Transposition cipher

In classical cryptography, a transposition cipher changes one character from the plaintext to another (to decrypt the reverse is done). That is, the order of the characters is changed. Mathematically a bijective function is used on the characters' positions to encrypt and an inverse function to decrypt.

Following are some implementations.

Rail fence

In the rail fence cipher, the plaintext is written downwards on successive "rails" of an imaginary fence, starting a new column when the top is reached. The message is then read off in rows. For example, if we have 3 "rails" and a message of 'WE ARE DISCOVERED. FLEE AT ONCE', the cipherer writes out: W R I O R F E O E P E E S V E L A N J D A D C E D E T C X Q The extra odd letters at the end are "nulls", added to round off the pattern, or to confuse a cryptanalyst. Then reads off:

WRIOR FEOEP EESVE LANJD ADCED ETCXQ

(Grouping letters into blocks of a standard size, typically five, was a practice developed for ease of transmission by telegraph.) The rail fence cipher is not very strong; the number of practical keys is small enough that a cryptanalyst can try them all by hand. See also scytale

The easiest way to decipher a rail fence cipher is to use the following method:

1) First, run all the letters into a long string. WRIORFEOEPEESVELANJDADCEDETCXQ

2) Next, divide the string of letters into a number of even groups equal to the number of rails. WRIORFEOEP|EESVELANJD|ADCEDETCXQ Since there are 30 letters, and we know there are 3 rails, we divide the group into 3 groups of 10.

3) Finally, write down the first letter from group 1, from group 2, and group 3, followed by the second letter from group 1, group 2, and group 3, etc. WEAREDISCOVEREDFLEEATONCEJXPDQ

4) Now just break the string of letters into easily identifyable words, separate the nulls, and the code is deciphered.

Route cipher

In a route cipher, the plaintext is first written out in a grid of given dimensions, then read off in a pattern given in the key. For example, using the same plaintext and grid that we used for rail fence: W R I O R F E O E E E S V E L A N J A D C E D E T C X The key might specify "spiral inwards, clockwise, starting from the top right". That would give a cipher text of:

EJX CTE DEC DAE WRI ORF EON ALE VSE

(The clerk has broken this ciphertext up into blocks of three to help avoid errors).

Route ciphers have many more keys than a rail fence. In fact, for messages of reasonable length, the number of possible keys is potentially too great to be enumerated even by modern machinery. However, not all keys are equally good. Badly chosen routes will leave excessive chunks of plaintext, or text simply reversed, and this will give cryptanalysts a clue as to the routes.

An interesting variation of the route cipher was the Union Route Cipher, used by Union forces during the American Civil War. This worked much like an ordinary route cipher, but transposed whole words instead of individual letters. Because this would leave certain highly sensitive words exposed, such words would first be concealed by code. The cipher clerk may also add entire null words, which were often chosen to make the ciphertext humorous. See ^* for an example.

Columnar transposition

In a columnar transposition, the message is written out in rows of a fixed length, and then read out again column by column, and the columns are chosen in some scrambled order. Both the length of the rows and the permutation of the columns are usually defined by a keyword. For example, the word ZEBRAS is of length 6 (so the rows are of length 6), and the permutation is defined by the alphabetical order of the letters in the keyword. In this case, the order would be "6 3 2 4 1 5".

In a regular columnar transposition cipher, any spare spaces are filled with nulls; in an irregular columnar transposition cipher, the spaces are left blank. Finally, the message is read off in columns, in the order specified by the keyword. For example, suppose we use the keyword ZEBRAS and the message WE ARE DISCOVERED. FLEE AT ONCE. In a regular columnar transposition, we write this into the grid as: 6 3 2 4 1 5 W E A R E D I S C O V E R E D F L E E A T O N C E Q K J E U Providing five nulls (QKJEU) at the end. The ciphertext is then read off as: EVLNE ACDTK ESEAQ ROFOJ DEECU WIREE

In the irregular case, the columns are not completed by nulls: 6 3 2 4 1 5 W E A R E D I S C O V E R E D F L E E A T O N C E This results in the following ciphertext: EVLNA CDTES EAROF ODEEC WIREE

To decipher it, the recipient has to work out the column lengths by dividing the message length by the key length. Then he can write the message out in columns again, then re-order the columns by reforming the key word.

Columnar transposition continued to be used for serious purposes as a component of more complex ciphers at least into the 1950's.

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 anagrams. 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.

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, 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

During World War I, the German military used a double columnar transposition cipher. The system was regularly solved by the French, naming it Übchi, who were typically able to find the key in a matter of days after a new one had been introduced. However, the French success became widely-known and, after a publication in Le Matin, the Germans changed to a new system on 18 November 1914.

During World War II, the double transposition cipher was used by Dutch Resistance groups, the French Maquis and the British Special Operations Executive (SOE). It was also used as an emergency cipher for the German Army and Navy.

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

Disrupted transposition

In a disrupted transposition, certain positions in a grid are blanked out, and not used when filling in the plaintext. This breaks up regular patterns and makes the cryptanalyst's job more difficult.

Detection and cryptanalysis

Since transposition does not affect the frequency of individual symbols, simple transposition can be easily detected by the cryptanalyst by doing a frequency count. If the ciphertext exhibits a frequency distribution very similar to plaintext, it is most likely a transposition. This can then often be attacked by anagramming - sliding pieces of ciphertext around, then looking for sections that look like anagrams of English words, and solving the anagrams. Once such anagrams have been found, they reveal information about the transposition pattern, and can consequently be extended.

Simpler transpositions also often suffer from the property that keys very close to the correct key will reveal long sections of legible plaintext interspersed by gibberish. Consequently such ciphers may be vulnerable to optimum seeking algorithms such as genetic algorithms.

Combinations

Transposition is often combined with other techniques. For example, a simple substitution cipher combined with a columnar transposition avoids the weakness of both. Replacing high frequency ciphertext symbols with high frequency plaintext letters does not reveal chunks of plaintext because of the transposition. Anagramming the transposition does not work because of the substitution. The technique is particularly powerful if combined with fractionation (see below). A disadvantage is that such ciphers are considerably more laborious and error prone than simpler ciphers.

Fractionation

Transposition is particularly effective when employed with fractionation - that is, a preliminary stage that divides each plaintext symbol into several ciphertext symbols. For example, the plaintext alphabet could be written out in a grid, then every letter in the message replaced by its co-ordinates (see Polybius square). Another method of fractionation is to simply convert the message to Morse code, with a symbol for spaces as well as dots and dashes.

When such a fractionated message is transposed, the components of individual letters become widely separated in the message, thus achieving Claude E. Shannon's diffusion. Examples of ciphers that combine fractionation and transposition include the bifid cipher, the trifid cipher, the ADFGVX cipher and the VIC cipher.

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