# Category: Elliptic curve cryptography

Doubling-oriented Doche–Icart–Kohel curve
In mathematics, the doubling-oriented Doche–Icart–Kohel curve is a form in which an elliptic curve can be written. It is a special case of Weierstrass form and it is also important in elliptic-curve c
X448
No description available.
Enhanced privacy ID
Enhanced Privacy ID (EPID) is Intel Corporation's recommended algorithm for attestation of a trusted system while preserving privacy. It has been incorporated in several Intel chipsets since 2008 and
Sakai–Kasahara scheme
The Sakai–Kasahara scheme, also known as the Sakai–Kasahara key encryption algorithm (SAKKE), is an identity-based encryption (IBE) system proposed by Ryuichi Sakai and Masao Kasahara in 2003. Alongsi
Elliptic-curve Diffie–Hellman
Elliptic-curve Diffie–Hellman (ECDH) is a key agreement protocol that allows two parties, each having an elliptic-curve public–private key pair, to establish a shared secret over an insecure channel.
Schoof–Elkies–Atkin algorithm
The Schoof–Elkies–Atkin algorithm (SEA) is an algorithm used for finding the order of or calculating the number of points on an elliptic curve over a finite field. Its primary application is in ellipt
Tate pairing
In mathematics, Tate pairing is any of several closely related bilinear pairings involving elliptic curves or abelian varieties, usually over local or finite fields, based on the Tate duality pairings
Sub-group hiding
The sub-group hiding assumption is a computational hardness assumption used in elliptic curve cryptography and pairing-based cryptography. It was first introduced in to build a 2-DNF homomorphic encry
KCDSA
KCDSA (Korean Certificate-based Digital Signature Algorithm) is a digital signature algorithm created by a team led by the Korea Internet & Security Agency (KISA). It is an ElGamal variant, similar to
Elliptic Curve Digital Signature Algorithm
In cryptography, the Elliptic Curve Digital Signature Algorithm (ECDSA) offers a variant of the Digital Signature Algorithm (DSA) which uses elliptic-curve cryptography.
Twisted Hessian curves
In mathematics, the Twisted Hessian curve represents a generalization of Hessian curves; it was introduced in elliptic curve cryptography to speed up the addition and doubling formulas and to have str
FourQ
In cryptography, FourQ is an elliptic curve developed by Microsoft Research. It is designed for key agreements schemes (elliptic-curve Diffie–Hellman) and digital signatures (Schnorr), and offers abou
Table of costs of operations in elliptic curves
Elliptic curve cryptography is a popular form of public key encryption that is based on the mathematical theory of elliptic curves. Points on an elliptic curve can be added and form a group under this
X25519
No description available.
Hessian form of an elliptic curve
In geometry, the Hessian curve is a plane curve similar to folium of Descartes. It is named after the German mathematician Otto Hesse.This curve was suggested for application in elliptic curve cryptog
Decision Linear assumption
The Decision Linear (DLIN) assumption is a computational hardness assumption used in elliptic curve cryptography. In particular, the DLIN assumption is useful in settings where the decisional Diffie–H
Pairing-based cryptography
Pairing-based cryptography is the use of a pairing between elements of two cryptographic groups to a third group with a mapping to construct or analyze cryptographic systems.
Hyperelliptic curve cryptography
Hyperelliptic curve cryptography is similar to elliptic curve cryptography (ECC) insofar as the Jacobian of a hyperelliptic curve is an abelian group in which to do arithmetic, just as we use the grou
Tripling-oriented Doche–Icart–Kohel curve
The tripling-oriented Doche–Icart–Kohel curve is a form of an elliptic curve that has been used lately in cryptography; it is a particular type of Weierstrass curve. At certain conditions some operati
Montgomery curve
In mathematics the Montgomery curve is a form of elliptic curve introduced by Peter L. Montgomery in 1987, different from the usual Weierstrass form. It is used for certain computations, and in partic
Jacobian 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 is used in cryptography instead of the Weierstr
Twisted Edwards curve
In algebraic geometry, the twisted Edwards curves are plane models of elliptic curves, a generalisation of Edwards curves introduced by Bernstein, Birkner, Joye, Lange and Peters in 2008. The curve se
Twists of elliptic curves
In the mathematical field of algebraic geometry, an elliptic curve E over a field K has an associated quadratic twist, that is another elliptic curve which is isomorphic to E over an algebraic closure
Bitcoin
Bitcoin (abbreviation: BTC; sign: ₿) is a decentralized digital currency that can be transferred on the peer-to-peer bitcoin network. Bitcoin transactions are verified by network nodes through cryptog
EdDSA
In public-key cryptography, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on twisted Edwards curves.It is designed to be fa
Decisional Diffie–Hellman assumption
The decisional Diffie–Hellman (DDH) assumption is a computational hardness assumption about a certain problem involving discrete logarithms in cyclic groups. It is used as the basis to prove the secur
Supersingular isogeny graph
In mathematics, the supersingular isogeny graphs are a class of expander graphs that arise in computational number theory and have been applied in elliptic-curve cryptography. Their vertices represent
Boneh–Franklin scheme
The Boneh–Franklin scheme is an identity-based encryption system proposed by Dan Boneh and Matthew K. Franklin in 2001. This article refers to the protocol version called BasicIdent. It is an applicat
Edwards curve
In 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 used in elliptic curve cryptography. A
DNSCurve
DNSCurve is a proposed secure protocol for the Domain Name System (DNS), designed by Daniel J. Bernstein.
ECC patents
Patent-related uncertainty around elliptic curve cryptography (ECC), or ECC patents, is one of the main factors limiting its wide acceptance. For example, the OpenSSL team accepted an ECC patch only i
MQV
MQV (Menezes–Qu–Vanstone) is an authenticated protocol for key agreement based on the Diffie–Hellman scheme. Like other authenticated Diffie–Hellman schemes, MQV provides protection against an active
Elliptic-curve cryptography
Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys compared to non-EC cryptogra
XDH assumption
The external Diffie–Hellman (XDH) assumption is a computational hardness assumption used in elliptic curve cryptography. The XDH assumption holds that there exist certain subgroups of elliptic curves
Schoof's algorithm
Schoof's algorithm is an efficient algorithm to count points on elliptic curves over finite fields. The algorithm has applications in elliptic curve cryptography where it is important to know the numb