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Computer Security and Cryptography by Alan G. Konheim

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2.2 THE RULES OF COLUMNAR TRANSPOSITION ENCIPHERMENT

Columnar transposition (CT) uses a key consisting of

  • K1. A (columnar) width N, and
  • K2. A transposition τ = (τ0, τ1, …, τN−1), a permutation of the integers 0, 1, …, N−1.

The encipherment of the plaintext x = (x0, x1, …, xn−1) of length n = (r − 1)N + N (0 < N) proceeds in two steps:

  • CT1. The plaintext x = (x0, x1, …, xn−l) is read by rows into an array X of width N.

    image

  • CT2. The ciphertext y results when X is read out by columns, the order in which the columns are read out being specified by the transposition τ.

The ciphertext is the concatenation of segments corresponding to the columns of X

image

We use the notation y = TNτ(x) to denote that the plaintext x has been enciphered to the ciphertext y by the columnar transposition TN,τ with key (N, τ).

2.2.1 The Shape of X

If n = (r − 1)N + with 0 < N, then X is a possibly ragged array, where X has1

  1. image
  2. A final partial row of letters, if 0 < N;
  3. long columns, each containing image letters; and
  4. c = n short columns, each containing letters.

We write L(j) for the length of the ...

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