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

problem" (ECDLP). The security of elliptic curve cryptography depends on the ability to compute a point multiplication and the inability to compute the...

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

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...

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...

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

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...

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...

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

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...

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...

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...

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

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...

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

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...

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...

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...

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

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...

algorithm is implemented over G F ( p ) {\displaystyle GF(p)} , but an elliptic curve variant (EC-KCDSA) is also specified. KCDSA requires a collision-resistant...

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...

summer of 1975. Together they worked on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory. He further worked with...

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