Transposition Ciphers - Columnar and Block Transpositions

Cryptology

The Similarity Between Columnar and Block Transpositions

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Example

The permutation (2413) transforms the text

  Vom Eise befreit sind Strom und Baeche

via the columnar transposition scheme

  2 4 1 3
  V O M E
  I S E B
  E F R E
  I T S I
  N D S T
  R O M U
  N D B A
  E C H E

into the ciphertext

  MERSS MBHVI EINRN EEBEI TUAEO SFTDO DC

If we write the latter in columns instead of rows—that is we go to the transposed mtrix—, we get the scheme

  M V E O
  E I B S
  R E E F
  S I I T
  S N T D
  M R U O
  B N A D
  H E E C

This is a block transposition of the plaintext of blocklength 4. Breaking it is trivial with a known plaintext of length at least 4. (For example there is only one possible position of the probable word Strom.)

Mathematical Description

As usual the mathematical description is a way of concealing the simplicity of this method that is very easily understood from the example. But it also leads to deeper insight (at least we hope so).

This is provided as PDF file. Content:

Permutation Matrices
Description of Block Transpositions by Matrices
Description of Columnar Transpositions by Matrices

Author: Klaus Pommerening, 2000-Jan-22; last change: 2014-Jul-24.