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.