Elliptic curve point multiplication information

Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself repeatedly. It is used in elliptic...

key curve point Q A = d A × G {\displaystyle Q_{A}=d_{A}\times G} . We use × {\displaystyle \times } to denote elliptic curve point multiplication by a...

mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over...

In mathematics, complex multiplication (CM) is the theory of elliptic curves E that have an endomorphism ring larger than the integers. Put another way...

In mathematics, the Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form...

In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods...

algebraic geometry, the twisted Edwards curves are plane models of elliptic curves, a generalisation of Edwards curves introduced by Bernstein, Birkner, Joye...

including elliptic curve point multiplication, Diffie–Hellman modular exponentiation over a prime, or an RSA signature calculation. Elliptic Curves and prime...

This curve was suggested for application in elliptic curve cryptography, because arithmetic in this curve representation is faster and needs less memory...

mathematics, the Edwards curves are a family of elliptic curves studied by Harold Edwards in 2007. The concept of elliptic curves over finite fields is widely...

An important aspect in the study of elliptic curves is devising effective ways of counting points on the curve. There have been several approaches to do...

The elliptic curve only hash (ECOH) algorithm was submitted as a candidate for SHA-3 in the NIST hash function competition. However, it was rejected in...

In mathematics, the moduli stack of elliptic curves, denoted as M 1 , 1 {\displaystyle {\mathcal {M}}_{1,1}} or M ell {\displaystyle {\mathcal {M}}_{\textrm...

mathematics, the Twisted Hessian curve represents a generalization of Hessian curves; it was introduced in elliptic curve cryptography to speed up the addition...

semistable elliptic curve may be described more concretely as an elliptic curve that has bad reduction only of multiplicative type. Suppose E is an elliptic curve...

In mathematics, the Jacobi curve is a representation of an elliptic curve different from the usual one defined by the Weierstrass equation. Sometimes it...

Egyptian multiplication (also known as Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication), one of two...

is the equation of an elliptic cylinder. Further simplification can be obtained by translation of axes and scalar multiplication. If ρ {\displaystyle \rho...

called elliptic modular forms to emphasize the point) are related to elliptic curves. Jacobi forms are a mixture of modular forms and elliptic functions...

cryptography, FourQ is an elliptic curve developed by Microsoft Research. It is designed for key agreements schemes (elliptic-curve Diffie–Hellman) and digital...

pairing (bilinear form, though with multiplicative notation) on the points of order dividing n of an elliptic curve E, taking values in nth roots of unity...

Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group...

In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see...

back to the studies of Pierre de Fermat on what are now recognized as elliptic curves; and has become a very substantial area of arithmetic geometry both...