Editing XOR cipher (section)

== Usefulness in cryptography ==
The primary reason XOR is so useful in cryptography is because it is "perfectly balanced"; for a given plaintext input 0 or 1, the ciphertext result is equally likely to be either 0 or 1 for a truly random key bit.{{sfn | Paar | Pelzl | 2009|pp=32–34}}

The table below shows all four possible pairs of plaintext and key bits. It is clear that if nothing is known about the key or plaintext, nothing can be determined from the ciphertext alone.{{sfn | Paar | Pelzl | 2009|pp=32–34}}
{| class="wikitable"
|+XOR Cipher Trace Table
!Plaintext
!Key
!Ciphertext
|-
|0
|0
|0
|-
|0
|1
|1
|-
|1
|0
|1
|-
|1
|1
|0
|}
Other logical operations such and [[Logical conjunction|AND]] or [[Logical disjunction|OR]] do not have such a mapping (for example, AND would produce three 0's and one 1, so knowing that a given ciphertext bit is a 0 implies that there is a 2/3 chance that the original plaintext bit was a 0, as opposed to the ideal 1/2 chance in the case of XOR){{efn|name=3ways}}