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Results on Algebraic Immunity for Cryptographically Significant Boolean Functions

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Progress in Cryptology - INDOCRYPT 2004 (INDOCRYPT 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3348))

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Abstract

Recently algebraic attack has received a lot of attention in cryptographic literature. It has been observed that a Boolean function f, interpreted as a multivariate polynomial over GF(2), should not have low degree multiples when used as a cryptographic primitive. In this paper we show that high nonlinearity is a necessary condition to resist algebraic attack and explain how the Walsh spectra values are related to the algebraic immunity (resistance against algebraic attack) of a Boolean function. Next we present enumeration results on linearly independent annihilators. We also study certain classes of highly nonlinear resilient Boolean functions for their algebraic immunity.

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Author information

Authors and Affiliations

  1. Applied Statistics Unit, Indian Statistical Institute, 203, B T Road, Calcutta, 700 108, India

    Deepak Kumar Dalai, Kishan Chand Gupta & Subhamoy Maitra

Authors
  1. Deepak Kumar Dalai
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  2. Kishan Chand Gupta
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  3. Subhamoy Maitra
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Editor information

Editors and Affiliations

  1. INRIA Rocquencourt, France

    Anne Canteaut

  2. SETS, 21 Mangadu Swamy Street, Nungambakkam, 600 034, Chennai, India

    Kapaleeswaran Viswanathan

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© 2004 Springer-Verlag Berlin Heidelberg

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Dalai, D.K., Gupta, K.C., Maitra, S. (2004). Results on Algebraic Immunity for Cryptographically Significant Boolean Functions. In: Canteaut, A., Viswanathan, K. (eds) Progress in Cryptology - INDOCRYPT 2004. INDOCRYPT 2004. Lecture Notes in Computer Science, vol 3348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30556-9_9

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  • DOI: https://doi.org/10.1007/978-3-540-30556-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24130-0

  • Online ISBN: 978-3-540-30556-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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