Boolean Functions Derived from Pseudorandom Binary Sequences

  • Gottlieb Pirsic
  • Arne Winterhof
Conference paper

DOI: 10.1007/978-3-642-30615-0_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7280)
Cite this paper as:
Pirsic G., Winterhof A. (2012) Boolean Functions Derived from Pseudorandom Binary Sequences. 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 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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations