New General Lower Bounds on the Information Rate of Secret Sharing Schemes
Douglas R. Stinson
- pp 168-182
TLDR
Two combinatorial techniques are used to apply a decomposition construction in obtaining general lower bounds on information rate and average information rate of certain general classes of access structures.Abstract:
We use two combinatorial techniques to apply a decomposition construction in obtaining general lower bounds on information rate and average information rate of certain general classes of access structures. The first technique uses combinatorial designs (in particular, Steiner systems S(t, k, v)). The second technique uses equitable edge-colourings of bipartite graphs. For uniform access structures of rank t, this second technique improves the best previous general bounds by a factor of t (asymptotically).read more
Citations
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Book
A First Course in Information Theory
TL;DR: This book provides the first comprehensive treatment of the theory of I-Measure, network coding theory, Shannon and non-Shannon type information inequalities, and a relation between entropy and group theory.
Journal ArticleDOI
An explication of secret sharing schemes
TL;DR: This paper presents numerous direct constructions for secret sharing schemes, such as the Shamir threshold scheme, the Boolean circuit construction of Benaloh and Leichter, the vector space construction of Brickell, and the Simmons geometric construction, emphasizing combinatorial construction methods.
Journal ArticleDOI
Decomposition constructions for secret-sharing schemes
TL;DR: It is shown that for any graph G of maximum degree d, there is a perfect secret-sharing scheme for G with information rate 2/(d+1), as a corollary, the maximum information rate of secret- sharing schemes for paths on more than three vertices and for cycles on morethan four vertices is shown to be 2/3.
Journal ArticleDOI
Graph decompositions and secret sharing schemes
TL;DR: This paper studies the information rate of secret sharing schemes for-access structures based on graphs, which measures how much information in being distributed as shares compared with the size of the secret key, and the average information rate, which is the ratio between the secret size and the arithmetic mean of the size the shares.
Journal ArticleDOI
On the information rate of perfect secret sharing schemes
TL;DR: A method to derive information-theoretical upper bounds on the optimal information rate and the optimal average information rate of perfect secret sharing schemes based on connected graphs on six vertices is discussed.
References
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How to share a secret
TL;DR: This technique enables the construction of robust key management schemes for cryptographic systems that can function securely and reliably even when misfortunes destroy half the pieces and security breaches expose all but one of the remaining pieces.
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.
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TL;DR: In an elementary text book, the reader gains an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject.
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Some ideal secret sharing schemes
TL;DR: This paper constructs ideal secret sharing schemes for more general access structures which include the multilevel and compartmented access structures proposed by Simmons.