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Second-Order Nonlinearity of a Boolean Function Class with Low Spectra

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Advances in Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 666))

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Abstract

In 2015, Cao and Hu (Cao, X., Hu, L.: Two boolean functions with five-valued walsh spectra and high nonlinearity. International Journal of Foundations of Computer Science, pp. 537–556 (2015)) introduced a certain class of Boolean functions, possessing low Walsh spectra, high nonlinearity, and high algebraic degree. For this class of Boolean functions, computation of higher-order nonlinearities (even second-order) is a tedious task. Therefore, in this article, we study the lower bound on the second-order nonlinearity of the above-mentioned class of Boolean functions for \(n=4.\) Also, we deduce that the bound, thus obtained is the maximum possible bound. We also demonstrated that our lower bound is greater than the lower bound on the second-order nonlinearity of other classes of cubic Boolean functions.

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Acknowledgment

The author would like to thank the Council of Scientific and Industrial Research for providing the financial support.

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Authors and Affiliations

  1. Department of Mathematics, The LNM Institute of Information Technology, Jaipur, 302031, Rajasthan, India

    Kezia Saini & Manish Garg

Authors
  1. Kezia Saini
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  2. Manish Garg
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Corresponding author

Correspondence to Kezia Saini .

Editor information

Editors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, India

    Jagdev Singh

  2. Department of Mathematics, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  3. Department of Mathematics, Cankaya University, Institute of space sciences, Bucharest, Ankara, Türkiye

    Dumitru Baleanu

  4. Department of Mathematics, University of Rajasthan, Jaipur, India

    Devendra Kumar

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Saini, K., Garg, M. (2023). Second-Order Nonlinearity of a Boolean Function Class with Low Spectra. In: Singh, J., Anastassiou, G.A., Baleanu, D., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation . ICMMAAC 2022. Lecture Notes in Networks and Systems, vol 666. Springer, Cham. https://doi.org/10.1007/978-3-031-29959-9_6

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  • DOI: https://doi.org/10.1007/978-3-031-29959-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-29958-2

  • Online ISBN: 978-3-031-29959-9

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