Two Classes Of Low Differential Uniform Permutation Polynomials Over Finite Fields Of Even Characteristic

The low differential uniform permutation functions play a very important role in the nonlinear component substitution boxes(S-boxes) of the block ciphers. In order to resist against the differential attacks, linear attacks and higher order differential attacks, the functions must have the low differential uniformity, high nonlinearity and high algebraic degree in block cipher algorithms. So constructing the differential uniformity less than6permutation functions, which have the high nonlinearity and algebraic degree, is a very important issue with practical significance in research of cryptographic functions. This thesis discusses the low differential uniform permutation polynomials, and it includes the following two parts:(1) By changing the values of the known functions x2k+2,x2k+2k+1,x2n-2in subfield or subgroup of the finite field F2n, we construct two classes of the new differential uniformity less than6permutation functions. At the same time, via computing the nonlinearity and algebraic degree, we prove that the proposed functions are inequivalent the known ones.(2) We propose a class of permutation polynomials, which is derived from the functions was given by Bracken C. et al. in the paper By modifying some conditions of their functions, we prove its permutation of the functions.