Merkle–Hellman knapsack cryptosystem
E434684
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Merkle–Hellman knapsack cryptosystem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4381583 — 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: Merkle–Hellman knapsack cryptosystem Context triple: [Ralph Merkle, knownFor, Merkle–Hellman knapsack cryptosystem]
-
A.
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.
-
B.
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.
-
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.
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.
-
E.
Shamir secret sharing scheme
The Shamir secret sharing scheme is a cryptographic method that divides a secret into multiple parts so that only a specified threshold of parts can reconstruct the original secret, while fewer parts reveal nothing.
- 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: Merkle–Hellman knapsack cryptosystem Target entity description: 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.
-
A.
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.
-
B.
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.
-
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.
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.
-
E.
Shamir secret sharing scheme
The Shamir secret sharing scheme is a cryptographic method that divides a secret into multiple parts so that only a specified threshold of parts can reconstruct the original secret, while fewer parts reveal nothing.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
encryption scheme
ⓘ
knapsack cryptosystem ⓘ public-key cryptosystem ⓘ |
| application | theoretical study of cryptanalytic techniques ⓘ |
| basedOn |
knapsack problem
ⓘ
subset sum problem NERFINISHED ⓘ |
| brokenBy | Adi Shamir NERFINISHED ⓘ |
| brokenIn | 1982 ⓘ |
| ciphertextType | integer ⓘ |
| cipherType |
asymmetric-key cipher
ⓘ
public-key cipher ⓘ |
| consideredSecure | false ⓘ |
| constructionStep |
choose a modulus larger than the sum of the superincreasing sequence
ⓘ
choose a multiplier relatively prime to the modulus ⓘ choose a superincreasing sequence as private key ⓘ compute public key by modular multiplication of private sequence ⓘ |
| creator |
Martin Hellman
NERFINISHED
ⓘ
Ralph Merkle NERFINISHED ⓘ |
| decryptionMethod |
multiply ciphertext by modular inverse of multiplier
ⓘ
solve superincreasing subset sum greedily ⓘ |
| encryptionMethod | encode bits as subset sums of public key weights ⓘ |
| field |
cryptography
ⓘ
public-key cryptography ⓘ |
| hasComponent |
decryption algorithm
ⓘ
encryption algorithm ⓘ key generation algorithm ⓘ |
| hasVariant |
general knapsack cryptosystem
NERFINISHED
ⓘ
multiple-iterated Merkle–Hellman knapsack cryptosystem NERFINISHED ⓘ |
| historicalSignificance |
demonstrated practicality of public-key cryptography
ⓘ
early example of public-key encryption ⓘ |
| inspiredBy | Diffie–Hellman key exchange NERFINISHED ⓘ |
| introducedIn | 1978 ⓘ |
| keyType |
private key
ⓘ
public key ⓘ |
| namedAfter |
Martin Hellman
NERFINISHED
ⓘ
Ralph Merkle NERFINISHED ⓘ |
| notableAs | one of the first practical public-key cryptosystems ⓘ |
| plaintextType | binary message ⓘ |
| problemType | NP-complete problem (subset sum) ⓘ |
| publicationYear | 1978 ⓘ |
| securityGoal | confidentiality ⓘ |
| status | broken ⓘ |
| taughtIn | cryptography courses ⓘ |
| uses |
modular inverse
ⓘ
modular multiplication ⓘ superincreasing sequence ⓘ |
| vulnerableTo |
Shamir’s attack
NERFINISHED
ⓘ
lattice-based attacks ⓘ low-density subset sum attacks ⓘ |
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: Merkle–Hellman knapsack cryptosystem Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.