Elements of information theory
Elements of information theory
Some improved bounds on the information rate of perfect secret sharing schemes
Journal of Cryptology
An explication of secret sharing schemes
Designs, Codes and Cryptography
On the information rate of perfect secret sharing schemes
Designs, Codes and Cryptography
On the information rate of secret sharing schemes
Theoretical Computer Science
Communications of the ACM
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Contemporary Cryptology: The Science of Information Integrity
Contemporary Cryptology: The Science of Information Integrity
Randomness in Distributed Protocols
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th 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
Lower bounds for monotone span programs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
New bounds on the information rate of secret sharing schemes
IEEE Transactions on Information Theory
Secret Sharing Schemes with Detection of Cheaters for a General Access Structure
Designs, Codes and Cryptography
Lower bounds on the information rate of secret sharing schemes with homogeneous access structure
Information Processing Letters
Sharing One Secret vs. Sharing Many Secrets: Tight Bounds for the Max Improvement Ratio
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Randomness Required for Linear Threshold Sharing Schemes Defined over Any Finite Abelian Group
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Requirements for Group Independent Linear Threshold Secret Sharing Schemes
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Secret Sharing Schemes with Detection of Cheaters for a General Access Structure
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Sharing one secret vs. sharing many secrets
Theoretical Computer Science - Mathematical foundations of computer science
A Linear Algebraic Approach to Metering Schemes
Designs, Codes and Cryptography
Secret sharing schemes with three or four minimal qualified subsets
Designs, Codes and Cryptography
Sharing Multiple Secrets: Models, Schemes and Analysis
Designs, Codes and Cryptography
Secret sharing schemes on access structures with intersection number equal to one
Discrete Applied Mathematics
A note on secret sharing schemes with three homogeneous access structure
Information Processing Letters
Ideal Multipartite Secret Sharing Schemes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
On Linear Secret Sharing for Connectivity in Directed Graphs
SCN '08 Proceedings of the 6th international conference on Security and Cryptography for Networks
Hypergraph decomposition and secret sharing
Discrete Applied Mathematics
Ideal secret sharing schemes whose minimal qualified subsets have at most three participants
Designs, Codes and Cryptography
Secret sharing schemes on access structures with intersection number equal to one
Discrete Applied Mathematics
An impossibility result on graph secret sharing
Designs, Codes and Cryptography
Weakly-private secret sharing schemes
TCC'07 Proceedings of the 4th conference on Theory of cryptography
On secret sharing schemes, matroids and polymatroids
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Secret sharing schemes on access structures with intersection number equal to one
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
On the optimization of bipartite secret sharing schemes
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Journal of Combinatorial Optimization
SIAM Journal on Discrete Mathematics
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
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Optimal complexity of secret sharing schemes with four minimal qualified subsets
Designs, Codes and Cryptography
Complexity of universal access structures
Information Processing Letters
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
On the optimization of bipartite secret sharing schemes
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Ideal secret sharing schemes whose minimal qualified subsets have at most three participants
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
Finding lower bounds on the complexity of secret sharing schemes by linear programming
Discrete Applied Mathematics
The complexity of the graph access structures on six participants
Designs, Codes and Cryptography
Information Sciences: an International Journal
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A secret sharing scheme is a protocol by means of whicha dealer distributes a secret s among a set of participantsP in such a way that only qualified subsets ofP can reconstruct the value of s whereasany other subset of P, non-qualified to know s,cannot determine anything about the value of the secret. In this paper we provide a general technique to prove upper boundson the information rate of secret sharing schemes. The informationrate is the ratio between the size of the secret and the sizeof the largest share given to any participant. Most of the recentupper bounds on the information rate obtained in the literaturecan be seen as corollaries of our result. Moreover, we provethat for any integer d there exists a d-regulargraph for which any secret sharing scheme has information rateupper bounded by 2/(d+1). This improves on van Dijk‘sresult dik and matches the corresponding lower bound proved byStinson in [22].