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International Conference on Cryptology in India

INDOCRYPT 2000: Progress in Cryptology —INDOCRYPT 2000 pp 19–30Cite as

On Resilient Boolean Functions with Maximal Possible Nonlinearity

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

Abstract

It is proved that the maximal possible nonlinearity of nvariable m-resilient Boolean function is 2n-1-2m+1 for 2n-7/3 ≤ m ≤ n- 2. This value can be achieved only for optimized functions (i. e. functions with an algebraic degree n - m - 1). For 2n-7/3 ≤ m ≤ n - log2n+2/3 - 2 it is suggested a method to construct an n-variable m-resilient function with maximal possible nonlinearity 2n-1 -2m+1 such that each variable presents in ANF of this function in some term of maximal possible length n -m - 1.

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Author information

Authors and Affiliations

  1. Mech. & Math. Department, Moscow State University, 119899, Moscow, Russia

    Yuriy V. Tarannikov

Authors
  1. Yuriy V. Tarannikov
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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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Tarannikov, Y.V. (2000). On Resilient Boolean Functions with Maximal Possible Nonlinearity. 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_3

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  • DOI: https://doi.org/10.1007/3-540-44495-5_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41452-0

  • Online ISBN: 978-3-540-44495-4

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