Yet another algorithm to compute the nonlinearity of a Boolean function

Abstract

We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and computing its evaluation vector requires a worst-case complexity of $O(n2^n)$ integer operations. This way, with a different approach, we reach the same complexity of established algorithms, such as those based on the fast Walsh transform.