递归构造多个具有最优代数免疫度的平衡布尔函数

代数免疫度是针对代数攻击而提出来的一个新的密码学概念.要能够有效地抵抗代数攻击,密码系统中使用的布尔函数必须具有平衡性、较高的代数次数、较高的非线性度和较高的代数免疫度等.为了提高布尔函数的密码学性能,通过布尔函数仿射等价的方法,找出了所有具有最优代数免疫度的三变元布尔函数.由这些具有最优代数免疫度的三变元非线性布尔函数,递归构造了一类代数免疫度最优、代数次数较高的平衡布尔函数.给出了这类布尔函数非线性度的一个下界,偶数变元时,其下界严格大于Lobanov给出的下界.     

代数免疫度为1的布尔函数

布尔函数的代数免疫度是在流密码的代数攻击中所产生的重要概念.研究了代数免疫度为1的布尔函数,得到的主要结果有:对代数免疫度为1的布尔函数给出了一个谱刻画,给出了其个数的精确计数公式,最后给出了此类函数的非线性度的紧的上界.     

用非线性方程组求解等式约束非线性规划问题的降维算法

本文研究线性和非线性等式约束非线性规划问题的降维算法.首先,利用一般等式约束问题的降维方法,将线性等式约束非线性规划问题转换成一个非线性方程组,解非线性方程组即得其解;然后,对线性和非线性等式约束非线性规划问题用Lagrange乘子法,将非线性约束部分和目标函数构成增广的Lagrange函数,并保留线性等式约束,这样便得到一个线性等式约束非线性规划序列,从而,又将问题转化为求解只含线性等式约束的非线性规划问题.     

布尔函数的迹Walsh谱

布尔函数线性Walsh谱和高阶Walsh谱的研究对构造能够抵抗线性逼近攻击和二次或较高次逼近攻击的密码函数发挥了重要作用.为了抵抗采样攻击,提出了布尔函数迹Walsh谱和迹Walsh循环谱概念,并给出该Walsh谱的一些简单性质.利用这一谱值的分布特性,可以很好地分析布尔函数的迹函数逼近问题,对序列密码采样攻击研究具有重要意义.     

巧用“线性规划”的方法求解问题

线性规划问题指的是在线性约束条件下,求线性目标函数的最大值或最小值的问题,其实质是通过线性约束条件和线性目标函数的几何表征,利用数形结合的思想方法把问题直观化、可视化,以图解的形式解决之．这种方法可以拓展运用到一些非线性规划的问题,即“约束条件非线性”或“目标函数非线性”的类似问题．下面就按照目标函数的几何含义分三类举例说明．     

Galois环和Z/(m)环上完全非线性函数的性质

本文把完全非线性函数推广到了有限Abel群上,利用特征谱讨论了Z/(m)上Bent函数与GF(pe)上bent函数以及完全非线性函数定义之间的关系;给出Galois环与Z/(m)上最佳线性逼近的特征谱表示,得到完全非线性函数在某种程度上能抵抗最佳线性逼近攻击的结论;并给出一种Galois环与Z/(m)环上完全非线性函数的构结方法.     

n维复形上一类具有线性分式目标函数的规划问题

ｎ维复形上一类具有线性分式目标函数的规划问题郑汉鼎（山东大学教学系，济南２５０１Ｏ０）文献［１，２］已经研究了ｎ维复形上的规划问题，本文将讨论。维复形上具有线性分式目标函数的规划问题．问题Ⅰ给定一个ｎ维复形Ｋｎ和一个ｒ－１维边缘链，要找一个ｒ维链。使...     

有限域上低差分置换的计算与构造

低差分置换是对称密码算法的重要组件,最近屈等先后提出了优先函数、优先布尔函数的概念,并用之构造4-差分置换.构造了一些具有较少项数的优先布尔函数,将交换法中的布尔函数推广为F_(2~n)到F_4的映射,进一步研究了广义的交换构造,构造了三类新的4-差分置换,并计算了它们的非线性度.     

一类二元低重线性码及其重量分布（英文）

线性码在秘密共享方案、认证码、强正则图以及结合方案等领域有广泛应用,已成为编码理论中重要的研究内容.本文利用布尔函数构造了一类二元线性码,并运用Walsh变换完全确定了这类线性码及其对偶码的重量分布.     

线性等式约束多目标规划的一个降维算法

本文提出具有线性等式约束多目标规划问题的一个降维算法．当目标函数全是二次或线性但至少有一个二次型时，用线性加权法转化原问题为单目标二次规划，再用降维方法转化为求解一个线性方程组．若目标函数非上述情形，首先用线性加权法将原问题转化为具有线性等式约束的非线性规划，然后，对这一非线性规划的目标函数二次逼近，构成线性等式约束二次规划序列，用降维法求解，直到满足精度要求为止．     

Exact relations between nonlinearity and algebraic immunity

We sharpen some lower bounds on the higher order nonlinearity of a Boolean function in terms of the value of its algebraic immunity and obtain new tight bounds. We prove a universal tight lower bound, which enables us to reduce the problem of estimating higher order nonlinearity to finding the dimension of certain linear subspaces in the space of Boolean functions. As a simple corollary of this result, we obtain all previously known estimates in this area. For polynomials with disjoint terms, finding the dimension of those linear subspaces reduces to a simple combinatorial inspection. We prove a tight lower bound on the second order nonlinearity of a Boolean function in terms of the value of its algebraic immunity.     

EXISTENCE TIME FOR SOLUTIONS OFSEMILINEAR DIFFERENT SPEED KLEIN-GORDONSYSTEM WITH WEAK DECAY DATA IN 1D

0 IntroductionWe know tliat tliere are a lot Of results on the lower bouud problem for the life-span ofsolutions to the following senillinear Klein-Gordoli equationDu + u = F(u, 0tu, 0xu), x E IRa,ult=0 = Ere, (0.0.1)0tuIt=o = eu1with sluall, smootli Cauchy data.For tl1e weak decay Caucl1y data, Delort studied tl1at question witl1 periodic Cauchy data inI41. He got a lOwer bound fOr tlie tinle of eristellce. of maghtude cE--2 f fOr a general nonlinearityalld there are exau1ples showili…     

Parity Dimension for Graphs - A Linear Algebraic Approach

For a graph G with closed neighborhood matrix N , the parity dimension of G , denoted PD( G ), is the dimension of the null space of N over the field ${\cal Z}_2$ . Equivalently, the number of vertex sets S in G with the property that S dominates each vertex an even number of times is 2 k for some value of k , and PD( G ) = k . Using primarily linear algebraic techniques, we investigate the parity dimension of graphs.     

Smoothness of the Functional Law Generated by a Nonlinear SPDE

The authors consider a stochastic heat equation in dimension d=1 driven by an additive space time white noise and having a mild nonlinearity.It is proved that the functional law of its solution is absolutely continuous and possesses a smooth density with respect to the functional law of the corresponding linear SPDE.     

Linear and Steiner Bundles on Projective Varieties

We generalize the theory of Horrocks monads to ACM varieties, and use the generalization to establish a cohomological characterization of linear and Steiner bundles on projective space and on quadric hypersurfaces. We also characterize Steiner bundles on the Grassmannian G(1, 4) of lines in ?⁴. Finally, we study linear resolutions of bundles on ACM varieties, and characterize linear homological dimension on quadric hypersurfaces.     

On the existence of a short pivoting sequence for a linear program

We show that given a feasible primal–dual pair of linear programs in canonical form, there exists a sequence of pivots, whose length is bounded by the minimum dimension of the constraint matrix, leading from the origin to the optimum. The sequence of pivots give a sequence of square and nonsingular submatrices of the constraint matrix. Solving two linear equations involving such a submatrix give primal–dual optimal solutions to the corresponding linear program in canonical form.     

Splitting Integrators for Nonlinear Schrödinger Equations Over Long Times

Conservation properties of a full discretization via a spectral semi-discretization in space and a Lie–Trotter splitting in time for cubic Schrödinger equations with small initial data (or small nonlinearity) are studied. The approximate conservation of the actions of the linear Schrödinger equation, energy, and momentum over long times is shown using modulated Fourier expansions. The results are valid in arbitrary spatial dimension.     

分形插值函数的分数阶微积分的分形维数

证明了线性分形插值函数的Riemann-Liouville分数阶微积分仍然是线性分形插值函数.在基于线性分形插值函数有关讨论的基础上,证明了线性分形插值函数的Box维数与Riemann-.Liouville分数阶微积分的阶之间成立着线性关系.文中给出的例子的图像和数值结果更进一步说明了这个结论.     

Rank preservers of matrices over max algebra

The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We consider the semimodules over max algebra and study the properties of the weak basis and weak dimension of the semi-modules. Moreover, we obtain the characterizations of those linear operators that preserve rank of matrices over max-algebra.