Elliptic curves over finite fields F2n play a prominent role in modern cryptography. Published quantum algorithms dealing with such curves build on a short Weierstrass form in combination with affine or projective coordinates. In this paper we show that changing the curve representation allows a substantial reduction in the number of T -gates needed to implement the curve arithmetic. As a tool,...

We present an algorithm which speeds scalar multiplication on a general elliptic curve by an estimated 3.8% to 8.5% over the best known general methods when using affine coordinates. This is achieved by eliminating a field multiplication when we compute 2P+Q from given points P , Q on the curve. We give applications to simultaneous multiple scalar multiplication and to the Elliptic Curve Method...

The Elliptic Curve Cryptography covers all relevant asymmetric cryptographic primitives like digital signatures and key agreement algorithms. In the present work, we develop a design of elliptic curve operations over binary Fields GF (2). The function used for this purpose is the scalar multiplication kP which is the core operation of ECCs. Where k is an integer and P is a point on an elliptic ...

This paper describes synthesizable VDHL implementation of elliptic curve Point Multiplication. Elliptic curves used for ECC are defined over mathematical structures called Galois fields. Based on the theory of ECC, this paper has carried out Modular addition/subtraction, EC Point doubling/addition, Modular multiplicative inversion, EC point multiplier, projective to affine coordinates conversio...

We present a novel algorithm for accurate, high quality point rendering, which is based on the formulation of splatting using homogeneous coordinates. In contrast to previous methods, this leads to perspective correct splat shapes, avoiding artifacts such as holes caused by the affine approximation of the perspective projection. Further, our algorithm implements the EWA resampling filter, hence...

Bi-Hamiltonian structures are of great importance in the theory of integrable Hamiltonian systems. The notion of compatibility of symplectic structures is a key aspect of bi-Hamiltonian systems. Because of this, a few different notions of compatibility have been introduced. In this paper we show that, under some additional assumptions, compatibility in the sense of Magri implies a notion of com...

In this paper an algorithm for robust extraction of leaf veins on plant leaf images is presented and tested on several images. It accomplishes a structure tracking by taking spatial information into account. The final result of the algorithm is a representation of the leaf veins as b-splines which contains the hierarchical information of the vein system. This allows to sample previously estimat...

A group code structure of a linear code is a description of the code as one-sided or two-sided ideal of a group algebra of a finite group. In these realizations, the group algebra is identified with the ambient space, and the group elements with the coordinates of the ambient space. It is well known that every affine-invariant code of length pm, with p prime, can be realized as an ideal of the ...

In this paper, we study and describe the universal Poisson deformation space of hypertoric varieties concretely. first application, show that affine as conical symplectic are classified by associated regular matroids (this is a partial generalization result Arbo Proudfoot). As corollary, obtain criterion when two quiver whose dimension vector have all coordinates equal to one isomorphic each ot...

Increasingly, geoscientists and biologists are monitoring the natural environment with total station and terrestrial laser scanning surveys. Due to the remote nature of many of the sites monitored (e.g., streams, rivers, glaciers, etc.) the surveys are often done in unprojected, Cartesian, local, assumed coordinate systems. However, without the survey data projected in real world coordinates th...