# Number of terms in Balanced boolean functions?

I know that balanced boolean functions are required for creating S-boxes. I want to create four balanced Boolean functions for 4X4 Sbox and as far as I’ve understood, the maximum order of the balanced Boolean function should be <= (number of var)/2.

But… how many terms should there be in my boolean functions?

• is the answer satisfactory? – kodlu Nov 2 '16 at 22:28

You can represent such an Sbox as a mapping from $GF(2^4)$ to itself as well as a univariate polynomial mapping from $GF(2)^4$ to itself and what's sparse or simple in one representation can be complex in the other.