Galois环和Z/(m)环上完全非线性函数的性质

Properties of Perfect Nonlinear Functions over Galois and Z/(m) Rings

中文关键词:  bent函数； 完全非线性函数  最佳线性逼近.

英文关键词:Beta function  perfect nonlinear function  the best linear approximation.

中文摘要:

      本文把完全非线性函数推广到了有限Abel群上，利用特征谱讨论了Z/(m)上Bent函数与GF(pe)上bent函数以及完全非线性函数定义之间的关系；给出Galois环与Z/(m)上最佳线性逼近的特征谱表示，得到完全非线性函数在某种程度上能抵抗最佳线性逼近攻击的结论；并给出一种Galois环与Z/(m)环上完全非线性函数的构结方法.

英文摘要:

      In this paper, the auther generalized perfect nonlinear functions, discussed the relationships among bent functions over defined by［2］， bent functions over GF (p^e) defined by 3］and perfect nonlinear fuctions, presented aspectal characterization of the Best Arrine Approximation over Galois and Zm rings, proved that perfect nonlinear functions can resist the BAA attack, and presented a method for contructing perfect nonlinear functions over GF(p^e).