A one-way function based on norm form equations

In this paper we present a new one-way function with collision resistance. The security of this function is based on the difficulty of solving a norm form equation. We prove that this function is collision resistant, so it can be used as a one-way hash function. We show that this construction probably provides a family of one-way functions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Increasing the security of hash functions

In this paper, we introduce a solution for ensuring data integrity using cryptographic one-way hash functions. The cryptographic security of such hash functions was estimated by us in detail for different kinds of attacks. We propose several new schemes for increasing the security of one-way hash functions without reformation of its internal algorithms. Also we outline schemes with the best speed and security level. We show that the Schneier method of suffix superposition has a serious drawback. In this article, we also suggest the method of constructing collision resistant one-way hash functions from standard well-known hash functions. Therefore, the proposed schemas can be used to upgrade the majority of cryptographic one-way functions, such as MD4, MD5, RIPEMD, SHA, GOST 34 11-94.     

The General Pay-Word: A Micro-payment Scheme Based on <Emphasis Type="BoldItalic">n</Emphasis>-dimension One-way Hash Chain

In this paper, we extend the Pay-Word micro-payment scheme using the 1-dimension one-way hash chain to generate an n-dimension one-way hash chain. According to the system requirements, a user can flexibly choose the number of dimensions to gain the best time/space trade off. The proposed scheme is based on an n-dimension one-way hash chain, which can improve the efficiency of deriving the pay-words but also increase the temporary storage space. In addition, this scheme is fit for real-time payment.AMS Classification: 14G50, 11T71     

Decomposition of Graphs into Chains

We establish a result on edge-disjoint paths with prescribedends in infinite trees and apply this to prove the conjectureof Eggleton and Skilton [1] that any connected graph has a decompositioninto chains such that at most one of these is one-way infiniteand each vertex is the end-vertex of at most one of the chainsand no vertex of infinite degree is such an end-vertex. We alsogive a necessary and sufficient condition for a graph to havea decomposition into one-way infinite chains.     

High Order Approximation of One-Way Wave Equations

In this article the high order approximation of the one-way wave equations are discussed. The approximate dispersion relations are expressed in explicit form of sums of simple fractions. By introducing new functions, the high order approximations of the one-way wave equations are put into the form of systems of lower order equations. The initial-boundary value problem of these systems which corresponds to the migration problem in seismic prospecting is discussed. The energy estimates for their solutions are obtained.     

The decomposition and measurement of the interdependency between second-order stationary processes

Summary For a given pair of multivariate stationary processes, the process of one-way effect is extracted from each of the processes. Each process is decomposed into two orthogonal processes, namely, into the process generated by the one-way effect of the other process and the process orthogonal to it. Based on the decomposition, three measures characterizing the interdependency of the pair of processes are introduced. They are the measure of association, the measure of one-way effect and the measure of reciprocity. Each of the measures is defined as overall as well as frequencywise measure. The paper shows that the measure of association is equal to the sum of the others. It discusses the relationships of those measures to the ones proposed by Gel'fand-Yaglom and by Geweke.This paper is partially supported by the Japanese Ministry of Education Grant for Scientific Research No. C02630010     

Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors

We consider a panel data semiparametric partially linear regression model with an unknown parameter vector for the linear parametric component, an unknown nonparametric function for the nonlinear component, and a one-way error component structure which allows unequal error variances (referred to as heteroscedasticity). We develop procedures to detect heteroscedasticity and one-way error component structure, and propose a weighted semiparametric least squares estimator (WSLSE) of the parametric component in the presence of heteroscedasticity and/or one-way error component structure. This WSLSE is asymptotically more efficient than the usual semiparametric least squares estimator considered in the literature. The asymptotic properties of the WSLSE are derived. The nonparametric component of the model is estimated by the local polynomial method. Some simulations are conducted to demonstrate the finite sample performances of the proposed testing and estimation procedures. An example of application on a set of panel data of medical expenditures in Australia is also illustrated.     

Incorporating one-way substitution policy into the newsboy problem with imprecise customer demand

This paper presents an approach for solving an inventory model for single-period products with maximizing its expected profit in a fuzzy environment, in which the retailer has the opportunity for substitution. Though various structures of substitution arise in real life, in this study we consider the fuzzy model for two-item with one-way substitution policy. This one-way substitutability is reasonable when the products can be stored according to certain attribute levels such as quality, brand or package size. Again, to describe uncertainty usually probability density functions are being used. However, there are many situations in real world that utilize knowledge-based information to describe the uncertainty. The objective of this study is to provide an analysis of single-period inventory model in a fuzzy environment that enables us to compute the expected resultant profit under substitution. An efficient numerical search procedure is provided to identify the optimal order quantities, in which the utilization of imprecise demand and the use of one-way substitution policy increase the average expected profit. The benefit of product substitution is illustrated through numerical example.     

One-way intervals of circle maps

An interval in the circle is one-way with respect to a map if under repeated applications of all points of the interval move in the same direction. The main result is that every locally one-way interval is either one-way or is the union of two overlapping one-way subintervals. An example is given which illustrates that the latter case can occur; however, it is proved that the latter case cannot occur if the interval is covered by the image of the map. As a corollary, it is shown that if has periodic points, then every interval which contains no periodic points is either one-way or is the union of two overlapping one-way subintervals.

     

ID-based cryptography using symmetric primitives

A general method for deriving an identity-based public key cryptosystem from a one-way function is described. We construct both ID-based signature schemes and ID-based encryption schemes. We use a general technique which is applied to multi-signature versions of the one-time signature scheme of Lamport and to a public key encryption scheme based on a symmetric block cipher which we present. We make use of one-way functions and block designs with properties related to cover-free families to optimise the efficiency of our schemes.      

An efficient multi-use multi-secret sharing scheme based on hash function

In this work, a renewable, multi-use, multi-secret sharing scheme for general access structure based on the one-way collision resistant hash function is presented in which each participant has to carry only one share. As it applies the collision resistant one-way hash function, the proposed scheme is secure against conspiracy attacks even if the pseudo-secret shares are compromised. Moreover, high complexity operations like modular multiplication, exponentiation and inversion are avoided to increase its efficiency. Finally, in the proposed scheme, both the combiner and the participants can verify the correctness of the information exchanged among themselves.     

Analysis of a fast method for solving the high frequency Helmholtz equation in one dimension

We propose and analyze a fast method for computing the solution of the high frequency Helmholtz equation in a bounded one-dimensional domain with a variable wave speed function. The method is based on wave splitting. The Helmholtz equation is split into one-way wave equations with source functions which are solved iteratively for a given tolerance. The source functions depend on the wave speed function and on the solutions of the one-way wave equations from the previous iteration. The solution of the Helmholtz equation is then approximated by the sum of the one-way solutions at every iteration. To improve the computational cost, the source functions are thresholded and in the domain where they are equal to zero, the one-way wave equations are solved with geometrical optics with a computational cost independent of the frequency. Elsewhere, the equations are fully resolved with a Runge–Kutta method. We have been able to show rigorously in one dimension that the algorithm is convergent and that for fixed accuracy, the computational cost is asymptotically just O(w^{1/ p})\mathcal {O}(\omega^{1/ p}) for a pth order Runge–Kutta method, where ω is the frequency. Numerical experiments indicate that the growth rate of the computational cost is much slower than a direct method and can be close to the asymptotic rate.     

Finitary isomorphism of some renewal processes to Bernoulli schemes

Using the marker and filler methods of Keane and Smorodinsky, we prove that entropy is a complete finitary isomorphism invariant for r-processes. It is conjectured that entropy is a complete finitary isomorphism invariant for finitary factors of Bernoulli schemes. We present a weaker version of this conjecture with hope that its proof is more attainable with present methods. In doing so, we define a one-way finitary isomorphism and prove one-way finitary results for random walks. We will also extend the marker and filler methods of Keane and Smorodinsky to a class of countable state processes.     

One way functions and pseudorandom generators

Pseudorandom generators transform in polynomial time a short random “seed” into a long “pseudorandom” string. This string cannot be random in the classical sense of [6], but testing that requires an unrealistic amount of time (say, exhaustive search for the seed). Such pseudorandom generators were first discovered in [2] assuming that the function (a ^x modb) is one-way, i.e., easy to compute, but hard to invert on a noticeable fraction of instances. In [12] this assumption was generalized to the existence of any one-way permutation. The permutation requirement is sufficient but still very strong. It is unlikely to be proven necessary, unless something crucial, like P=NP, is discovered. Below, among other observations, a weaker assumption about one-way functions is proposed, which is not only sufficient, but also necessary for the existence of pseudorandom generators. Supported by NSF grant #DCR-8304498, DCR-8607492.     

An extension of whitney’s theorem to infinite strong triangulations

In this paper, the existence of one-way infinite Hamiltonian paths in an infinite 4-connected strong triangulation is constructively verified, which is an extension of WHITNEY’S theorem to infinite graphs.     

单向环同态的一个新构造及两个多签名方案

本文对单向环同态提出了一种新的构造方法 ,即直接定义 Zn× U与 Zn× Imf( U,V是有限可换群 ,f 是 U→V的同态映射 )的两种运算而使 Zn× U与 Zn× Imf 是环 ,不必利用 U与 Imf是 Zn-模 ,这可避免某些运算在形式上易造成的混乱 ,并把单向环同态应用于椭圆曲线上 ,提出了一种基于椭圆曲线上单向环同态的多签名方案 .另外 ,本文对 Kazuo Ohta和 Tatsuaki Okamoto提出的一个多签名方案进行了改进 ,使原来需经过两个轮次而完成的多签名过程只需经一个轮次即可完成     

ONE-WAY MULTIVARIATE REPEATED MEASUREMENTS ANALYSIS OF VARIANCE MODEL

The one-way multivariate repeated measurements analysis of variance (1-way MRM ANOVA) model for complete data and the sphericity test are studied.     

平衡单向分类模型中几种同时置信区间的比较

在平衡单向分类模型中,通过对对照的三种同时置信区间长度表达式的分析,可以看到,在不同情况下,三种区间的优劣.     

Improving Penalized Least Squares through Adaptive Selection of Penalty and Shrinkage

Estimation of the mean function in nonparametric regression is usefully separated into estimating the means at the observed factor levels—a one-way layout problem—and interpolation between the estimated means at adjacent factor levels. Candidate penalized least squares (PLS) estimators for the mean vector of a one-way layout are expressed as shrinkage estimators relative to an orthogonal regression basis determined by the penalty matrix. The shrinkage representation of PLS suggests a larger class of candidate monotone shrinkage (MS) estimators. Adaptive PLS and MS estimators choose the shrinkage vector and penalty matrix to minimize estimated risk. The actual risks of shrinkage-adaptive estimators depend strongly upon the economy of the penalty basis in representing the unknown mean vector. Local annihilators of polynomials, among them difference operators, generate penalty bases that are economical in a range of examples. Diagnostic techniques for adaptive PLS or MS estimators include basis-economy plots and estimates of loss or risk.     

谱分析在我国经济波动理论中的应用

本文讨论经济波动研究的谱分析方法。在对我国主要宏观经济指标的数据序列进行一元、二元谱分析的基础上，对于我国经济波动的机制及运行规律进行定量分析