Triple
T9931833
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Curve25519-based schemes |
E192664
|
entity |
| Predicate | usesScalarMultiplicationAlgorithm |
P91192
|
FINISHED |
| Object |
Montgomery ladder
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.
|
E831071
|
NE FINISHED |
How this triple was built (5 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Montgomery ladder | Statement: [Curve25519-based schemes, usesScalarMultiplicationAlgorithm, Montgomery ladder]
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.
-
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
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Montgomery ladder Triple: [Curve25519-based schemes, usesScalarMultiplicationAlgorithm, Montgomery ladder]
Generated 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.
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
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: usesScalarMultiplicationAlgorithm Context triple: [Curve25519-based schemes, usesScalarMultiplicationAlgorithm, Montgomery ladder]
-
A.
hasMultiplicationFormula
Indicates that there exists a specific multiplication-based formula or rule that defines or computes the value or behavior of the related entity.
-
B.
multiplicativeInverse
Indicates that one quantity is the multiplicative inverse of another, meaning their product equals the multiplicative identity (typically 1).
-
C.
usesMultiaxialSystem
Indicates that one entity applies or operates according to a multiaxial classification or measurement system in relation to another entity or context.
-
D.
isScalarUnit
Indicates that a given unit represents a single, non-vector (one-dimensional) quantity rather than a composite or vector-valued unit.
-
E.
usesEliminationMethod
Indicates that one entity applies an elimination-based method or process to solve, simplify, or remove elements in relation to another entity or problem.
- F. None of above. chosen
Provenance (7 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69ca82dd978c8190947124ab0d3315ac |
completed | March 30, 2026, 2:04 p.m. |
| NER | Named-entity recognition | batch_69cdb5b54f348190b8e70e7beff6098a |
completed | April 2, 2026, 12:17 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d228d1620c8190ac7125b268dd6832 |
completed | April 5, 2026, 9:18 a.m. |
| NEDg | Description generation | batch_69d22c3a6fc0819083a376736325a04e |
completed | April 5, 2026, 9:32 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d22cabf39881908f45667751384df5 |
completed | April 5, 2026, 9:34 a.m. |
| PD | Predicate disambiguation | batch_69cd1d90b8a8819081748f129c0c6ab6 |
completed | April 1, 2026, 1:28 p.m. |
| PDg | Predicate description generation | batch_69cd3581a9688190a00cef4c3eebb0ae |
completed | April 1, 2026, 3:10 p.m. |
Created at: March 30, 2026, 8:43 p.m.