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Cryptography and Communications

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25-06-2020

A note on the distinctness of some Kloosterman sums

Authors: Yuri Borissov, Lyubomir Borissov

Published in: Cryptography and Communications | Issue 5/2020

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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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Zinoviev, V.A.: On classical Kloosterman sums. Cryptography and Communications 11(3), 461–496 (2019)MathSciNetCrossRef

Hurt, N.E.: Exponential sums and coding theory: a review. Acta Appl. Math. 46(1), 49–91 (1997)MathSciNetCrossRef

Fischer, B.: Distinctness of Kloosterman sums. Contemporary Mathematics 133, 81–102 (1992)MathSciNetCrossRef

Wan, D.: Minimal polynomials and distinctness of Kloosterman sums. Finite Fields Appl. 1, 189–203 (1995)MathSciNetCrossRef

Cao, X., Hollmann, H.D.L., Xiang, Q.: New Kloosterman sum identities and equalities over finite fields. Finite Fields Appl. 14, 823–833 (2008)MathSciNetCrossRef

Lisonek, P., Moisio, M.: On zeros of Kloosterman sums. Designs, Codes and Cryptography 59(3), 223–230 (2011)MathSciNetCrossRef

Kononen, K.P., Rinta-aho, M., Väänänen, K.: On integer values of Kloosterman sums. IEEE IT 56(8), 4011–4013 (2010)MathSciNetCrossRef

Moisio, M.: On certain values of Kloosterman sums. IEEE IT 55 (8), 3563–3564 (2009)MathSciNetCrossRef

Salié, Hans: Über die Kloostermanschen Summen S(u, v; q). Math. Zeit. 34(1932), 91–109 (1932)MathSciNetCrossRef

10.

Carlitz, L.: Kloosterman sums and finite field extensions. Acta Arithmetika XVI. 2, 179–193 (1969)MathSciNetCrossRef

11.

Lachaud, G., Wolfman, J.: The weights of the orthogonals of the extended quadratic binary Goppa codes. IEEE IT 36(3), 686–692 (1990)MathSciNetCrossRef

12.

Helleseth, T., Zinoviev, V.A.: On z₄-linear Goethals codes and Kloosterman sums. Designs, Codes and Cryptography 17(1-3), 246–262 (1999)MATH

Title: A note on the distinctness of some Kloosterman sums
Authors: Yuri Borissov
Lyubomir Borissov
Publication date: 25-06-2020
Publisher: Springer US
Published in: Cryptography and Communications / Issue 5/2020
Print ISSN: 1936-2447
Electronic ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-020-00443-1

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