Polynomial interpolation to data on flats in Rd
Journal of Approximation Theory
Communications of the ACM
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Hierarchical Threshold Secret Sharing
Journal of Cryptology
Characterizing ideal weighted threshold secret sharing
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
Ideal Multipartite Secret Sharing Schemes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Secret-sharing schemes: a survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
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Given a set of participants that is partitioned into distinct compartments, a multipartite access structure is an access structure that does not distinguish between participants that belong to the same compartment. We examine here three types of such access structures – compartmented access structures with lower bounds, compartmented access structures with upper bounds, and hierarchical threshold access structures. We realize those access structures by ideal perfect secret sharing schemes that are based on bivariate Lagrange interpolation. The main novelty of this paper is the introduction of bivariate interpolation and its potential power in designing schemes for multipartite settings, as different compartments may be associated with different lines in the plane. In particular, we show that the introduction of a second dimension may create the same hierarchical effect as polynomial derivatives and Birkhoff interpolation were shown to do in [13]