STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
How to share a secret with cheaters
Journal of Cryptology
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Prepositioned shared secret and/or shared control schemes
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
A protocol to set up shared secret schemes without the assistance of mutually trusted party
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
The detection of cheaters in threshold schemes
SIAM Journal on Discrete Mathematics
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
Some Improved Bounds on the Information Rate of Perfect Secret Sharing Schemes
CRYPTO '90 Proceedings of the 10th 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
On the Size of Shares for Secret Sharing Schemes
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Size of shares and probability of cheating in threshold schemes
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Nonperfect secret sharing schemes and matroids
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the Information Rate of Secret Sharing Schemes (Extended Abstract)
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
New General Lower Bounds on the Information Rate of Secret Sharing Schemes
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Fully Dynamic Secret Sharing Schemes
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Visual cryptographic protocols using the trusted initializer
ICICS'05 Proceedings of the 7th international conference on Information and Communications Security
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In this paper, we continue a study of secret sharing schemes for access structures based on graphs. Given a graph G, we require that a subset of participants can compute a secret key if they contain an edge of G otherwise, they can obtain no information regarding the key. We study the information rate of such schemes, which measures how much information is being distributed as shares as compared to the size of the secret key, and the average information rate, which is the ratio between the secret size and the arithmetic mean of the size of the shares. We give both upper and lower bounds on the optimal information rate and average information rate that can be obtained. Upper bounds arise by applying entropy arguments due to Capocelli et al [10]. Lower bounds come from constructions that are based on graph decompositions. Application of these constructions requires solving a particular linear programming problem. We prove some general results concerning the information rate and average information rate for paths, cycles and trees. Also, we study the 30 (connected) graphs on at most five vertices, obtaining exact values for the optimal information rate in 26 of the 30 cases, and for the optimal avebage information rate in 28 of the 30 cases.