short integer solution (SIS) problem
E639078
average-case hard problem
computational problem
lattice problem
post-quantum cryptography assumption
The short integer solution (SIS) problem is a fundamental lattice-based computational problem that underpins many modern cryptographic constructions, especially in post-quantum cryptography.
All labels observed (1)
| Label | Occurrences |
|---|---|
| short integer solution (SIS) problem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7046855 — 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: short integer solution (SIS) problem Context triple: [Daniele Micciancio, knownFor, short integer solution (SIS) problem]
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A.
Computing short vectors in lattices
"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.
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B.
Merkle–Hellman knapsack cryptosystem
The Merkle–Hellman knapsack cryptosystem is an early public-key encryption scheme based on the subset sum (knapsack) problem, historically significant as one of the first practical public-key systems though later found to be insecure.
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C.
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.
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D.
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.
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E.
Merkle puzzles
Merkle puzzles are an early cryptographic protocol that introduced the concept of public-key exchange by allowing two parties to establish a shared secret over an insecure channel using computationally asymmetric “puzzle” problems.
- 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: short integer solution (SIS) problem Target entity description: The short integer solution (SIS) problem is a fundamental lattice-based computational problem that underpins many modern cryptographic constructions, especially in post-quantum cryptography.
-
A.
Computing short vectors in lattices
"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.
-
B.
Merkle–Hellman knapsack cryptosystem
The Merkle–Hellman knapsack cryptosystem is an early public-key encryption scheme based on the subset sum (knapsack) problem, historically significant as one of the first practical public-key systems though later found to be insecure.
-
C.
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.
-
D.
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.
-
E.
Merkle puzzles
Merkle puzzles are an early cryptographic protocol that introduced the concept of public-key exchange by allowing two parties to establish a shared secret over an insecure channel using computationally asymmetric “puzzle” problems.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
average-case hard problem
ⓘ
computational problem ⓘ lattice problem ⓘ post-quantum cryptography assumption ⓘ |
| abbreviation | SIS ⓘ |
| alsoKnownAs | short integer solutions problem ⓘ |
| basedOn | integer lattices ⓘ |
| considered |
hard for classical computers
ⓘ
hard for quantum computers ⓘ |
| constraint | matrix-vector product equals zero modulo q ⓘ |
| definedOver | integer matrix modulo q ⓘ |
| field |
computational complexity theory
ⓘ
cryptography ⓘ |
| hardnessType | worst-case to average-case reduction ⓘ |
| hasVariant |
approximate SIS problem
ⓘ
inhomogeneous SIS problem ⓘ module-SIS problem ⓘ ring-SIS problem ⓘ |
| introducedInContextOf | lattice-based cryptography ⓘ |
| involves | finding short nonzero integer vector ⓘ |
| motivation | design of post-quantum secure primitives ⓘ |
| parameter |
dimension n
ⓘ
modulus q ⓘ norm bound for short vector ⓘ number of columns m ⓘ |
| relatedTo |
NTRU cryptosystem
ⓘ
linked to:
NTRU Cryptosystems
bounded distance decoding problem ⓘ closest vector problem ⓘ learning with errors problem ⓘ shortest vector problem ⓘ |
| securityBasisFor |
Fiat–Shamir with aborts signatures
ⓘ
Lyubashevsky-style lattice signatures ⓘ SIS-based hash functions ⓘ SIS-based identification schemes ⓘ |
| typicalNorm |
Euclidean norm
ⓘ
infinity norm ⓘ |
| underpins |
lattice-based cryptography
ⓘ
post-quantum cryptography schemes ⓘ |
| usedIn |
attribute-based signatures
ⓘ
collision-resistant hash functions ⓘ commitment schemes ⓘ digital signature schemes ⓘ group signatures ⓘ hash-and-sign signatures ⓘ homomorphic authenticators ⓘ identification schemes ⓘ lattice-based identification protocols ⓘ ring signatures ⓘ zero-knowledge proofs ⓘ |
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: short integer solution (SIS) problem Description of subject: The short integer solution (SIS) problem is a fundamental lattice-based computational problem that underpins many modern cryptographic constructions, especially in post-quantum cryptography.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.