Computer Security and Cryptography

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 128^N 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 . We suppose the length n of plaintext x = (x₀, x₁,…, x_n−1) is a multiple of N; various modifications are possible when n ≠ kN and will be mentioned later. x is divided into N-grams whose components are integers in :

The Hill encipherment of ASCII plaintext x denoted by

is defined by

where

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