Bent函数具有最高的非线性度，能最好的抵抗线性攻击和仿射逼近攻击，从而使得Bent函数在数学和信息安全学方面都占据着非常重要的地位。有关Bent函数的研究一直是密码学的热点问题，并有学者对Bent函数的概念进行了推广。Partial Spread Bent函数类(简记为PS)是最经典的Bent函数类之一，但是已知的能给出具体表达式的PS Bent函数却很少，而且它们的有些密码学性质也并不清楚。本项目主要对PS Bent函数和Bent-Negabent函数进行研究：（1）分析如何从有限几何的角度来构造得到新的PS Bent函数，分析它们的密码学性质，试图找到新的Hyperbent函数；（2）分析已知构造得到的Bent-Ngebent函数的密码学性质，研究如何从有限域上构造密码学性质好的Bent-Negabent函数。这些问题的解决对Bent函数的研究有一定的促进作用。

Bent functions achieve the maximum possible nonlinearities and have the best resistance to linear attack and affine linear approximation attack. Since they were introduced, bent functions have attracted a lot of attention in various areas of mathematics and information science. There are some generalized bent criteria for Boolean functions, such as negabent. Partial spread bent function class is one of the most classic bent classes, but functions belonging to this class that can be explicitly represented are only the PSap functions and the partial spread bent functions based on some pre-quasifield and pre-semifield. Moreover, their cryptographic properties are also not clear. In the project, we study the partial spread bent functions and bent-negabent functions: (1) construct new PS bent functions from finite geometry, give their explicitly representation, analyze their cryptographic properties, and try to find new hyperbent functions. (2) analyze the cryptographic properties of the known bent-ngabent functions and construct bent-negabent functions over finite fields. The results of this project will play an important role in the research of bent functions.