Generalized oblivious transfer by secret sharing
Designs, Codes and Cryptography
ICCOMP'10 Proceedings of the 14th WSEAS international conference on Computers: part of the 14th WSEAS CSCC multiconference - Volume I
Ideal secret sharing schemes for useful multipartite access structures
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
A hierarchical threshold secret image sharing
Pattern Recognition Letters
A probabilistic secret sharing scheme for a compartmented access structure
ICICS'11 Proceedings of the 13th international conference on Information and communications security
Ideal secret sharing schemes with share selectability
ICICS'11 Proceedings of the 13th international conference on Information and communications security
Multipartite secret sharing by bivariate interpolation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Ideal hierarchical secret sharing schemes
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
On the optimization of bipartite secret sharing schemes
Designs, Codes and Cryptography
Natural generalizations of threshold secret sharing
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Short attribute-based signatures for threshold predicates
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Secured hierarchical secret sharing using ECC based signcryption
Security and Communication Networks
A multi-threshold secret image sharing scheme based on MSP
Pattern Recognition Letters
Efficient integer span program for hierarchical threshold access structure
Information Processing Letters
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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.