Coherent functions and program checkers
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Amortized communication complexity (Preliminary version)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
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
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
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
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
Products and help bits in decision trees
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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Asecret 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. Am ulti 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. Am ulti secret sharing scheme can be trivially realized by realizing a secret sharing scheme for each of the secrets. An atural question in the area is whether this simple construction is the most efficient as well, and, if not, how much improvement is possible over it. In this paper we address and answer this question, with respect to the most widely used efficiency measure, that is, the maximum piece of information distributed among all the parties. Although no improvement is possible for several instances of multi secret sharing, we present the first instance for which some improvement is possible, and, in fact, we show that for this instance an improvement factor equal to the number of secrets over the above simple construction is possible. The given improvement is also proved to be the best possible, thus showing that the achieved bound is tight.