Substitutions and Permutations

Related Concepts

Alphabet; Encryption; Symmetric Cryptosystem

Definition

A substitution cipher is usually described by a sequence or list of single substitutions, each of which is commonly denoted by an arrow, like p ↦π.

Example: The Russian-English ISO transliteration (using diacritical marks) is a substitution.

A substitution may have homophones (Encryption).

A permutation is a one-to-one mapping from an alphabet to itself.

A substitution may be described by two lines: the first one being the standard alphabet and the second one being a mixed alphabet (Alphabet). An example is given below:

Note that small letters are used for the plaintext and capital letters for the ciphertext.

In mathematics, there is a commonly used, simplified notation with two lines bracketed together:

This is convenient for encryption. For decryption, it is worth while to rearrange the list:

or

There is also the cycle notation which is shorter

$$(\textrm{ a}\,\textrm{ b}\,\textrm{ e}\,\textrm{ i}\,\textrm{...