**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**232

# Search results for: Dickson Polynomial

##### 232 Cryptographic Attack on Lucas Based Cryptosystems Using Chinese Remainder Theorem

**Authors:**
Tze Jin Wong,
Lee Feng Koo,
Pang Hung Yiu

**Abstract:**

_{4,6}) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC

_{3}cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC

_{4,6}cryptosystem than LUC

_{3}and LUC cryptosystems. Current study concludes that LUC

_{4,6}cryptosystem is more secure than LUC and LUC

_{3}cryptosystems in sustaining against Lenstra’s attack.

**Keywords:**
Lucas sequence,
Dickson Polynomial,
faulty signature,
corresponding signature,
congruence.

##### 231 Transformations between Bivariate Polynomial Bases

**Authors:**
Dimitris Varsamis,
Nicholas Karampetakis

**Abstract:**

It is well known, that any interpolating polynomial p (x, y) on the vector space Pn,m of two-variable polynomials with degree less than n in terms of x and less than m in terms of y, has various representations that depends on the basis of Pn,m that we select i.e. monomial, Newton and Lagrange basis e.t.c.. The aim of this short note is twofold : a) to present transformations between the coordinates of the polynomial p (x, y) in the aforementioned basis and b) to present transformations between these bases.

**Keywords:**
Bivariate interpolation polynomial,
Polynomial basis,
Transformations.

##### 230 A Novel Deinterlacing Algorithm Based on Adaptive Polynomial Interpolation

**Authors:**
Seung-Won Jung,
Hye-Soo Kim,
Le Thanh Ha,
Seung-Jin Baek,
Sung-Jea Ko

**Abstract:**

**Keywords:**
Deinterlacing,
polynomial interpolation.

##### 229 Factoring a Polynomial with Multiple-Roots

**Authors:**
Feng Cheng Chang

**Abstract:**

**Keywords:**
Polynomial roots,
greatest common divisor,
Longhand polynomial division,
Euclidean GCD Algorithm.

##### 228 Reduction of Peak Input Currents during Charge Pump Boosting in Monolithically Integrated High-Voltage Generators

**Authors:**
Jan Doutreloigne

**Abstract:**

**Keywords:**
Bi-stable display driver,
Dickson charge pump,
highvoltage
generator,
peak current reduction,
sub-pump boosting,
variable frequency boosting.

##### 227 Designing FIR Filters with Polynomial Approach

**Authors:**
Sunil Bhooshan,
Vinay Kumar

**Abstract:**

**Keywords:**
FIR filter,
Polynomial.

##### 226 Blow up in Polynomial Differential Equations

**Authors:**
Rudolf Csikja,
Janos Toth

**Abstract:**

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

**Keywords:**
blow up,
finite escape time,
polynomial ODE,
singularity,
Lotka–Volterra equation,
Painleve analysis,
Ψ-series,
global existence

##### 225 An Attack on the Lucas Based El-Gamal Cryptosystem in the Elliptic Curve Group Over Finite Field Using Greater Common Divisor

**Authors:**
Lee Feng Koo,
Tze Jin Wong,
Pang Hung Yiu,
Nik Mohd Asri Nik Long

**Abstract:**

Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

**Keywords:**
Decryption,
encryption,
elliptic curve,
greater common divisor.

##### 224 On Generalized New Class of Matrix Polynomial Set

**Authors:**
Ghazi S. Kahmmash

**Abstract:**

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

**Keywords:**
Generating functions,
Recurrences relation and Generalization of the new class matrix polynomial set.

##### 223 Evolutionary Design of Polynomial Controller

**Authors:**
R. Matousek,
S. Lang,
P. Minar,
P. Pivonka

**Abstract:**

**Keywords:**
Evolutionary design,
Genetic algorithms,
PID controller,
Pole placement,
Polynomial controller

##### 222 Discrete Polynomial Moments and Savitzky-Golay Smoothing

**Authors:**
Paul O'Leary,
Matthew Harker

**Abstract:**

**Keywords:**
Gram polynomials,
Savitzky-Golay Smoothing,
Discrete Polynomial Moments

##### 221 Segmentation of Piecewise Polynomial Regression Model by Using Reversible Jump MCMC Algorithm

**Authors:**
Suparman

**Abstract:**

Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.

**Keywords:**
Piecewise,
Bayesian,
reversible jump MCMC,
segmentation.

##### 220 Fuzzy Fingerprint Vault using Multiple Polynomials

**Authors:**
Daesung Moon,
Woo-Yong Choi,
Kiyoung Moon

**Abstract:**

Fuzzy fingerprint vault is a recently developed cryptographic construct based on the polynomial reconstruction problem to secure critical data with the fingerprint data. However, the previous researches are not applicable to the fingerprint having a few minutiae since they use a fixed degree of the polynomial without considering the number of fingerprint minutiae. To solve this problem, we use an adaptive degree of the polynomial considering the number of minutiae extracted from each user. Also, we apply multiple polynomials to avoid the possible degradation of the security of a simple solution(i.e., using a low-degree polynomial). Based on the experimental results, our method can make the possible attack difficult 2192 times more than using a low-degree polynomial as well as verify the users having a few minutiae.

**Keywords:**
Fuzzy vault,
fingerprint recognition multiple polynomials.

##### 219 Computable Function Representations Using Effective Chebyshev Polynomial

**Authors:**
Mohammed A. Abutheraa,
David Lester

**Abstract:**

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

**Keywords:**
Approximation Theory,
Chebyshev Polynomial,
Computable Functions,
Computable Real Arithmetic,
Integration,
Numerical Analysis.

##### 218 Implementation and Analysis of Elliptic Curve Cryptosystems over Polynomial basis and ONB

**Authors:**
Yong-Je Choi,
Moo-Seop Kim,
Hang-Rok Lee,
Ho-Won Kim

**Abstract:**

**Keywords:**
Elliptic Curve Cryptosystem,
Crypto Algorithm,
Polynomial Basis,
Optimal Normal Basis,
Security.

##### 217 A New Approach to Polynomial Neural Networks based on Genetic Algorithm

**Authors:**
S. Farzi

**Abstract:**

**Keywords:**
GMDH,
GPNN,
GA,
PNN.

##### 216 A Deterministic Polynomial-time Algorithm for the Clique Problem and the Equality of P and NP Complexity Classes

**Authors:**
Zohreh O. Akbari

**Abstract:**

**Keywords:**
Clique problem,
Deterministic Polynomial-time
Algorithm,
Equality of P and NP Complexity Classes.

##### 215 Numerical Inverse Laplace Transform Using Chebyshev Polynomial

**Authors:**
Vinod Mishra,
Dimple Rani

**Abstract:**

In this paper, numerical approximate Laplace transform inversion algorithm based on Chebyshev polynomial of second kind is developed using odd cosine series. The technique has been tested for three different functions to work efficiently. The illustrations show that the new developed numerical inverse Laplace transform is very much close to the classical analytic inverse Laplace transform.

**Keywords:**
Chebyshev polynomial,
Numerical inverse Laplace transform,
Odd cosine series.

##### 214 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation

**Authors:**
Tsun-Hui Huang,
Shyue-Cheng Yang,
Chiou-Fen Shieh

**Abstract:**

In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

**Keywords:**
Polynomial constitutive equation,
solitary.

##### 213 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

**Authors:**
Azita Tajaddini,
Ramleh Shamsi

**Abstract:**

**Keywords:**
Linear matrix equation,
Block GMRES,
matrix Krylov
subspace,
polynomial preconditioner.

##### 212 On CR-Structure and F-Structure Satisfying Polynomial Equation

**Authors:**
Manisha Kankarej

**Abstract:**

**Keywords:**
CR-submainfolds,
CR-structure,
Integrability condition & Nijenhuis tensor.

##### 211 New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

**Authors:**
Oleksandr Poliakov,
Yevgen Pashkov,
Marina Kolesova,
Olena Chepenyuk,
Mykhaylo Kalinin,
Vadym Kramar

**Abstract:**

**Keywords:**
Iterative method,
Laguerre's method,
Newton's
method,
polynomial equation,
system of equations

##### 210 Particle Filter Applied to Noisy Synchronization in Polynomial Chaotic Maps

**Authors:**
Moussa Yahia,
Pascal Acco,
Malek Benslama

**Abstract:**

Polynomial maps offer analytical properties used to obtain better performances in the scope of chaos synchronization under noisy channels. This paper presents a new method to simplify equations of the Exact Polynomial Kalman Filter (ExPKF) given in [1]. This faster algorithm is compared to other estimators showing that performances of all considered observers vanish rapidly with the channel noise making application of chaos synchronization intractable. Simulation of ExPKF shows that saturation drawn on the emitter to keep it stable impacts badly performances for low channel noise. Then we propose a particle filter that outperforms all other Kalman structured observers in the case of noisy channels.

**Keywords:**
Chaos synchronization,
Saturation,
Fast ExPKF,
Particlefilter,
Polynomial maps.

##### 209 An Interval Type-2 Dual Fuzzy Polynomial Equations and Ranking Method of Fuzzy Numbers

**Authors:**
Nurhakimah Ab. Rahman,
Lazim Abdullah

**Abstract:**

According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.

**Keywords:**
Dual fuzzy polynomial equations,
Interval type-2,
Ranking method,
Value.

##### 208 On the Construction of m-Sequences via Primitive Polynomials with a Fast Identification Method

**Authors:**
Abhijit Mitra

**Abstract:**

**Keywords:**
Finite field,
irreducible polynomial,
primitive polynomial,
maximal length sequence,
additive shift register,
multiplicative
shift register.

##### 207 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra

**Authors:**
Z. Altawallbeh

**Abstract:**

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

**Keywords:**
Exterior algebra,
free resolution,
free and projective
modules,
Hochschild homology,
homotopic function,
symmetric
algebra.

##### 206 Non-Polynomial Spline Solution of Fourth-Order Obstacle Boundary-Value Problems

**Authors:**
Jalil Rashidinia,
Reza Jalilian

**Abstract:**

**Keywords:**
Quintic non-polynomial spline,
Boundary formula,
Convergence,
Obstacle problems.

##### 205 Comparison of the Existing Methods in Determination of the Characteristic Polynomial

**Authors:**
Mohammad Saleh Tavazoei,
Mohammad Haeri

**Abstract:**

**Keywords:**
Characteristic Polynomial,
Transient Response,
Filters,
Stability.

##### 204 On Chromaticity of Wheels

**Authors:**
Zainab Yasir Al-Rekaby,
Abdul Jalil M. Khalaf

**Abstract:**

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique.

**Keywords:**
Chromatic Polynomial,
Chromatically Equivalent,
Chromatically Unique,
Wheel.

##### 203 Generalized Chebyshev Collocation Method

**Authors:**
Junghan Kim,
Wonkyu Chung,
Sunyoung Bu,
Philsu Kim

**Abstract:**

In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

**Keywords:**
Generalized Chebyshev Collocation method,
Generalized Chebyshev Polynomial,
Initial value problem.