Piecewise constructions of inverses of cyclotomic mapping permutation polynomials

Given a permutation polynomial of a large finite field, finding its inverse is usually a hard problem. Based on a piecewise interpolation formula, we construct the inverses of cyclotomic mapping permutation polynomials of arbitrary finite fields.

[1]  Michael E. Zieve.  Some families of permutation polynomials over finite fields , 2007, 0707.1111.

[2]  Baofeng Wu,et al.  The compositional inverse of a class of bilinear permutation polynomials over finite fields of characteristic 2 , 2013, Finite Fields Their Appl..

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

[4]  Qiang Wang.  On inverse permutation polynomials , 2009, Finite Fields Their Appl..

[5]  Dingyi Pei,et al.  Piecewise constructions of inverses of some permutation polynomials , 2015, Finite Fields Their Appl..

[6]  Lei Hu,et al.  Constructing permutation polynomials from piecewise permutations , 2014, Finite Fields Their Appl..

[7]  Qiang Wang,et al.  On the inverses of some classes of permutations of finite fields , 2013, Finite Fields Their Appl..

[8]  Baofeng Wu,et al.  The compositional inverse of a class of linearized permutation polynomials over 𝔽2n, n odd , 2014, Finite Fields Their Appl..

[9]  Cunsheng Ding,et al.  Further results on permutation polynomials over finite fields , 2013, Finite Fields Their Appl..

[10]  Amela Muratovic-Ribic.  A note on the coefficients of inverse polynomials , 2007, Finite Fields Their Appl..

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

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

[13]  Tor Helleseth,et al.  Further results on a class of permutation polynomials over finite fields , 2013, Finite Fields Their Appl..

[14]  Qiang Wang,et al.  Cyclotomy and permutation polynomials of large indices , 2012, Finite Fields Their Appl..

[15]  Marie Henderson,et al.  The compositional inverse of a class of permutation polynomials over a finite field , 2002, Bulletin of the Australian Mathematical Society.

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

[17]  L. Carlitz,et al.  Some theorems on permutation polynomials , 1962 .

[18]  Baofeng Wu,et al.  Linearized polynomials over finite fields revisited , 2012, Finite Fields Their Appl..

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

[20]  Xiang-dong Hou,et al.  A piecewise construction of permutation polynomials over finite fields , 2012, Finite Fields Their Appl..

[21]  Qiang Wang,et al.  On Polynomials of the Form xrf(x(q-1)/l) , 2007, Int. J. Math. Math. Sci..

[22]  H. Niederreiter,et al.  Complete mappings of finite fields , 1982, Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics.

[23]  Harald Niederreiter,et al.  Cyclotomic R-orthomorphisms of finite fields , 2005, Discret. Math..

[24]  Michael E. Zieve.  On some permutation polynomials over Fq of the form x^r h(x^{(q-1)/d}) , 2007, 0707.1110.

[25]  Xiang-dong Hou,et al.  Two classes of permutation polynomials over finite fields , 2011, J. Comb. Theory, Ser. A.