Twisted Edwards curve
E831082
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Curve25519 in Edwards form | 1 |
| Edwards-curve Digital Signature Algorithm | 1 |
| Twisted Edwards curve canonical | 1 |
| twisted Edwards curves | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9932066 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Twisted Edwards curve Context triple: [Ed25519, basedOn, Twisted Edwards curve]
-
A.
Koblitz curves
Koblitz curves are a special class of elliptic curves defined over binary fields that enable particularly efficient and fast implementations of elliptic curve cryptography.
-
B.
Curve25519-based schemes
Curve25519-based schemes are cryptographic protocols and algorithms that use the Curve25519 elliptic curve to provide efficient, high-security public-key operations such as key exchange and digital signatures.
-
C.
Elliptic Curve Digital Signature Algorithm
Elliptic Curve Digital Signature Algorithm is a public-key cryptographic method that uses elliptic curve mathematics to create compact, secure digital signatures for authentication and data integrity.
-
D.
Elliptic Curve Cryptography
Elliptic Curve Cryptography is a public-key cryptographic approach that uses the mathematics of elliptic curves over finite fields to provide strong security with relatively small key sizes.
-
E.
Schoof–Elkies–Atkin (SEA) point-counting algorithm
The Schoof–Elkies–Atkin (SEA) point-counting algorithm is an efficient method in computational number theory and elliptic curve cryptography for determining the number of points on an elliptic curve over a finite field.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Twisted Edwards curve Target entity description: 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.
-
A.
Koblitz curves
Koblitz curves are a special class of elliptic curves defined over binary fields that enable particularly efficient and fast implementations of elliptic curve cryptography.
-
B.
Curve25519-based schemes
Curve25519-based schemes are cryptographic protocols and algorithms that use the Curve25519 elliptic curve to provide efficient, high-security public-key operations such as key exchange and digital signatures.
-
C.
Elliptic Curve Digital Signature Algorithm
Elliptic Curve Digital Signature Algorithm is a public-key cryptographic method that uses elliptic curve mathematics to create compact, secure digital signatures for authentication and data integrity.
-
D.
Elliptic Curve Cryptography
Elliptic Curve Cryptography is a public-key cryptographic approach that uses the mathematics of elliptic curves over finite fields to provide strong security with relatively small key sizes.
-
E.
Schoof–Elkies–Atkin (SEA) point-counting algorithm
The Schoof–Elkies–Atkin (SEA) point-counting algorithm is an efficient method in computational number theory and elliptic curve cryptography for determining the number of points on an elliptic curve over a finite field.
- F. None of above. chosen
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
ⓘ
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
ⓘ
complete Edwards curve ⓘ |
| isBirationallyEquivalentTo |
Montgomery curve
ⓘ
linked to:
Montgomery curves
Weierstrass elliptic curve ⓘ
linked to:
Weierstrass form
|
| isGeneralizationOf | Edwards curve ⓘ |
| relatedTo |
Curve25519
ⓘ
linked to:
Curve25519-based schemes
Curve448 ⓘ Ed25519 ⓘ Ed448 ⓘ |
| requiresConditionOnParameter |
a ≠ 0
ⓘ
a ≠ d ⓘ d ≠ 0 ⓘ |
| studiedIn |
computational number theory
ⓘ
elliptic curve cryptography ⓘ |
| supportsGroupLaw | elliptic curve group law ⓘ |
| usedIn |
Diffie–Hellman key exchange
ⓘ
EdDSA ⓘ Elliptic Curve Diffie–Hellman ⓘ
linked to:
Diffie–Hellman key exchange
digital signatures ⓘ key exchange ⓘ public-key cryptography ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Twisted Edwards curve Description of subject: 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.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Twisted Edwards curve
linked to: Twisted Edwards curve