Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity
Construction of rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity
复制标题
DOI：
10.1007/s10623-012-9727-x
复制
发表时间：
2012-07
期刊：
影响因子：
--
通讯作者：
Sihong Su;Xiaohu Tang
中科院分区：
文献类型：
--
作者：
Sihong Su;Xiaohu Tang
最近的研究表明，旋转对称布尔函数类可能包含丰富的具有密码学意义的函数。在本文中，基于整数组合的知识，我们提出了两种新的旋转对称布尔函数的构造，对于奇数变量或偶数变量具有最佳代数免疫性。我们的新函数比所有现有的具有最佳代数免疫性的旋转对称布尔函数的理论结构具有更好的非线性。此外，我们的旋转对称布尔函数的代数次数也足够高。
Recent research shows that the class of rotation symmetric Boolean functions is potentially rich in functions of cryptographic significance. In this paper, based on the knowledge of compositions of an integer, we present two new kinds of construction of rotation symmetric Boolean functions having optimal algebraic immunity on either odd variables or even variables. Our new functions are of much better nonlinearity than all the existing theoretical constructions of rotation symmetric Boolean functions with optimal algebraic immunity. Further, the algebraic degree of our rotation symmetric Boolean functions are also high enough.