Editing Playfair cipher (section)

== Description ==
[[Image:Charles Wheatstone - Project Gutenberg etext 13103.jpg|thumbnail|left|The Playfair system was invented by [[Charles Wheatstone]], who first described it in 1854.]]
The Playfair cipher uses a 5 × 5 table containing a [[Key (cryptography)|key word or phrase]]. Memorization of the keyword and 4 simple rules was all that was required to create the 5 by 5 table and use the cipher.

To generate the key table, one would first fill in the spaces in the table (a modified [[Polybius square]]) with the letters of the keyword (dropping any duplicate letters), then fill the remaining spaces with the rest of the letters of the alphabet in order (usually omitting "J" or "Q" to reduce the alphabet to fit; other versions put both "I" and "J" in the same space). The key can be written in the top rows of the table, from left to right, or in some other pattern, such as a spiral beginning in the upper-left-hand corner and ending in the center.  The keyword together with the conventions for filling in the 5 by 5 table constitute the cipher key.

To encrypt a message, one would break the message into digrams (groups of 2 letters) such that, for example, "HelloWorld" becomes "HE LL OW OR LD". These digrams will be substituted using the key table. Since encryption requires pairs of letters, messages with an odd number of characters usually append an uncommon letter, such as "X", to complete the final digram. The two letters of the digram are considered opposite corners of a rectangle in the key table. To perform the substitution, apply the following 4 rules, in order, to each pair of letters in the plaintext:

#If both letters are the same (or only one letter is left), add an "X" after the first letter. Encrypt the new pair and continue. Some variants of Playfair use "Q" instead of "X", but any letter, itself uncommon as a repeated pair, will do.
#If the letters appear on the same row of your table, replace them with the letters to their immediate right respectively (wrapping around to the left side of the row if a letter in the original pair was on the right side of the row).
#If the letters appear on the same column of your table, replace them with the letters immediately below respectively (wrapping around to the top side of the column if a letter in the original pair was on the bottom side of the column).
#If the letters are not on the same row or column, replace them with the letters on the same row respectively but at the other pair of corners of the rectangle defined by the original pair. The order is important – the first letter of the encrypted pair is the one that lies on the same '''row''' as the first letter of the plaintext pair.

To decrypt, use the ''inverse'' (opposite) of the two shift rules, selecting the letter to the left or upwards as appropriate. The last rule remains unchanged, as the transformation switches the selected letters of the rectangle to the opposite diagonal, and a repeat of the transformation returns the selection to its original state. The first rule can only be reversed by dropping any extra instances of the chosen insert letter — generally  "X"s or "Q"s — that do not make sense in the final message when finished.

There are several minor variations{{which|date=November 2022}} of the original Playfair cipher.<ref>{{harvnb|Gaines|1956|page=201}}</ref>