A note on homogeneous bent functions
A note on homogeneous bent functions
复制标题
关于齐次弯曲函数的注释
DOI：
10.1109/snpd.2007.113
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Yubing Zang
中科院分区：
文献类型：
--
作者：
Xiaolin Wang;Jianqin Zhou;Yubing Zang
Bent函数用于构建密码学强S盒和扩频系统的模块。提出了半Bent函数和四分之一Bent函数的概念。在此基础上，提出了一种构造Bent函数的方法.本文给出了一种较简单的方法，可求出以前用计算机搜索发现的全部30个由6个布尔变量组成的3次齐次Bent函数。证明了在2m个布尔变元中不存在m次齐次Bent函数（m > 3），这与差集理论的结果无关.
Bent functions are used to build blocks for cryptographically strong S-boxes and spread spectrum systems. The concept of semi bent functions and quarter bent functions is presented. Based on the new concept, an approach to construct bent functions is proposed. A simpler method to find all 30 homogeneous bent functions of degree 3 in 6 Boolean variables, which were previously discovered by a computer search, is given. It is proved that there do not exist homogeneous bent functions of degree m in 2 m Boolean variables for m > 3, without invoicing results from the difference set theory.