Elliptic Curve Cryptography (ECC) is one of the public key cryptosystems that works based on the algebraic models in the form of elliptic curves. Usually, in ECC to implement the encryption, the encoding of data must be carried out on the elliptic curve, which seems to be a preprocessing step. Similarly, after the decryption a post processing step must be conducted for mapping or decoding the corresponding data to the exact point on the elliptic curves. The Memory Mapping (MM) and Koblitz Encoding (KE) are the commonly used encoding models. But both encoding models have drawbacks as the MM needs more memory for processing and the KE needs more computational resources. To overcome these issues the proposed enhanced Koblitz encodi

With simple and undirected connected graph Φ, the Schultz and modified Schultz polynomials are defined as  and , respectively, where the summation is taken over all unordered pairs of distinct vertices in V(Φ), where V(Φ) is the vertex set of Φ, degu  is the degree of vertex u and d(v,u) is the ordinary distance between v and u, u≠v. In this study, the Shultz distance, modified Schultz distance, the polynomial, index, and average for both have been generalized, and this generalization has been applied  to some special graphs.

In this paper, the effective computational method (ECM) based on the standard monomial polynomial has been implemented to solve the nonlinear Jeffery-Hamel flow problem. Moreover, novel effective computational methods have been developed and suggested in this study by suitable base functions, namely Chebyshev, Bernstein, Legendre, and Hermite polynomials. The utilization of the base functions converts the nonlinear problem to a nonlinear algebraic system of equations, which is then resolved using the Mathematica^®12 program. The development of effective computational methods (D-ECM) has been applied to solve the nonlinear Jeffery-Hamel flow problem, then a comparison between the methods has been shown. Furthermore, the maximum

It has become necessary to change from a traditional system to an automated system in production processes, because it has high advantages. The most important of them is improving and increasing production. But there is still a need to improve and develop the work of these systems. The objective of this work is to study time reduction by combining multiple sequences of operations into one process. To carry out this work, the pneumatic system is designed to decrease\ increase the time of the sequence that performs a pick and place process through optimizing the sequences based on the obstacle dimensions. Three axes are represented using pneumatic cylinders that move according to the sequence used. The system is implemented and

  In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation.  The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation