Computing the weight of a boolean function from its algebraic normal form

Authors:
Çağdaş Çalık;Ali Doğanaksoy
Affiliations:
Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey;Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey,Department of Mathematics, Middle East Technical University, Ankara, Turkey
Venue:
SETA'12 Proceedings of the 7th international conference on Sequences and Their Applications
Year:
2012

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Abstract

We present an algorithm that computes the weight of a Boolean function from its Algebraic Normal Form (ANF). For functions acting on high number of variables (n30) and having low number of monomials in its ANF, the algorithm is advantageous over the standard method of computing weight which requires the transformation of function's ANF to its truth table with a complexity of $\mathcal{O}(n2^n)$ operations. A relevant attempt at computing the Walsh coefficients of a function from its ANF by Gupta and Sarkar required the function to be composed of high degree monomials [1]. The proposed algorithm overcomes this limitation for particular values of n, enabling the weight and Walsh coefficient computation for functions that could be of more interest for practical applications.