摘要
为了防止存在有效的低次函数逼近,对于较小的正整数r,用于对称密码系统中的布尔函数应具有较高的r-阶非线性度.当r>1时,准确计算布尔函数的r-阶非线性度十分困难,已有的研究工作主要是通过分析其导函数的(r-1)-阶非线性度来确定布尔函数的r-阶非线性度下界.对于整数n≡2(mod 4),文中确定了一类由Niho指数生成的Bent函数的二阶非线性度下界.与相同变元个数的两类Bent函数和三类布尔函数相比,这类Bent函数具有更紧的二阶非线性度下界.
The Boolean functions used in symmetric ciphers should have high rth-order nonlinearity to resist against the low-degree approximation cryptanalysis. For an integer r〉1, it is quite difficult to compute the rth-order nonlinearity of a Boolean function, and the known literatures mainly utilize the （r-1）th-order nonlinearity of its derivatives to deduce the lower bound on the rtb-order nonlinearity. For an integer n≡ 2 （mod4）, this paper investigates the nonlinearities of the corresponding derivative functions for a class of Bent functions constructed from Niho exponents, and then determines the lower bound of the second-order nonlinearity for this class of Bent functions. Compared with two Bent functions and three classes of Boolean functions with the same number of variables, this class of Bent functions has a tighter lower bound on the second-order nonlinearity.
出处
《计算机学报》
EI
CSCD
北大核心
2012年第8期1588-1593,共6页
Chinese Journal of Computers
基金
国家自然科学基金(60970115
60970116
61003267
91018008
61003268)资助~~
