一类长周期的伪随机数序列

１．引 言 近年来,随着计算技术的迅猛发展,在计算机上利用 Ｍｏｎｔｅ－Ｃａｒｌｏ方法（亦称随机模拟）解决科学及工程实际问题已经成为现实．不过对此还要涉及到随机数ξ～（０,１）．然而生成真正的ξ～（０,１）却十分困难．一般都是依照一定的规则在计算机上生成伪随机数序列取代ξ（～０,１）,以用于随机模拟工作． 为获取品质优良的伪随机数序列以提高随机模拟结果的有效性,人们不断地提出多种伪随机数发生器即生成方法［１］．特别地,九十年代初由Ｍａｒｓａｇｌｉａ等［２］问提出的进位加法（ａｄｄ－ｗｉｔｈ－ｃａｒｒ…     

组合序列的若干优良性质

随机模拟技术在科学和工程中应用相当广泛［‘，‘］实际经验与理论分析均表明，伪随机数序列的性质（主要是独立性与均匀性）同模拟结果的可靠性有密切关系．自Lehmer门提出同余法以来，为高效率地生成优质伪随机数序列，多种伪随机数发生器及生成方法相继提出＊，组合法便是其中之一．该法的一种普通形式为问：假定｛（。（k），nEN｝，k二1，…，M川是M个取值于”1］的伪随机数序列，其中N表自然数集．以饲表实数x的分数部分，称为由（1）中的M个组成序列生成的组合序列．经验表明组合序列常优于它的组成序列，但对此缺乏理论根据．因…     

巧用8051单片机的奇偶校验位

利用８０５１单片机的奇偶校验位实现伪随机序列发生器和［８，４］扩展汉明解码的方法     

通用简约验证测试集U（p,w）矩阵的广义构造公式

本文是在文献［１］的基础上进行的研究，通过将文献［１］的三条定理推广到多进制情况以及对多进制ｐ中取ｉ矢量矩阵生成关系图的研究，提出Ｕ（ｐ，ｗ）矩阵的广义构造公式，利用本文公式可直接生成多值逻辑电路在进行伪穷举测试时需要的通用简约验证测试集。     

关于M=2^β的乘同余发生器

模数Ｍ＝２＾β的乘同余发生器常被应用作伪随和发生源。本文讨论了由此种发生器生成的伪随机数序列的整体结构及参数，Ａ，Ｘ０的作用，并说明了正确的实现方式，有利于随机模拟效果的改进。     

检验0,1数字序列随机性的多重异或法

１．引言在电信技术中,常常需要检验０,１数字序列｛Ｘｊ,ｊ＝１,…;Ｎ｝（１）的随机性［１］．在随机模拟工作中,对由一般反馈移位寄存器（ＧＦＳＲ）生成的０,１数字序列亦常需作同样的检验．检验序列（１）的随机性就是检验是否可以把它当作某０－１分布随机变量的Ｎ个独立观察值,即的容量为Ｎ的样本（２）的一个现实．异或是一种极易实现的运算,常用于分析序列（１）的结构［２,３］．以ｙ表示对ｘ,ｙ施行异或运算,令Ｘ－Ｘｊ－（３）取适当的Ｎ－１,从序列（１）开始,按式（３）可依次生成Ｎ＊＋１个序列其中Ｘｊ’‘－…     

字长对一类伪随机数序列周期的影响

提出了在字长限制下，按方法Ｕ１＝｛ａｕｉ－１｝实际生成的伪随机数序列的周期计算公式；通过理论分析与数字实例表明该方法可在ＲＥＡＬ＊８之下普通的随机模拟问题，但不宜在大型模拟问题中使用。     

复合非线性混沌系统伪随机数发生器产生算法

基于传统的特征多项式和寄存器设计的伪随机数发生器具有速度慢、生成代价高和周期短等缺点,通过非线性Logistic映射系统和分段映射描述了复合混沌系统的基本性质,设计了一种基于复合非线性混沌系统的伪随机数发生器的产生算法,基于此设计了新的复合混沌流密码的加密系统。理论和实验结果证明该伪随机数发生器产生的随机序列具有良好的密码学性能,产生密钥空间大,能有效抵御穷举和统计分析攻击。该复合系统具有安全性高、代价低和伪随机特性好的特点。     

基于单向函数的伪随机数发生器

伪随机数发生器(pseudorandom number generator,PRNG)是重要的密码学概念.基于单向函数的伪随机数发生器起始于1982年的BMY发生器,将单向函数反复迭代,周期性地输出伪随机序列.单向函数的性质和种子长度关系到发生器的可实现性和安全性,是此类发生器的2个重要参数.在分析现有工作的基础上,改进了单向函数的随机化迭代方式,基于不可逆性证明了迭代过程的安全性.迭代方式的改进消除了单向函数的长度保持性质,采用一般的压缩规范单向函数和通用散列函数构建伪随机数发生器.输出级与BMY发生器结构类似,以迭代函数的核心断言作为伪随机序列.基于与真随机序列的不可区分性,证明了伪随机数发生器的安全性.所构建的伪随机数发生器与现有同类发生器结构类似,但放松了对单向函数性质的要求,增强了可实现性,减小了种子长度,提高了效率.     

对伪随机数发生器一种强度分析方法

本文建立了对伪随机数据发生器的强度进行描述的概率方法，用这种方法对伪随机数发生器问题的一些方面着重进行了探讨，并得到了由伪随机函数（置换）发生器构造伪随机数发生器一个具有一定实际意义的结果，本文认为此种方法为在密码不或进行较规范的数学化分析提供了一个工具。     

GENETIC ALGORITHMS CAN BE USED TO OBTAIN GOOD LINEAR CONGRUENTIAL GENERATORS

Linear Congruential Generators (LCGs) are one model of pseudorandom number generators used in a great number of applications. They strongly depend on, and are completely characterized by, some critical parameters. The selection of good parameters to define a LCG is a difficult task mainly done, nowadays, by consulting tabulated values [10] or by trial and error. In this work, the authors present a method based on genetic algorithms that can automatically solve the problem of finding good parameters for a LCG. They also show that the selection of an evaluation function for the generated solutions is critical to the problem and how a seemingly good function such as entropy could lead to poor results. Finally, other fitness functions are proposed and one of them is shown to produce very good results. Some other possibilities and variations that may produce fine linear congruential generators are also mentioned.     

一种新的随机数组合发生器的研究

提出基于Mersenne Twister法和素数模乘同余法的随机数组合发生器。针对目前组合发生器理论多是对线性同余类中不同方法的组合的情况,结合两种类型的发生器的优点,得到一种新的随机数发生器。实验表明得到的组合发生器具有相对优越的统计性质,均匀性和独立性都有很大的提高。     

An exhaustive search for good 64-bit linear congruential random number generators with restricted multiplier

This paper explores that the different prime moduli can affect both the number of primitive root and the spectral test performance for 64-bit linear congruential generators (LCGs). Three forms of prime modulus and two types restriction on multiplier are considered in this paper. We perform computerized experiments that indicate significant differences exist among the number of primitive root of three forms of prime modulus. These differences can affect the performance of the spectral test. Two good 64-bit LCGs with significantly better spectral values and excellent empirical performance are presented. They are suitable for the requirements of today?s computer simulation studies.     

The microcomputer performance of uniform variate random number generators expressed in FORTRAN

The microcomputer performance of random number generators is an important component of uncertainty analysis in environmental modeling. The results of a performance study of 110 uniform variate pseudo-random number generators expressed in FORTRAN are presented. The algorithms tested include multiplicative, mixed, additive and quadratic congruential generators plus example combined and generalized feedback shift register generators. Results are presented for generator speed, period, and 17 statistical measures of number randomness quality. These results indicate that, based on both speed and number quality, the multiplicative linear congruential generator can yield superior performance. Specific moduli and multipliers are recommended for this generator. For relatively low period generators, explicit use of the integer modulus function provides superior performance. When high period generators are implemented, they should be based on the Schrage (1979) or Bongiovanni (1987) computational procedure for accomplishing the modulus operation with arithmetic that avoids explicit use of the modulus function.     

Multi-loop control of liquid cooling garment systems

In this study the effects of multi-loop control of liquid cooling garments (LCGs) under exercise heat stress conditions were investigated by experiments and theoretical analysis. A triple-loop LCG, by which the torso, arms and legs could be independently cooled, was used in the two series of experiments carried out in a hot environment (35 degrees C/40% RH). The experiment consisted of rest, exercise on an ergometer at 70 W and exercise at 110 W. In the first experiment, each water inlet temperature (TWI) was adjusted according to the local thermal sensation. In the second experiment, TWI for the torso including arms and TWI for the legs were regulated by a skin temperature controller with set-point adjustment via heart rate. The experiments showed that a multi-loop LCG is more effective than a single-loop LCG in providing thermal sensation and comfort adjusted to the requirements of the different parts of the body, and that a skin temperature controller could be applied to a multi-loop system. The theoretical analysis was carried out using a mathematical model of thermoregulation. The results showed that a strong cooling of the surface over the working muscles (legs) provided the greatest thermoregulatory advantage during low body exercise, because most of the heat generated within the working muscles can be removed directly by heat conduction to the skin. Optimization of a human/LCG system could be attained by an optimal configuration and control. However, an optimal configuration always depends on the application purpose of an LCG system.     

A random number generator based on the combination of four LCGs

A portable package for uniform random number generation is proposed, based on a backbone generator with period length near 2¹²¹, which combines four linear congruential generators. The package provides for multiple (virtual) generators evolving in parallel. Each generator has many disjoint subsequences, and software tools are provided to reset the state of any generator to the beginning of its first, previous, or current subsequence. An implementations is given in the C language.     

格蕴涵代数中的极小素理想及α-理想

在格蕴涵代数中,证明了极小素理想与极小格素理想的等价性,继而给出了极小素理想与零化子的相互表示定理。提出了格蕴涵代数中的[α]-理想概念并给出其若干等价刻画,证明了极小素理想是[α]-理想。证明了全体素[α]-理想之集[Sα(L)]是一个紧的Stone空间,进一步给出[Sα(L)]分别是[T1、][T2]拓扑空间的充要条件。     

Extending Lambek grammars to basic categorial grammars

Pentus (1992) proves the equivalence of LCG's and CFG's, and CFG's are equivalent to BCG's by the Gaifman theorem (Bar-Hillel et al., 1960). This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen (1967), but it was deficient (Buszkowski, 1985). We use a modification of Pentus' proof and a new proof of the Gaifman theorem on the basis of the Lambek calculus.     

综述:产生伪随机数的若干新方法

产生随机数是 Ｍｏｎｔｅ－Ｃａｒｌｏ方法的基础．本文简要综述有关方法,重点是近年来国际上热门的一些新方法与评论,包括作者们的一些工作．除了线性同余法外,还将涉及非线性同余法,Ｆｉｂｏｎａｃｃｉ,Ｔａｕｓｗｏｒｔｈｅ序列,进位加－借位减发生器法,以及乘子和增量也在递推中变化的复合素数发生器和基于混沌映射产生随机数的方法．除此之外,也介绍组合发生器,特别是介绍用于证明组合发生器优于单个发生器的一些理论结果,基于这些理论可实际地构造优良的随机数发生器．在本文中,我们也注意收集和指出某些发生器在应用中可…     

Architectures for vibration-driven micropower generators

Several forms of vibration-driven MEMS microgenerator are possible and are reported in the literature, with potential application areas including distributed sensing and ubiquitous computing. This paper sets out an analytical basis for their design and comparison, verified against full time-domain simulations. Most reported microgenerators are classified as either velocity-damped resonant generators (VDRGs) or Coulomb-damped resonant generators (CDRGs) and a unified analytical structure is provided for these generator types. Reported generators are shown to have operated at well below achievable power densities and design guides are given for optimising future devices. The paper also describes a new class-the Coulomb-force parametric generator (CFPG)-which does not operate in a resonant manner. For all three generators, expressions and graphs are provided showing the dependence of output power on key operating parameters. The optimization also considers physical generator constraints such as voltage limitation or maximum or minimum damping ratios. The sensitivity of each generator architecture to the source vibration frequency is analyzed and this shows that the CFPG can be better suited than the resonant generators to applications where the source frequency is likely to vary. It is demonstrated that mechanical resonance is particularly useful when the vibration source amplitude is small compared to the allowable mass-to-frame displacement. The CDRG and the VDRG generate the same power at resonance but give better performance below and above resonance respectively. Both resonant generator types are unable to operate when the allowable mass frame displacement is small compared to the vibration source amplitude, as is likely to be the case in some MEMS applications. The CFPG is, therefore, required for such applications.