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.
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
NERFINISHED
ⓘ
Omer Reingold NERFINISHED ⓘ |
| basedOn |
Decisional Diffie–Hellman assumption
NERFINISHED
ⓘ
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
NERFINISHED
ⓘ
Omer Reingold NERFINISHED ⓘ |
| property | length-preserving on the group representation ⓘ |
| provenUnder | Decisional Diffie–Hellman assumption NERFINISHED ⓘ |
| relatedTo |
Diffie–Hellman key exchange
NERFINISHED
ⓘ
Goldreich–Goldwasser–Micali pseudorandom function NERFINISHED ⓘ |
| 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 ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.