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International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2012: Advances in Cryptology – ASIACRYPT 2012 pp 172–189Cite as

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Perfect Algebraic Immune Functions

Perfect Algebraic Immune Functions

  • Meicheng Liu18,
  • Yin Zhang18 &
  • Dongdai Lin18 
  • Conference paper
  • 3793 Accesses

  • 21 Citations

Part of the Lecture Notes in Computer Science book series (LNSC,volume 7658)

Abstract

A perfect algebraic immune function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. The main results are that for a perfect algebraic immune balanced function the number of input variables is one more than a power of two; for a perfect algebraic immune unbalanced function the number of input variables is a power of two. Also, for n equal to a power of two, the Carlet-Feng functions on n + 1 variables and the modified Carlet-Feng functions on n variables are shown to be perfect algebraic immune functions.

Keywords

  • Boolean functions
  • Algebraic immunity
  • Fast algebraic attacks

Supported by the National 973 Program of China under Grant 2011CB302400, the National Natural Science Foundation of China under Grants 10971246, 60970152, and 61173134, the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant XDA06010701, and the CAS Special Grant for Postgraduate Research, Innovation and Practice.

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Author information

Authors and Affiliations

  1. SKLOIS, Institute of Information Engineering, CAS, Beijing, 100195, P.R. China

    Meicheng Liu, Yin Zhang & Dongdai Lin

Authors
  1. Meicheng Liu
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  2. Yin Zhang
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  3. Dongdai Lin
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Editor information

Editors and Affiliations

  1. Tsinghua University, 30 Shuangqing Road, 100084, Beijing, China

    Xiaoyun Wang

  2. Central Research Laboratories, NEC, 1754 Shimonumabe Nakahara, 211-8666, Kawasaki, Japan

    Kazue Sako

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© 2012 International Association for Cryptologic Research

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Liu, M., Zhang, Y., Lin, D. (2012). Perfect Algebraic Immune Functions. In: Wang, X., Sako, K. (eds) Advances in Cryptology – ASIACRYPT 2012. ASIACRYPT 2012. Lecture Notes in Computer Science, vol 7658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34961-4_12

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  • DOI: https://doi.org/10.1007/978-3-642-34961-4_12

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  • Print ISBN: 978-3-642-34960-7

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