Shamir secret sharing scheme
E195491
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.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Shamir secret sharing scheme canonical | 3 |
| Shamir secret sharing | 2 |
| (t,n)-threshold scheme | 1 |
| How to share a secret | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1762031 — 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: Shamir secret sharing scheme Context triple: [Adi Shamir, knownFor, Shamir secret sharing scheme]
-
A.
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.
-
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.
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.
-
D.
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.
-
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: Shamir secret sharing scheme Target entity description: 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.
-
A.
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.
-
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.
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.
-
D.
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.
-
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 (49)
| Predicate | Object |
|---|---|
| instanceOf |
cryptographic protocol
ⓘ
information-theoretic security scheme ⓘ secret sharing scheme ⓘ threshold scheme ⓘ |
| advantage |
flexible choice of threshold and number of participants
ⓘ
simple to implement ⓘ unconditional security against computationally unbounded adversaries ⓘ |
| application |
access control
ⓘ
backup and recovery of cryptographic keys ⓘ cryptographic wallets with social recovery ⓘ distributed key management ⓘ secure multiparty computation ⓘ threshold cryptography ⓘ |
| assumption | participants know distinct public x-coordinates ⓘ |
| basedOn |
Lagrange interpolation
ⓘ
linked to:
Lagrange interpolation polynomial
polynomial interpolation ⓘ |
| designGoal |
distribute trust among multiple parties
ⓘ
prevent single point of failure for secrets ⓘ |
| extendedBy |
proactive secret sharing schemes
ⓘ
verifiable secret sharing schemes ⓘ |
| inventedBy | Adi Shamir ⓘ |
| limitation |
does not inherently provide verifiability of shares
ⓘ
requires secure channel to distribute shares ⓘ |
| mainIdea |
distribute points on a polynomial to participants as shares
ⓘ
encode the secret as the constant term of a random polynomial ⓘ |
| mathematicalTool | univariate polynomials of degree t-1 ⓘ |
| numberOfParticipantsParameter | n ⓘ |
| originalPaperTitle |
How to share a secret
ⓘ
linked to:
Shamir secret sharing scheme
|
| property |
ideal secret sharing scheme
ⓘ
perfect secret sharing scheme ⓘ |
| publishedIn | Communications of the ACM ⓘ |
| reconstructionMethod | interpolate the polynomial from t shares ⓘ |
| reconstructionRequirement | t or more shares are required to reconstruct the secret ⓘ |
| relatedTo |
Blakley secret sharing scheme
ⓘ
threshold access structures ⓘ |
| requirement | all computations are done modulo a prime or field size ⓘ |
| resilience | robust against collusion of fewer than t participants ⓘ |
| secretEncoding | secret is the value f(0) ⓘ |
| securityGuarantee | any set of fewer than t shares reveals no information about the secret ⓘ |
| securityType | information-theoretic ⓘ |
| shareSize | each share has size equal to the secret size ⓘ |
| shareStructure | each share is a point (x, f(x)) on a polynomial f ⓘ |
| thresholdParameter | t ⓘ |
| typicalField | GF(p) ⓘ |
| usedIn |
distributed key generation protocols
ⓘ
threshold decryption schemes ⓘ threshold signature schemes ⓘ |
| worksOver | finite field ⓘ |
| yearProposed | 1979 ⓘ |
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: Shamir secret sharing scheme Description of subject: 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.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Shamir secret sharing scheme
linked to: Shamir secret sharing scheme
linked to: Shamir secret sharing scheme
linked to: Shamir secret sharing scheme