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On the linear structures of balanced functions and quadratic APN functions

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Abstract

The set of linear structures of most known balanced Boolean functions is non-trivial. In this paper, some balanced Boolean functions whose set of linear structures is trivial are constructed. We show that any APN function in even dimension must have a component whose set of linear structures is trivial. We determine a general form for the number of bent components in quadratic APN functions in even dimension and some bounds on the number are produced. We also count bent components in any quadratic power functions.

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Acknowledgments

The results in this paper appear in the first author’s PhD thesis supervised by the second author.

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Authors and Affiliations

  1. Mzuzu University, P/Bag 201, Luwinga, Mzuzu 2, Malawi

    A. Musukwa

  2. University of Trento, Via Sommarive, 14, Povo, 38123, Trento, Italy

    M. Sala

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  1. A. Musukwa
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  2. M. Sala
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Correspondence to A. Musukwa.

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This article belongs to the Topical Collection: Boolean Functions and Their Applications IV

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Musukwa, A., Sala, M. On the linear structures of balanced functions and quadratic APN functions. Cryptogr. Commun. 12, 859–880 (2020). https://doi.org/10.1007/s12095-020-00431-5

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  • DOI: https://doi.org/10.1007/s12095-020-00431-5

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