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．
In this paper, the auther generalized perfect nonlinear functions, discussed the relationships among bent functions over defined by [2], bent functions over GF (pe) 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(pe).
基金
国家自然科学基金资助项目!(19771088)
