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.

An example of a balanced boolean function is the function that assigns a 1 to every even number and 0 to all odd numbers (likewise the other way around). The same applies for functions assigning 1 to all positive numbers and 0 otherwise.

A Boolean function of n bits is balanced if it takes the value 1 with probability 1⁄2.

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