扩散准则与相关免疫

对于布尔函数f(x),设不满足扩散准则的元素之集为Rf,不满足相关免疫的元素之集为zf ,即Rf={ai|(ai)0,0≤i≤2n-1},zf={ai|0,0≤i≤2n-1}。本文首先讨论了集合zf中元素的相关性, 并讨论了|zf|=1,2,3,4时函数的结构和性质。其次讨论了Rf构成线性子空间时,Rf和线性结构之集Lf之间的关系,其中Lf={ai||(ai)|=2n, 0≤I≤2n-1},给出Rf构成线性子空间时,Rf中的元素全部是线性结构的充要条件。还给出一种2阶扩散准则函数的构造方法。     

布尔函数扩散性的矩阵刻画

该文利用布尔函数的特征矩阵, 给出了n(3) 元布尔函数在sGFn(2) 满足扩散准则的充分必要条件, 在此基础上得到了布尔函数满足严格雪崩准则(SAC)的一个充分必要条件和n元平衡布尔函数满足严格雪崩准则、代数次数达到最大且不含有非零线性结构的一个充分必要条件, 最后提出了平衡且满足严格雪崩准则的布尔函数的两种特殊的递补构造法。     

Hamming重量为k的布尔函数的全局特征和非线性度

该文给出了布尔函数的自相关系数和互相关系数的一些性质,得到n元布尔函数f (x)满足t 阶扩散准则时,n,t 和Hamming重量wt(f)的制约关系,给出了任意Hamming重量为k的布尔函数的平方和指标下界表达式,推出了仅由布尔函数Hamming重量所确定的非线性度的上界表达式。这些结论推广了已有结果。     

代数次数为2的Bent函数的性质及其应用

本文证明了任意代数次数为2的n元Bent函数都与形式为x₁x₂+x₃x₄+…+x_n-1x_n的Bent函数线性等价;给出了以任意已知代数次数为2的n元Bent函数为分量的多维Bent函数的构造法;利用本文所给的方法,对任一主对角线上元素全为0的n阶可逆对称矩阵M₁,都可以构造k-1个主对角线上元素全为0的n阶可逆对称矩阵M₂…,M_k,使得M₁,M₂…,M_k的任意非零线性组合仍是主对角线上元素全为0的阶可逆对称矩阵.     

环Z_q~n上函数线性结构及其谱特征

在环Z_q~q(q≥2)上研究函数f(x)的线性结构点性质并对函数f(x)的恒变线性结构点进行了分类,讨论了它们之间的相互关系,并给出了函数f(x)的线性结构点的谱刻划。     

环Z_q~n上函数线性结构及其性质的研究

本文在Z_q~n(q=p_1*p_2,p_1、p_2是素数)上研究了函数f(x)的线性结构点性质并对函数f(x)的恒变线性结构点进行了分类,提出了零因子、非零因子恒变线性结构点两个全新的概念,讨论了恒变线性结构点之间的相互关系,指出了函数f(x)的非零谱值点与线性结构点之间的内在关系。     

相关免疫函数和Hamming重量之间的关系

相关免疫性是设计流密码和分组密码的重要准则之一.在对布尔函数的特征矩阵研究的基础上,利用Hamming重量分析法和相关免疫的充要条件从Hamming角度方面给出了相关免疫的一些性质,同时得到一个n元布尔函数f(x)是m阶相关免疫的充要条件,该充要条件进一步扩充了Siegenthaler关于相关免疫的,必要条件.     

布尔"复合函数"的密码学性质分析

本文探讨了布尔"复合函数"G(f1,L,fk)的有关密码学性质,分别给出了布尔"复合函数"是平衡函数、m阶相关免疫函数、(n,l.m)弹性函数,m阶广义ε-相关免疫函数的条件及其满足严格雪崩准则的条件.     

一类布尔函数的某些性质

本文给出对于某一自变量线性的布尔函数的一些性质;举例说明:当n>2时,“重量w(f)=2~(n-1)”不能导出“f(x_1,…x_n)对于某一自变量是线性的”;给出了函数f(x_1,…x_n)的重量w(f)=2~(n-1)的一个充分必要条件。     

k元de Bruijn序列的反馈函数的一个升级算法

本文定义了k个从k元n级de Bruijn-Good图到k元n-1级de Bruijn-Good图的满同态映射D_a,利用这些同态映射,我们证明了n级非奇反馈函数f(x₁,x₂,…,x_n)与以D_a(G_f)为状态图的n-1级非奇反馈函数g(x₁,x₂,…,x_n-1)的一个关系定理,给出了k元de Bruijn序列的反馈函数的一个升级算法,特别当k=2,a=0时,利用映射D在 Z ₂上运算的简单性,本文给出了一个从2元n-2^r级de Bruijn序列反馈函数直接生成2元n级de Bruijn序列的反馈函数的有效算法.     

Fault detection for multiple-valued logic circuits with fanout-free

The single fault and multiple fault detections for multiple-valued logic circuits are studied in this paper. Firstly, it is shown that the cardinality of optimal single fault test set for fanout-free m-valued circuits with n primary inputs is not more than n + 1, for linear tree circuits is two, and for multiplication modulo circuits is two if n is an odd number or if n is an even number and m > 3, where the optimal test set of a circuit has minimal number of test vectors. Secondly, it is indicated that the cardinality of optimal multiple fault test set for linear tree circuits with n primary inputs is 1 + [n/(m - 1)], for multiplication modulo circuits is n + 1, for fanout-free circuits that consist of 2-input linear tree circuits and 2-input multiplication modulo circuits is not greater than n+ 1, where [x] denotes the smallest integer greater than or equal to x. Finally, the single fault location approaches of linear tree circuits and multiplication modulo circuits are presented, and all faults in th     

A unique solution for the exact differential equation of nonuniform lines

The purpose of this letter is to establish that the general solution of the telegraphists' equation for any nonautonomic line is uniquely given by V = [f(x)]²[A + B ∫ dx/{f(x)}³], A and B being boundary constant, if and only if the propagation factor Γ(x) of the line may be expressible as Γ(x) = √2f'(x)/f(x) where the primes denote derivatives with respect to the distance variable x, and f(x) is any arbitrary function of x characterizing the distributing of nonuniformity of per-unit-length series impedance Z(x) = Z0f(x), Z0being a constant for impedence.     

The L(2,1)-labeling and operations of graphs

Motivated by a variation of the channel assignment problem, a graph labeling analogous to the graph vertex coloring has been presented and is called an L(2,1)-labeling. More precisely, an L(2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x)-f(y)| /spl ges/ 2 if d(x,y)=1 and |f(x)-f(y)| /spl ges/ 1 if d(x,y) = 2. The L(2,1)-labeling number /spl lambda/(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v):v/spl isin/V(G)}=k. A conjecture states that /spl lambda/(G) /spl les/ /spl Delta//sup 2/ for any simple graph with the maximum degree /spl Delta//spl ges/2. This paper considers the graphs formed by the Cartesian product and the composition of two graphs. The new graph satisfies the conjecture above in both cases(with minor exceptions).     

旋转对称布尔函数线性结构的2个公开问题

证明了代数次数为 的偶变元平衡旋转对称布尔函数不存在非零线性结构这个公开问题,给出了代数次数为 的奇变元旋转对称布尔函数不存在非零线性结构这个公开问题成立的充分条件和不成立的必要条件。     

模2n加法最佳线性逼近关系研究

该文研究了模2n加法运算的最佳线性逼近问题。利用权位分量函数的线性逼近关系,该文首先给出了模2n加法最佳线性逼近相关值的计算公式。其次通过递归构造得到了模2n加法最佳线性逼近集的生成方法。该文的研究从理论上更清楚地刻画了二元模2n加法最佳线性逼近的内在规律,有助于更好地利用该线性逼近关系实现对实际密码算法的有效分析。     

Generalized sampling: stability and performance analysis

Generalized sampling provides a general mechanism for recovering an unknown input function f(x)ϵℋ from the samples of the responses of m linear shift-invariant systems sampled at 1/mth the reconstruction rate. The system can be designed to perform a projection of f(x) onto the reconstruction subspace V(φ)=span {φ(x-k)}_kϵZ; for example, the family of bandlimited signals with φ(x)=sinc(x). This implies that the reconstruction will be perfect when the input signal is included in V(φ): the traditional framework of Papoulis' (1977) generalized sampling theory. Otherwise, one recovers a signal approximation f(x)ϵV(φ) that is consistent with f(x) in the sense that it produces the same measurements. To characterize the stability of the algorithm, we prove that the dual synthesis functions that appear in the generalized sampling reconstruction formula constitute a Riesz basis of V(φ), and we use the corresponding Riesz bounds to define the condition number of the system. We then use these results to analyze the stability of various instances of interlaced and derivative sampling. Next, we consider the issue of performance, which becomes pertinent once we have extended the applicability of the method to arbitrary input functions, that is, when ℋ is considerably larger than V(φ), and the reconstruction is no longer exact. We show that the generalized sampling solution is essentially equivalent to the optimal minimum error approximation. We then perform a detailed analysis for the case in which the analysis filters are in L₂ and determine all relevant bound constants explicitly. Finally, we use an interlaced sampling example to illustrate these various calculations     

Irreducible Polynomials Which Divide Trinomials Over GF (2)

The simplest linear shift registers to generate binary sequences involve only two taps, which corresponds to a trinomial over GF(2). It is therefore of interest to know which irreducible polynomials f(x) divide trinomials over GF(2), since the output sequences corresponding to f(x) can be obtained from a two-tap linear feedback shift register (with a suitable initial state) if and only if f(x) divides some trinomial t(x)=x^m+x^a+1 over GF(2). In this paper, we develop the theory of which irreducible polynomials do, or do not, divide trinomials over GF(2). Then some related problems such as Artin's conjecture about primitive roots, and the conjectures of Blake, Gao, and Lambert, as well as of Tromp, Zhang, and Zhao are discussed     

The q-ary image of a qm-ary cyclic code

For (n, q)=1 V a q^m-ary cyclic code of length n and with generator polynomial g(x), we show that there exists a basis for F(q^m) over F_q with respect to which the q-ary image of V is cyclic, if and only if: (i) g(x) is over F_q; or (ii) g(x)=g₀(x)(x-γ^-q(μ)), g₀(x) is over F_q, F_q≠F(q^k)=F_q(γ)⊂F(q^m ), μ an integer modulo k, and w^m-γ has a divisor over F(q^k) of degree e=m/k; or (iii) g(x)=g₀ (x) Π_μϵs(x-γ(-q^μ)), g ₀(x) is over F_q, F_q≠F(q^k)=F_q(γ)⊂F(q^m ), S a set of integers module k of cardinality k-1 and w^m -μ has a divisor over F(q^k) of degree e=m/k. In all of the above cases, we determine all of the bases with respect to which the q-ary image of V is cyclic     

Monomial and quadratic bent functions over the finite fields of odd characteristic

Considered are p-ary bent functions having the form f(x)=Tr/sub n/(/spl sigma//sub i=0//sup s/a/sub i/x/sup di/). A new class of ternary monomial regular bent function with the Dillon exponent is discovered. The existence of Dillon bent functions in the general case is an open problem of deciding whether a certain Kloosterman sum can take on the value -1. Also described is the general Gold-like form of a bent function that covers all the previously known monomial quadratic cases. The (weak) regularity of the new as well as of known monomial bent functions is discussed and the first example of a not weakly regular bent function is given. Finally, some criteria for an arbitrary quadratic function to be bent are proven.     

介质波导阵列电磁特性分析

根据已提出的二维周期介质严格理论,比较详细地分析和研究了介质波导阵列的电磁特性．首先,对存在纵向波传播时(kz≠0)的空间谐波相互作用特征进行了分析,得出了横向波传播色散特性．其次,在横向平面上的两互相垂直方向的波数相等(kx=ky)时,对不同波频率下空间谐波相互作用特性及其产生的阻带分布特征作了详细研究,并对横向纵向波传播色散关系进行了分析和计算．最后,得出介质波导阵列存在纯纵向导波的十分有意义的结论,具有实用价值．