Piecewise constructions of inverses of some permutation polynomials

It is a hard problem to find the inverse of a nontrivial class of permutation polynomials of finite fields. In this paper the piecewise method is employed to construct the inverses of permutation polynomials, although piecewise constructing permutation polynomials is not a new idea. A formula for the inverses of some permutation polynomials of finite fields is presented.

[1]  R. Lidl,et al.  When does a polynomial over a finite field permute the elements of the fields , 1988 .

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

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

[4]  Jack Levine,et al.  Some Cryptographic Applications of Permutation Polynomials , 1977, Cryptologia.

[5]  Lei Hu,et al.  Two classes of permutation polynomials over finite fields , 2012, Finite Fields Their Appl..

[6]  Rudolf Lidl,et al.  On Cryptosystems Based on Polynomials and Finite Fields , 1985, EUROCRYPT.

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

[8]  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..

[9]  Jack Levine,et al.  Some Further Cryptographic Applications of Permutation Polynomials , 1987, Cryptologia.

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

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

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

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

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

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

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

[17]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

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

[19]  Rudolf Lidl,et al.  Permutation Polynomials in RSA-Cryptosystems , 1983, CRYPTO.

[20]  Rudolf Lide,et al.  Finite fields , 1983 .

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

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

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