Blakley secret sharing scheme
E831737
The Blakley secret sharing scheme is a threshold cryptographic method that hides a secret as the intersection point of multiple hyperplanes, requiring a minimum number of shares (hyperplanes) to reconstruct it.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Blakley | 2 |
| Blakley secret sharing scheme canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9958020 — 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: Blakley secret sharing scheme Context triple: [Shamir secret sharing scheme, relatedTo, Blakley secret sharing scheme]
-
A.
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.
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B.
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.
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C.
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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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.
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E.
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.
- 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: Blakley secret sharing scheme Target entity description: The Blakley secret sharing scheme is a threshold cryptographic method that hides a secret as the intersection point of multiple hyperplanes, requiring a minimum number of shares (hyperplanes) to reconstruct it.
-
A.
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.
-
B.
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.
-
C.
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.
-
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.
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.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
information-theoretic secret sharing scheme
ⓘ
secret sharing scheme ⓘ threshold cryptographic scheme ⓘ |
| advantage | conceptually simple geometric interpretation ⓘ |
| application |
distributed trust
ⓘ
key management ⓘ secure multiparty control of cryptographic keys ⓘ |
| basedOn | intersection of hyperplanes ⓘ |
| category | key management protocol ⓘ |
| comparedWith | Shamir secret sharing scheme NERFINISHED ⓘ |
| condition | t ≤ n ⓘ |
| contemporaryWith | Shamir secret sharing scheme NERFINISHED ⓘ |
| differenceFromShamirScheme | uses geometric hyperplanes instead of polynomial interpolation ⓘ |
| disadvantage | shares may leak geometric information about the secret space if not over large fields ⓘ |
| field |
cryptography
ⓘ
information security ⓘ information theory NERFINISHED ⓘ |
| generalizationOf | geometric secret sharing ⓘ |
| goal | distribute trust among multiple participants ⓘ |
| hasProperty |
information-theoretic security
ⓘ
linear secret sharing ⓘ perfect secret sharing ⓘ threshold property ⓘ |
| influenced | later geometric secret sharing schemes ⓘ |
| introducedBy | George R. Blakley NERFINISHED ⓘ |
| introducedIn | 1979 ⓘ |
| protects | cryptographic keys ⓘ |
| publishedIn | Proceedings of the National Computer Conference NERFINISHED ⓘ |
| reconstructionMethod | compute unique point common to all given hyperplanes ⓘ |
| reconstructionRequires | intersection of at least t hyperplanes ⓘ |
| representsSecretAs | point in a vector space ⓘ |
| representsSharesAs | hyperplanes containing the secret point ⓘ |
| requires | minimum number of shares to reconstruct secret ⓘ |
| requiresComputation | solving systems of linear equations ⓘ |
| requiresParameter |
number of participants n
ⓘ
threshold t ⓘ |
| secret | unique intersection point of hyperplanes ⓘ |
| securityGuarantee | fewer than t shares reveal no information about the secret ⓘ |
| securityModel | honest-but-curious adversaries for basic construction ⓘ |
| share | equation of a hyperplane ⓘ |
| shareGenerationMethod | choose random hyperplanes through secret point ⓘ |
| shareSpace | t-dimensional or higher-dimensional vector space ⓘ |
| thresholdType | (t,n)-threshold scheme NERFINISHED ⓘ |
| titleOfOriginalPaper | Safeguarding cryptographic keys ⓘ |
| typicalImplementationDomain | finite field GF(q) GENERATED ⓘ |
| uses |
finite fields
ⓘ
geometric construction ⓘ hyperplanes ⓘ linear algebra ⓘ |
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: Blakley secret sharing scheme Description of subject: The Blakley secret sharing scheme is a threshold cryptographic method that hides a secret as the intersection point of multiple hyperplanes, requiring a minimum number of shares (hyperplanes) to reconstruct it.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Blakley
this entity surface form:
Blakley