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Computer Security and Cryptography by Alan G. Konheim

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3.8 HILL ENCIPHERMENT OF ASCII N-GRAMS

Monoalphabetic encipherment of N-grams of ASCII plaintext with N > 1 is attractive for two reasons:

  1. The probability distribution of N-grams with N ≈ 4 is much flatter than for 1-grams, making it harder to recognize letter fragments; and
  2. There is a very large number 128N of N-grams with N ≥ 4.

Lester Hill [1929] described a simple and elegant way to encipher N-grams of ASCII plaintext. Each character will be identified by its ordinal position in the ASCII character alphabet, integers in image. We suppose the length n of plaintext x = (x0, x1,…, xn−1) is a multiple of N; various modifications are possible when nkN and will be mentioned later. x is divided into N-grams whose components are integers in image:

image

The Hill encipherment of ASCII plaintext x denoted by

image

is defined by

image

image

where

and A = (ai,j) is an N × N matrix with entries in and which is invertible. ...

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