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International Conference on Information Security and Cryptology

Inscrypt 2010: Information Security and Cryptology pp 404–414Cite as

A Note on Fast Algebraic Attacks and Higher Order Nonlinearities

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6584))

Abstract

In this note, we deduce a bound between fast algebraic immunity and higher order nonlinearity (it is the first time that a bound between these two cryptographic criteria is given), and find that a Boolean function should have high r-order nonlinearity to resist fast algebraic attacks. As a corollary, we find that no matter how much effort we make, the Tu-Deng functions cannot be repaired in a standard way to behave well against fast algebraic attacks. Therefore, we should give up repairing this class of Boolean functions and try to find other classes of functions with good cryptographic properties or to prove that the Carlet-Feng function behaves well.

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Author information

Authors and Affiliations

  1. The Shanghai Key Lab of Intelligent Information Processing, School of Computer Science, Fudan University, Shanghai, 200433, P.R. China

    Qichun Wang

  2. Dept. of Electrical and Information Technology, Lund University, P.O. Box 118, 221 00, Lund, Sweden

    Qichun Wang & Thomas Johansson

Authors
  1. Qichun Wang
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  2. Thomas Johansson
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Shanghai Jiaotong University, Dongchuan Road 800, 200240, Shanghai, China

    Xuejia Lai

  2. Columbia University, USA

    Moti Yung

  3. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Wang, Q., Johansson, T. (2011). A Note on Fast Algebraic Attacks and Higher Order Nonlinearities. In: Lai, X., Yung, M., Lin, D. (eds) Information Security and Cryptology. Inscrypt 2010. Lecture Notes in Computer Science, vol 6584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21518-6_28

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  • DOI: https://doi.org/10.1007/978-3-642-21518-6_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21517-9

  • Online ISBN: 978-3-642-21518-6

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