Vectorial Algorithm Research Articles

Vectorial Decoding Algorithm for Fast Correlation Attack and Its Applications to Stream Cipher Grain-128a

Fast correlation attack, pioneered by Meier and Staffelbach, is an important cryptanalysis tool for LFSR-based stream cipher, which exploits the correlation between the LFSR state and key stream and targets at recovering the initial state of LFSR via a decoding algorithm. In this paper, we develop a vectorial decoding algorithm for fast correlation attack, which is a natural generalization of the original binary approach. Our approach benefits from the contributions of all correlations in a subspace. We propose two novel criteria to improve the iterative decoding algorithm. We also give some cryptographic properties of the new FCA which allows us to estimate the efficiency and complexity bounds. Furthermore, we apply this technique to the well-analyzed stream cipher Grain-128a. Based on a hypothesis, an interesting result for its security bound is deduced from the perspective of iterative decoding. Our analysis reveals the potential vulnerability for LFSRs over matrix ring and also for nonlinear functions with biased multidimensional linear approximations such as Grain-128a.

On the properties of a single vortex solution of Ginzburg–Landau model of superconductivity

We closely examine a single vortex formation in an infinitely long cylinder with a rectangular crossection through field-cooling process with Temperature and Time-dependent Ginzburg–Landau model. We identify a solution for which components of vector potential and order function display a certain symmetry, which we name symmetric vortex solution. Furthermore, we observe that single vortex formation is associated with a jump discontinuity in all components of solution and associated observables, and illustrate graphically dynamics of transition. We carry out simulations in a vectorial algorithm using a variable order stiff ODE integration scheme of MATLAB.

Environmental pollution monitoring: a novel vectorial algorithm technique for oil detection in wastewater

This work presents a new technique based on converting IR absorbance of each element and that of a mixture into phasors. Projecting the mixture phasor vector on that of each component results in the concentration of this component in the mixture. This novel technique, when compared with existing pattern recognition techniques, makes it easy to analyze the constituents of a mixture with high accuracy in the presence of traces of unknown components. It is found that the new algorithm is capable of detecting the presence of oil in water samples containing many other unknown polluting elements up to 0.1 mg/L. This new algorithm is tested on laboratory contaminated samples and then used to monitor pollution by lubricating oil in an industrial zone.

Analysis of Leaky Modes in Photonic Crystal Fibers Using the Surface Integral Equation Method

A fully vectorial algorithm based on the surface integral equation method for the modelling of leaky modes in photonic crystal fibers (PCFs) by solely solving the complex propagation constants of characteristic equations is presented. It can be used for calculations of the complex effective index and confinement losses of photonic crystal fibers. As complex root examination is the key technique in the solution, the new algorithm which possesses this technique can be used to solve the leaky modes of photonic crystal fibers. The leaky modes of solid-core PCFs with a hexagonal lattice of circular air-holes are reported and discussed. The simulation results indicate how the confinement loss by the imaginary part of the effective index changes with air-hole size, the number of rings of air-holes, and wavelength. Confinement loss reductions can be realized by increasing the air-hole size and the number of air-holes. The results show that the confinement loss rises with wavelength, implying that the light leaks more easily for longer wavelengths; meanwhile, the losses are decreased significantly as the air-hole size d/Λ is increased.

Unitary Polynomial Propagator Solving Maxwell’s Equations Allowing Arbitrarily Large Time Steps

A novel fully explicit vectorial time-domain algorithm for the analysis of photonic devices capable of solving Maxwell’s equations with arbitrarily large time steps is presented. Furthermore, the time-domain propagation algorithm ensures energy conservation and stability. For this purpose, a unitary time-domain propagation scheme is defined by a suitable polynomial expansion of the propagator.

Simulation of birefringence effects on the dominant transversal laser resonator mode caused by anisotropic crystals.

Birefringence effects can have a significant influence on the polarization state as well as on the transversal mode structure of laser resonators. This work introduces a flexible, fast and fully vectorial algorithm for the analysis of resonators containing homogeneous, anisotropic optical components. It is based on a generalization of the Fox and Li algorithm by field tracing, enabling the calculation of the dominant transversal resonator eigenmode. For the simulation of light propagation through the anisotropic media, a fast Fourier Transformation (FFT) based angular spectrum of plane waves approach is introduced. Besides birefringence effects, this technique includes intra-crystal diffraction and interface refraction at crystal surfaces. The combination with numerically efficient eigenvalue solvers, namely vector extrapolation methods, ensures the fast convergence of the method. Furthermore a numerical example is presented which is in good agreement to experimental measurements.

Reduction of product platform complexity by vectorial Euclidean algorithm

In traditional machine, equipment and devices design, technical solutions are practically independent, thus increasing designs cost and complexity. Overcoming this situation has been tackled just using designer’s experience. In this work, a product platform complexity reduction is presented based on a matrix representation of technical solutions versus product properties. This matrix represents the product platform. From this matrix, the Euclidean distances among technical solutions are obtained. Thus, the vectorial distances among technical solutions are identified in a new matrix of order of the number of technical solutions identified. This new matrix can be reorganized in groups with a hierarchical structure, in such a way that modular design of products is now more tractable. As a result of this procedure, the minimum vector distances are found thus being possible to identify the best technical solutions for the design problem raised. Application of these concepts is shown with two examples.

Vectorial total variation model for multi-channel SAR image denoising

The vectorial total variation model and algorithm are studied for multi-channel SAR image denoising.After introducing the vectorial total variation model,an accelerative fix-point iterative algorithm was proposed and its convergence was proved.By improving the filter coefficient of the fix-point iterative process,an adaptive vectorial total variation model was developed for multi-channel SAR image denoising,whose iterative algorithm and convergence theorem were present.The performance of denoising and resolution preservation of our models was tested by multi-polarimetric,multi-temporal RADARSAT-2 images,in addition to the validation of the convergence and the convergent speed of the proposed algorithms.

A vectorial algorithm with finite element method for prediction of powder segregation in metal injection molding

SUMMARYThe design of the mold and the choice of the injection parameters for metal injection molding (MIM) is required to maintain homogeneity of the filled mixture. However, powder segregation is unavoidable in MIM because of the significant difference in densities of the metallic powder and the polymer binder. To achieve an effective prediction of segregation effect, a biphasic model based on mixture theory is employed. The viscous behaviors of each phase and the interaction coefficient between the flows of the two phases should be determined. The solution of two coupled Navier–Stokes equations results in a tremendous computation effort. The previous development of an explicit algorithm makes the biphasic simulation much faster than that of the classic methods. However, it is strongly desired to reduce or even eliminate the numerous global solutions for pressure fields at each time step. Hence, a new vectorial algorithm is proposed and developed to perform the simulation only by vectorial operations. It provides the anticipated efficiency in the simulation of biphasic modeling, and the advantage to use the classic elements of equal‐order interpolations. Some results produced by the two algorithms are compared with the experimental values to validate the new vectorial algorithm. Copyright © 2012 John Wiley & Sons, Ltd.

Usability limits of the scalar effective frequency method used to determine modes distributions in oxide-confined vertical-cavity surface-emitting diode lasers

The accuracy of the commercially used, simplified scalar optical effective frequency method (EFM) is verified by comparing its results with those obtained using more accurate vectorial models represented by the method of lines (MoL). Both EFM and MoL methods are applied to the modern telecommunication oriented GaAs-based oxide-confined vertical-cavity surface-emitting diode laser (VCSEL) emitting 1.3 µm radiation from the InGaAsN/GaAs double quantum well active region. Although both methods are applied to the specific laser structure, the conclusion remains valid for a broad range of different VCSEL designs. The scalar EFM approach has been found to remain surprisingly often quite exact; nevertheless, it fails for structures violating its fundamental assumption of plane wave propagation within the laser cavity. Therefore, a noteworthy discrepancy between modes calculated with the aid of scalar and vectorial approaches occurs for weaker guidance, i.e. for higher-order modes, smaller aperture diameters, thinner oxidation layers and/or apertures shifted from the antinode position. These cases need an exclusive use of the more exact but also more time-consuming vectorial algorithms.

Vectorial languages and linear temporal logic

Determining for a given deterministic complete automaton the sequence of visited states while reading a given word is the core of important problems with automata-based solutions, such as approximate string matching. The main difficulty is to do this computation efficiently. Considering words as vectors and working on them using vectorial operations allows to solve the problem faster than using local operations. In this paper, we show first that the set of vectorial operations needed by an algorithm representing a given automaton depends on the language accepted by the automaton. We give precise characterizations for star-free, solvable and regular languages using vectorial algorithms. We also study classes of languages associated with restricted sets of vectorial operations and relate them with languages defined by fragments of linear temporal logic. Finally, we consider the converse problem of constructing an automaton from a given vectorial algorithm. As a byproduct, we show that the satisfiability problem for some extensions of LTL characterizing solvable and regular languages is PSPACE-complete.

A vectorial algorithm for tracing discrete straight lines in N-dimensional generalized grids

This paper presents an algorithm to trace discrete straight lines in regular grids of any dimension. Most known line tracing algorithms have been developed in Z/sup 2/ and Z/sup 3/ orthogonal grids. The contribution of this paper is the definition of a method to trace lines in nonorthogonal grids in any dimension. This method is not restricted to being used with a specific grid connectivity as other widespread methods are. Good performance can be achieved because only additions are used during line tracing.

On capacitated stochastic chain problems in a network

This paper considers two basic problems relating to capacitated chains in a stochastic network in which each arc has a discrete arbitrary probability distribution for its capacity. Given a source-sink pair, the first problem is to find an optimal capacity chain subject to a chance constraint. By treating the right-hand side of the chance constraint also as a decision variable, the complete spectrum of optimal solutions is found by a polynomial algorithm. The second problem is to find a chain with the highest expected capacity. A vectorial labeling algorithm which exploits a certain dominance property and an effective bound is presented for solving this problem. Both are illustrated by an example, and computational results on the second are included. © 1998 John Wiley & Sons, Inc. Networks 31: 19–27, 1998

An extension of Lagrange’s theorem to interval exchange transformations over quadratic fields

LetT be an interval exchange transformation onN intervals whose lengths lie in a quadratic number field. Let {Tn}n=1∞ be any sequence of interval exchange transformations such thatT1 =T andTn is the first return map induced byTn-1 on one of its exchanged intervals In-1. We prove that {Tn}n=1∞ contains finitely many transformations up to rescaling. If the interval In is chosen according to a consistent pattern of induction, e.g., the first interval is chosen, then there existk,n0 ∈ ℤ+, λ ∈R+ such that for alln ≥n0,In = λIn+k andTn,Tn+k are the same up to rescaling. Rephrased arithmetically, this says that a certain family of vectorial division algorithms, applied to quadratic vector spaces, yields sequences of remainders that are eventually periodic. WhenN = 2 the assertion reduces to Lagrange’s classical theorem that the simple continued fraction expansion of a quadratic irrational is eventually periodic. We also discuss the case of periodic induced sequences.

Fast algorithms for multi-grid solvers of three-dimensional boundary value problems in structural analysis

A large number of analyses in structural mechanics may be treated using the three-dimensional boundary value formulation of the problem. The use of the standard finite element techniques, typically comprising local stiffness matrix assembling and a direct eliminating procedure for solving resulting systems of equations, is usually computationally very demanding. It is natural to employ here multi-grid methods giving a good convergence in solving boundary value elliptic problems. But in spite of the fact that these methods avoid a costly eliminating procedure, the difficulties associated with programming costs, grid generation, storage requirements and introducing a coarse problem concept, remain acute. There are some potential methods to overcome these difficulties by allowing some simplifications. We propose one of them associated with constructing a simplified data structure based on logically rectangular grids which leads to developing efficient vectorial algorithms for executing basic multi-grid operations. These algorithms appeared to be easy to program and good for pre- and post-processing, suitable for parallel processing and very efficient when implemented as a software package for heat condition and stress-strain state analyses of various engineering structures, such as reactor vessels, dam structures, building fragments and others. We propose the substructuring algorithm in the framework of a multi-grid method which is useful for treating problems with cyclic and complicated domains. It is based on dividing the domain into simple parts each admitting the simplified data structure. We also represent the multi-grid method previously developed to demonstrate the possibility of using the algorithmic approaches. In conclusion we consider the example of an actual problem illustrating the 3-D finite element analysis of a reactor vessel.

On the multi‐grid technique for solving three‐dimensional boundary value engineering problems

AbstractThe paper proposes an iterative technique with a similar multi‐grid operator for solving complex spatial bounctary value problems. The description of the method and efficient vectorial algorithms based on a simple ctata structure applicable to solving three‐dimensional engineering problems are presented. The discussion of the method's convergence includes theoretical grounds and practical aspects. We give a general proof of convergence and consider the model cases to estimate the rate of convergence. We also address the histories of convergence derived from the numerical tests and consider two examples of practical problems.

An error analysis for absolute and relative approximation

We consider the vectorial algorithm for finding best polynomial approximationsp ∈Pn to a given function ƒ ∈C[a, b], with respect to the norm ‖·‖s, defined by ‖p -ϕ‖s = ‖w1(p -f)‖∞ + ‖w2(p - ƒ)‖∞. A bound for the modulus of continuity of the best vectorial approximation operator is given, and using the floating point calculus of J. H. Wilkinson, a bound for the rounding error in the algorithm is derived. For given ƒ, these estimates provide an indication ol the conditioning of the problem, an estimate of the obtainable accuracy, and a practical method for terminating the iteration.