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
On the information rate of perfect secret sharing schemes
Designs, Codes and Cryptography
Lower bounds for monotone span programs
Computational Complexity
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
A Linear Construction of Secret Sharing Schemes
Designs, Codes and Cryptography
Access Control and Signatures via Quorum Secret Sharing
IEEE Transactions on Parallel and Distributed Systems
On arithmetic branching programs
Journal of Computer and System Sciences
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
A note on monotone complexity and the rank of matrices
Information Processing Letters
Undirected ST-connectivity in log-space
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Separating the Power of Monotone Span Programs over Different Fields
SIAM Journal on Computing
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
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
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 schemes: a survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
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In this work we study linear secret sharing schemes for s-tconnectivity in directed graphs. In such schemes the parties are edges of a complete directed graph, and a set of parties (i.e., edges) can reconstruct the secret if it contains a path from node sto node t. We prove that in every linear secret sharing scheme realizing the st-con function on a directed graph with nedges the total size of the shares is ï戮驴(n1.5). This should be contrasted with s-tconnectivity in undirected graphs, where there is a scheme with total share size n. Our result is actually a lower bound on the size monotone span programs for st ï戮驴 con, where a monotone span program is a linear-algebraic model of computation equivalent to linear secret sharing schemes. Our results imply the best known separation between the power of monotone and non-monotone span programs. Finally, our results imply the same lower bounds for matching.