Journal ArticleDOI
Hierarchical Threshold Secret Sharing
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TLDR
A perfect secret sharing scheme for threshold secret sharing in groups with hierarchical structure that uses Birkhoff interpolation, i.e., the construction of a polynomial according to an unstructured set of point and derivative values.Abstract:
We consider the problem of threshold secret sharing in groups with hierarchical structure. In such settings, the secret is shared among a group of participants that is partitioned into levels. The access structure is then determined by a sequence of threshold requirements: a subset of participants is authorized if it has at least k0 0 members from the highest level, as well as at least k1 > k0 members from the two highest levels and so forth. Such problems may occur in settings where the participants differ in their authority or level of confidence and the presence of higher level participants is imperative to allow the recovery of the common secret. Even though secret sharing in hierarchical groups has been studied extensively in the past, none of the existing solutions addresses the simple setting where, say, a bank transfer should be signed by three employees, at least one of whom must be a department manager. We present a perfect secret sharing scheme for this problem that, unlike most secret sharing schemes that are suitable for hierarchical structures, is ideal. As in Shamir's scheme, the secret is represented as the free coefficient of some polynomial. The novelty of our scheme is the usage of polynomial derivatives in order to generate lesser shares for participants of lower levels. Consequently, our scheme uses Birkhoff interpolation, i.e., the construction of a polynomial according to an unstructured set of point and derivative values. A substantial part of our discussion is dedicated to the question of how to assign identities to the participants from the underlying finite field so that the resulting Birkhoff interpolation problem will be well posed. In addition, we devise an ideal and efficient secret sharing scheme for the closely related hierarchical threshold access structures that were studied by Simmons and Brickell.read more
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.
Book ChapterDOI
Short attribute-based signatures for threshold predicates
TL;DR: This work proposes the first two attribute-based signature schemes with constant size signatures, which are proven in the selective-predicate and adaptive-message setting, in the standard model, under chosen message attacks, with respect to some algorithmic assumptions related to bilinear groups.
Journal ArticleDOI
Counting-based secret sharing technique for multimedia applications
TL;DR: This work presented two different modeling variations that are mainly different in the secret-sharing keys generation where both are studied elaborating their pros and cons.
Journal ArticleDOI
Multipartite Secret Sharing by Bivariate Interpolation
Tamir Tassa,Nira Dyn +1 more
TL;DR: It is shown that the introduction of a second dimension may create the same hierarchical effect as polynomial derivatives and Birkhoff interpolation were shown to do in Tassa (J. Cryptol. 20:237–264, 2007).
Journal ArticleDOI
Generalized oblivious transfer by secret sharing
TL;DR: This work proposes a simple and efficient GOT protocol that employs secret sharing and compares it to another secret sharing based solution for that problem that was recently proposed in Shankar et al. (Proceeding of ICDCN08, LNCS 4904, pp 304–309, 2008).
References
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Proceedings ArticleDOI
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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.
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Contemporary Cryptology: The Science of Information Integrity
TL;DR: This book provides the engineer and scientist with algorithms, protocols, and applications of the science of information integrity, with an emphasis on the cryptographic elements of the subject.