中文摘要：

完全非线性（perfect nonlinear,PN）函数在密码学和代数组合等领域中具有重要的应用价值。从已有的两个基本完全非线性函数出发,通过确定一类有限域上线性化多项式方程的解,构造了奇数特征有限域上一类2次完全非线性函数,证明了该函数不等价于形式为x2的完全非线性函数,并通过一个实例分析了它与完全非线性函数xps＋1的等价性问题。

英文摘要：

Perfect nonlinear functions are widely used in cryptography and algebra combinatorics.By using two known perfect nonlinear functions,a quadratic perfect nonlinear function over finite fields of odd characteristic was constructed based on determining the root of a linearized function.This quadratic function was proved to be inequivalent to x2,and then an example was used to analyzed its inequivalence to xps＋1.