Local method for compositional inverses of permutation polynomials

References

• Akbary, A., Ghioca, D., Wang, Q. (2001). On constructing permutations of finite fields. Finite Fields Appl. 17:51–67. DOI: 10.1016/j.ffa.2010.10.002.
   Google Scholar
• Coulter, R. S., Henderson, M. (2002). The compositional inverse of a class of permutation polynomials over a finite field. Bull. Austral. Math. Soc. 65:521–526. DOI: 10.1017/S0004972700020578.
   Web of Science ®Google Scholar
• Ding, C., Yuan, J. (2006). A family of skew Hadamard difference sets. J. Comb. Theory, Ser. A 113:1526–1535. DOI: 10.1016/j.jcta.2005.10.006.
   Web of Science ®Google Scholar
• Laigle-Chapuy, Y. (2007). Permutation polynomials and applications to coding theory. Finite Fields Appl. 13:58–70. DOI: 10.1016/j.ffa.2005.08.003.
   Web of Science ®Google Scholar
• Li, K., Qu, L., Wang, Q. (2019). Compositional inverses of permutation polynomials of the form xrh(xs) over finite fields. Cryptogr. Commun. 11:279–298.
   Google Scholar
• Lidl, R., Niederreiter, H. (1997). Finite Fields. Cambridge: Cambridge University Press.
   Google Scholar
• Mullen, G. L. (1991). Permutation polynomials over finite fields. In: Finite Fields, Coding Theory, and Advances in Communication and Computing. Las Vegas, NY: CRC Press, pp. 131–151.
   Google Scholar
• Niu, T., Li, K., Qu, L., Wang, Q. (2021). Finding compositional inverses of permutations from the AGW creterion. IEEE Trans. Inf. Theory 67:4975–4985. DOI: 10.1109/TIT.2021.3089145.
   Web of Science ®Google Scholar
• Park, Y. H., Lee, J. B. (2001). Permutation polynomials and group permutation polynomials. Bull. Austral. Math. Soc. 63:67–74. DOI: 10.1017/S0004972700019110.
   Web of Science ®Google Scholar
• Tuxanidy, A., Wang, Q. (2014). On the inverses of some classes of permutations of finite fields. Finite Fields Appl. 28:244–281. DOI: 10.1016/j.ffa.2014.02.006.
   Web of Science ®Google Scholar
• Tuxanidy, A., Wang, Q. (2017). Compositional inverses and complete mappings over finite fields. Discrete Appl. Math. 217:318–329. DOI: 10.1016/j.dam.2016.09.009.
   Web of Science ®Google Scholar
• Wang, Q. (2007). Cyclotomic mapping permutation polynomials over finite fields. In: Sequences, Subsequences, Consequences. Berlin, Germany: Springer, pp. 119–128.
   Google Scholar
• Wang, Q. (2017). A note on inverses of cyclotomic mapping permutation polynomials over finite fields. Finite Fields Appl. 45:422–427. DOI: 10.1016/j.ffa.2017.01.006.
   Web of Science ®Google Scholar
• Wu, B. (2014). The compositional inverse of a class of linearized permutation polynomials over F2n,n odd. Finite Fields Appl. 29:34–48.
   Web of Science ®Google Scholar
• Wu, B., Liu, Z. (2013). The compositional inverse of a class of bilinear permutation polynomials over finite fields of characteristic 2. Finite Fields Appl. 24:136–147. DOI: 10.1016/j.ffa.2013.05.003.
   Web of Science ®Google Scholar
• Wu, B., Liu, Z. (2013). Linearized polynomials over finite fields revisited. Finite Fields Appl. 22:79–100. DOI: 10.1016/j.ffa.2013.03.003.
   Web of Science ®Google Scholar
• Yuan, P. (2022). Compositional inverses of AGW-PPs. Adv. Math. Commun. 16(4): 1185–1195. DOI: 10.3934/amc.2022045.
   Web of Science ®Google Scholar
• Yuan, P. (2022). Permutation polynomials and their compositional inverses. arXiv:2206.04252. Algebra Colloq. (to appear)
   Google Scholar
• Yuan, P., Ding, C. (2011). Permutation polynomials over finite fields from a powerful lemma. Finite Fields Appl. 17:560–574. DOI: 10.1016/j.ffa.2011.04.001.
   Web of Science ®Google Scholar
• Yuan, P., Ding, C. (2014). Further results on permutation polynomials over finite fields. Finite Fields Appl. 27:88–103. DOI: 10.1016/j.ffa.2014.01.006.
   Web of Science ®Google Scholar
• Zheng, D., Yuan, M., Li, N., Hu, L., Zeng, X. (2019). Constructions of involutions over finite fields. IEEE Trans. Inf. Theory 65:7876–7883. DOI: 10.1109/TIT.2019.2919511.
   Web of Science ®Google Scholar
• Zheng, Y., Yu, Y. (2018). On inverse of permutation polynomials of small degree over finite fields, II. arXiv:1812.11812.
   Google Scholar
• Zheng, Y., Wang, Q., Wei, W. (2020). On inverses of permutation polynomials of small degree over finite fields. IEEE Trans. Inf. Theory 66:914–922. DOI: 10.1109/TIT.2019.2939113.
   Web of Science ®Google Scholar
• Zieve, M. (2009). On some permutation polynomials over Fq of the form xrh(x(q−1)/d). Proc. Amer. Math. Soc. 137:2209–2216.
   Web of Science ®Google Scholar