Computer Security and Cryptography

3.1 MONOALPHABETIC SUBSTITUTION

A monoalphabetic substitution T : x = (x₀, x₁,…, x_n−1) → y = (y₀, y₁,…, y_n−1) on plaintext with letters in the alphabet is a rule specifying the substitute θ(x_i) for the letter x_i. Here θ = (θ(0), θ(1),…, θ(m − 1)) is a permutation on the letters in the alphabet

We begin by examining substitutions encipherment for plaintext written with letters in the alphabet of 26 Latin letters. Uppercase letters will be used to display plaintext and lowercase letters for ciphertext. As before, letters will also be referred to by their ordinal positions in the alphabet with m = 26. Even though there are 26! ≈ 4 × 10²⁶ different monoalphabetic substitutions on , approximately a key space of 80 bits, William Friedman [1944] estimated that the key would be determined by ∼25 characters of monoalphabetic ciphertext.

A monoalphabetic substitution may be specified in a substitution table such as Table 3.1. A key word provides a simple mnemonic to construct a substitution table. For example, the letter repetitions in GOODWORD are first deleted, yielding GODWR. The substitution ...