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The Correlation of a Boolean Function with Its Variables

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Progress in Cryptology —INDOCRYPT 2000 (INDOCRYPT 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1977))

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Abstract

The correlation of a Boolean function with its variables is closely related to the correlation attack on stream cipher. The Walsh transformation is the main tool to study the correlation of Boolean functions. The Walsh transformation of a Boolean function with r variables has 2r coefficients. Let k denote the number of non-zero coefficients of the Walsh Transformations. The paper studies the functions with 1 ≤k ≤ 8. It is proved that the functions with k = 1 are the linear functions only, there are no functions with k = 2, 3, 5, 6, 7, and finally we construct all functions with k = 4 or 8.

Supported by NNSF under contract No. 19931010

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References

  1. V. Chepyzhov and B. Smeets, On a fast correlation attack on certain stream cipher, Advance in Cryptology-Eurocrypt’91 (LNCS 547) (1991), 176–185.

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Author information

Authors and Affiliations

  1. State Key Laboratory of Information Security, Graduate School of Chinese Academy of Science, China

    Dingyi Pei & Wenliang Qin

Authors
  1. Dingyi Pei
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  2. Wenliang Qin
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Editor information

Editors and Affiliations

  1. Indian Statistical Institute, Calcutta, India

    Bimal Roy

  2. Department of Computer Science, University of Wisconsin, Milwaukee, Wisconsin, USA

    Eiji Okamoto

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© 2000 Springer-Verlag Berlin Heidelberg

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Pei, D., Qin, W. (2000). The Correlation of a Boolean Function with Its Variables. In: Roy, B., Okamoto, E. (eds) Progress in Cryptology —INDOCRYPT 2000. INDOCRYPT 2000. Lecture Notes in Computer Science, vol 1977. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44495-5_1

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  • DOI: https://doi.org/10.1007/3-540-44495-5_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41452-0

  • Online ISBN: 978-3-540-44495-4

  • eBook Packages: Springer Book Archive

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