【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.更多还原

【Abstract】 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 rth-order nonlinearity.For an integer n ≡ 2(mod 4),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.更多还原