Gold型Bent函数的两个注记

Two notes on Bent functions of Gold case

Bent函数一直是密码学研究中的重要课题,如何判断给出的布尔函数是否为bent函数是必须要解决的问题.通过对Gold型函数中指数的分析,得到了Gold型函数成为bent函数的充要条件,此充要条件是Leander文献中定理的部分推广,用该结论判断bent函数更加简便.同时还讨论了多个迹函数之和成为bent函数的一个充要条件.

Bent functions are important in cryptography, and one must know how to judge whether a Boolean function is bent. We obtain a sufficient and necessary condition by analyzing the power in functions of Gold case. This sufficient and necessary condition is a partial generalization of the theorem in Leander＇s reference. Our result makes the judgement of bentness of Gold ease much easier. We also discuss a sufficient and necessary condition for that the sum of a few trace functions is bent.