A combinatorial approach to threshold schemes
SIAM Journal on Discrete Mathematics
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
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
Journal of Combinatorial Theory Series B
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On the information rate of perfect secret sharing schemes
Designs, Codes and Cryptography
Combinatorial lower bounds for secret sharing schemes
Information Processing Letters
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
Anonymous secret sharing schemes
Discrete Applied Mathematics
A Linear Construction of Secret Sharing Schemes
Designs, Codes and Cryptography
Perfectly secure key distribution for dynamic conferences
Information and Computation
Access Control and Signatures via Quorum Secret Sharing
IEEE Transactions on Parallel and Distributed Systems
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Communications of the ACM
On the bound for anonymous secret sharing schemes
Discrete Applied Mathematics
A combinatorial characterization of regular anonymous perfect threshold schemes
Information Processing Letters
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
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
On the Power of Nonlinear Secret-Sharing
SIAM Journal on Discrete Mathematics
Attribute-based encryption for fine-grained access control of encrypted data
Proceedings of the 13th ACM conference on Computer and communications security
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
On private computation in incomplete networks
Distributed Computing
General short computational secret sharing schemes
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
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
Linear integer secret sharing and distributed exponentiation
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
On matroids and non-ideal secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Communication in key distribution schemes
IEEE Transactions on Information Theory
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
New bounds on the information rate of secret sharing schemes
IEEE Transactions on Information Theory
Secret Sharing and Non-Shannon Information Inequalities
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Group signature implies PKE with non-interactive opening and threshold PKE
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
Attribute-based strong designated-verifier signature scheme
Journal of Systems and Software
On partial anonymity in secret sharing
EuroPKI'07 Proceedings of the 4th European conference on Public Key Infrastructure: theory and practice
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Secret-sharing schemes are an important tool in cryptography that is used in the construction of many secure protocols. However, the shares' size in the best known secret-sharing schemes realizing general access structures is exponential in the number of parties in the access structure, making them impractical. On the other hand, the best lower bound known for sharing of an l-bit secret with respect to an access structure with n parties is ω(ln/ log n) (Csirmaz, EUROCRYPT 94). No major progress on closing this gap has been obtained in the last decade. Faced by our lack of understanding of the share complexity of secret sharing schemes, we investigate a weaker notion of privacy in secrets sharing schemes where each unauthorized set can never rule out any secret (rather than not learn any "probabilistic" information on the secret). Such schemes were used previously to prove lower bounds on the shares' size of perfect secret-sharing schemes. Our main results is somewhat surprising upper-bounds on the shares' size in weakly-private schemes. - For every access structure, we construct a scheme for sharing an l-bit secret with (l+c)-bit shares, where c is a constant depending on the access structure (alas, c can be exponential in n). Thus, our schemes become more efficient as l - the secret size - grows. For example, for the above mentioned access structure of Csirmaz, we construct a scheme with shares' size l + n log n. - We construct efficient weakly-private schemes for threshold access structures for sharing a one bit secret. Most impressively, for the 2- out-of-n threshold access structure, we construct a scheme with 2-bit shares (compared to ω(log n) in any perfect secret sharing scheme).