Ciphers

An encryption algorithm ($e$), also called a cipher, transforms a plaintext ($m$) into a ciphertext ($c$) under the control of a secret key ($k$).

The reverse process, decryption ($d$) or decipherment, recovers the plaintext:

Secret Key

The secrecy of plaintext $m$ is totally dependent on the secrecy of the key $k$.

Algorithms with this property are called symmetric cryptosystems or secret key cryptosystems. Both parties to a secret communication must know $k$ and keep it secret.

Security also depends on Kerckhoffs’s principle, covered in a dedicated note, for what a cryptosystem may safely assume is public.

Categorization

Ciphers are classified along several axes, not mutually exclusive. A modern cipher often falls into multiple categories at once.

Classical Ciphers

The ciphers used in the pre-computer era are called historical ciphers or classical ciphers.

Historical ciphers used plaintext linked to:

• A particular language.
• The alphabet of symbols or characters used.
• The peculiar statistical characteristics of the language.

For English:

• A 26 character alphabet (A to Z).
• Higher usage of characters e, t, a, o, i.
• Higher appearance of bigrams (th, he, an, in) and trigrams (the, ing, and, her, ere).

Mono-alphabetic Ciphers

A plaintext character is replaced with a ciphertext character according to a fixed rule.

Preserves the language’s statistical characteristics in the ciphertext.

The shift and substitution ciphers are examples of mono-alphabetic ciphers.

Poly-alphabetic Ciphers

Uses multiple substitution alphabets, e.g. one alphabet for odd-numbered positions and a different one for even-numbered positions, flattening the character frequency graph.

Using $n$ alphabets in a poly-alphabetic cipher gives a key space of $(26!)^n$ at the cost of remembering a key of length $26n$ characters.