Bent-Negabent函数、2-旋转对称Bent-Negabent函数及其对偶的系统构造
Systematic Constructions of Bent-Negabent Functions, 2-Rotation Symmetric Bent-Negabent Functions and Their Duals
摘要：
Bent-negabent函数在Walsh-Hadamard变换和负Hadamard变换下都具有平坦的绝对谱，因此具有许多重要的性质，这对它们在密码学中的应用具有重要意义。本文通过对两类具有简单形式的二次正负函数的真值表的修改，分别给出了关于$4k, 8k, 4k+2$和$8k+2$变量的四个新的正负函数的系统构造.确定了所构造函数的代数范式和代数形式。我们进一步确定的必要条件和充分条件，这些n-negabent功能，有最大的代数次数。最后，通过对一类二次2-旋转对称负函数的真值表的修改，给出了任意代数次数的2-旋转对称负函数的构造.考虑到在旋转对称类中可能不存在π-negabent函数，在广义旋转对称类中构造π-negabent函数是首次有意义的尝试.
英文摘要：
Bent-negabent functions have many important properties for their application in cryptography since they have the flat absolute spectrum under the both Walsh-Hadamard transform and nega-Hadamard transform. In this paper, we present four new systematic constructions of bent-negabent functions on $4k, 8k, 4k+2$ and $8k+2$ variables, respectively, by modifying the truth tables of two classes of quadratic bent-negabent functions with simple form. The algebraic normal forms and duals of these constructed functions are also determined. We further identify necessary and sufficient conditions for those bent-negabent functions which have the maximum algebraic degree. At last, by modifying the truth tables of a class of quadratic 2-rotation symmetric bent-negabent functions, we present a construction of 2-rotation symmetric bent-negabent functions with any possible algebraic degrees. Considering that there are probably no bent-negabent functions in the rotation symmetric class, it is the first significant attempt to construct bent-negabent functions in the generalized rotation symmetric class.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
