Telegrams in ADFGX appeared for the first time on 5 March, and 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.</blockquote>

The ADFGX and ADFGVX ciphers are now regarded as insecure.