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Two new permutation polynomials with the form \({\left(x^{2^k}+x+\delta\right)^{s}+x}\) over \({\mathbb{F}_{2^n}}\). (English) Zbl 1215.11116
Summary: This note presents two new permutation polynomials of the form \[ {p(x)=\left(x^{2^k}+x+\delta\right)^{s}+x} \] over the finite field \({\mathbb{F}_{2^n}}\) as a supplement of the recent work of J. Yuan, C. Ding, H. Wang and J. Pieprzyk [Finite Fields Appl. 14, No. 2, 482–493 (2008; Zbl 1211.11136)].

11T06 Polynomials over finite fields
Full Text: DOI
[1] Ball, S., Zieve, M.: Symplectic spreads and permutation polynomials. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds.) International Conference on Finite Fields and Applications, Lecture Notes in Computer Science, vol. 2948, pp. 79–88. Springer (2004) · Zbl 1066.51005
[2] Blokhuis, A., Coulter, R.S., Henderson, M., OKeefe, 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) · Zbl 1009.11064
[3] Beth, T., Ding, C.: On almost perfect nonlinear permutations. In: Goos, G., Hartmanis, J. (eds.) Advances in Cryptology-EUROCRYPT’93, Lecture Notes in Computer Science, vol. 765, pp. 65–76. Springer (1993) · Zbl 0951.94524
[4] Cohen, S.D.: Permutation group theory and permutation polynomials. In: Algebras and Combinatorics, Hong Kong (1997), pp. 133–146. Springer, Singapore (1999) · Zbl 0958.12001
[5] Coulter R.S.: On the equivalence of a class of Weil sums in characteristic 2. N. Z. J. Math. 28, 171–184 (1999) · Zbl 0979.11055
[6] Corrada Bravo, C.J., Kumar, P.V.: Permutation polynomials for interleavers in turbo codes. In: Proceedings of the IEEE International Symposium on Information Theory, Yokohama, Japan, p. 318. 29 June–4 July (2003)
[7] Dobbertin, H.: Kasami power functions, permutation polynomials and cyclic difference sets, difference sets, sequences and their correlation properties (Bad Windsheim, 1998), NATO Advanced Science Institute Series C: Mathematical and Physical Science, vol. 542, pp. 133–158. Kluwer Academic Publishers, Dordrecht (1999) · Zbl 0946.05010
[8] Helleseth T., Zinoviev V.: New Kloosterman sums identities over \({\mathbb{F}_{2^m}}\) for all m. Finite Fields Appl. 9(2), 187–193 (2003) · Zbl 1081.11077 · doi:10.1016/S1071-5797(02)00028-X
[9] Hollmann H.D., Xiang Q.: A class of permutation polynomials of \({\mathbb{F}_{2^m}}\) related to Dickson polynomials. Finite Fields Appl. 11(1), 111–122 (2005) · Zbl 1073.11074 · doi:10.1016/j.ffa.2004.06.005
[10] Lidl R., Mullen G.L.: When does a polynomial over a finite field permute the elements of the field?. Am. Math. Mon. 95(3), 243–246 (1988) · Zbl 0653.12010 · doi:10.2307/2323626
[11] Lidl R., Mullen G.L.: When does a polynomial over a finite field permute the elements of the field? II. Am. Math. Mon. 100(1), 71–74 (1993) · Zbl 0777.11054 · doi:10.2307/2324822
[12] Lidl R., Niederreiter H.: Finite Fields, Encyclopedia of Mathematics and its Applications, 2nd ed., vol. 20. Cambridge University Press, Cambridge (1997)
[13] Mullen, G.L.: Permutation polynomials over finite fields. In: Finite Fields, Coding Theory, and Advances in Communications and Computing (Las Vegas, NV, 1991), Lecture Notes in Pure and Applied Mathematics, vol. 141, pp. 131–151. Dekker, New York (1993) · Zbl 0808.11069
[14] Yuan J., Ding C.: Four classes of permutation polynomials of \({\mathbb{F}_{2^m}}\) . Finite Fields Appl. 13(4), 869–876 (2007) · Zbl 1167.11045 · doi:10.1016/j.ffa.2006.05.006
[15] Yuan J., Ding C., Wang H., Pieprzyk J.: Permutation polynomials of the form (x p + \(\delta\)) s + L(x). Finite Fields Appl. 14, 482–493 (2008) · Zbl 1211.11136 · doi:10.1016/j.ffa.2007.05.003
[16] Zhang W., Wu C., Li S.: Construction of cryptographically important Boolean permutations. Appl. Algebra Eng. Commun. Comput. 15, 173–177 (2004) · Zbl 1062.94043 · doi:10.1007/s00200-004-0163-7
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