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Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity

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Cryptology and Network Security (CANS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5888))

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Abstract

Rotation symmetric Boolean functions (RSBFs) which are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, we study the construction of RSBFs with maximum algebraic immunity. First, a new construction of RSBFs on odd number of variables with maximum possible Algebraic Immunity is given. Then by using the relationship between some flats and support of a n-variables Boolean function f, we prove that a construction of RSBFs on even number of variables has maximum possible Algebraic Immunity. Furthermore, we study the nonlinearity of functions by our construction.

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Author information

Authors and Affiliations

  1. Department of Mathematics and System Science, National University of Defence Technology, Changsha, China

    Shaojing Fu, Chao Li & Longjiang Qu

  2. Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505, Japan

    Shaojing Fu & Kanta Matsuura

  3. State Key Laboratory of Information Security, Beijing, China

    Chao Li

Authors
  1. Shaojing Fu
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  2. Chao Li
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  3. Kanta Matsuura
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  4. Longjiang Qu
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Editor information

Editors and Affiliations

  1. AT&T Labs Research, Florham Park, NJ, USA

    Juan A. Garay

  2. Japan Advanced Institute of Science and Technology (JAIST), Nomi, Ishikawa, Japan

    Atsuko Miyaji

  3. National Institute of Advanced Industrial Science and Technoloy (AIST), Tokyo, Japan

    Akira Otsuka

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© 2009 Springer-Verlag Berlin Heidelberg

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Fu, S., Li, C., Matsuura, K., Qu, L. (2009). Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity. In: Garay, J.A., Miyaji, A., Otsuka, A. (eds) Cryptology and Network Security. CANS 2009. Lecture Notes in Computer Science, vol 5888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10433-6_27

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  • DOI: https://doi.org/10.1007/978-3-642-10433-6_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10432-9

  • Online ISBN: 978-3-642-10433-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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