Balanced boolean function

In mathematics and computer science, a balanced boolean function is a boolean function whose output yields as many 0s as 1s over its 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 of the input bits.

Usage

Balanced boolean functions are primarily used in cryptography. If a function is not balanced, it will have a statistical bias, making it subject to cryptanalysis such as the correlation attack.

See also

• Bent function

References

• Balanced boolean functions that can be evaluated so that every input bit is unlikely to be read, Annual ACM Symposium on Theory of Computing