Twisted Edwards curve

E831082
algebraic curve elliptic curve

A Twisted Edwards curve is a type of elliptic curve with a specific algebraic form that enables especially fast and secure implementations of cryptographic operations such as digital signatures and key exchange.

Try in SPARQL Jump to: Surface forms Statements Referenced by

Observed surface forms (3)

Surface form Occurrences
Curve25519 in Edwards form 1
Edwards-curve Digital Signature Algorithm 1
twisted Edwards curves 1

Statements (47)

Predicate Object
instanceOf algebraic curve ⓘ
elliptic curve ⓘ
advantage high performance in hardware ⓘ
high performance in software ⓘ
resistance to certain side-channel attacks ⓘ
simple and unified addition formulas ⓘ
appliedIn TLS NERFINISHED ⓘ
cryptographic libraries ⓘ
secure messaging protocols ⓘ
definedOver field ⓘ
enables constant-time implementations ⓘ
efficient point addition ⓘ
efficient point doubling ⓘ
fast elliptic curve scalar multiplication ⓘ
groupLawIs complete addition law under certain parameter conditions ⓘ
hasGeneralEquation ax^2 + y^2 = 1 + dx^2y^2 ⓘ
hasNeutralElement (0,1) ⓘ
hasParameter a ⓘ
d ⓘ
hasProperty can be defined over binary fields ⓘ
can be defined over extension fields ⓘ
can be defined over prime fields ⓘ
forms an abelian group with respect to point addition ⓘ
often admits complete addition formulas ⓘ
suitable for high-security parameter sizes ⓘ
supports unified addition and doubling formulas ⓘ
hasSpecialCase Edwards curve NERFINISHED ⓘ
complete Edwards curve ⓘ
isBirationallyEquivalentTo Montgomery curve NERFINISHED ⓘ
Weierstrass elliptic curve NERFINISHED ⓘ
isGeneralizationOf Edwards curve NERFINISHED ⓘ
relatedTo Curve25519 NERFINISHED ⓘ
Curve448 NERFINISHED ⓘ
Ed25519 NERFINISHED ⓘ
Ed448 NERFINISHED ⓘ
requiresConditionOnParameter a ≠ 0 ⓘ
a ≠ d ⓘ
d ≠ 0 ⓘ
studiedIn computational number theory ⓘ
elliptic curve cryptography ⓘ
supportsGroupLaw elliptic curve group law GENERATED ⓘ
usedIn Diffie–Hellman key exchange NERFINISHED ⓘ
EdDSA NERFINISHED ⓘ
Elliptic Curve Diffie–Hellman NERFINISHED ⓘ
digital signatures ⓘ
key exchange ⓘ
public-key cryptography ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Ed25519 → basedOn → Twisted Edwards curve ⓘ
EdDSA → fullName → Twisted Edwards curve ⓘ
this entity surface form: Edwards-curve Digital Signature Algorithm
EdDSA → usesCurveType → Twisted Edwards curve ⓘ
this entity surface form: twisted Edwards curves
EdDSA → curveForEd25519 → Twisted Edwards curve ⓘ
this entity surface form: Curve25519 in Edwards form