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Enumeration of Even-Variable Boolean Functions with Maximum Algebraic Immunity

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Part of the Lecture Notes in Computer Science book series (LNSC,volume 7690)

Abstract

Enumerating the Boolean functions satisfying one or several cryptographic criteria is useful. However, for a given number of variables, the number of Boolean functions with maximum AI is not known, either the previous known bound on the number is not good. In this paper, we investigate the enumeration of Boolean functions with maximum AI. First, we improve the lower bound on the number of even-variable Boolean functions with maximum AI, our new lower bound is better than the previous lower bounds. Then, for the first time, a significant lower bound on the number of 1-resilient Boolean functions with maximum AI is provided.

Keywords

  • Stream cipher
  • Boolean Function
  • Algebraic Attacks
  • Algebraic Immunity
  • Resiliency

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Zhao, W., Hai, X., Fu, S., Li, C., Wang, Y. (2012). Enumeration of Even-Variable Boolean Functions with Maximum Algebraic Immunity. In: Lee, D.H., Yung, M. (eds) Information Security Applications. WISA 2012. Lecture Notes in Computer Science, vol 7690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35416-8_4

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  • DOI: https://doi.org/10.1007/978-3-642-35416-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35415-1

  • Online ISBN: 978-3-642-35416-8

  • eBook Packages: Computer ScienceComputer Science (R0)