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布尔函数是许多密码系统的核心部件,其密码学性质的优劣决定着整个密码系统的安全性.因此研究和构造满足各种密码学性质的布尔函数是密码学研究领域的热点问题.旋转对称(Rotation Symmetric)函数也称幂等函数,是一类输出值在输入的循环移位下保持不变的布尔函数,具有结构简单、运算速度快、资源利用率高等优点,目前已被应用于分组密码S盒和压缩函数的设计中.本文综述了旋转对称函数的研究成果,具体包括:密码学性质优良的旋转对称布尔函数的搜索、旋转对称bent和semi-bent函数的构造、有限域上幂等函数的性质、代数免疫最优的旋转对称布尔函数的构造、线性结构特征、汉明重量和非线性度计算以及仿射等价性.其中重点归纳了近年来利用线性子空间构造旋转对称bent和semi-bent函数的构造方法,介绍了计算低次旋转对称布尔函数汉明重量以及非线性度的递归方法,提出了若干值得研究的公开问题.
Boolean functions are the core components of many cryptosystems whose cryptographic properties determine the security of the entire cryptosystem. Therefore, it is a hot issue in the field of cryptography to study and construct Boolean functions that satisfy various cryptographic properties. (Rotation Symmetric) function is also called the idempotent function. It is a kind of Boolean function whose output value remains unchanged under the input cyclic shift. It has the advantages of simple structure, high computing speed and high resource utilization. It has been applied to grouping S-boxes, S-boxes, and S-boxes, and so on.In this paper, the research results of rotational symmetry functions are reviewed, including the search of rotationally symmetric Boolean functions with good cryptographic properties, the construction of rotationally symmetric bent and semi- bent functions, Such as the structure of the rotationally symmetric Boolean function, the linear structure feature, the Hamming weight and nonlinearity calculation, and the affine equivalence of the algebraic immune optimal rotational symmetric Boolean function, which focus on the use of linear subspace in recent years to construct rotational symmetry bent And semi-bent function of the construction method, introduced the calculation of low-order rotational symmetry Boolean Hamming weight and nonlinearity Recursive method, put forward a number of open issues worthy of study.