scholarly journals Asymmetric key Cryptography using Laplace Transform

2020 ◽  
Vol 9 (4) ◽  
pp. 3083-3087
Keyword(s):  
Network Security ◽  
Laplace Transform ◽  
Inverse Laplace Transform ◽  
Text File ◽  
Key Recovery ◽  
Public And Private ◽  
Plain Text ◽  
Private Key ◽  
Coefficient Corrélation ◽  
Key Recovery Attack

This paper presents a method of Asymmetric key cryptography using Laplace transform and inverse Laplace transform respectively on Maclaurin’s series to attain information and network Security. The public key and private key are used to encrypt and decrypt data in Asymmetric cryptography. Public and private key are generated using Encryption and Decryption algorithms with a numerical example. Frequency allocations of characters in plain text file and cipher text file with proposed algorithm are analyzed using bar diagrams. It has been observed that the repeated character in encipher file has same frequency while running ElGamal and RSA encryption algorithms but differ in proposed algorithm. Time complexity of each algorithm is tested for distinct file size and is presented in a suitable table. Statistical analysis for the proposed algorithm is performed using coefficient correlation and compared with ElGamal, RSA algorithms. All these tests ensure that the proposed algorithm provide network security and key recovery attack.

scholarly journals Novel Key Recovery Attack on Secure ECDSA Implementation by Exploiting Collisions between Unknown Entries

2021 ◽  
pp. 1-26
Author(s):  
Sunghyun Jin ◽  
Sangyub Lee ◽  
Sung Min Cho ◽  
HeeSeok Kim ◽  
Seokhie Hong
Keyword(s):  
Power Consumption ◽  
Digital Signatures ◽  
Scalar Multiplication ◽  
Side Channel ◽  
Validation Process ◽  
Key Recovery ◽  
Private Key ◽  
Signature Generation ◽  
Fixed Base ◽  
Key Recovery Attack

In this paper, we propose a novel key recovery attack against secure ECDSA signature generation employing regular table-based scalar multiplication. Our attack exploits novel leakage, denoted by collision information, which can be constructed by iteratively determining whether two entries loaded from the table are the same or not through side-channel collision analysis. Without knowing the actual value of the table entries, an adversary can recover the private key of ECDSA by finding the condition for which several nonces are linearly dependent by exploiting only the collision information. We show that this condition can be satisfied practically with a reasonable number of digital signatures and corresponding traces. Furthermore, we also show that all entries in the pre-computation table can be recovered using the recovered private key and a sufficient number of digital signatures based on the collision information. As case studies, we find that fixed-base comb and T_SM scalar multiplication are vulnerable to our attack. Finally, we verify that our attack is a real threat by conducting an experiment with power consumption traces acquired during T_SM scalar multiplication operations on an ARM Cortex-M based microcontroller. We also provide the details for validation process.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

scholarly journals Quadrature Integration Techniques for Random Hyperbolic PDE Problems

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 160
Author(s):  
Rafael Company ◽  
Vera N. Egorova ◽  
Lucas Jódar
Keyword(s):  
Numerical Methods ◽  
Laplace Transform ◽  
Quadrature Rule ◽  
Inverse Laplace Transform ◽  
Process Time ◽  
Efficient Computation ◽  
Hyperbolic Pde ◽  
Numerical Convergence ◽  
Laplace Transform Technique ◽  
Integration Techniques

In this paper, we consider random hyperbolic partial differential equation (PDE) problems following the mean square approach and Laplace transform technique. Randomness requires not only the computation of the approximating stochastic processes, but also its statistical moments. Hence, appropriate numerical methods should allow for the efficient computation of the expectation and variance. Here, we analyse different numerical methods around the inverse Laplace transform and its evaluation by using several integration techniques, including midpoint quadrature rule, Gauss–Laguerre quadrature and its extensions, and the Talbot algorithm. Simulations, numerical convergence, and computational process time with experiments are shown.

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

Modeling electro-osmotic flow and thermal transport of Caputo fractional Burgers fluid through a micro-channel

2021 ◽  
pp. 095440892110259
Author(s):  
Mohammed Abdulhameed ◽  
Garba Tahiru Adamu ◽  
Gulibur Yakubu Dauda
Keyword(s):  
Electric Field ◽  
Laplace Transform ◽  
Inverse Laplace Transform ◽  
Micro Channel ◽  
Osmotic Flow ◽  
Sine Transform ◽  
Fourier Sine ◽  
Fourier Sine Transform ◽  
Burgers Fluid ◽  
Electro Osmotic Flow

In this paper, we construct transient electro-osmotic flow of Burgers’ fluid with Caputo fractional derivative in a micro-channel, where the Poisson–Boltzmann equation described the potential electric field applied along the length of the microchannel. The analytical solution for the component of the velocity profile was obtained, first by applying the Laplace transform combined with the classical method of partial differential equations and, second by applying Laplace transform combined with the finite Fourier sine transform. The exact solution for the component of the temperature was obtained by applying Laplace transform and finite Fourier sine transform. Further, due to the complexity of the derived models of the governing equations for both velocity and temperature, the inverse Laplace transform was obtained with the aid of numerical inversion formula based on Stehfest's algorithms with the help of MATHCAD software. The graphical representations showing the effects of the time, retardation time, electro-kinetic width, and fractional parameters on the velocity of the fluid flow and the effects of time and fractional parameters on the temperature distribution in the micro-channel were presented and analyzed. The results show that the applied electric field, electro-osmotic force, electro-kinetic width, and relaxation time play a vital role on the velocity distribution in the micro-channel. The fractional parameters can be used to regulate both the velocity and temperature in the micro-channel. The study could be used in the design of various biomedical lab-on-chip devices, which could be useful for biomedical diagnosis and analysis.

MACSYMS's inverse Laplace transform

1989 ◽  
Vol 23 (1) ◽  
pp. 33-38
Author(s):  
M. Clarkson
Keyword(s):  
Laplace Transform ◽  
Inverse Laplace Transform

Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. Toutain ◽  
J.-L. Battaglia ◽  
C. Pradere ◽  
J. Pailhes ◽  
A. Kusiak ◽  
...  
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Periodic Function ◽  
Thermal Characterization ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Time Resolved ◽  
Reliable Technique ◽  
Numerical Inverse Laplace Transform ◽  
Thermal Disturbance

The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.

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