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In [[Mathematics|mathematics]] and [[Computer science|computer science]], a '''balanced boolean function''' is a [[Boolean function|boolean function]] whose output yields as many '''0'''s as '''1'''s over its [[Domain of a function|input set]]. This means that for a uniformly random input string of bits, the probability of getting a '''1''' is 1/2.
Examples of balanced boolean functions are the function that copies the first bit of its input to the output,
and the function that produces the [[Exclusive or|exclusive or]] of the input bits.

== Usage ==
Balanced boolean functions are primarily used in [[Cryptography|cryptography]].  If a function is not balanced, it will have a statistical bias, making it subject to [[Cryptanalysis|cryptanalysis]] such as the [[Correlation attack|correlation attack]].

== See also ==
* [[Bent function]]

== References ==
* [http://portal.acm.org/citation.cfm?id=1060627 Balanced boolean functions that can be evaluated so that every input bit is unlikely to be read], Annual ACM Symposium on Theory of Computing

[[Category:Boolean algebra]]


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