Some classes of complete permutation polynomials in the form of (x^pm − x + δ )^s + ax^pm + bx over F_{p 2m}

[1] Akbary, A., Ghioca, D., & Wang, Q. (2011). On constructing permutations of finite fields. Finite Fields Appl. 17, 51-67. Search in Google Scholar

[2] Bartoli, D., Giulietti, M., Quoos, L., & Zini, G. (2017). Complete permutation polynomials from exceptional polynomials. J. Number Theory. 176, 46-66. Search in Google Scholar

[3] Diffie, W., & Ledin, G. (translators). (2008). SMS4 encryption algorithm for wireless networks. From https://eprint.iacr.org/2008/329.pdf. Search in Google Scholar

[4] Feng, D., Feng, X., & Zhang, W., et al. (2011). Loiss: a byte-oriented stream cipher. IWCC’11 Proceedings of the Third international conference on Coding and Cryptology, Springer, 109-125. Search in Google Scholar

[5] Gupta, R., & Sharma, R. K. (2018). Further results on permutation polynomials of the form (x^pm − x+ δ)^s + x over F_p2m. Finite Fields Appl. 50, 196-208. Search in Google Scholar

[6] Li, N., Helleseth, T., & Tang, X. (2013). Further results on a class of permutation polynomials over finite fields. Finite Fields Appl. 22, 16-23. Search in Google Scholar

[7] Li, L., Li, C., Li, C., & Zeng, X. (2019). New classes of complete permutation polynomials. Finite Fields Appl. 55, 177-201. Search in Google Scholar

[8] Li, L., Wang, S., Li, C., & Zeng, X. (2018). Permutation polynomials (x^pm − x+ δ )^s1 + (x^pm − x+ δ )^s2 + x over F_pn Finite Fields Appl. 51, 31-61. Search in Google Scholar

[9] Lidl, R., & Niederreiter, H. (1997). Finite Fields, second ed. Encyclopedia of Mathematics and its Applications, vol. 20, Cambridge University Press, Cambridge. Search in Google Scholar

[10] Mann, H. B. (1942). The construction of orthogonal Latin squares. Annals of Mathematical Statistics 13 (4), 418-423. Search in Google Scholar

[11] Mittenthal, L. (1995). Block substitutions using orthomorphic mappings. Adv. in Appl. Math. 16 (10), 59-71. Search in Google Scholar

[12] Mileva, A., & Markovski, S. (2012). Shapeless quasigroups derived by Feistel orthomorphisms. Glasnik Matematicki 47 (67), 333-349. Search in Google Scholar

[13] Niederreiter, H., & Robinson, K. H. (1982). Complete mappings of finite fields. J. Aust. Math. Soc. A 33(2), 197-212. Search in Google Scholar

[14] Ongan, P., & Temür, B. G. (2019). Some permutations and complete permutation polynomials over finite fields. Turk. J. Math., 43, 2154-2160. Search in Google Scholar

[15] Samardjiska, S., & Gligoroski, D. (2017). Quadratic permutation polynomials, complete mappings and mutually orthogonal Latin squares. Math. Slovaca, 67(5), 1129-1146. Search in Google Scholar

[16] Schnorr, C. P., & Vaudenay, S. (1995). Black box cryptanalysis of hash networks based on multipermutations. Advances in Cryptology-Eurocrypt’94, Springer, 47-57. Search in Google Scholar

[17] Tu, Z., Zeng, X., & Hu, L. (2014). Several classes of complete permutation polynomials. Finite Fields Appl. 25, 182-193. Search in Google Scholar

[18] Tu, Z., Zeng, X., & Jiang, Y. (2015). Two classes of permutation polynomials having the form (x^2m + x+ δ )^s +x. Finite Fields Appl. 31, 12-24. Search in Google Scholar

[19] Tuxanidy, A., & Wang, Q. (2017). Compositional inverses and complete mappings over finite fields. Discrete Appl. Math. 217, 318-329. Search in Google Scholar

[20] Wu, G., Li, N., Helleseth, T., & Zhang, Y. (2015). Some classes of complete permutation polynomials over F_q. Sci. China math. 58, 2081-2094. Search in Google Scholar

[21] Wu, B., & Lin, D. (2015). On constructing complete permutation polynomials over finite fields of even characteristic. Discrete Applied Mathematics 184, 213-222. Search in Google Scholar

[22] Xu, X., Feng, X., & Zeng, X. (2019). Complete permutation polynomials with the form (x^pm − x+ δ )^s + ax^pm + bxover F_pn. Finite Fields Appl., 57, 309-343. Search in Google Scholar

[23] Xu, X., Li, C., Zeng, X., & Helleseth, T. (2018). Constructions of complete permutation polynomials. Designs, Codes and Cryptography, 86(12), 2869-2892. Search in Google Scholar

[24] Yuan, P., & Zheng, Y. (2015). Permutation polynomials from piecewise functions. Finite Fields Appl. 35, 215-230. Search in Google Scholar

[25] Zheng, D., & Chen, Z. (2017). More classes of permutation polynomials of the form (x^pm − x+ δ) ^s +L(x). App Algebra Engrg Comm Comp. 28(3), 215-223. Search in Google Scholar

[26] Zheng, Y., Yuan, P., & Pei, D. (2016). Large classes of permutation polynomials over F_q2 . Designs Codes and Cryptography, 81(3), 505-521. Search in Google Scholar

[27] Zhou, Y., & Qu, L. (2017). Constructions of negabent functions over finite fields. Cryptography and Communications, 9(2), 165-180. Search in Google Scholar