This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobiquartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobiquartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (...

For classical discretizations of elliptic partial differential equations, like conforming finite elements or finite differences, block Jacobi methods are equivalent to classical Schwarz methods with minimal overlap, see for example [4]. This is different when the linear system (1) is obtained using DG methods. Our paper is organized as follows: in section 2 we describe several DG methods for li...

The reductive perturbation technique is used to obtain the Modified KP equation at critical densities distinguished by MKPE in plasma ion pair with fast electron positron. new structures reveal that super-solitary and period waveforms are derived via mathematical analysis of Jacobi-elliptic function expansions (MJEFE) for MKPE. electrostatic such as super-soliton, cnoidals, shock-like, super-di...

The article discusses and expands the known elements of eight-vertex model, paying special attention to parameterization matrix. matrix values are interconnected with knot through braids this model is valid on finite square lattices in two-dimensional space. A new solution parametrized free fermions a complex version elliptic functions, which lattice, will be constructed. range applicability Ja...

In 1967 Durrmeyer introduced a modiication of the Bernstein polynomials as a selfadjoint polynomial operator on L 2 0; 1] which proved to be an interesting and rich object of investigation. Incorporating Jacobi weights Berens and Xu obtained a more general class of operators, sharing all the advantages of Durrmeyer's modiication, and identiied these operators as de la Vall ee{Poussin means with...

In this paper, we investigate solitary wave solutions of the nonlinear electrical transmission line by using Jacobi elliptic function and auxiliary equation methods. We obtain as well kink, bright, dark, W-shaped solitons a result. For specific values modulus, depict soliton suitable parameters structure. Using method gives combined bright–bright dark–dark optical in fibers. One result emerges ...

Abstract A hierarchy of integrable semi-discrete equations is deduced in terms the discrete zero curvature equation as well its bi-Hamiltonian structure gotten through trace identity. The above separated into soluble ordinary differential according to relationship between elliptic variables and potentials, from which continuous flow straightened out via Abel–Jacobi coordinates resorting algebra...

This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 = dX +Z. We improve the doubling and addition steps in Miller’s algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific point representation to obtain the best resu...

We present an efficient null space free Jacobi-Davidson method to compute the positive eigenvalues of the degenerate elliptic operator arising from Maxwell’s equations. We consider spatial compatible discretizations such as Yee’s scheme which guarantee the existence of a discrete vector potential. During the Jacobi-Davidson iteration, the correction process is applied to the vector potential in...

This paper proposes the computation of the Tate pairing, Ate pairing and its variations on the special Jacobi quartic elliptic curve Y 2 D dX C Z. We improve the doubling and addition steps in Miller’s algorithm to compute the Tate pairing. We use the birational equivalence between Jacobi quartic curves and Weierstrass curves, together with a specific point representation to obtain the best res...