Transposition (cryptography)

In cryptography , transposition is one of the two basic classes of encryption . The characters of a message (of the plain text ) are rearranged . Each character remains unchanged, but the position at which it stands is changed. This is in contrast to the class of ( monoalphabetic or polyalphabetic ) substitution , in which each character in the plain text retains its place, but is replaced ("substituted") by another character.

method

For example, a word with only three letters (“from”) can only be rearranged (“ permuted ”) in six different ways , namely: from, asu, uas, usa, sua, sau . However, with the length of the character string, the number of possible arrangements increases more than exponentially .

A random transposition of longer strings creates a relatively high degree of security, but a recipient is faced with the same puzzle as a possible eavesdropper, namely how to decipher the encrypted message (see also: anagram ). Therefore, manageable systems of transposition must be agreed - these are called regulated transpositions .

Every transposition can be traced back to a polyalphabetic substitution . To do this, the Hill cipher is used with a permutation matrix of the size that contains exactly one one in each row and each column and only zeros otherwise. This results in an image that is identical to the original transposition. ${\displaystyle n\times n}$

example

The “garden fence” transposition should serve as a very simple and clear example of a regulated transposition: The letters of the text are written alternately on two lines, so that the first on the upper, the second on the lower, the third letter again on the at the top and so on. Finally, the character string of the lower line is added to that of the upper line:

A really confusing garden fence , in capital letters A REALLY CONFUSING GARDEN FENCE is encoded:

E  N  I  K  I  H  E  W  R  E  D  R  A  T  N  A  N
 I  W  R  L  C  V  R  I  R  N  E  G  R  E  Z  U

ENIKIHEWREDRATNAN IWRLCVRIRNEGREZU  - the encryption by transposition is done. The recipient can decrypt the message by simply reversing the procedure, i.e. rewriting the two blocks of characters in two lines.

See also

• Column transposition
• Seriation
• Skytale
• Fleissner stencil
• ADFGX

literature

• Friedrich L. Bauer : Deciphered Secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin et al. 2000, ISBN 3-540-67931-6 .
• Simon Singh : Secret Messages . The art of encryption from antiquity to the times of the Internet (= dtv 33071). Deutscher Taschenbuch-Verlag, Munich 2001, ISBN 3-42333-071-6 .

Individual evidence

1. ↑ Friedrich L. Bauer: Deciphered secrets. Methods and maxims of cryptology. 3rd, revised and expanded edition. Springer, Berlin et al. 2000, p. 46 ff.