Constructions Of Differentially 4-uniform Permutations Over F_2^2k

Differentially 4-uniform permutation polynomials over F22k are a class of impor-tant cryptographic functions.It plays a key role in the nonlinear component S-boxes of the block ciphers.For example,the S-box of the Advanced Encryption Standard(AES)is constructed from the inverse function x-1(0-1 = 0)over F28,which is just a differentially 4-uniform permutation.In this thesis,we defined and studied the per-fect trace-1 element over F22fk,and obtained some special partitions of the finite field.Based on that,we constructed a lot of differentially 4-uniform permutations.Our work generalizes that of[1].In addition,we proved that the method of constructing differentially 4-uniform permutations over F2n via preferred Boolean functions of[27]is essentially the same as that of constructing differentially 4-uniform permutations of F2n by Corollary 1 of[1].Finally,we solved a conjecture of[27]cm the number of differentially 4-uniform permutations constructed by Theorem 3 of that paper.