A randomized protocol for signing contracts
Communications of the ACM
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
One-way functions are necessary and sufficient for secure signatures
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Elements of information theory
Elements of information theory
On the information rate of perfect secret sharing schemes
Designs, Codes and Cryptography
On the information rate of secret sharing schemes
Theoretical Computer Science
Lower bounds for monotone span programs
Computational Complexity
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
Communication complexity
Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Information Processing Letters
Designs, Codes and Cryptography
Access Control and Signatures via Quorum Secret Sharing
IEEE Transactions on Parallel and Distributed Systems
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Communications of the ACM
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Shared Generation of Authenticators and Signatures (Extended Abstract)
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
A Construction of Practical Secret Sharing Schemes using Linear Block Codes
ASIACRYPT '92 Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
A characterization of span program size and improved lower bounds for monotone span programs
Computational Complexity
A note on monotone complexity and the rank of matrices
Information Processing Letters
Monotone Circuits for Weighted Threshold Functions
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Separating the Power of Monotone Span Programs over Different Fields
SIAM Journal on Computing
On the Power of Nonlinear Secret-Sharing
SIAM Journal on Discrete Mathematics
Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions
Information Processing Letters
Attribute-based encryption for fine-grained access control of encrypted data
Proceedings of the 13th ACM conference on Computer and communications security
Robust computational secret sharing and a unified account of classical secret-sharing goals
Proceedings of the 14th ACM conference on Computer and communications security
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Verifiable secret sharing and achieving simultaneity in the presence of faults
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
On Linear Secret Sharing for Connectivity in Directed Graphs
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Information Theory and Network Coding
Information Theory and Network Coding
Secret Sharing and Non-Shannon Information Inequalities
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
On secret sharing schemes, matroids and polymatroids
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Alternative protocols for generalized oblivious transfer
ICDCN'08 Proceedings of the 9th international conference on Distributed computing and networking
Matroids can be far from ideal secret sharing
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Generalized oblivious transfer by secret sharing
Designs, Codes and Cryptography
Multipartite secret sharing by bivariate interpolation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Fuzzy identity-based encryption
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
On characterization of entropy function via information inequalities
IEEE Transactions on Information Theory
Natural generalizations of threshold secret sharing
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Optimum general threshold secret sharing
ICITS'12 Proceedings of the 6th international conference on Information Theoretic Security
Finding lower bounds on the complexity of secret sharing schemes by linear programming
Discrete Applied Mathematics
Information Sciences: an International Journal
Witness encryption and its applications
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Secret sharing schemes based on graphical codes
Cryptography and Communications
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A secret-sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret. Secret-sharing schemes are an important tool in cryptography and they are used as a building box in many secure protocols, e.g., general protocol for multiparty computation, Byzantine agreement, threshold cryptography, access control, attribute-based encryption, and generalized oblivious transfer. In this survey, we describe the most important constructions of secret-sharing schemes; in particular, we explain the connections between secret-sharing schemes and monotone formulae and monotone span programs. We then discuss the main problem with known secret-sharing schemes - the large share size, which is exponential in the number of parties. We conjecture that this is unavoidable. We present the known lower bounds on the share size. These lower bounds are fairly weak and there is a big gap between the lower and upper bounds. For linear secret-sharing schemes, which is a class of schemes based on linear algebra that contains most known schemes, super-polynomial lower bounds on the share size are known. We describe the proofs of these lower bounds. We also present two results connecting secret-sharing schemes for a Hamiltonian access structure to the NP vs. coNP problem and to a major open problem in cryptography - constructing oblivious-transfer protocols from one-way functions.