algorithmic number theory
E898460
Algorithmic number theory is a branch of mathematics and computer science that designs and analyzes efficient algorithms for solving problems involving integers, prime numbers, and related number-theoretic structures.
All labels observed (1)
| Label | Occurrences |
|---|---|
| algorithmic number theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991100 — 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: algorithmic number theory Context triple: [generalized Riemann hypothesis, usedIn, algorithmic number theory]
-
A.
algebraic number theory
Algebraic number theory is a branch of mathematics that studies algebraic structures related to algebraic integers and number fields, focusing on properties of integers through tools from abstract algebra.
-
B.
analytic number theory
Analytic number theory is a branch of mathematics that uses tools from mathematical analysis to study the distribution and properties of integers, especially prime numbers.
-
C.
A Course in Number Theory and Cryptography
A Course in Number Theory and Cryptography is a widely used textbook that introduces fundamental concepts of number theory with a strong emphasis on their applications to modern cryptography.
-
D.
Algebraic Aspects of Cryptography
Algebraic Aspects of Cryptography is a graduate-level textbook that develops modern public-key cryptography using tools from algebraic number theory, algebraic geometry, and finite fields.
-
E.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
- 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: algorithmic number theory Target entity description: Algorithmic number theory is a branch of mathematics and computer science that designs and analyzes efficient algorithms for solving problems involving integers, prime numbers, and related number-theoretic structures.
-
A.
algebraic number theory
Algebraic number theory is a branch of mathematics that studies algebraic structures related to algebraic integers and number fields, focusing on properties of integers through tools from abstract algebra.
-
B.
analytic number theory
Analytic number theory is a branch of mathematics that uses tools from mathematical analysis to study the distribution and properties of integers, especially prime numbers.
-
C.
A Course in Number Theory and Cryptography
A Course in Number Theory and Cryptography is a widely used textbook that introduces fundamental concepts of number theory with a strong emphasis on their applications to modern cryptography.
-
D.
Algebraic Aspects of Cryptography
Algebraic Aspects of Cryptography is a graduate-level textbook that develops modern public-key cryptography using tools from algebraic number theory, algebraic geometry, and finite fields.
-
E.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
- F. None of above. chosen
Statements (57)
| Predicate | Object |
|---|---|
| instanceOf |
academic discipline
ⓘ
subfield of number theory ⓘ subfield of theoretical computer science ⓘ |
| appliedIn |
coding theory
ⓘ
computational algebraic geometry ⓘ computational complexity theory ⓘ computer algebra systems ⓘ cryptanalysis ⓘ public-key cryptography ⓘ |
| fieldOfStudy |
Diophantine equations
ⓘ
algebraic number fields ⓘ algorithms ⓘ arithmetic of integers ⓘ computational complexity ⓘ elliptic curves ⓘ finite fields ⓘ lattices in number theory ⓘ modular arithmetic ⓘ number theory ⓘ prime numbers ⓘ |
| goal |
analysis of correctness of number-theoretic algorithms
ⓘ
analysis of running time of arithmetic algorithms ⓘ design of efficient number-theoretic algorithms ⓘ |
| historicalDevelopment | grew rapidly with the rise of modern cryptography in the late 20th century ⓘ |
| notableAlgorithm |
AKS primality test
ⓘ
LLL lattice basis reduction algorithm ⓘ Lenstra elliptic-curve factorization method ⓘ Miller–Rabin primality test ⓘ
linked to:
Miller primality test
Pollard rho discrete logarithm algorithm ⓘ Pollard rho factorization algorithm ⓘ baby-step giant-step algorithm ⓘ number field sieve ⓘ quadratic sieve ⓘ |
| relatedTo |
arithmetic geometry
ⓘ
complexity theory of numerical algorithms ⓘ computational number theory ⓘ symbolic computation ⓘ |
| studies |
Diophantine approximation algorithms
ⓘ
algorithms for computing class groups ⓘ algorithms for computing unit groups ⓘ computational aspects of algebraic number theory ⓘ discrete logarithm algorithms ⓘ efficient algorithms for arithmetic problems ⓘ greatest common divisor algorithms ⓘ integer factorization algorithms ⓘ integer relation algorithms ⓘ lattice basis reduction algorithms ⓘ modular exponentiation algorithms ⓘ point counting on elliptic curves ⓘ polynomial factorization over finite fields ⓘ primality testing algorithms ⓘ |
| usesConcept |
asymptotic complexity
ⓘ
deterministic algorithms ⓘ lattice reduction ⓘ probabilistic algorithms ⓘ randomized primality tests ⓘ sieve methods ⓘ |
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: algorithmic number theory Description of subject: Algorithmic number theory is a branch of mathematics and computer science that designs and analyzes efficient algorithms for solving problems involving integers, prime numbers, and related number-theoretic structures.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.