Generalized linear threshold scheme
Proceedings of CRYPTO 84 on Advances in cryptology
Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
Communications of the ACM
Verifiable secret-ballot elections
Verifiable secret-ballot elections
A practical scheme for non-interactive verifiable secret sharing
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Verifiable secret sharing for monotone access structures
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
Access control and signatures via quorum secret sharing
CCS '96 Proceedings of the 3rd ACM conference on Computer and communications security
On the Dealer‘s Randomness Required in Secret Sharing Schemes
Designs, Codes and Cryptography
Protecting data privacy in private information retrieval schemes
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Existence of multiplicative secret sharing schemes with polynomial share expansion
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Sharing one secret vs. sharing many secrets: tight bounds on the average improvement ratio
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Lower bounds on the information rate of secret sharing schemes with homogeneous access structure
Information Processing Letters
Information-Theoretic Private Information Retrieval: A Unified Construction
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Geometric Shared Secret and/or Shared Control Schemes
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Sharing one secret vs. sharing many secrets
Theoretical Computer Science - Mathematical foundations of computer science
A Linear Algebraic Approach to Metering Schemes
Designs, Codes and Cryptography
On perfect secret sharing schemes and coalitional game forms
TARK '01 Proceedings of the 8th conference on Theoretical aspects of rationality and knowledge
Concealing complex policies with hidden credentials
Proceedings of the 11th ACM conference on Computer and communications security
Practical secret sharing scheme realizing generalized adversary structure
Journal of Computer Science and Technology
Establishment of Ad-Hoc Communities through Policy-Based Cryptography
Electronic Notes in Theoretical Computer Science (ENTCS)
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
An improved watermarking technique for multi-user, multi-right environments
Multimedia Tools and Applications
Classification of ideal homomorphic threshold schemes over finite Abelian groups
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
A method for sending confidential messages to a group without trusted parties
ISPA'03 Proceedings of the 2003 international conference on Parallel and distributed processing and applications
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Secret Sharing from the perspective of threshold schemes has been well-studied over the past decade. Threshold schemes, however, can only handle a small fraction of the secret sharing functions which we may wish to form. For example, if it is desirable to divide a secret among four participants A, B, C, and D in such a way that either A together with B can reconstruct the secret or C together with D can reconstruct the secret, then threshold schemes (even with weighting) are provably insufficient.This paper will present general methods for constructing secret sharing schemes for any given secret sharing function. There is a natural correspondence between the set of "generalized" secret sharing functions and the set of monotone functions, and tools developed for simplifying the latter set can be applied equally well to the former set.