Journal ArticleDOI
The Size of a Share Must Be Large
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TLDR
It is proved that for each n there exists an access structure on n participants so that any perfect sharing scheme must give some participant a share which is at least about $n/\log n times the secret size.Citations
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Book ChapterDOI
Secret-sharing schemes: a survey
TL;DR: This survey describes the most important constructions of secret-sharing schemes and explains the connections between secret- sharing schemes and monotone formulae and monOTone span programs, and presents the known lower bounds on the share size.
DissertationDOI
Entropy measures and unconditional security in cryptography
TL;DR: Information-theoretic meth¬ ods are used for proving the security of unconditionally secure cryptosystems, and a new information measure, smooth entropy, is introduced to quantify the number of almost uniform random bits that can be extracted from a source by probabilistic algorithms.
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.
Journal ArticleDOI
Tight Bounds on the Information Rate of Secret SharingSchemes
TL;DR: It is proved that for any integer d there exists a d-regular graph for which any secret sharing scheme has information rate upper bounded by 2/(d+1), which improves on van Dijk's result dik and matches the corresponding lower bound proved by Stinson in [22].
Journal ArticleDOI
Superpolynomial Lower Bounds for Monotone Span Programs
TL;DR: The results give the first superpolynomial lower bounds for linear secret sharing schemes and show that the perfect matching function can be computed by polynomial size (non-monotone) span programs over arbitrary fields.
References
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Book
Information Theory: Coding Theorems for Discrete Memoryless Systems
I. Csiszar,János Körner +1 more
TL;DR: This new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics.
Book ChapterDOI
Security of ramp schemes
G. R. Blakley,Catherine Meadows +1 more
TL;DR: A k out of n p/s/r process [AS81] is a very efficient way to convey information (k words suffice to reclaim k words), but it provides virtually no cryptographic security for the information it deals with.
Journal ArticleDOI
On the size of shares for secret sharing schemes
TL;DR: This work shows that there are access structures with four participants for which any secret sharing scheme must give to a participant a share at least 50% greater than the secret size, the first proof that there exist access structures for which the best achievable information rate is bounded away from 1.
Journal ArticleDOI
On the classification of ideal secret sharing schemes
TL;DR: In this article, the authors show a relationship between ideal secret sharing schemes and matroids, and show that the set of possible shares in a secret sharing scheme is matroid-like.