Boolean Functions Derived from Pseudorandom Binary Sequences

  • Gottlieb Pirsic
  • Arne Winterhof
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)

Abstract

We study measures used to assess Boolean functions, where the functions are understood to be derived from binary sequences. We prove relations between two complexity measures for these Boolean functions and the correlation measure of order k of the corresponding sequence. More precisely, we study sparsity and combinatorial complexity of the Boolean function. Moreover, for a sequence with ’typical’ values of the correlation measure of order k we apply these relations to derive bounds on the complexity measures for the corresponding Boolean function. Finally, we apply our results to Sidelnikov sequences for which nice upper bounds on the correlation measure are known.

Keywords

Boolean functions sparsity correlation measure combinatorial complexity cryptography nonlinearity pseudorandomness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Gottlieb Pirsic
    • 1
  • Arne Winterhof
    • 2
  1. 1.Institute for Financial MathematicsKepler University LinzLinzAustria
  2. 2.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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