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Cryptology

Transposition Ciphers
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General Definition

Transposition ciphers don't transform the plaintext letters but rearrange (or permute) them. There are two basic methods:

  1. Aperiodic transposition: A text of length r is transformed by a permutation of length r.
  2. Periodic transposition: A text of arbitrary length is partitioned into blocks of length l – the last one padded with any letters if necessary – and each of these blocks is transformed by the same permutation.

Examples: 1. An aperiodic example is provided by the spiral [Spiral] The plaintext is written along the path, and the ciphertext is read off by rows.

                                         ISOPSN
                                         TPANAA
This is an aperiodic transposition. ---> IEHTSR ---> ISOPS NTPAN AAIEH TSROR ISITN IODIC
                                         ORISIT
                                         NIODIC

2. For a periodic transposition we take the period l = 5 and let the permutation defined by the keyword APPLE the alphabetic order of whose letters is (14532).

This is a periodic transposition. ---> THISI SAPER IODIC TRANS POSIT IONXX
                                       TSIIH SERPA IICDO TNSAR PITSO IXXNO

Properties

+Transposition breaks patterns in the plaintext.
+In general there is no unique cryptanalytic solution because each string has a lot of anagrams.
–Letter frequencies, MFL score, LW score, and coincidence index φ are invariant.
–This observation easily reveals the encryption method.

For a compehensive treatment of transposition ciphers and their cryptanalysis consult the books by F. L. Bauer, Gaines, Sinkov, and Nichols (Vol. II), see the reference list.

The earliest known hostorical appearances of transposition ciphers are the Scytale used by the Spartans and the work by AL-KINDI about 850.

Author: Klaus Pommerening, 2000-Jan-21; last change: 2014-Jul-22.