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Algebraic Construction of Near-Bent and APN Functions

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A Correction to this article was published on 12 March 2020

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Abstract

Boolean functions play an important role in symmetric cryptosystems. In this paper, we have constructed near-bent Boolean functions algebraically with the help of Niho power function exponent in the trace form over a finite field. Specific cryptographic properties which may gain attention with suitable modifications are observed using these functions. If exponents are either Mersenne numbers or Fermat numbers, then the resulting functions are found to be APN (almost perfect nonlinear).

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Change history

  • 12 March 2020

    Remark 4.1 and Remark 4.5 in Section 4 will be true only if a is a power of two.

  • 12 March 2020

    Remark 4.1 and Remark 4.5 in Section 4 will be true only if a is a power of two.

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Acknowledgements

The authors would like to thank the Editor-in-chief and the anonymous referees for their valuable comments and suggestions, which helped us to improve the quality of this manuscript. The corresponding author and the second author acknowledges Manipal Institute of Technology (MIT), Manipal Academy of Higher Education, India, for their kind encouragement. The first author is grateful to Manipal Academy of Higher Education for their support through the Dr. T. M. A. Pai Ph. D. scholarship program.

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Authors and Affiliations

  1. Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India

    Prasanna Poojary & Harikrishnan Panackal

  2. Department of Mathematics, Center for Cryptography, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, Karnataka, India

    Vadiraja G. R. Bhatta

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  1. Prasanna Poojary
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  2. Harikrishnan Panackal
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  3. Vadiraja G. R. Bhatta
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Correspondence to Vadiraja G. R. Bhatta.

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Communicated by Rafał Abłamowicz

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Poojary, P., Panackal, H. & Bhatta, V.G.R. Algebraic Construction of Near-Bent and APN Functions. Adv. Appl. Clifford Algebras 29, 93 (2019). https://doi.org/10.1007/s00006-019-1012-x

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