关于“停走”生成器概率模型中的符合率问题

本文首先建立了“停走”生成器辅出序列的概率模型,给出了“停走”生成器输出序列与其线性移位寄存器序列之间的符合率的计算公式。     

一类"停走"生成器输出序列符合率的计算

本文考察了"停走"生成器输出序列{Xn}的一个子列{X2n}与原序列{Zn}的符合率问题,并在此基础上推广到更一般的情况,证明了在本文所指的一类钟控模型中,当g(n)=2n时,其输出序列与原序列的符合率达到最大     

关于广义“缩减生成器”的概率模型

本文建立了以2值密钥流“缩减生成器”为特例的广义“缩减生成器”的概率模型,研究了它们的输出序列的概率性质,特别得到了其输出序列和原输入序列之间的符合率的表达式,据此可从概率论的角度对此类生成器的性能和得失进行分析.     

变系数反馈移位寄存器及其序列的几个性质

本文给出了一类新的密钥流生成器一变系数反馈移位寄存器,得到了该密钥流生成器序列的几个重要的密码学性质,并在文中给出了严格的数学证明。     

小木偶漫游记——非多拉森林的奇遇

(一)鹤之舞 听说外面的世界很精彩,小木偶决定去看看.他朝着太阳升起的方向一直走,走啊走啊,走到路的尽头,看见了一片大森林.森林中心,一个高高的石台上,两只白鹤正翩翩起舞,台下鸦雀无声,所有的动物都看得如痴如醉!小木偶看呆了,真是太美了! “停,停,停!你们!”一只乌鸦飞过来,气势汹汹,指着台下的动物们,“赶紧走,火烈狐大人驾到,闲杂人等速速避开!”     

“特殊与一般”思想在“函数的单调性”教学中的应用

单调性是函数最重要的性质之一,也是高中数学教学的重点内容.结合沪教版新编高中数学必修一教材的章节安排,采用从“特殊到一般”,再从“一般到特殊”的辩证思想,引导学生对函数的单调性进行探究,全面提升学生掌握抽象数学概念的能力.     

一般矩条件下随机变量的收敛性

本文在一般矩条件下研究了同分布的NA随机变量序列和独立同分布的随机变量序列的收敛性,得到了推广形式的Baum-Katz定理和强大数律,这些结果推广了已知的一些文献中相应的结果.     

特殊与一般思想在初中数学解题中的应用

从特殊到一般,再从一般到特殊,是认识事物的一般规律,这一规律在数学的认识活动中有着重要的应用.特殊与一般思想是初中数学重要的思想方法之一,本文中旨在通过举例探讨“特殊与一般”思想在解题中的应用策略.     

巧构空间模型解题三例

高考中立体几何主要考查概念辨析、位置关系探究、空间几何量的计算,并考查画图、识图、用图的能力,一般综合考查空间想象能力、推理论证能力和运算能力．近几年高考试卷涉及动点和动直线的试题较多,此类试题比较抽象,难以捉摸,是考生难以突破的问题之一．本文尝试构建空间模型,以“静”制“动”来解决这类问题．     

多个移位寄存器级联产生的互钟控序列

本文在文[1]的基础上,提出了两种互钟控序列模型,即Ⅰ型 LSR[k,d]~l 序列和Ⅱ型 LSR[k,d]~l 序列,并对Ⅱ型 LSR[k,d]~l 序列证明了它的极小多项可以达到 h(x~(q_1…q_l)),复杂度为 n·q_1…q_l,其中 h(x)为 GF(2)上某一 n 次不可约多项式,q_1、q_2、…,q_l 分别为l 个参加 LSR[k,d]~l 运算的 LSR 序列之周期.     

Probability model of Gunther generator

This paper constructs the probability model of Gunther generator at first,and the finite dimension union distribution of the output sequence is presented.The result shows that the output sequence is an independent and uniformly distributed 0,1 random variable sequence. It gives the theoretical foundation about why Gunther generator can avoid the statistic weakness of the output sequence of stop-and-go generator,and analyzes the coincidence between output sequence and input sequences of Gunther generator.The conclusions of this paper would offer theoretical references for designers and analyzers of clock-controlled generators.     

多值KM_1M_2生成器的概率模型(英文）

This paper constructs the probability model of the multi-valued KM_1M_2 clock controlled generator,and discusses the probability distributing,homogeneous Markov property,ergodic property,strict placidity,numeral character and the property of large numbers of the random variables with this kind of output sequence.It gets the probability formula of the coincidence of the output sequence with the input sequence,and gives important reference to the design and analysis of the multi-valued key stream clock controlled generator in cryptography.     

Hidden symmetries and nonlocal group generators for ordinary differential equations

Hidden symmetries of ordinary differential equations (ODEs)are studied with nonlocal group generators. General forms aregiven for an exponential nonlocal group generator of an ODEthat is reduced from a higher-order ODE, which is expressedin canonical variables and which is invariant under a two-parameterLie group. The nonlocal group generator identifies a type Ihidden symmetry. Type II hidden symmetries are found in somereduction pathways of an ODE invariant under a solvable, nonabelian,three-parameter Lie group. The algorithm for the appearanceof the type II hidden symmetry is stated. General forms forthe reduced nonlocal group generator, which identifies the typeII hidden symmetry, are presented when the other two commutingoriginal group generators are in normal form.     

On a nonlinear congruential pseudorandom number generator

A nonlinear congruential pseudorandom number generator with modulus is proposed, which may be viewed to comprise both linear as well as inversive congruential generators. The condition for it to generate sequences of maximal period length is obtained. It is akin to the inversive one and bears a remarkable resemblance to the latter.

     

On the structure of digital explicit nonlinear and inversive pseudorandom number generators

We analyze the lattice structure and distribution of the digital explicit inversive pseudorandom number generator introduced by Niederreiter and Winterhof as well as of a general digital explicit nonlinear generator. In particular, we extend a lattice test designed for this class of pseudorandom number generators to parts of the period and arbitrary lags and prove that these generators pass this test up to very high dimensions. We also analyze the behavior of digital explicit inversive and nonlinear generators under another very strong lattice test which in its easiest form can be traced back to Marsaglia and provides a complexity measure essentially equivalent to linear complexity.     

On the Linear Complexity of the Power Generator

We obtain a lower bound on the linear complexity of the powergenerator of pseudo-random numbers, which in some special cases is alsoknown as the RSA generator and as the Blum–Blum–Shubgenerator. In some very important cases this bound is essentially thebest possible. In particular, this implies that lattice reductionattacks on such generators are not feasible.     

分圆域Q(ζ_(33))的幂元整基

伽罗华数域L称有一个幂元整基,如果其代数整数环具有形式Ζα,其中α∈L.此时称α是L的幂元整基生成元.设α,β是L的两个幂元整基生成元,若β=m±σ(α),m∈Z,σ∈Gal(L/Q),则称α与β等价.本文主要研究分圆域Q(ζ33)的幂元整基问题.分圆域Q(ζ33)的代数整环是Z[ζ33],所以ζ33是Q(ζ33)的幂元整基生成元.设α是Q(ζ33)的幂元整基生成元,证明了当α+ā■Z时,α与ζ33等价.从而给出在此条件下分圆域Q(ζ33)的所有幂元整基生成元.     

分圆域Q（ζ33）的幂元整基

伽罗华数域L称有一个幂元整基,如果其代数整数环具有形式Ζα,其中α∈L.此时称α是L的幂元整基生成元.设α,β是L的两个幂元整基生成元,若β=m±σ（α）,m∈Z,σ∈Gal（L/Q）,则称α与β等价.本文主要研究分圆域Q（ζ33）的幂元整基问题.分圆域Q（ζ33）的代数整环是Z[ζ33],所以ζ33是Q（ζ33）的幂元整基生成元.设α是Q（ζ33）的幂元整基生成元,证明了当α＋ā Z时,α与ζ33等价.从而给出在此条件下分圆域Q（ζ33）的所有幂元整基生成元.     

Varieties without minimal generators

While many familiar varieties have a minimal varietal generator, i.e., a regular projective finitely presentable regular generator such that none of its retracts is a regular generator, and even a unique one, we present (a) a variety having no minimal varietal generator at all and (b) a variety having two non-isomorphic minimal varietal generators. Moreover we demonstrate that the same effects can happen with respect to a weaker notion of minimality and are common even in module categories. Received April 7, 1999; accepted in final form July 10, 2000.