Elliptic curve cryptosystems, proposed by Koblitz ((11]) and Miller ((15]), can be constructed over a smaller eld of deenition than the ElGamal cryptosystems ((5]) or the RSA cryptosystems ((19]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate eecient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinat...

The aim of this report is to illustrate the issues in implementing a practical elliptic curve cryptographic system. Before doing the implementation, I will review group operation defined on elliptic curve over finite field. From that perspective, the efficiency of elliptic curve cryptographic system can be improved in two steps. The first step is to find a good representation of field element s...

a modified f-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (nlpdes) is discussed. we use this method to construct many new solutions to the nonlinear whitham-broer-kaup system (1+1)-dimensional. the solutions obtained include jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

Nutlets of 20 taxa of the tribe Marrubieae were examined by scanning electron microscopy (SEM) and detailed descriptions of nutlet micromorphological features for all examined taxa are provided. The nutlets exhibited variation in size, shape, color and surface sculpturing. The nutlets shape of most species studied is ovate, but rounded, broad ovate, elliptic, lanceolate, triangular and oblong c...

A Vehicular Ad hoc NETwork (VANET) is a type of mobile Peer-To-Peer wireless network that allows providing communication among nearby vehicles and between vehicles and nearby fixed roadside equipment. The lack of centralized infrastructure, high node mobility and increasing number of vehicles in VANETs result in several problems discussed in this paper, such as interrupting connections, difficu...

Discontinuous Galerkin (DG) and matrix-free finite element methods with a novel projective pressure estimation are combined to enable the numerical modeling of magma dynamics in 2D and 3D using the library deal.II . The physical model is an advection-reaction type system consisting of two hyperbolic equations to evolve porosity and soluble mineral abundance and one elliptic equation to recover ...

In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm altern...

A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur complement system that arises by eliminating the velocity. Each of the arising finite element problems...

in this paper, gaussian and elliptic high pass filters are analyzed for image sharpening qualitatively and quantatively . the filters are implemented in frequency domain using matlab software. experiments are performed to compare the performance of both the filters ,processed images are presented. the results demonstrate that elliptic yields better results.

Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA and its extensions to elliptic curves. Over elliptic curves, the analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in...