Editing Involution (mathematics) (section)

=== Computer science ===
The [[XOR]] [[bitwise operation]] with a given value for one parameter is an involution on the other parameter. XOR [[Mask (computing)|masks]] in some instances were used to draw graphics on images in such a way that drawing them twice on the background reverts the background to its original state.

Two special cases of this, which are also involutions, are the [[bitwise NOT]] operation which is XOR with an all-ones value, and [[stream cipher]] [[encryption]], which is an XOR with a secret [[keystream]].

This predates binary computers; practically all mechanical cipher machines implement a [[reciprocal cipher]], an involution on each typed-in letter.
Instead of designing two kinds of machines, one for encrypting and one for decrypting, all the machines can be identical and can be set up (keyed) the same way.<ref>{{cite book
 |title=Classical Cryptology
 |first=Greg |last=Goebel
 |chapter-url=http://vc.airvectors.net/ttcode_05.html
 |chapter=The Mechanization of Ciphers
 |year=2018
}}</ref>

Another involution used in computers is an order-2 bitwise permutation.  For example. a color value stored as integers in the form {{math|(''R'', ''G'', ''B'')}}, could exchange {{math|''R''}} and {{math|''B''}}, resulting in the form {{math|(''B'', ''G'', ''R'')}}: {{math|1=''f''(''f''(RGB)) = RGB, ''f''(''f''(BGR)) = BGR}}.