Blum–Micali pseudorandom number generator
E117703
cryptographic primitive
number-theoretic algorithm
pseudorandom number generator
stream cipher primitive
The Blum–Micali pseudorandom number generator is a foundational cryptographic algorithm that produces provably secure pseudorandom bits based on number-theoretic hardness assumptions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Blum–Micali pseudorandom number generator canonical | 1 |
| “How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits” | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T990927 — 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: Blum–Micali pseudorandom number generator Context triple: [Manuel Blum, notableWork, Blum–Micali pseudorandom number generator]
-
A.
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.
-
B.
New Directions in Cryptography
New Directions in Cryptography is a landmark 1976 paper that introduced the concepts of public-key cryptography and digital signatures, fundamentally reshaping modern cryptography and secure communications.
-
C.
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.
-
D.
Secrecy, Authentication, and Public Key Systems
"Secrecy, Authentication, and Public Key Systems" is Ralph Merkle's influential doctoral thesis that helped lay the foundations of modern public-key cryptography and secure communication protocols.
-
E.
Merkle–Damgård construction
The Merkle–Damgård construction is a fundamental method for building collision-resistant cryptographic hash functions from fixed-size compression functions, used in many classic hash algorithms like MD5 and SHA-1.
- 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: Blum–Micali pseudorandom number generator Target entity description: The Blum–Micali pseudorandom number generator is a foundational cryptographic algorithm that produces provably secure pseudorandom bits based on number-theoretic hardness assumptions.
-
A.
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.
-
B.
New Directions in Cryptography
New Directions in Cryptography is a landmark 1976 paper that introduced the concepts of public-key cryptography and digital signatures, fundamentally reshaping modern cryptography and secure communications.
-
C.
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.
-
D.
Secrecy, Authentication, and Public Key Systems
"Secrecy, Authentication, and Public Key Systems" is Ralph Merkle's influential doctoral thesis that helped lay the foundations of modern public-key cryptography and secure communication protocols.
-
E.
Merkle–Damgård construction
The Merkle–Damgård construction is a fundamental method for building collision-resistant cryptographic hash functions from fixed-size compression functions, used in many classic hash algorithms like MD5 and SHA-1.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
cryptographic primitive
ⓘ
number-theoretic algorithm ⓘ pseudorandom number generator ⓘ stream cipher primitive ⓘ |
| assumes | existence of one-way permutations ⓘ |
| basedOn |
discrete logarithm problem
ⓘ
one-way function ⓘ |
| category | provably secure pseudorandom generator ⓘ |
| constructionType | bit-by-bit generator ⓘ |
| designedFor |
cryptographic applications
ⓘ
key stream generation ⓘ |
| developedBy |
Manuel Blum
ⓘ
Silvio Micali ⓘ |
| field |
computational number theory
ⓘ
cryptography ⓘ theoretical computer science ⓘ |
| formalizedIn | complexity-theoretic framework ⓘ |
| hasAbbreviation | BM generator ⓘ |
| hasComplexity | polynomial time per output bit ⓘ |
| hasProperty |
bitwise output
ⓘ
computationally indistinguishable from uniform ⓘ next-bit unpredictable ⓘ provably secure under standard assumptions ⓘ |
| influenced |
Yao’s pseudorandom generator construction
ⓘ
subsequent number-theoretic PRGs ⓘ |
| input | secret seed ⓘ |
| introducedIn |
“How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits”
ⓘ
linked to:
Blum–Micali pseudorandom number generator
|
| namedAfter |
Manuel Blum
ⓘ
Silvio Micali ⓘ |
| output |
pseudorandom bit sequence
ⓘ
pseudorandom bitstream ⓘ |
| publicationYear | 1984 ⓘ |
| relatedTo |
Blum–Blum–Shub pseudorandom number generator
ⓘ
Yao’s next-bit test ⓘ |
| requires |
large prime modulus
ⓘ
primitive root modulo prime ⓘ |
| securityGuarantee | next-bit test implies all polynomial-time statistical tests ⓘ |
| securityModel | polynomial-time adversary ⓘ |
| securityReliesOn | hardness of computing discrete logarithms ⓘ |
| securityType | computational security ⓘ |
| seedSpace | elements of the underlying group ⓘ |
| typicalGroup | multiplicative group of integers modulo a large prime ⓘ |
| uses |
cyclic group modulo a prime
ⓘ
generator of a multiplicative group ⓘ modular exponentiation ⓘ |
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: Blum–Micali pseudorandom number generator Description of subject: The Blum–Micali pseudorandom number generator is a foundational cryptographic algorithm that produces provably secure pseudorandom bits based on number-theoretic hardness assumptions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
Blum–Micali pseudorandom number generator
→
introducedIn
→
“How to Generate Cryptographically Strong Sequences of Pseudo-Random Bits”
ⓘ
linked to: Blum–Micali pseudorandom number generator