中文摘要：

APN函数是特征为2的有限域上达到最低差分均匀度的函数,其中最经典的是APN幂函数。在F2^2n上的APN幂函数都是3-1函数。推广了前人在奇特征有限域上由2-1函数构造置换的思想,得到偶特征域上由3-1函数构造置换的方法,并由F2^2n上的APN幂函数构造置换。根据这种构造,研究了此类置换的差分性质。

英文摘要：

APN functions have the lowest differential uniform over finite fields with characteristic 2 and the APN power functions are the most classical ones. APN power functions are all 3-1 functions over F2^2n. By generalizing the idea of changing 2-1 functions to 1-1 functions over finite fields with odd characteristics, methods to change 3-1 functions over finite fields with even characteristics into permutations were obtained and permutations from APN power functions over F2^2n were constructed. According to the construction, the differential properties of permutations obtained by this method were discussed.