Editing Caesar cipher (section)

==Example==
{{Wikifunctions|Z12812|Latin alphabet Caesar cipher}}
The transformation can be represented by aligning two alphabets; the cipher is the plain alphabet rotated left or right by some number of positions. For instance, here is a Caesar cipher using a left rotation of three places, equivalent to a right shift of 23 (the shift parameter is used as the [[key (cryptography)|key]]):

{{Aligned table|cols=27|class=wikitable|col1header=on
|  Plain|  A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z
|  Cipher| X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W
}}

When encrypting, a person looks up each letter of the message in the "plain" line and writes down the corresponding letter in the "cipher" line.
 
 Plaintext:  THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG
 Ciphertext: QEB NRFZH YOLTK CLU GRJMP LSBO QEB IXWV ALD

Deciphering is done in reverse, with a right shift of 3.

The encryption can also be represented using [[modular arithmetic]] by first transforming the letters into numbers, according to the scheme, A → 0, B → 1, ..., Z → 25.<ref>{{cite journal |last=Luciano |first=Dennis |author2=Gordon Prichett |date=January 1987 |title=Cryptology: From Caesar Ciphers to Public-Key Cryptosystems |journal=The College Mathematics Journal |volume=18 |issue=1 |pages=2–17 |doi=10.2307/2686311 |jstor=2686311 |citeseerx=10.1.1.110.6123 }}</ref> Encryption of a letter ''x'' by a shift ''n'' can be described mathematically as,<ref>{{cite book |title=Cryptology Unlocked |url=https://archive.org/details/Cryptology_Unlocked |last=Wobst |first=Reinhard |year=2001 |publisher=Wiley |isbn=978-0-470-06064-3 |page=19 }}</ref>

: <math>E_n(x) = (x + n) \mod {26}.</math>

Decryption is performed similarly,

: <math>D_n(x) = (x - n) \mod {26}.</math>

(Here, "mod" refers to the [[modulo operation]]. The value ''x'' is in the range 0 to 25, but if {{nowrap|''x'' + ''n''}} or {{nowrap|''x'' − ''n''}} are not in this range then 26 should be added or subtracted.)

The replacement remains the same throughout the message, so the cipher is classed as a type of ''[[monoalphabetic substitution]]'', as opposed to ''[[polyalphabetic substitution]]''.