论文标题
弯曲的函数的系统构造，2旋转对称弯曲函数及其双重函数
Systematic Constructions of Bent-Negabent Functions, 2-Rotation Symmetric Bent-Negabent Functions and Their Duals
论文作者
论文摘要
弯曲的函数在密码学中的应用具有许多重要的特性，因为它们在Walsh-Hadamard变换和Nega-Hadamard变换下都具有平坦的绝对频谱。在本文中，我们分别以$ 4K，8K，4K，4K+2 $和$ 8K+2 $变量的价格介绍了四个新的系统构造，该功能分别通过简单形式修改了两类二次弯曲的弯曲式函数的真实表，分别为$ 4K，4K+2 $和$ 8K+2 $变量。还确定了这些构建功能的代数正常形式和二元组。我们进一步确定了具有最大代数程度的弯曲型功能的必要条件。最后，通过修改一类二次2旋转对称弯曲式功能的真实表，我们提出了具有任何可能的代数度的2个复位对称弯曲式函数的结构。考虑到旋转对称类别中可能没有弯曲的函数，这是在广义旋转对称类中构造弯曲的不良函数的第一次重要尝试。
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.
