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.

Contents

1 Rail fence 2 Route cipher 3 Columnar transposition 4 Double transposition 5 Disrupted transposition 6 Detection and cryptanalysis 7 Combinations 8 Fractionation 9 See also

Rail fence

In the rail fence cipher, the plaintext is written downwards on successive "rails" of an imaginary fence, starting a new column when we get to the top. 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.

   [ WEAREDISCOVEREDFLEEATONCEXPDQ ]

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 [1] (http://pages.cthome.net/fwc/CODE.HTM) and [2] (http://www.vectorsite.net/ttcode3.html#m3) for examples.

Columnar transposition

The standard columnar transposition consists of writing the key out as column headers, then writing the message out in successive rows beneath these headers (filling in any spare spaces with nulls), finally, the message is read off in columns, in alphabetical order of the headers. For example suppose we have a key of 'ZEBRAS' and a message of 'WE ARE DISCOVERED. FLEE AT ONCE'. We start with:

Z E B R A S
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 

Then read it off as:

EVLNE ACDTK ESEAQ ROFOJ DEECU 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, with two different keys of different (preferably relatively prime) length. Double transposition was generally regarded as the most complicated cipher that an agent could operate reliably under difficult field conditions. It was in actual use at least as late as World War II (e.g. see poem code).

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.

See also

• Permutation cipher
• Substitution cipher
• Topics in cryptography

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