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Cryptography and Communications

Erschienen in:

28.12.2016

Several classes of permutation trinomials from Niho exponents

verfasst von: Nian Li, Tor Helleseth

Erschienen in: Cryptography and Communications | Ausgabe 6/2017

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Abstract

Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field \({\mathbb F}_{2^n}\), where n is a positive even integer, we focus on the construction of permutation trinomials over \({\mathbb F}_{2^n}\) from Niho exponents. As a consequence, several new classes of permutation trinomials over \({\mathbb F}_{2^n}\) are constructed from Niho exponents based on some subtle manipulation of solving equations with low degrees over finite fields.

Vorheriger Artikel Design sequences with high linear complexity over finite fields using generalized cyclotomy

Nächster Artikel Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions

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Akbary, A., Wang, Q.: On polynomials of the form x ^r h(x ^{(q − 1)/l}), International Journal of Mathematics and Mathematical Sciences. Article ID 23408 (2007)

Blokhuis, A., Coulter, R.S., Henderson, M., O’Keefe, C.M.: Permutations amongst the Dembowski-Ostrom polynomials. In: Jungnickel, D., Niederreiter, H. (eds.) Finite Fields and Applications: Proceedings of the Fifth International Conference on Finite Fields and Applications, pp 37–42 (2001)

Dickson, L.E.: The analytic representation of substitutions on a power of a prime number of letters with a discussion of the linear group. Ann. Math. 11, 65–120 (1896)MathSciNetCrossRefMATH

Ding, C., Qu, L., Wang, Q., Yuan, J., Yuan, P.: Permutation trinomials over finite fields with even characteristic. SIAM J. Discret. Math. 29, 79–92 (2015)MathSciNetCrossRefMATH

Dobbertin, H.: Almost perfect nonlinear power functions on G F(2ⁿ): The Welch case. IEEE Trans. Inf. Theory 45, 1271–1275 (1999)MathSciNetCrossRefMATH

Dobbertin, H.: Almost perfect nonlinear power functions on G F(2ⁿ): the Niho case. Inf. Comput. 151(1-2), 57–72 (1999)MathSciNetCrossRefMATH

Helleseth, T.: Some results about the cross-correlation function between two maximal linear sequences. Discret. Math. 16(3), 209–232 (1976)MathSciNetCrossRefMATH

Hermite, C.h.: Sur les fonctions de sept lettres. C. R. Acad. Sci. Paris 57, 750–757 (1863)

Hou, X.: A survey of permutation binomials and trinomials over finite fields. In: Kyureghyan, G., Mullen, G.L., Pott, A. (eds.) Topics in Finite Fields, Proceedings of the 11th International Conference on Finite Fields and Their Applications, Contemp. Math., Magdeburg, Germany, July 2013, vol. 632, AMS, pp 177–191 (2015)

10.

Hou, X.: A class of permutation trinomials over finite fields. Acta Arith 162, 51–64 (2014)MathSciNetCrossRefMATH

11.

Hou, X.: Permutation polynomials over finite fields–A survey of recent advances. Finite Fields Appl. 32, 82–119 (2015)MathSciNetCrossRefMATH

12.

Hou, X.: Determination of a type of permutation trinomials over finite fields, II. Finite Fields Appl. 35, 16–35 (2015)MathSciNetCrossRefMATH

13.

Lahtonen, J.: On the odd and the aperiodic correlation properties of the Kasami sequences. IEEE Trans. Inf. Theory 41(5), 1506–1508 (1995)MathSciNetCrossRefMATH

14.

Leonard, P.A., Williams, K.S.: Quartics over GF (2ⁿ). Proc. Am. Math. Soc., 347–350 (1972)

15.

Lee, J.B., Park, Y.H.: Some permutation trinomials over finite fields. Acta Math. Sci. 17, 250–254 (1997)MATH

16.

Li, K., Qu, L., Chen, X.: New classes of permutation binomials and permutation trinomials over finite fields, available online: http://arxiv.org/pdf/1508.07590.pdf

17.

Lidl, R., Niederreiter, H.: Finite Fields, 2nd ed. Cambridge Univ. Press, Cambridge (1997)MATH

18.

Niho, Y.: Multivalued cross-correlation functions between two maximal linear recursive sequence, Ph.D. dissertation. Univ Southern Calif., Los Angeles (1972)

19.

Park, Y.H., Lee, J.B.: Permutation polynomials and group permutation polynomials. Bull. Austral. Math. Soc. 63, 67–74 (2001)MathSciNetCrossRefMATH

20.

Tu, Z., Zeng, X., Hu, L., Li, C.: A class of binomial permutation polynomials, available online: http://arxiv.org/pdf/1310.0337v1.pdf

21.

Tu, Z., Zeng, X., Hu, L.: Several classes of complete permutation polynomials. Finite Fields and Appl. 25, 182–193 (2014)MathSciNetCrossRefMATH

22.

Wan, D., Lidl, R.: Permutation polynomials of the form x ^r h(x ^{(q − 1)/d}) and their group structure. Monatsh. Math. 112, 149–163 (1991)MathSciNetCrossRefMATH

23.

Zeng, X., Tian, S., Tu, Z.: Permutation polynomials from trace functions over finite fields. Finite Fields Appl. 35, 36–51 (2015)MathSciNetCrossRefMATH

24.

Zhu, X., Zeng, X., Chen, Y.: Some binomial and trinomial differentially 4-uniform permutation polynomials. Int. J. Found. Comput. Sci. 26(4), 487–498 (2015)MathSciNetCrossRefMATH

25.

Zieve, M.: Permutation polynomials on \(\mathbb {F}_{q}\) induced form Rédei function bijections on subgroups of \(\mathbb {F}_{q}^{*}\), available online: http://arxiv.org/pdf/1310.0776v2.pdf

26.

Zieve, M.: On some permutation polynomials over \(\mathbb {F}_{q}\) of the form x ^r h(x ^{(q − 1)/d}). Proc. Amer. Math. Soc. 137, 2209–2216 (2009)MathSciNetCrossRefMATH

Titel: Several classes of permutation trinomials from Niho exponents
verfasst von: Nian Li
Tor Helleseth
Publikationsdatum: 28.12.2016
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 6/2017
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-016-0210-9

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