Editing Transposition cipher (section)

== Double transposition ==
A single columnar transposition could be attacked by guessing possible column lengths, writing the message out in its columns (but in the wrong order, as the key is not yet known), and then looking for possible [[anagram]]s. Thus to make it stronger, a double transposition was often used. This is simply a columnar transposition applied twice. The same key can be used for both transpositions, or two different keys can be used.

=== Visual demonstration of double transposition ===
In the following example, we use the keys '''JANEAUSTEN''' and '''AEROPLANES''' to encrypt the following plaintext: "'''Transposition ciphers scramble letters like puzzle pieces to create an indecipherable arrangement."'''<gallery perrow="5">
File:Transposition step 1.png|'''Step 1:''' The plaintext message is written into the first grid (which has the key JANEAUSTEN).
File:Transposition step 1.5.png|The columns are read off in alphabetical order according to the key, into the next grid (see step 2).
File:Transposition step 2.png|'''Step 2:''' The columns from step 1 are written into the second grid (which has the key AEROPLANES).
File:Transposition step 2.5.png|The columns are read off in alphabetical order according to the key, into the next grid (see step 3).
File:Transposition step 3.png|'''Step 3:''' The ciphertext is often written out in blocks of 5, e.g. '''RIAES NNELI EEIRP''' etc.
</gallery>The colors show how the letters are scrambled in each transposition step. While a single step only causes a minor rearrangement, the second step leads to a significant scrambling effect if the last row of the grid is incomplete.

=== Another example ===
As an example, we can take the result of the irregular columnar transposition in the previous section, and perform a second encryption with a different keyword, {{mono|STRIPE}}, which gives the permutation "564231":
 5 6 4 2 3 1 
 E V L N A C
 D T E S E A
 R O F O D E
 E C W I R E
 E

As before, this is read off columnwise to give the ciphertext:

 CAEEN SOIAE DRLEF WEDRE EVTOC

If multiple messages of exactly the same length are encrypted using the same keys, they can be anagrammed simultaneously.  This can lead to both recovery of the messages, and to recovery of the keys (so that every other message sent with those keys can be read).

During [[World War I]], the German military used a double columnar transposition cipher, changing the keys infrequently. The system was regularly solved by the French, naming it Übchi, who were typically able to quickly find the keys once they'd intercepted a number of messages of the same length, which generally took only a few days. However, the French success became widely known and, after a publication in ''[[Le Matin (France)|Le Matin]]'', the Germans changed to a new system on 18 November 1914.<ref>Kahn, pp. 301-304.</ref>

During World War II, the double transposition cipher was used by [[Netherlands in World War II#Oppression and resistance|Dutch Resistance]] groups, the French [[Maquis (World War II)|Maquis]] and the British [[Special Operations Executive]] (SOE), which was in charge of managing underground activities in Europe.<ref>Kahn, pp. 535 and 539.</ref> It was also used by agents of the American [[Office of Strategic Services]]<ref>Kahn, p. 539.</ref> and as an emergency cipher for the German Army and Navy.

Until the invention of the [[VIC cipher]], double transposition was generally regarded as the most complicated cipher that an agent could operate reliably under difficult field conditions.

=== Cryptanalysis ===

The double transposition cipher can be treated as a single transposition with a key as long as the product of the lengths of the two keys.<ref>{{cite book |last1=Barker |first1=Wayne |title=Cryptanalysis of the Double Transposition Cipher: Includes Problems and Computer Programs |date=1995 |publisher=Aegean Park Press}}</ref>

In late 2013, a double transposition challenge, regarded by its author as undecipherable, was solved by George Lasry using  a divide-and-conquer approach where each transposition was attacked individually.<ref>{{cite journal |first=George |last=Lasry |title=Solving the Double Transposition Challenge with a Divide-and-Conquer Approach |date=2014-06-13 |journal= Cryptologia|volume = 38|issue=3 |pages=197–214 |doi=10.1080/01611194.2014.915269 |s2cid=7946904 }}</ref>