Search results for: singular elliptic divisibilitysequences
128 A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type
Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long
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This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.
Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1615127 Efficient Hardware Implementation of an Elliptic Curve Cryptographic Processor Over GF (2 163)
Authors: Massoud Masoumi, Hosseyn Mahdizadeh
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A new and highly efficient architecture for elliptic curve scalar point multiplication which is optimized for a binary field recommended by NIST and is well-suited for elliptic curve cryptographic (ECC) applications is presented. To achieve the maximum architectural and timing improvements we have reorganized and reordered the critical path of the Lopez-Dahab scalar point multiplication architecture such that logic structures are implemented in parallel and operations in the critical path are diverted to noncritical paths. With G=41, the proposed design is capable of performing a field multiplication over the extension field with degree 163 in 11.92 s with the maximum achievable frequency of 251 MHz on Xilinx Virtex-4 (XC4VLX200) while 22% of the chip area is occupied, where G is the digit size of the underlying digit-serial finite field multiplier.
Keywords: Elliptic curve cryptography, FPGA implementation, scalar point multiplication.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2508126 Novel Method for Elliptic Curve Multi-Scalar Multiplication
Authors: Raveen R. Goundar, Ken-ichi Shiota, Masahiko Toyonaga
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The major building block of most elliptic curve cryptosystems are computation of multi-scalar multiplication. This paper proposes a novel algorithm for simultaneous multi-scalar multiplication, that is by employing addition chains. The previously known methods utilizes double-and-add algorithm with binary representations. In order to accomplish our purpose, an efficient empirical method for finding addition chains for multi-exponents has been proposed.Keywords: elliptic curve cryptosystems, multi-scalar multiplication, addition chains, Fibonacci sequence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1566125 Analysis of a Singular Perturbed Synchronous Generator with a Bond Graph Approach
Authors: Gilberto Gonzalez-A, Noe Barrera-G
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An analysis of a synchronous generator in a bond graph approach is proposed. This bond graph allows to determine the simplified models of the system by using singular perturbations. Firstly, the nonlinear bond graph of the generator is linearized. Then, the slow and fast state equations by applying singular perturbations are obtained. Also, a bond graph to get the quasi-steady state of the slow dynamic is proposed. In order to verify the effectiveness of the singularly perturbed models, simulation results of the complete system and reduced models are shown.Keywords: Bond graph modelling, synchronous generator, singular perturbations
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1655124 Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space
Authors: Li Xiguang
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In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1420123 Effects of Geometry on Intensity of Singular Stress Fields at the Corner of Single-Lap Joints
Authors: Yu Zhang, Nao-Aki Noda, Kentaro Takaishi
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This paper discusses effects of adhesive thickness, overlap length and material combinations on the single-lap joints strength from the point of singular stress fields. A useful method calculating the ratio of intensity of singular stress is proposed using FEM for different adhesive thickness and overlap length. It is found that the intensity of singular stress increases with increasing adhesive thickness, and decreases with increasing overlap length. The increment and decrement are different depending on material combinations between adhesive and adherent.Keywords: Adhesive thickness, Overlap length, Intensity ofsingular stress, Single-lap joint
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1719122 Parallel Multisplitting Methods for Singular Linear Systems
Authors: Guangbin Wang, Fuping Tan
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In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.
Keywords: Singular H-matrix, linear systems, extrapolated iterative method, GMAOR method, convergence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1305121 Positive Solutions for Boundary Value Problems of Fourth-Order Nonlinear Singular Differential Equations in Banach Space
Authors: Li Xiguang
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In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1637120 Alternative Key Exchange Algorithm Based on Elliptic Curve Digital Signature Algorithm Certificate and Usage in Applications
Authors: A. Andreasyan, C. Connors
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The Elliptic Curve Digital Signature algorithm-based X509v3 certificates are becoming more popular due to their short public and private key sizes. Moreover, these certificates can be stored in Internet of Things (IoT) devices, with limited resources, using less memory and transmitted in network security protocols, such as Internet Key Exchange (IKE), Transport Layer Security (TLS) and Secure Shell (SSH) with less bandwidth. The proposed method gives another advantage, in that it increases the performance of the above-mentioned protocols in terms of key exchange by saving one scalar multiplication operation.
Keywords: Cryptography, elliptic curve digital signature algorithm, key exchange, network security protocols.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 523119 The Elliptic Curves y2 = x3 - t2x over Fp
Authors: Ahmet Tekcan
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Let p be a prime number, Fp be a finite field and t ∈ F*p= Fp- {0}. In this paper we obtain some properties of ellipticcurves Ep,t: y2= y2= x3- t2x over Fp. In the first sectionwe give some notations and preliminaries from elliptic curves. In the second section we consider the rational points (x, y) on Ep,t. Wegive a formula for the number of rational points on Ep,t over Fnp for an integer n ≥ 1. We also give some formulas for the sum of x?andy?coordinates of the points (x, y) on Ep,t. In the third section weconsider the rank of Et: y2= x3- t2x and its 2-isogenous curve Et over Q. We proved that the rank of Etand Etis 2 over Q. In the last section we obtain some formulas for the sums Σt∈F?panp,t for an integer n ≥ 1, where ap,t denote the trace of Frobenius.
Keywords: Elliptic curves over finite fields, rational points onelliptic curves, rank, trace of Frobenius.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1996118 Implementing Authentication Protocol for Exchanging Encrypted Messages via an Authentication Server Based on Elliptic Curve Cryptography with the ElGamal-s Algorithm
Authors: Konstantinos Chalkias, George Filiadis, George Stephanides
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In this paper the authors propose a protocol, which uses Elliptic Curve Cryptography (ECC) based on the ElGamal-s algorithm, for sending small amounts of data via an authentication server. The innovation of this approach is that there is no need for a symmetric algorithm or a safe communication channel such as SSL. The reason that ECC has been chosen instead of RSA is that it provides a methodology for obtaining high-speed implementations of authentication protocols and encrypted mail techniques while using fewer bits for the keys. This means that ECC systems require smaller chip size and less power consumption. The proposed protocol has been implemented in Java to analyse its features and vulnerabilities in the real world.
Keywords: Elliptic Curve Cryptography, ElGamal, authentication protocol.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1986117 The Symmetric Solutions for Boundary Value Problems of Second-Order Singular Differential Equation
Authors: Li Xiguang
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In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1257116 Existence of Solution for Singular Two-point Boundary Value Problem of Second-order Differential Equation
Authors: Xiguang Li
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In this paper, by constructing a special set and utilizing fixed point theory in coin, we study the existence of solution of singular two point’s boundary value problem for second-order differential equation, which improved and generalize the result of related paper.
Keywords: Singular differential equation, boundary value problem, coin, fixed point theory.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1088115 The Symmetric Solutions for Three-Point Singular Boundary Value Problems of Differential Equation
Authors: Li Xiguang
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In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.
Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1370114 Solving Linear Matrix Equations by Matrix Decompositions
Authors: Yongxin Yuan, Kezheng Zuo
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In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.
Keywords: Matrix equation, Generalized inverse, Generalized singular-value decomposition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2006113 Multiple Soliton Solutions of (2+1)-dimensional Potential Kadomtsev-Petviashvili Equation
Authors: Mohammad Najafi, Ali Jamshidi
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We employ the idea of Hirota-s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived.
Keywords: Hirota bilinear method, potential Kadomtsev-Petviashvili equation, multiple soliton solutions, multiple singular soliton solutions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1323112 Encryption Image via Mutual Singular Value Decomposition
Authors: Adil Al-Rammahi
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Image or document encryption is needed through egovernment data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal basis, and spectral diagonal basis. Product of the two row basis is calculated. Similarly the product of the two column basis is achieved. Finally we transform or save the files of public, row product and column product. In decryption stage, the original image is deduced by mutual method of the three public files.
Keywords: Image cryptography, Singular values decomposition.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2039111 Deniable Authentication Protocol Resisting Man-in-the-Middle Attack
Authors: Song Han, Wanquan Liu, Elizabeth Chang
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Deniable authentication is a new protocol which not only enables a receiver to identify the source of a received message but also prevents a third party from identifying the source of the message. The proposed protocol in this paper makes use of bilinear pairings over elliptic curves, as well as the Diffie-Hellman key exchange protocol. Besides the security properties shared with previous authentication protocols, the proposed protocol provides the same level of security with smaller public key sizes.Keywords: Deniable Authentication, Man-in-the-middleAttack, Cryptography, Elliptic Curves.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1576110 Principal Component Analysis using Singular Value Decomposition of Microarray Data
Authors: Dong Hoon Lim
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A series of microarray experiments produces observations of differential expression for thousands of genes across multiple conditions. Principal component analysis(PCA) has been widely used in multivariate data analysis to reduce the dimensionality of the data in order to simplify subsequent analysis and allow for summarization of the data in a parsimonious manner. PCA, which can be implemented via a singular value decomposition(SVD), is useful for analysis of microarray data. For application of PCA using SVD we use the DNA microarray data for the small round blue cell tumors(SRBCT) of childhood by Khan et al.(2001). To decide the number of components which account for sufficient amount of information we draw scree plot. Biplot, a graphic display associated with PCA, reveals important features that exhibit relationship between variables and also the relationship of variables with observations.
Keywords: Principal component analysis, singular value decomposition, microarray data, SRBCT
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3210109 Robust Fuzzy Control of Nonlinear Fuzzy Impulsive Singular Perturbed Systems with Time-varying Delay
Authors: Caigen Zhou, Haibo Jiang
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The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1653108 Fingerprint Image Encryption Using a 2D Chaotic Map and Elliptic Curve Cryptography
Authors: D. M. S. Bandara, Yunqi Lei, Ye Luo
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Fingerprints are suitable as long-term markers of human identity since they provide detailed and unique individual features which are difficult to alter and durable over life time. In this paper, we propose an algorithm to encrypt and decrypt fingerprint images by using a specially designed Elliptic Curve Cryptography (ECC) procedure based on block ciphers. In addition, to increase the confusing effect of fingerprint encryption, we also utilize a chaotic-behaved method called Arnold Cat Map (ACM) for a 2D scrambling of pixel locations in our method. Experimental results are carried out with various types of efficiency and security analyses. As a result, we demonstrate that the proposed fingerprint encryption/decryption algorithm is advantageous in several different aspects including efficiency, security and flexibility. In particular, using this algorithm, we achieve a margin of about 0.1% in the test of Number of Pixel Changing Rate (NPCR) values comparing to the-state-of-the-art performances.Keywords: Arnold cat map, biometric encryption, block cipher, elliptic curve cryptography, fingerprint encryption, Koblitz’s Encoding.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1029107 Lifting Wavelet Transform and Singular Values Decomposition for Secure Image Watermarking
Authors: Siraa Ben Ftima, Mourad Talbi, Tahar Ezzedine
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In this paper, we present a technique of secure watermarking of grayscale and color images. This technique consists in applying the Singular Value Decomposition (SVD) in LWT (Lifting Wavelet Transform) domain in order to insert the watermark image (grayscale) in the host image (grayscale or color image). It also uses signature in the embedding and extraction steps. The technique is applied on a number of grayscale and color images. The performance of this technique is proved by the PSNR (Pick Signal to Noise Ratio), the MSE (Mean Square Error) and the SSIM (structural similarity) computations.Keywords: Color image, grayscale image, singular values decomposition, lifting wavelet transform, image watermarking, watermark, secure.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 976106 Optimal Placement of Piezoelectric Actuators on Plate Structures for Active Vibration Control Using Modified Control Matrix and Singular Value Decomposition Approach
Authors: Deepak Chhabra, Gian Bhushan, Pankaj Chandna
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The present work deals with the optimal placement of piezoelectric actuators on a thin plate using Modified Control Matrix and Singular Value Decomposition (MCSVD) approach. The problem has been formulated using the finite element method using ten piezoelectric actuators on simply supported plate to suppress first six modes. The sizes of ten actuators are combined to outline one actuator by adding the ten columns of control matrix to form a column matrix. The singular value of column control matrix is considered as the fitness function and optimal positions of the actuators are obtained by maximizing it with GA. Vibration suppression has been studied for simply supported plate with piezoelectric patches in optimal positions using Linear Quadratic regulator) scheme. It is observed that MCSVD approach has given the position of patches adjacent to each-other, symmetric to the centre axis and given greater vibration suppression than other previously published results on SVD.
Keywords: Closed loop Average dB gain, Genetic Algorithm (GA), LQR Controller, MCSVD, Optimal positions, Singular Value Decomposition (SVD) Approaches.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3035105 An Algorithm for Computing the Analytic Singular Value Decomposition
Authors: Drahoslava Janovska, Vladimir Janovsky, Kunio Tanabe
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A proof of convergence of a new continuation algorithm for computing the Analytic SVD for a large sparse parameter– dependent matrix is given. The algorithm itself was developed and numerically tested in [5].
Keywords: Analytic Singular Value Decomposition, large sparse parameter–dependent matrices, continuation algorithm of a predictorcorrector type.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1414104 A Study on the Quality of Hexapod Machine Tool's Workspace
Authors: D. Karimi, M.J. Nategh
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One of the main concerns about parallel mechanisms is the presence of singular points within their workspaces. In singular positions the mechanism gains or loses one or several degrees of freedom. It is impossible to control the mechanism in singular positions. Therefore, these positions have to be avoided. This is a vital need especially in computer controlled machine tools designed and manufactured on the basis of parallel mechanisms. This need has to be taken into consideration when selecting design parameters. A prerequisite to this is a thorough knowledge about the effect of design parameters and constraints on singularity. In this paper, quality condition index was introduced as a criterion for evaluating singularities of different configurations of a hexapod mechanism obtainable by different design parameters. It was illustrated that this method can effectively be employed to obtain the optimum configuration of hexapod mechanism with the aim of avoiding singularity within the workspace. This method was then employed to design the hexapod table of a CNC milling machine.Keywords: Hexapod, Machine Tool, Singularity, Workspace.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1916103 Numerical Study of Iterative Methods for the Solution of the Dirichlet-Neumann Map for Linear Elliptic PDEs on Regular Polygon Domains
Authors: A. G. Sifalakis, E. P. Papadopoulou, Y. G. Saridakis
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A generalized Dirichlet to Neumann map is one of the main aspects characterizing a recently introduced method for analyzing linear elliptic PDEs, through which it became possible to couple known and unknown components of the solution on the boundary of the domain without solving on its interior. For its numerical solution, a well conditioned quadratically convergent sine-Collocation method was developed, which yielded a linear system of equations with the diagonal blocks of its associated coefficient matrix being point diagonal. This structural property, among others, initiated interest for the employment of iterative methods for its solution. In this work we present a conclusive numerical study for the behavior of classical (Jacobi and Gauss-Seidel) and Krylov subspace (GMRES and Bi-CGSTAB) iterative methods when they are applied for the solution of the Dirichlet to Neumann map associated with the Laplace-s equation on regular polygons with the same boundary conditions on all edges.Keywords: Elliptic PDEs, Dirichlet to Neumann Map, Global Relation, Collocation, Iterative Methods, Jacobi, Gauss-Seidel, GMRES, Bi-CGSTAB.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1673102 A New Design Partially Blind Signature Scheme Based on Two Hard Mathematical Problems
Authors: Nedal Tahat
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Recently, many existing partially blind signature scheme based on a single hard problem such as factoring, discrete logarithm, residuosity or elliptic curve discrete logarithm problems. However sooner or later these systems will become broken and vulnerable, if the factoring or discrete logarithms problems are cracked. This paper proposes a secured partially blind signature scheme based on factoring (FAC) problem and elliptic curve discrete logarithms (ECDL) problem. As the proposed scheme is focused on factoring and ECDLP hard problems, it has a solid structure and will totally leave the intruder bemused because it is very unlikely to solve the two hard problems simultaneously. In order to assess the security level of the proposed scheme a performance analysis has been conducted. Results have proved that the proposed scheme effectively deals with the partial blindness, randomization, unlinkability and unforgeability properties. Apart from this we have also investigated the computation cost of the proposed scheme. The new proposed scheme is robust and it is difficult for the malevolent attacks to break our scheme.
Keywords: Cryptography, Partially Blind Signature, Factoring, Elliptic Curve Discrete Logarithms.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1734101 Cryptanalysis of Chang-Chang-s EC-PAKA Protocol for Wireless Mobile Networks
Authors: Hae-Soon Ahn, Eun-Jun Yoon
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With the rapid development of wireless mobile communication, applications for mobile devices must focus on network security. In 2008, Chang-Chang proposed security improvements on the Lu et al.-s elliptic curve authentication key agreement protocol for wireless mobile networks. However, this paper shows that Chang- Chang-s improved protocol is still vulnerable to off-line password guessing attacks unlike their claims.
Keywords: Authentication, key agreement, wireless mobile networks, elliptic curve, password guessing attacks.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1474100 A Nonoblivious Image Watermarking System Based on Singular Value Decomposition and Texture Segmentation
Authors: Soroosh Rezazadeh, Mehran Yazdi
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In this paper, a robust digital image watermarking scheme for copyright protection applications using the singular value decomposition (SVD) is proposed. In this scheme, an entropy masking model has been applied on the host image for the texture segmentation. Moreover, the local luminance and textures of the host image are considered for watermark embedding procedure to increase the robustness of the watermarking scheme. In contrast to all existing SVD-based watermarking systems that have been designed to embed visual watermarks, our system uses a pseudo-random sequence as a watermark. We have tested the performance of our method using a wide variety of image processing attacks on different test images. A comparison is made between the results of our proposed algorithm with those of a wavelet-based method to demonstrate the superior performance of our algorithm.Keywords: Watermarking, copyright protection, singular value decomposition, entropy masking, texture segmentation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 171999 Numerical Analysis of the Influence of Tip Devices on the Power Coefficient of a VAWT
Authors: Federico Amato, Gabriele Bedon, Marco Raciti Castelli, Ernesto Benini
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The aerodynamic performances of vertical axis wind turbines are highly affected by tip vortexes. In the present work, different tip devices are considered and simulated against a baseline rotor configuration, with the aim of identifying the best tip architecture. Three different configurations are tested: winglets, an elliptic termination and an aerodynamic bulkhead. A comparative analysis on the most promising architectures is conducted, focusing also on blade torque evolution during a full revolution of the rotor blade. The most promising technology is concluded to be a well designed winglet.Keywords: Darrieus Wind Turbine, Tip Devices, Tip Vortexes, Winglet, Elliptic Termination, Aerodynamic Bulkhead
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2192