中文摘要：

密码学中所涉及的函数包括布尔函数和向量值函数,这两类函数的安全性指标包括差分一致性和非线性度等。构造密码学性质良好的低差分一致性函数是密码学中的热点问题。构造了两类偶特征有限域上的、新的几乎完全非线性（ almost perfect nonlinear,APN）函数,并分别证明了它们与偶特征有限域上已知的单项式APN函数EA不等价。

英文摘要：

Boolean function and vector function were two classes of functions involved in cryptography. It contained differential uniformity, nonlinearity, etc. as their safety indicator. Constructing low differential uniformity functions with good cryptography property was always a hot topic. Two new types of almost per-fect nonlinear （ APN） polynomial function over even characteristic finite fields were constructed, moreo-ver, it was proved that the presented functions were EA-inequivalent to the previously known monomial APN functions over even characteristic finite fields.