一类2^t-差分置换多项式

A class of 2~t-difference uniform permutation polynomials

构造了有限域F23k(k≥1)上一类二项式函数,利用有限域上单变元方程化为多变元方程组的方法证明了该函数是差分均匀度为2t(t≥1)的置换.由此得到一类APN置换和4-差分置换,并发现该两类低差分置换是已有结果的推广.

By using the multivariate method solving system of equations over finite fields F23k （k≥1）, a class of permutation polynomials with 2t-difference uniformity was constructed, where t≥1. A class of APN permutations and a class of 4-difference uniform permutations were obtained. Moreover, it is discovered that the two classes of low difference uniform permutations were generalizations of some known results.