Proceedings of CRYPTO 84 on Advances in cryptology
Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
How to share a secret with cheaters
Proceedings on Advances in cryptology---CRYPTO '86
How to withstand mobile virus attacks (extended abstract)
PODC '91 Proceedings of the tenth annual ACM symposium on Principles of distributed computing
Nonperfect secret sharing schemes and matroids
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Anonymous secret sharing schemes
Discrete Applied Mathematics
Communications of the ACM
A nonlinear secret sharing scheme
ACISP '96 Proceedings of the First Australasian Conference on Information Security and Privacy
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Proactive Secret Sharing Or: How to Cope With Perpetual Leakage
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
On the Power of Nonlinear Secret-Sharing
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Verifiable secret sharing and achieving simultaneity in the presence of faults
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
General short computational secret sharing schemes
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
A Strong Ramp Secret Sharing Scheme Using Matrix Projection
WOWMOM '06 Proceedings of the 2006 International Symposium on on World of Wireless, Mobile and Multimedia Networks
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In a secret sharing protocol, a dealer shares the secret such that only the subsets of players in the (monotone) access structure can reconstruct the secret, while subsets of players that are not in the access structure cannot reconstruct the secret. The sharing is perfect if the players of any set not in the access structure have no information about the secret. Non-perfect secret sharing slackens the requirement as: the players of any set not in the access structure can have some information about the secret but cannot reconstruct the secret. All known schemes in the literature for non-perfect secret sharing are directed toward specific classes of the access hierarchy like threshold, ramp, multiple-level hierarchy etc. In this work, we initiate the study of a more general nonperfect secret sharing. We model the access hierarchy via a weighted lattice. We first give a necessary condition and a sufficient condition for the existence of a secret sharing scheme for any given weighted lattice (that defines the access hierarchy). Subsequently, we provide a framework for designing non-perfect secret sharing schemes, using generalized monotone span programs (GenMSPs). We also show how to construct new nonperfect secret sharing schemes by composition of known GenMSPs, and design an exemplary secret sharing algorithm that is based on and illustrates the above framework.