Key exchange based on Dickson polynomials over finite field with 2m

Give a survey of the important properties of Dickson polynomial Dn(x,1), and prove that Dickson polynomial  Dn(x,1) over finite field with 2m is a permutation polynomial if and only  if  n is odd. Use this fact to construct a new key agreement protocol which is secure, feasible and extensible.

[1]  Tang Yong-min,et al.  New public-key system replaced the LUC system , 2006 .

[2]  Song Han,et al.  Chaotic map based key agreement with/out clock synchronization , 2009 .

[3]  Tao Xiang,et al.  On the security of a novel key agreement protocol based on chaotic maps , 2009 .

[4]  Alfredo De Santis,et al.  Security of public-key cryptosystems based on Chebyshev polynomials , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Krishna M. Sivalingam,et al.  Cryptographic key exchange based on locationing information , 2007, Pervasive Mob. Comput..

[6]  Xiaofeng Liao,et al.  A novel key agreement protocol based on chaotic maps , 2007, Inf. Sci..

[7]  Don Coppersmith,et al.  Discrete logarithms inGF(p) , 2005, Algorithmica.

[8]  Hari M. Srivastava,et al.  Topics in polynomials of one and several variables and their applications : volume dedicated to the memory of P.L. Chebyshev (1821-1894) , 1993 .

[9]  Leandro Tortosa,et al.  Analysis and design of a secure key exchange scheme , 2009, Inf. Sci..

[10]  Joel V. Brawley,et al.  Polynomials which permute the matrices over a field , 1987 .

[11]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[12]  Kwok-Wo Wong,et al.  An efficient entire chaos-based scheme for deniable authentication , 2005 .

[13]  Henk D. L. Hollmann,et al.  A class of permutation polynomials of F2m related to Dickson polynomials , 2005, Finite Fields Their Appl..