Naor–Reingold pseudorandom function
E833448
The Naor–Reingold pseudorandom function is a foundational cryptographic construction that provides a simple, efficient, and provably secure method for generating pseudorandom outputs from secret keys based on number-theoretic assumptions.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Naor–Reingold pseudorandom function canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T9958184 — 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: Naor–Reingold pseudorandom function Context triple: [Moni Naor, notableWork, Naor–Reingold pseudorandom function]
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A.
Naor–Yung encryption paradigm
The Naor–Yung encryption paradigm is a foundational cryptographic framework that uses double encryption and zero-knowledge proofs to transform semantically secure public-key schemes into ones secure against chosen-ciphertext attacks.
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B.
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.
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C.
Blum–Micali pseudorandom number generator
The Blum–Micali pseudorandom number generator is a foundational cryptographic algorithm that produces provably secure pseudorandom bits based on number-theoretic hardness assumptions.
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D.
Fiat–Shamir heuristic
The Fiat–Shamir heuristic is a cryptographic technique that transforms interactive proof systems into non-interactive ones using hash functions, widely used in digital signatures and zero-knowledge proofs.
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E.
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.
- 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: Naor–Reingold pseudorandom function Target entity description: The Naor–Reingold pseudorandom function is a foundational cryptographic construction that provides a simple, efficient, and provably secure method for generating pseudorandom outputs from secret keys based on number-theoretic assumptions.
-
A.
Naor–Yung encryption paradigm
The Naor–Yung encryption paradigm is a foundational cryptographic framework that uses double encryption and zero-knowledge proofs to transform semantically secure public-key schemes into ones secure against chosen-ciphertext attacks.
-
B.
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.
-
C.
Blum–Micali pseudorandom number generator
The Blum–Micali pseudorandom number generator is a foundational cryptographic algorithm that produces provably secure pseudorandom bits based on number-theoretic hardness assumptions.
-
D.
Fiat–Shamir heuristic
The Fiat–Shamir heuristic is a cryptographic technique that transforms interactive proof systems into non-interactive ones using hash functions, widely used in digital signatures and zero-knowledge proofs.
-
E.
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.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
number-theoretic construction
ⓘ
pseudorandom function ⓘ |
| application |
keyed cryptographic constructions
ⓘ
pseudorandom function families ⓘ theoretical foundations of PRFs ⓘ |
| assumes | hardness of distinguishing Diffie–Hellman tuples ⓘ |
| author |
Moni Naor
ⓘ
Omer Reingold ⓘ |
| basedOn |
Decisional Diffie–Hellman assumption
ⓘ
number-theoretic assumptions ⓘ |
| category | public-key–based pseudorandom function ⓘ |
| codomain | multiplicative group of a finite field ⓘ |
| constructionMethod | iterated group exponentiation controlled by input bits ⓘ |
| domain | {0,1}^n ⓘ |
| efficiency |
efficient
ⓘ
simple ⓘ |
| field |
cryptography
ⓘ
theoretical computer science ⓘ |
| formalizedIn | standard cryptographic security definitions for PRFs ⓘ |
| hasInput | bit string ⓘ |
| hasKey | vector of group exponents ⓘ |
| hasOutput | group element ⓘ |
| hasProperty |
simple algebraic structure
ⓘ
well-understood security proof ⓘ |
| influenced | subsequent PRF constructions ⓘ |
| introducedInPublication | Naor and Reingold paper on number-theoretic constructions of efficient pseudorandom functions ⓘ |
| keySizeDependsOn | input length n ⓘ |
| namedAfter |
Moni Naor
ⓘ
Omer Reingold ⓘ |
| property | length-preserving on the group representation ⓘ |
| provenUnder | Decisional Diffie–Hellman assumption ⓘ |
| relatedTo |
Diffie–Hellman key exchange
ⓘ
Goldreich–Goldwasser–Micali pseudorandom function ⓘ |
| reliesOn | uniformly random exponents as secret key ⓘ |
| requires | group with efficiently computable exponentiation ⓘ |
| securityModel |
computational security
ⓘ
provable security ⓘ |
| securityProperty |
indistinguishability from a random function
ⓘ
pseudorandomness ⓘ |
| typeOf | keyed function ⓘ |
| usedFor |
constructing secure encryption schemes (as a component)
ⓘ
message authentication (as a component) ⓘ theoretical study of pseudorandomness ⓘ |
| uses |
exponentiation in a cyclic group
ⓘ
multiplicative group modulo a prime ⓘ |
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: Naor–Reingold pseudorandom function Description of subject: The Naor–Reingold pseudorandom function is a foundational cryptographic construction that provides a simple, efficient, and provably secure method for generating pseudorandom outputs from secret keys based on number-theoretic assumptions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.