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On the Menezes-Teske-Weng conjecture

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Abstract

In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conjecture on properties of the solutions of a type of quadratic equations over the binary extension fields, which had been confirmed by extensive experiments but the proof was unknown until now. We prove that this conjecture is correct. Furthermore, using this proved conjecture, we have completely determined the null space of a class of linearized polynomials.

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Acknowledgments

The authors deeply thank Alfred Menezes for checking our proof of the Menezes-Teske-Weng conjecture. They also thank the Assoc. Edit. and the anonymous reviewers for their valuable comments which have highly improved the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Paris VIII, University of Paris XIII, LAGA, UMR 7539, CNRS and Telecom ParisTech, Paris, France

    Sihem Mesnager

  2. Institute of Mathematics, State Academy of Sciences, Pyongyang, DPR, Korea

    Kwang Ho Kim & Junyop Choe

  3. PGItech Corp., Pyongyang, DPR, Korea

    Kwang Ho Kim

  4. School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, China

    Chunming Tang

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  1. Sihem Mesnager
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  2. Kwang Ho Kim
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  3. Junyop Choe
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  4. Chunming Tang
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Correspondence to Sihem Mesnager.

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Mesnager, S., Kim, K.H., Choe, J. et al. On the Menezes-Teske-Weng conjecture. Cryptogr. Commun. 12, 19–27 (2020). https://doi.org/10.1007/s12095-019-00359-5

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  • DOI: https://doi.org/10.1007/s12095-019-00359-5

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