2-分解H布尔函数和高非线性度布尔函数  

H Boolean Functions with Divided into Two Parts and High Nonlinearity Boolean Functions

作　　者：黄景廉[1] 王卓[1] 李娟[1] 

机构地区：[1]西北民族大学电气工程学院,兰州730030

出　　处：《计算机科学》2016年第7期166-170,202,共6页Computer Science

基　　金：国家自然科学基金项目(61262085)资助

摘　　要：以布尔函数的导数和自定义的e-导数为主要研究工具,研究满足一次扩散准则、可2-分解为两个子函数乘积的一类H布尔函数的非线性度、相关免疫性和代数免疫性等密码学性质。得到了这类H布尔函数的相关免疫阶与两个子函数的关系,以及这类H布尔函数的相关免疫阶可达到■n/2■-1的结论。还得到了利用两个子函数使布尔函数的非线性度易于求解的方法,以及这类H布尔函数的最低代数次数零化子与两个子函数的关系。进一步地,在这类H布尔函数上述特点的基础上,利用导数和e-导数构造出了非线性度提高到2^(n-2)+2^(n-3)、具有相关免疫性和2阶代数免疫性的一族H布尔函数。由此,解决了提高布尔函数的非线性度问题,以及同时具有较高非线性度、扩散性、相关免疫性和较高阶代数免疫性的布尔函数的存在性问题。Using the derivative of the Boolean functions and the e-derivative defined by ourselves as research tools, we studied the cryptographic properties of a class of H Boolean function which satisfy one degree propagation and are divided into the product of two subfunctions, including nonlinearity, correlation immunity and algebraic immunity and so on. We achieved the relationship between the correlation immunity of this kind of H Boolean function and the two sub- functions, and also arrived at a conclusion on the correlation immunity of this kind of H Boolean function which can reach [n/2]-1.Moreover,we obtained the relationship between the lowest algebraic degree annihilator of this kind of an H Boolean function and the two subfunctions. Further, using e-derivative and derivative of a Boolean function, we con- structed a cluster of H Boolean function which has the nonlinearity 2^n-2 ＋2^n-3 , the correlation immunity and 2-order al- gebraic immunity from obtained H Boolean functions. In this way, we resolved the problem of improving the nonlinearity of a Boolean function,and the existence problem of a Boolean function having higher nonlinearity, propagation, correlation immunity and higher algebraic immunity.

关 键 词：H布尔函数 2-分解 e-导数 非线性度 代数免疫性 相关免疫性 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]