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Science China Information Sciences

, Volume 56, Issue 3, pp 1–9 | Cite as

Construction of even-variable rotation symmetric Boolean functions with maximum algebraic immunity

  • ShaoJing FuEmail author
  • Chao Li
  • Kanta Matsuura
  • LongJiang Qu
Research Paper

Abstract

Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. In this paper, we investigate n-variable (n even and n ⩾ 12) RSBFs to achieve maximum algebraic immunity (AI), and provide a construction of RSBFs with maximum AI and nonlinearity. These functions have higher nonlinearity than the previously known nonlinearity of RSBFs with maximum AI. We also prove that our construction provides high algebraic degree in some case.

Keywords

Boolean function rotation symmetry algebraic immunity nonlinearity 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • ShaoJing Fu
    • 1
    • 2
    Email author
  • Chao Li
    • 1
    • 3
  • Kanta Matsuura
    • 2
  • LongJiang Qu
    • 1
  1. 1.Department of Mathematics and System ScienceNational University of Defense TechnologyChangshaChina
  2. 2.Institute of Industrial ScienceUniversity of TokyoTokyoJapan
  3. 3.State Key Laboratory of Information SecurityGraduate University of Chinese Academy of SciencesBeijingChina

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