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Construction of Resilient and Nonlinear Boolean Functions with Almost Perfect Immunity to Algebraic and Fast Algebraic Attacks

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Information Security and Cryptology (Inscrypt 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7763))

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Abstract

In this paper, we study a class of Boolean functions with good cryptographic properties. We show that the functions of this class are 1-resilient and have optimal algebraic degree and good nonlinearity. Further, we prove that the functions of this class have at least sub-maximum algebraic immunity. We also check that, at least for small values of the number of variables, the functions of this class have very good nonlinearity, maximum algebraic immunity and almost perfect immunity to 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, and the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant XDA06010701.

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Author information

Authors and Affiliations

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

    Tianze Wang, Meicheng Liu & Dongdai Lin

  2. University of Chinese Academy of Sciences, Beijing, 100049, P.R. China

    Tianze Wang & Meicheng Liu

Authors
  1. Tianze Wang
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  2. Meicheng Liu
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  3. Dongdai Lin
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Editor information

Editors and Affiliations

  1. Department of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Mirosław Kutyłowski

  2. Computer Science Department, Columbia University and Google Inc., Amsterdam Avenue 1214, 10027, New York, NY, USA

    Moti Yung

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Wang, T., Liu, M., Lin, D. (2013). Construction of Resilient and Nonlinear Boolean Functions with Almost Perfect Immunity to Algebraic and Fast Algebraic Attacks. In: Kutyłowski, M., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2012. Lecture Notes in Computer Science, vol 7763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38519-3_18

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  • DOI: https://doi.org/10.1007/978-3-642-38519-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38518-6

  • Online ISBN: 978-3-642-38519-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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