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Duality of Boolean functions and its cryptographic significance

  • Session 5: Boolean Functions and Stream Ciphers
  • Conference paper
  • First Online:
Information and Communications Security (ICICS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1334))

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Abstract

Recent advances in interpolation and high order differential cryptanalysis have highlighted the cryptographic significance of Boolean functions with a high algebraic degree. However, compared with other nonlinearity criteria such propagation, resiliency, differential and linear characteristics, apparently little progress has been made in relation to algebraic degree in the context of cryptography. The aim of this work is to research into relationships between algebraic degree and other nonlinearity criteria. Making use of duality properties of Boolean functions, we have obtained several results that are related to lower bounds on nonlinearity, as well as on the number of terms, of Boolean functions. We hope that these results would stimulate the research community's interest in further exploring this important area.

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Author information

Authors and Affiliations

  1. The University of Wollongong, 2522, Wollongong, NSW, Australia

    Xian-Mo Zhang

  2. Monash University, 3199, Frankston, Melbourne, VIC, Australia

    Yuliang Zheng

  3. The University of Tokyo, 7-22-1 Roppongi, 106, Minato-ku, Tokyo, Japan

    Hideki Imai

Authors
  1. Xian-Mo Zhang
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  2. Yuliang Zheng
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  3. Hideki Imai
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Editor information

Yongfei Han Tatsuaki Okamoto Sihan Qing

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© 1997 Springer-Verlag

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Zhang, XM., Zheng, Y., Imai, H. (1997). Duality of Boolean functions and its cryptographic significance. In: Han, Y., Okamoto, T., Qing, S. (eds) Information and Communications Security. ICICS 1997. Lecture Notes in Computer Science, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028472

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  • DOI: https://doi.org/10.1007/BFb0028472

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63696-0

  • Online ISBN: 978-3-540-69628-5

  • eBook Packages: Springer Book Archive

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