Ideal secret sharing schemes for useful multipartite access structures
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
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
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
Secured hierarchical secret sharing using ECC based signcryption
Security and Communication Networks
Efficient integer span program for hierarchical threshold access structure
Information Processing Letters
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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 belonging to the same compartment. We examine here three types of such access structures: two that were studied before, compartmented access structures and hierarchical threshold access structures, and a new type of compartmented access structures that we present herein. We design ideal perfect secret sharing schemes for these types of access structures that are based on bivariate interpolation. The secret sharing schemes for the two types of compartmented access structures are based on bivariate Lagrange interpolation with data on parallel lines. The secret sharing scheme for the hierarchical threshold access structures is based on bivariate Lagrange interpolation with data on lines in general position. The main novelty of this paper is the introduction of bivariate Lagrange interpolation and its potential power in designing schemes for multipartite settings, as different compartments may be associated with different lines or curves 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 Tassa (J. Cryptol. 20:237–264, 2007).