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On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices

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Progress in Cryptology — INDOCRYPT 2001 (INDOCRYPT 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2247))

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Abstract

In this paper we consider matrices of special form introduced in [11] and used for the constructing of resilient functions with cryptographically optimal parameters. For such matrices we establish lower bound 1/log2(√5+1) = 0.5902... for the important ratio t/t+k of its parameters and point out that there exists a sequence of matrices for which the limit of ratio of these parameters is equal to lower bound. By means of these matrices we construct m-resilient n-variable functions with maximum possible nonlinearity 2n-1-2m+1 for m = 0.5902 . . . n+O (log2 n). This result supersedes the previous record.

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Author information

Authors and Affiliations

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

    Maria Fedorova & Yuriy Tarannikov

Authors
  1. Maria Fedorova
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  2. Yuriy Tarannikov
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology, Madras, Chennai, India

    C. Pandu Rangan

  2. Department of Computer Science, Hong Kong University of Science and Technology, Hong Kong

    Cunsheng Ding

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© 2001 Springer-Verlag Berlin Heidelberg

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Fedorova, M., Tarannikov, Y. (2001). On the Constructing of Highly Nonlinear Resilient Boolean Functions by Means of Special Matrices. In: Rangan, C.P., Ding, C. (eds) Progress in Cryptology — INDOCRYPT 2001. INDOCRYPT 2001. Lecture Notes in Computer Science, vol 2247. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45311-3_24

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  • DOI: https://doi.org/10.1007/3-540-45311-3_24

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43010-0

  • Online ISBN: 978-3-540-45311-6

  • eBook Packages: Springer Book Archive

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