Book ChapterDOI
Nonperfect Secret Sharing Schemes
Wakaha Ogata,Kaoru Kurosawa,Shigeo Tsujii +2 more
- pp 56-66
TLDR
This paper characterizes nonperfect secret sharing schemes and derives a lower bound of ¦Vi¦ in terms of a distance between Γ1 and Γ3.Abstract:
A nonperfect secret sharing scheme (NSS) consists of a family of access subsets Γ1, a family of semi-access subsets Γ2 and a family of non-access subsets Γ3. In an NSS, it is possible that ¦Vi¦<¦S¦, where ¦Vi¦ is the size of the share and ¦S¦ is the size of the secret. This paper characterizes nonperfect secret sharing schemes. First, we show that (Γ1, Γ2, Γ3) is realizable if and only if Γ1 is monotone and Γ1 ∪ Γ2 is monotone. Then, we derive a lower bound of ¦Vi¦ in terms of a distance between Γ1 and Γ3. Finally, we show a condition for (Γ1, Γ2, Γ3) to achieve ¦V i ¦=¦S¦/2 for all i.read more
Citations
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Book ChapterDOI
Nonperfect secret sharing schemes and matroids
TL;DR: This paper shows that nonperfect secret sharing schemes (NSS) have matroid structures and presents a direct link between the secret sharing matroids and entropy for both perfect and nonperfect schemes.
Journal Article
Secret Sharing Schemes with Applications in Security Protocols.
TL;DR: It is proved, using the concept of entropy, that in any perfect threshold secret sharing scheme the shares must be at least as long as the secret and, later on, Capocelli, De Santis, Gargano, and Vaccaro have extended this result to the …
Journal Article
Some basic properties of general nonperfect secret sharing schemes
Wakaha Ogata,Kaoru Kurosawa +1 more
TL;DR: It is shown that a compact NSS has some special access hierarchy and it is closely related to a matroid, which means that it meets the equalities of both the bounds and the entropy type bound.
Book ChapterDOI
General short computational secret sharing schemes
Philippe Béguin,Antonella Cresti +1 more
TL;DR: A secret sharing scheme permits a secret to be shared among participants in such a way that only qualified subsets of participants can recover the secret if any non qualified subset has absolutely no information about the secret, then the scheme is called perfect.
Journal ArticleDOI
A General Decomposition Construction for Incomplete SecretSharing Schemes
TL;DR: This paper presents a more precise definition of secret sharing schemes in terms of information theory, and a new decomposition theorem that generalizes previous decomposition theorems and also works for a more general class of access structures.
References
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Journal ArticleDOI
How to share a secret
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Proceedings ArticleDOI
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Journal ArticleDOI
Secret sharing scheme realizing general access structure
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Book ChapterDOI
Generalized secret sharing and monotone functions
Josh Benaloh,Jerry Leichter +1 more
TL;DR: This paper will present general methods for constructing secret sharing schemes for any given secret sharing function using the set of monotone functions and tools developed for simplifying the latter set can be applied equally well to the former set.