Computing short vectors in lattices
E224030
"Computing short vectors in lattices" is Daniel J. Bernstein's doctoral thesis, focusing on algorithms and complexity issues related to finding short vectors in mathematical lattices, a central problem in computational number theory and cryptography.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Computing short vectors in lattices canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2002192 — 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: Computing short vectors in lattices Context triple: [Daniel J. Bernstein, thesisTitle, Computing short vectors in lattices]
-
A.
Shamir’s attack on RSA with low decryption exponent
Shamir’s attack on RSA with low decryption exponent is a cryptanalytic method that exploits unusually small private exponents in RSA to efficiently recover the secret key and break the encryption.
-
B.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
-
C.
Modern Cryptography, Probabilistic Proofs and Pseudorandomness
"Modern Cryptography, Probabilistic Proofs and Pseudorandomness" is a foundational textbook that systematically develops the theoretical underpinnings of modern cryptography, focusing on probabilistic proof techniques and the theory of pseudorandomness.
-
D.
Håstad’s switching lemma
Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
-
E.
Probabilistic Encryption
Probabilistic Encryption is a cryptographic technique that uses randomness in the encryption process so that the same message encrypts to different ciphertexts, enhancing security against attackers.
- 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: Computing short vectors in lattices Target entity description: "Computing short vectors in lattices" is Daniel J. Bernstein's doctoral thesis, focusing on algorithms and complexity issues related to finding short vectors in mathematical lattices, a central problem in computational number theory and cryptography.
-
A.
Shamir’s attack on RSA with low decryption exponent
Shamir’s attack on RSA with low decryption exponent is a cryptanalytic method that exploits unusually small private exponents in RSA to efficiently recover the secret key and break the encryption.
-
B.
Blum–Blum–Shub pseudorandom number generator
The Blum–Blum–Shub pseudorandom number generator is a cryptographically secure generator based on the hardness of factoring large composite numbers, widely studied in theoretical computer science and cryptography.
-
C.
Modern Cryptography, Probabilistic Proofs and Pseudorandomness
"Modern Cryptography, Probabilistic Proofs and Pseudorandomness" is a foundational textbook that systematically develops the theoretical underpinnings of modern cryptography, focusing on probabilistic proof techniques and the theory of pseudorandomness.
-
D.
Håstad’s switching lemma
Håstad’s switching lemma is a fundamental result in computational complexity theory that provides powerful bounds on the simplification of Boolean formulas under random restrictions, with major applications in circuit lower bounds.
-
E.
Probabilistic Encryption
Probabilistic Encryption is a cryptographic technique that uses randomness in the encryption process so that the same message encrypts to different ciphertexts, enhancing security against attackers.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
PhD dissertation
ⓘ
doctoral thesis ⓘ |
| academicInstitution | University of Amsterdam ⓘ |
| addressesProblem |
computing short vectors in high-dimensional lattices
ⓘ
efficiency of lattice reduction algorithms ⓘ hardness assumptions for lattice-based cryptography ⓘ |
| author | Daniel J. Bernstein ⓘ |
| authorFullName | Daniel Julius Bernstein ⓘ |
| contributor | Daniel J. Bernstein ⓘ |
| countryOfInstitution | Netherlands ⓘ |
| degree | Doctor of Philosophy ⓘ |
| doctoralAdvisor |
Hendrik Willem Lenstra Jr.
ⓘ
linked to:
Hendrik Lenstra
|
| field |
computational complexity theory
ⓘ
computational number theory ⓘ cryptography ⓘ lattice theory ⓘ |
| focusesOn |
algorithms for finding short lattice vectors
ⓘ
complexity of lattice problems ⓘ practical computation in high-dimensional lattices ⓘ |
| hasApplication |
computational number theory algorithms
ⓘ
cryptanalysis of lattice-based schemes ⓘ design of lattice-based cryptographic primitives ⓘ |
| hasAuthor | Daniel J. Bernstein ⓘ |
| hasAuthorORCID | 0000-0002-0165-0007 ⓘ |
| isAbout |
Euclidean lattices
ⓘ
NP-hard lattice problems ⓘ approximation algorithms for lattice problems ⓘ geometry of numbers ⓘ |
| language | English ⓘ |
| mainTopic |
algorithmic number theory
ⓘ
closest vector problem ⓘ lattice algorithms ⓘ lattice basis reduction ⓘ short vectors in lattices ⓘ shortest vector problem ⓘ |
| relatedTo |
LLL algorithm
ⓘ
basis reduction algorithms ⓘ cryptographic constructions based on lattices ⓘ |
| subjectArea |
discrete mathematics
ⓘ
public-key cryptography ⓘ theoretical computer science ⓘ |
| typeOfWork |
computer science thesis
ⓘ
mathematics thesis ⓘ |
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: Computing short vectors in lattices Description of subject: "Computing short vectors in lattices" is Daniel J. Bernstein's doctoral thesis, focusing on algorithms and complexity issues related to finding short vectors in mathematical lattices, a central problem in computational number theory and cryptography.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.