Further results on permutation trinomials with Niho exponents

In this paper, we prove a conjecture proposed by Deng and Zheng about a class of permutation trinomials over finite fields F22m${\mathbb {F}}_{2^{2m}}$. In addition, we also construct four classes of permutation trinomials with Niho exponents over F32m${\mathbb {F}}_{3^{2m}}$.

[1]  Gohar M. M. Kyureghyan,et al.  Permutation polynomials of the form X + γ Tr(Xκ) , 2016 .

[2]  Kangquan Li,et al.  New constructions of permutation polynomials of the form $$x^rh\left( x^{q-1}\right) $$xrhxq-1 over $${\mathbb F}_{q^2}$$Fq2 , 2018 .

[3]  Yoji Niho.  Multi-Valued Cross-Correlation Functions between Two Maximal Linear Recursive Sequences , 1972 .

[4]  Xiangyong Zeng,et al.  Two classes of permutation polynomials having the form (x2m+x+δ)s+x , 2015, Finite Fields Their Appl..

[5]  Kangquan Li,et al.  New Permutation Trinomials Constructed from Fractional Polynomials , 2016, ArXiv.

[6]  Tor Helleseth,et al.  Several classes of permutation trinomials from Niho exponents , 2016, Cryptography and Communications.

[7]  V. A. Zinoviev,et al.  Permutation and complete permutation polynomials , 2015, Finite Fields Their Appl..

[8]  Tor Helleseth,et al.  New permutation trinomials from Niho exponents over finite fields with even characteristic , 2018, Cryptography and Communications.

[9]  June-Bok Lee,et al.  Permutation polynomials and group permutation polynomials , 2001, Bulletin of the Australian Mathematical Society.

[10]  R. K. Sharma,et al.  Some new classes of permutation trinomials over finite fields with even characteristic , 2016, Finite Fields Their Appl..

[11]  John J. Cannon,et al.  The Magma Algebra System I: The User Language , 1997, J. Symb. Comput..

[12]  Xiang-dong Hou,et al.  Permutation polynomials over finite fields - A survey of recent advances , 2015, Finite Fields Their Appl..

[13]  Dabin Zheng,et al.  More classes of permutation trinomials with Niho exponents , 2018, Cryptography and Communications.

[14]  Lei Hu,et al.  Further results on permutation trinomials over finite fields with even characteristic , 2017, Finite Fields Their Appl..

[15]  Long Yu,et al.  Two types of permutation polynomials with special forms , 2018, Finite Fields Their Appl..

[16]  Daniele Bartoli,et al.  Permutation polynomials, fractional polynomials, and algebraic curves , 2017, Finite Fields Their Appl..

[17]  Nian Li,et al.  Several classes of permutation trinomials over F5n$\mathbb {F}_{5^{n}}$ from Niho exponents , 2018, Cryptography and Communications.

[18]  David A. Cox,et al.  Ideals, Varieties, and Algorithms , 1997 .

[19]  涂自然.  Two classes of permutation polynomials having the form (x2m+x +δ)s+x , 2015 .

[20]  Yongbo Xia,et al.  A new class of permutation trinomials constructed from Niho exponents , 2017, Cryptography and Communications.

[21]  Gennian Ge,et al.  A note on permutation polynomials over finite fields , 2017, Finite Fields Their Appl..

[22]  R. K. Sharma,et al.  Further results on permutation polynomials of the form (xpm-x+δ)s+x over Fp2m , 2018, Finite Fields Their Appl..

[23]  Baofeng Wu,et al.  A general construction of permutation polynomials of the form (x2m+x+δ)i(2m-1)+1+x over F22m , 2017, ArXiv.

[24]  Qiang Wang,et al.  Cyclotomic Mapping Permutation Polynomials over Finite Fields , 2007, SSC.

[25]  Nian Li,et al.  On two conjectures about permutation trinomials over 𝔽32k , 2017, Finite Fields Their Appl..

[26]  Tao Zhang,et al.  Some new results on permutation polynomials over finite fields , 2015, Des. Codes Cryptogr..

[27]  Xi Chen,et al.  New classes of permutation binomials and permutation trinomials over finite fields , 2015, Finite Fields Their Appl..

[28]  June-Bok Lee,et al.  SOME PERMUTING TRINOMIALS OVER FINITE FIELDS , 1997 .

[29]  Rudolf Lidl,et al.  Permutation polynomials of the formxrf(xq−1)/d) and their group structure , 1991 .

[30]  Daniel Panario,et al.  Handbook of Finite Fields , 2013, Discrete mathematics and its applications.

[31]  Xiang-dong Hou,et al.  Determination of a type of permutation trinomials over finite fields, II , 2013, Finite Fields Their Appl..

[32]  Cunsheng Ding,et al.  Permutation polynomials of the form cx+Trql/q(xa)$cx+\text {Tr}_{q^{l}/ q}(x^{a})$ and permutation trinomials over finite fields with even characteristic , 2014, Cryptography and Communications.

[33]  Xiang-dong Hou.  Determination of a type of permutation trinomials over finite fields , 2013 .

[34]  Cunsheng Ding,et al.  Permutation trinomials over F2m , 2017, Finite Fields Their Appl..