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...

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC...

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

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

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...

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

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...

The Lenstra elliptic-curve factorization or the elliptic-curve factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer...

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

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

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

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

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...

In mathematics, twisted Hessian curves are a generalization of Hessian curves; they were introduced in elliptic curve cryptography to speed up the addition...

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...

by Deuring (1941) for elliptic curves with complex multiplication. It was subsequently shown to be true for all elliptic curves over Q, as a consequence...

Over the open subscheme where q is invertible, the Tate curve is an elliptic curve. The Tate curve can also be defined for q as an element of a complete...

Doche–Icart–Kohel curve is a form in which an elliptic curve can be written. It is a special case of the Weierstrass form and it is also important in elliptic-curve cryptography...

an elliptic curve over a number field K, the Hasse–Weil zeta function is conjecturally related to the group of rational points of the elliptic curve over...

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

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

definition of elliptic curve from algebraic geometry is connected non-singular projective curve of genus 1 with a given rational point on it. By the Riemann–Roch...

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

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...

A multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient...

varieties and fields are open. Let E be an elliptic curve defined over the rational numbers without complex multiplication. For a prime number p, define θp as...

that can also be applied to multiplication. The method for general multiplication is a method to achieve multiplications a × b {\displaystyle a\times...

= b. In elliptic curve cryptography, the multiplication in a finite field is replaced by the operation of adding points on an elliptic curve, i.e., the...