Curve25519-based schemes

E192664

cryptographic scheme family public-key cryptography

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.

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All labels observed (12)

Label	Occurrences
Curve25519	5
Curve25519 family	1
Curve25519 for key agreement	1
Curve25519-based Diffie–Hellman key exchange	1
Curve25519-based schemes canonical	1
ECIES over Curve25519	1
Elliptic Curve Diffie–Hellman	1
NaCl cryptographic library	1
SSH X25519 key exchange	1
WireGuard design family of patterns	1
X25519	1
elliptic curve Diffie–Hellman	1

Statements (52)

Predicate	Object
instanceOf	cryptographic scheme family ⓘ public-key cryptography ⓘ
advantage	fast key agreement ⓘ fast key generation ⓘ fast signature verification ⓘ good performance on constrained devices ⓘ small key sizes compared to RSA ⓘ
avoids	branch-based side channels (in well-written implementations) ⓘ timing side channels (in well-written implementations) ⓘ
basedOn	elliptic-curve cryptography ⓘ
commonlyUsedIn	SSH implementations ⓘ TLS implementations ⓘ VPN protocols ⓘ end-to-end encrypted storage systems ⓘ secure messaging applications ⓘ
coordinateSystem	Montgomery form ⓘ
designedFor	high performance ⓘ side-channel resistance ⓘ
field	prime field GF(2^255-19) ⓘ
keyExchangeVariant	X25519 ⓘ
property	cofactor 8 ⓘ constant-time scalar multiplication implementations ⓘ rigidly defined curve parameters ⓘ twist security ⓘ
provides	digital signatures ⓘ key exchange ⓘ public-key encryption ⓘ
securityAssumption	elliptic-curve discrete logarithm problem ⓘ
securityLevel	approximately 128-bit security ⓘ
signatureVariant	Ed25519 ⓘ Ed25519ctx ⓘ Ed25519ph ⓘ
standardizedIn	Noise protocol framework ⓘ surface form: Noise Protocol Framework specification OpenSSH ⓘ surface form: OpenSSH protocol extensions RFC 7748 ⓘ RFC 8032 ⓘ RFC 8446 ⓘ surface form: TLS 1.3 (RFC 8446)
supportsProtocol	Curve25519-based schemes self-linksurface differs ⓘ surface form: ECIES over Curve25519 Ed25519 ⓘ Noise protocol framework ⓘ surface form: Noise protocol framework handshakes Curve25519-based schemes self-linksurface differs ⓘ surface form: SSH X25519 key exchange Signal protocol Double Ratchet ⓘ Signal protocol X3DH ⓘ TLS 1.3 X25519 key exchange ⓘ EdDSA ⓘ surface form: VXEdDSA WireGuard key exchange ⓘ X25519 ⓘ age file encryption format ⓘ
typicalKeySize	256-bit public keys ⓘ
typicalPrivateKeySize	256-bit private scalars with clamping ⓘ
usesCurve	Curve25519-based schemes self-linksurface differs ⓘ surface form: Curve25519
usesScalarMultiplicationAlgorithm	Montgomery ladder ⓘ

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: Curve25519-based schemes
Description of subject: 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.

Referenced by (16)

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

Elliptic Curve Cryptography → hasVariant → Curve25519-based schemes ⓘ

Daniel J. Bernstein → notableWork → Curve25519-based schemes ⓘ

this entity surface form: Curve25519

Daniel J. Bernstein → notableWork → Curve25519-based schemes ⓘ

this entity surface form: NaCl cryptographic library

Daniel J. Bernstein → notableWork → Curve25519-based schemes ⓘ

this entity surface form: Curve25519-based Diffie–Hellman key exchange

Simultaneous Authentication of Equals → uses → Curve25519-based schemes ⓘ

this entity surface form: elliptic curve Diffie–Hellman

libsodium → implementsPrimitive → Curve25519-based schemes ⓘ

this entity surface form: Curve25519

libsodium → implementsPrimitive → Curve25519-based schemes ⓘ

this entity surface form: X25519

ECC → canBeUsedWith → Curve25519-based schemes ⓘ

this entity surface form: Elliptic Curve Diffie–Hellman

ECC → notableCurveFamilies → Curve25519-based schemes ⓘ

this entity surface form: Curve25519 family

Curve25519-based schemes → usesCurve → Curve25519-based schemes self-linksurface differs ⓘ

this entity surface form: Curve25519

Curve25519-based schemes → supportsProtocol → Curve25519-based schemes self-linksurface differs ⓘ

this entity surface form: ECIES over Curve25519

Curve25519-based schemes → supportsProtocol → Curve25519-based schemes self-linksurface differs ⓘ

this entity surface form: SSH X25519 key exchange

Ed25519 → usesCurve → Curve25519-based schemes ⓘ

this entity surface form: Curve25519

WireGuard VPN protocol → usesCryptography → Curve25519-based schemes ⓘ

subject surface form: WireGuard

this entity surface form: Curve25519

Noise_XX pattern → usedIn → Curve25519-based schemes ⓘ

this entity surface form: WireGuard design family of patterns

CFRG → standardized → Curve25519-based schemes ⓘ

this entity surface form: Curve25519 for key agreement