New Collective Signatures Based on the Elliptic Curve Discrete Logarithm Problem

There have been many digital signature schemes were developed based on the discrete logarithm problem on a finite field. In this study, we use the elliptic curve discrete logarithm problem to build new collective signature schemes. The cryptosystem on elliptic curve allows to generate digital signatures with the same level of security as other cryptosystems but with smaller keys. To extend practical applicability and enhance the security level of the group signature protocols, we propose two new types of collective digital signature schemes based on the discrete logarithm problem on the elliptic curve: i) the collective digital signature scheme shared by several signing groups and ii) the collective digital signature scheme shared by several signing groups and several individual signers. These two new types of collective signatures have combined the advantages of group digital signatures and collective digital signatures. These signatures have a fixed size and do not depend on the number of members participating in the creation of the final collective signature. One of the advantages of the proposed collective signature protocols is that they can be deployed on top of the available public key infrastructures.     

Weil bounds for singular curves

We give explicit bounds useful in estimating the number of points on a (possibly singular) space curve defined over a finite field. Our estimates involve the degrees of the polynomials defining the curve set-theoretically, and reduce to Weil's well-known estimate for nonsingular complete intersection curves.     

On the low hamming weight discrete logarithm problem for nonadjacent representations

So-called nonadjacent representations are commonly used in elliptic curve cryptography to facilitate computing a scalar multiple of a point on an elliptic curve. A nonadjacent representation having few non-zero coefficients would further speed up the computations. However, any attempt to use these techniques must also consider the impact on the security of the cryptosystem. The security is studied by examining a related discrete logarithm problem, the topic of this paper. We describe an algorithm to solve the relevant discrete logarithm problem in time that is approximately the square root of the search space. This algorithm is of the familiar ``baby-step giant-step' type. In developing our algorithm we use two tools of independent interest; namely, a combinatorial set system called a ``splitting system' and a new type of combinatorial Gray code.     

A note on discrete logarithms in finite fields

In this note we provide a number of polynomial formulas for the discrete logarithm problem in an arbitrary multiplicative subgroup of a finite field. These formulas generalize previous formulas for computing logarithms in the multiplicative group of all nonzero elements.This author would like to thank the NSA for partial support under grant agreement #MDA904-87-H-2023.     

Phase‐field material point method for brittle fracture

The material point method for the analysis of deformable bodies is revisited and originally upgraded to simulate crack propagation in brittle media. In this setting, phase‐field modelling is introduced to resolve the crack path geometry. Following a particle in cell approach, the coupled continuum/phase‐field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, ie, non‐evolving, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying finite element mesh and relieved from corresponding mesh‐distortion errors. A staggered incremental procedure is implemented for the solution of the discrete coupled governing equations of the phase‐field brittle fracture problem. The proposed method is verified through a series of benchmark tests while comparisons are made between the proposed scheme, the corresponding finite element implementation, and experimental results.     

Plotting missing points and branches of real parametric curves

This paper is devoted to the study (from the theoretic and algorithmic point of view) of the existence of points and branches non-reachable by a parametric representation of a rational algebraic curve (in n-dimensional space) either over the field of complex numbers or over the field of real numbers. In particular, we generalize some of the results on missing points in (J. Symbolic Comput. 33, 863–885, 2002) to the case of space curves. Moreover, we introduce for the first time and we solve the case of missing branches. Another novelty is the emphasis on topological conditions over the curve for the existence of missing points and branches. Finally, we would like to point out that, by developing an “ad hoc” and simplified theory of valuations for the case of parametric curves, we approach in a new and unified way the analysis of the missing points and branches, and the proposal of the algorithmic solution to these problems. First author partially supported by MTM2005-02865. Second author partially supported by MTM2005-08690-C02-02. Both also partially supported by EU contract HPRN-CT-2001-00271.     

平面转弯带式输送机启动过程计算机仿真

针对大型平面转弯带式输送机动态设计问题,通过平面转弯带式输送机转弯部分的导向力和阻力分析,得出转弯段输送带运行的阻力计算方法,采用离散模型建立了系统的动力学方程。开发了平面转弯带式输送机动态分析软件,通过对实际系统的仿真,得出输送机启动过程各单元的位移、速度、加速度和张力等数值结果,绘制出相应的曲线,证明了其正确性。通过对直线运行输送机和转弯运行输送机仿真结果的比较,得出了转弯运行对带式输送机的影响。     

Mathematical construction and perturbation analysis of Zernike discrete orthogonal points

Zernike functions are orthogonal within the unit circle, but they are not over the discrete points such as CCD arrays or finite element grids. This will result in reconstruction errors for loss of orthogonality. By using roots of Legendre polynomials, a set of points within the unit circle can be constructed so that Zernike functions over the set are discretely orthogonal. Besides that, the location tolerances of the points are studied by perturbation analysis, and the requirements of the positioning precision are not very strict. Computer simulations show that this approach provides a very accurate wavefront reconstruction with the proposed sampling set.     

Computational hardness of IFP and ECDLP

The RSA cryptosystem and elliptic curve cryptography (ECC) have been used practically and widely in public key cryptography. The security of RSA and ECC respectively relies on the computational hardness of the integer factorization problem (IFP) and the elliptic curve discrete logarithm problem (ECDLP). In this paper, we give an estimate of computing power required to solve each problem by state-of-the-art of theory and experiments. By comparing computing power required to solve the IFP and the ECDLP, we also estimate bit sizes of the two problems that can provide the same security level.     

Lin-Wu(t,n)-门限防欺诈多秘密共享方案的改进

最近,Lin和Wu提出了一个防欺诈多秘共享方案。在该方案中,他们声称该方案是基于求解大整数分解和离散对数问题是不可行的。本文对Lin-Wu方案进行了分析,指出他们的方案有两个缺点：一．它不能抵抗来自内部参加者的攻击,二．它的安全性只相当于求解离散对数问题。针对该方案中存在的缺点,我们对其进行了改进。改进后的方案不仅可以抵抗来自内部参加者的攻击,而且使它的安全性真正建立在大整数分解和求解离散对数问题的双重困难数学问题上。     

A method for the numerical solution of singular integral equations with a principal value integral

A method for the numerical solution of singular integral equations with kernels having a singularity of the Cauchy type is presented. The singular behavior of the unknown function is explicitly built into the solution using the index theorem. The integral equation is replaced by integral relations at a discrete set of points. The integrand is then approximated by piecewise linear functions involving the value of the unknown function at a finite set of points. This permits integration in a closed form analytically. Thus the problem is reduced to a system of linear algebraic equations. The results obtained in this way are compared with the more sophisticated procedures based on Gauss-Chebyshev and Lobatto-Chebyshev quadrature formulae. An integral equation arising in a crack problem of the classical theory of elasticity is used for this purpose.     

A stochastic programming approach to manufacturing flow control

This paper proposes and tests an approximation of the solution of a class of piecewise deterministic control problems, typically used in the modeling of manufacturing flow processes. This approximation uses a stochastic programming approach on a suitably discretized and sampled system. The method proceeds through two stages: (i) the Hamilton-Jacobi-Bellman (HJB) dynamic programming equations for the finite horizon continuous time stochastic control problem are discretized over a set of sampled times; this defines an associated discrete time stochastic control problem which, due to the finiteness of the sample path set for the Markov disturbance process, can be written as a stochastic programming problem; and (ii) the very large event tree representing the sample path set is replaced with a reduced tree obtained by randomly sampling over the set of all possible paths. It is shown that the solution of the stochastic program defined on the randomly sampled tree converges toward the solution of the discrete time control problem when the sample size increases to infinity. The discrete time control problem solution converges to the solution of the flow control problem when the discretization mesh tends to zero. A comparison with a direct numerical solution of the dynamic programming equations is made for a single part manufacturing flow control model in order to illustrate the convergence properties. Applications to larger models affected by the curse of dimensionality in a standard dynamic programming techniques show the possible advantages of the method.     

Multi-objective sequence optimization of PCB component assembly with GA based on the discrete Fréchet distance

A new mechanism,namely a combination of curve matching method based on the discrete Fréchet distance and evolutionary algorithms,is proposed to solve pick-and-place sequence optimisation problems as a multi-objective optimisation problem. The essence of the mechanism is to accomplish the comparison of objective vectors with curve matching method. The objective vector is mapped into the array of points with a binary mapping operator and the discrete Fréchet distance is utilised to measure the similarity between the reference array of points and the comparison array of points. The genetic algorithm based on the discrete Fréchet distance (FGA) is proposed. To test the new mechanism, together with FGA, three other test algorithms are selected to solve the sequence optimisation problem. The simulation results indicate that FGA outperforms other algorithms. This new mechanism is rational and feasible for multi-objective pick-and-place sequence optimisation problems.     

A combined finite element and loop analysis for nonlinearly interacting magnetic fields and circuits

A general technique is described for combining a finite element representation of a quasi-stationary nonlinear magnetic field problem and the loop equations for all circuits, moving or stationary, which interact with the field. Various power quantities associated with the field and with each independent circuit loop can be estimated directly. Methods are presented for time integration of the first-order matrix differential equation describing both field and circuits. Saturating nonlinearities are treated iteratively. In particular, a transient problem in an idealized induction motor is solved. When permitted to reach steady state this solution yields points on the torque versus slip curve for the motor.     

力法非线性梁柱单元的合理单元长度划分

针对目前结构非线性分析中最常用的力法非线性梁柱单元模型,从理论上分析出了能消除其计算失真问题的合理单元长度及对应积分点数量。然后基于OpenSees有限元程序,使用该理论分析结果建立了一组单墩循环推倒试验的数值分析模型,通过加载点力-位移滞回曲线的对比分析和墩底截面曲率滞回曲线的对比分析验证了理论结果的正确性。结果表明:使用力法非线性梁柱单元模型进行结构的非线性数值分析时,其单元长度划分应根据积分点数量确定,确定原则应基于使单元屈服后变形增长的分布长度与塑性铰长度相等进行计算;在实际使用中,可利用等效塑性铰长度计算积分点数量与单元长度的关系,初步确定单元划分的合理长度;在保证单元长度与积分点数量的对应关系前提下,力法非线性单元的积分点数量越多,计算结果越稳定。     

A Simple Point Counting Algorithm for Hessian Elliptic Curves in Characteristic Three

Given an ordinary elliptic curve on Hesse form over a finite field of characteristic three, we give a sequence of elliptic curves which leads to an effective construction of the canonical lift, and obtain an algorithm for computing the number of points. Our methods are based on the study of an explicitly and naturally given 3-isogeny between elliptic curves on Hesse form.     

An evolution strategy in structural optimization problems for plates and shells

For multilayered plated and shell structures the formulation of the optimization problem is strongly dependant on the definition of the design variables. Therefore, the first part of the work is devoted to the definition of design variables and the forms of objective functions. Those design variables define stacking sequences of structures have discrete fiber orientations 0°, ±45°, 90° and a finite number of key points that are required in the evaluation of the curve Γ characterizing an external boundary of the structure or a structural shape understood in the sense of a structural geometry representing a shell/plate mid-surface or thickness distribution of structures. For the curve definition we have adopted one dimensional B-splines. Each curve is formed by an assembly of subsegments passing through certain key points. The positions of key points are randomly generated so that in the generation process it is possible to fulfill the required set of equality or inequality constraints. It is necessary to emphasize that the proposed method is very general and can be applicable to a very broad class of optimization problems. The generality of the approach is confirmed by the proof of the direct equivalence and mapping between discrete fiber orientations and continuous angle ply orientations. The evolution strategy is proposed herein as the optimization algorithm. Similarly as classical ones (e.g. ACO, SS, PS or ISM) it combines all features and advantages of evolution algorithms. It is worth to note that in the evolution strategy the number of children produced in one generation is not limited and it is not necessary to conduct mutation operations as in genetic algorithms. It simplifies significantly the effectiveness of numerical procedures. Then, two numerical examples have been solved to demonstrate the effectiveness of the proposed formulations and the optimization algorithm. They deal with thickness and stacking sequence optimization problems for circular cylindrical shells subjected to various dynamic and static constraints, respectively.     

力-变位关系全过程模拟的有限元位移控制新方法

材料、构件及结构的力-变位关系非线性全过程曲线有限元数值模拟中,极限强度和其后的软化下降段模拟一直是未得到较好解决的难题。位移增量控制法可以方便跨越力-变位关系中的极值点,因此它常被用于求解材料、构件及结构包含极限强度后软化下降段的力-变位关系非线性全过程曲线。但是,传统的位移增量控制法需要重新排列有限元方程的刚度矩阵,并存在求解非对称和非带状系数方程的问题,因而限制了其推广应用。该文提出了求解材料、构件及结构的力-变位关系非线性全过程曲线的一种新的位移增量控制方法,该方法通过修改刚度矩阵中相关对角系数的方式,将边界和力作用点的控制位移条件隐含到有限元方程中,从而可以采用有限元荷载控制方法同样的方式进行求解,保证了有限元方程系数矩阵在求解过程中的对称性和带状性,并可方便地在现有通用商业有限元软件中实现。算例分析表明了该文方法的有效性。     

The complexity of sparse polynomial interpolation over finite fields

We consider the problem of interpolating and zero testing sparse multivariate polynomials over finite fields from their values given by a black box. We give an estimate of the size of a test set constructed by Clausen, Dress, Grabmeier, and Karpinski [2] and improve the previously known lower bounds on the size of a minimal test set. Further, we present for arbitrary finite fields a new interpolation algorithm that uses only evaluations over the ground field, thereby answering an open question of Dür and Grabmeier [3].     

Exact solutions for the viscous sintering of multiply-connected fluid domains

Exact solutions for the viscous sintering of multiply-connected fluid domains are found. The approach is based on a recent observation by the author connecting viscous sintering and quadrature identities. The solutions are exact in that the evolution can be described in terms of a finite set of time-dependent parameters; it is shown that the evolution of certain initial fluid domains under the equations of Stokes flow driven by surface tension can be calculated by following the evolution of the coefficients of an algebraic curve. These coefficients satisfy a finite system of first-order nonlinear ordinary differential equations. Practical methods for solving this system are described. By way of example, explicit calculations of the sintering of unit cells deriving from square packings involving both unimodal and bimodal distributions of particles are given.