二次完备非线性函数的构造

On the construction of quadratic perfect nonlinear functions

完备非线性函数能很好地抵抗差分密码分析,在密码和通信领域中有重要应用.构造了一族代数次数为二次的完备非线性函数,该函数为具有四项的Dembowski-Ostrom多项式.证明了新构造的完备非线性函数不但EA-不等价于已知的完备非线性方幂函数,而且也不等价于所有已知的完备非线性函数.

Perfect nonlinear functions can provide good protection for differential cryptanalysis,so they have important applications in cryptology and communications.A new family of quadratic perfect nonlinear functions is constructed.They are Dembowski-Ostrom polynomials with four terms.It is proven that the new quadratic perfect nonlinear functions are EA-inequivalent not only to known perfect nonlinear power functions but also to all known perfect nonlinear functions.