Generalized secret sharing and monotone functions
CRYPTO '88 Proceedings on Advances in cryptology
Coherent functions and program checkers
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Communication complexity of secure computation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Elements of information theory
Elements of information theory
An explication of secret sharing schemes
Designs, Codes and Cryptography
On the information rate of perfect secret sharing schemes
Designs, Codes and Cryptography
Amortized Communication Complexity
SIAM Journal on Computing
On the information rate of secret sharing schemes
Theoretical Computer Science
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A Construction for Multisecret Threshold Schemes
Designs, Codes and Cryptography
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
Sharing one secret vs. sharing many secrets: tight bounds on the average improvement ratio
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Communications of the ACM
Efficient Sharing of Many Secrets
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Proofs of Membership vs. Proofs of Knowledge
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
New bounds on the information rate of secret sharing schemes
IEEE Transactions on Information Theory
A new multi-secret images sharing scheme using Largrange's interpolation
Journal of Systems and Software
Strongly secure ramp secret sharing schemes for general access structures
Information Processing Letters
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
Strongly secure ramp secret sharing schemes for general access structures
Information Processing Letters
A comprehensive study of visual cryptography
Transactions on data hiding and multimedia security V
Journal of Combinatorial Optimization
An improved multi-stage (t, n)-threshold secret sharing scheme
WAIM'05 Proceedings of the 6th international conference on Advances in Web-Age Information Management
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A secret sharing scheme is a method for distributing a secret among several parties in such a way that only qualified subsets of the parties can reconstruct it and unqualified subsets receive no information about the secret. A multi-secret sharing scheme is the natural extension of a secret sharing scheme to the case in which many secrets need to be shared, each with respect to possibly different subsets of qualified parties. A multi-secret sharing scheme can be trivially realized by realizing a secret sharing scheme for each of the secrets.In this paper we address the natural questions of whether this simple construction is the most efficient as well, and, if not, how much improvement is possible over it, with respect to both efficiency measures used in the literature; namely, the maximum piece of information and the sum of all pieces of information distributed to all parties. We completely answer these questions, as follows. We show the first instance for which an improvement is possible; we prove a bound on how much improvement is possible with respect to both measures; and we show instances of multi-secret sharing schemes which achieve this improvement, with respect to both measures, thus showing that the above bound is tight.