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A note on the distinctness of some Kloosterman sums

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Abstract

The Fischer result about distinctness of the Kloosterman sums on F∗p is extended for the finite fields of degrees of extension that are powers of 2. To obtain the desired outcome, we give an elementary proof of the fact that there does not exist a pair of Kloosterman sums on same odd characteristic fields which are opposite to each other.

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Acknowledgments

We would like to thank the reviewers for their valuable suggestions and comments which substantially improved this paper.

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 G. Bontchev Str., 1113, Sofia, Bulgaria

    Yuri Borissov & Lyubomir Borissov

Authors
  1. Yuri Borissov
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  2. Lyubomir Borissov
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Correspondence to Yuri Borissov.

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Dedicated to Prof. Claude Carlet’s 70th Birthday

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

Guest Editors: Lilya Budaghyan and Tor Helleseth

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Borissov, Y., Borissov, L. A note on the distinctness of some Kloosterman sums. Cryptogr. Commun. 12, 1051–1056 (2020). https://doi.org/10.1007/s12095-020-00443-1

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  • DOI: https://doi.org/10.1007/s12095-020-00443-1

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