Transposition Cipher

Transposition cipher is the name given to any encryption that involves rearranging the plain text letters in a new order.

However, in the literature, the term transposition cipher is generally associated with a subset: columnar transposition (or rectangular transposition) which consists of writing the plain message in a table / grid / rectangle, then arranging the columns of this table according to a defined permutation.

The permutation key is a series of numbers (often generated from a word) which indicates in which order to arrange the columns.

Example: The word KEY makes the permutation 2,1,3 :

In particular, the columnar transposition cipher consists to write a message in a table of width N (with N, the size of the permutation), row by row (or column by column), to permute the columns according to the order of the key and read the result in columns (or by lines).

Example: Encrypt MESSAGE by columnar transposition with the key CODE (permutation 1,3,4,2) gives MASESEG (writing in rows and reading the table by columns)

Some variants consist in reading the table in rows and not in columns, in this case, the encrypted message with a reading in column would be MSSEAEG.

If the grid contains empty boxes, it is possible to complete them with a neutral letter X (or other more frequent letter) in order to facilitate manual decryption.

Transposition cipher decryption is identical to encryption except that the order of the columns is changed/reversed.

If the message has a length (number of characters) which is not a multiple of the size of the permutation, then it is necessary to pre-calculate the position of the empty boxes in the grid (by simulating a filling similar to encryption).

Example: A permutation 2,1,3 has been used to get the message CDOEDX (read by row):

Example: The plain text is DCODEX.

If the message was read in columns, first write the table by columns

Example: A permutation 2,1,3 has been used to get the message CEDDOX (read by column):

Example: The plain text is DCODEX.

The message consists of the letters of the original message but in a different order.

The index of coincidence is identical to that of the one of the language of the plaintext.

It is possible to test all the permutations if the key is not too long, but the most effective method is to have or try to guess a word from the plain text and to deduce the permutations of the columns.

If the encrypted message is composed of very few words (1, 2 or 3) then an anagram solver can make it possible to find them.

The transposition cipher is, along with the substitution cipher, one of the most used bricks for more elaborate ciphers. There are dozens of ciphers that use it like ADFGVX, Amsco, Double Transposition, Redefence, etc.

The empty squares of the grid introduce an additional difficulty, rather time-consuming, when deciphering. Because the receiver of the message must calculate the position of these, which requires among other things, to count the number of characters of the message. If the empty boxes are not completed and the pre-calculation is not done, errors could appear in the reorganization of certain letters (especially the last ones).