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
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
Information Processing Letters
Access Control and Signatures via Quorum Secret Sharing
IEEE Transactions on Parallel and Distributed Systems
Communications of the ACM
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 characterization of span program size and improved lower bounds for monotone span programs
Computational Complexity
Attribute-based encryption for fine-grained access control of encrypted data
Proceedings of the 13th ACM conference on Computer and communications security
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
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
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
Weakly-private secret sharing schemes
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Matroids can be far from ideal secret sharing
TCC'08 Proceedings of the 5th conference on Theory of cryptography
On characterization of entropy function via information inequalities
IEEE Transactions on Information Theory
On a relation between information inequalities and group theory
IEEE Transactions on Information Theory
Two Constructions on Limits of Entropy Functions
IEEE Transactions on Information Theory
Networks, Matroids, and Non-Shannon Information Inequalities
IEEE Transactions on Information Theory
On the optimization of bipartite secret sharing schemes
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Secret-sharing schemes: a survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Ideal secret sharing schemes for useful multipartite access structures
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Finding lower bounds on the complexity of secret sharing schemes by linear programming
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Finding lower bounds on the complexity of secret sharing schemes by linear programming
Discrete Applied Mathematics
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The known secret-sharing schemes for most access structures are not efficient; even for a one-bit secret the length of the shares in the schemes is 2 O (n ), where n is the number of participants in the access structure. It is a long standing open problem to improve these schemes or prove that they cannot be improved. The best known lower bound is by Csirmaz (J. Cryptology 97), who proved that there exist access structures with n participants such that the size of the share of at least one party is n /logn times the secret size. Csirmaz's proof uses Shannon information inequalities, which were the only information inequalities known when Csirmaz published his result. On the negative side, Csirmaz proved that by only using Shannon information inequalities one cannot prove a lower bound of *** (n ) on the share size. In the last decade, a sequence of non-Shannon information inequalities were discovered. This raises the hope that these inequalities can help in improving the lower bounds beyond n . However, in this paper we show that all the inequalities known to date cannot prove a lower bound of *** (n ) on the share size.