Computing the Weight of a Boolean Function from Its Algebraic Normal Form

  • Çağdaş Çalık
  • Ali Doğanaksoy
Conference paper

DOI: 10.1007/978-3-642-30615-0_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)
Cite this paper as:
Çalık Ç., Doğanaksoy A. (2012) Computing the Weight of a Boolean Function from Its Algebraic Normal Form. In: Helleseth T., Jedwab J. (eds) Sequences and Their Applications – SETA 2012. SETA 2012. Lecture Notes in Computer Science, vol 7280. Springer, Berlin, Heidelberg

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 (n > 30) 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.

Keywords

Boolean Functions Algebraic Normal Form Weight 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Çağdaş Çalık
    • 1
  • Ali Doğanaksoy
    • 1
    • 2
  1. 1.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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