Montgomery ladder
E831071
The Montgomery ladder is a scalar multiplication algorithm on elliptic curves that provides efficient, uniform, and side-channel-resistant computation for cryptographic protocols such as those based on Curve25519.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Montgomery ladder canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9931833 — 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: Montgomery ladder Context triple: [Curve25519-based schemes, usesScalarMultiplicationAlgorithm, Montgomery ladder]
-
A.
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.
-
B.
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.
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C.
Diffie–Hellman key exchange
Diffie–Hellman key exchange is a foundational cryptographic protocol that enables two parties to securely establish a shared secret over an insecure communication channel.
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D.
Benettin algorithm
The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
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E.
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.
- 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: Montgomery ladder Target entity description: The Montgomery ladder is a scalar multiplication algorithm on elliptic curves that provides efficient, uniform, and side-channel-resistant computation for cryptographic protocols such as those based on Curve25519.
-
A.
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.
-
B.
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.
-
C.
Diffie–Hellman key exchange
Diffie–Hellman key exchange is a foundational cryptographic protocol that enables two parties to securely establish a shared secret over an insecure communication channel.
-
D.
Benettin algorithm
The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
-
E.
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.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
cryptographic algorithm
ⓘ
elliptic curve algorithm ⓘ scalar multiplication algorithm ⓘ |
| advantageOver | naive double-and-add with secret-dependent branches ⓘ |
| describedIn | "Speeding the Pollard and elliptic curve methods of factorization" ⓘ |
| designedFor |
efficient implementation on constrained devices
ⓘ
implementation without secret-dependent branches ⓘ implementation without secret-dependent memory access patterns ⓘ |
| field | cryptography ⓘ |
| hasProperty |
amenable to constant-time implementation
ⓘ
binary ladder structure ⓘ bit-by-bit scalar processing ⓘ constant-time conditional operations ⓘ iterative algorithm ⓘ performs one point addition and one point doubling per bit ⓘ regular structure ⓘ resistance to simple power analysis ⓘ resistance to timing attacks ⓘ side-channel resistance ⓘ simple control flow ⓘ uniform execution pattern ⓘ uses two running points ⓘ |
| implementedIn |
BoringSSL
NERFINISHED
ⓘ
OpenSSL NERFINISHED ⓘ TLS libraries ⓘ libsodium NERFINISHED ⓘ |
| introducedBy | Peter L. Montgomery NERFINISHED ⓘ |
| notableApplication |
Curve25519
NERFINISHED
ⓘ
RFC 7748 elliptic curves ⓘ X25519 key exchange NERFINISHED ⓘ |
| operatesOn |
Montgomery curves
NERFINISHED
ⓘ
elliptic curves over finite fields ⓘ x-coordinates of points on Montgomery curves ⓘ |
| publicationYear | 1987 ⓘ |
| relatedTo |
Montgomery curve
NERFINISHED
ⓘ
constant-time cryptographic implementations ⓘ double-and-add algorithm ⓘ windowed scalar multiplication ⓘ |
| securityGoal |
mitigation of power analysis side channels
ⓘ
mitigation of timing side channels ⓘ |
| usedFor |
Curve25519-based key exchange
ⓘ
Diffie–Hellman key exchange NERFINISHED ⓘ Elliptic Curve Diffie–Hellman NERFINISHED ⓘ constant-time scalar multiplication ⓘ key agreement protocols ⓘ scalar multiplication on elliptic curves ⓘ side-channel-resistant scalar multiplication ⓘ |
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: Montgomery ladder Description of subject: The Montgomery ladder is a scalar multiplication algorithm on elliptic curves that provides efficient, uniform, and side-channel-resistant computation for cryptographic protocols such as those based on Curve25519.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.