Cryptography

4 Symmetric CipheringHistorical Ciphers

Shift and substitution ciphers have been used for written text transmission and dominated the art of secret writing for at least two millenniums (and maybe more). The most known historical ciphers in this category, include Caesar’s, Vigenere’s, affine, OTP, and Enigma ciphers. With the advent of computers, shift and substitution ciphering were abandoned, because it has become easy to break them. However, it is important to learn them since they had inspired the modern cryptography. The material below is mostly collected from [1–5].

4.1 Definitions

Definition 4.1 Alphabet: it is a set of elements, which may be letters, words, or any other form of bit strings that are used to generate plaintexts and ciphertexts.

In the sequel, the alphabet elements are either Latin letters or bits.

Definition 4.2 Substitution cipher: it is a cipher in which an alphabet element is replaced by another alphabet element to yield a ciphertext.

Definition 4.3 Shift cipher: it is a special type of substitution cipher in which a letter is replaced by another letter located a few positions away.

Definition 4.4 Monoalphabetic cipher: it is a cipher in which the letters of the plaintext are mapped to ciphertext letters based on a single substitution key and each letter is always replaced by the same letter. The transformation is bijective.

Definition 4.5 Polyalphabetic cipher: it is a cipher, which makes use of multiple alphabets and a letter may be replaced by ...