Explicit construction of exponential sized families of K-independent sets
Discrete Mathematics
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STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
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Elements of information theory
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An explication of secret sharing schemes
Designs, Codes and Cryptography
On the upper bound of the size of the r-cover-free families
Journal of Combinatorial Theory Series A
Secure hypergraphs: privacy from partial broadcast
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Universal Hashing and Geometric Codes
Designs, Codes and Cryptography
Theoretical Computer Science
Optimal linear perfect hash families
Journal of Combinatorial Theory Series A
Some new bounds for cover-free families
Journal of Combinatorial Theory Series A
Communications of the ACM
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '93 Proceedings of the 13th Annual International Cryptology Conference on Advances in Cryptology
Secret Sharing with Public Reconstruction (Extended Abstract)
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
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ISW '97 Proceedings of the First International Workshop on Information Security
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ICON '99 Proceedings of the 7th IEEE International Conference on Networks
Efficient multiplicative sharing schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Strongly universal hashing and identification codes via channels
IEEE Transactions on Information Theory
Constructions of authentication codes from algebraic curves over finite fields
IEEE Transactions on Information Theory
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In a conventional secret sharing scheme a dealer uses secure point-to-point channels to distribute the shares of a secret to a number of participants. At a later stage an authorised group of participants send their shares through secure point-to-point channels to a combiner who will reconstruct the secret. In this paper, we assume no point-to-point channel exists and communication is only through partial broadcast channels. A partial broadcast channel is a point-to-multipoint channel that enables a sender to send the same message simultaneously and privately to a fixed subset of receivers. We study secret sharing schemes with partial broadcast channels, called partial broadcast secret sharing schemes. We show that a necessary and sufficient condition for the partial broadcast channel allocation of a (t, n)-threshold partial secret sharing scheme is equivalent to a combinatorial object called a cover-free family. We use this property to construct a (t, n)-threshold partial broadcast secret sharing scheme with O(log n) partial broadcast channels. This is a significant reduction compared to n point-to-point channels required in a conventional secret sharing scheme. Next, we consider communication rate of a partial broadcast secret sharing scheme defined as the ratio of the secret size to the total size of messages sent by the dealer. We show that the communication rate of a partial broadcast secret sharing scheme can approach 1/O(log n) which is a significant increase over the corresponding value, 1/n, in the conventional secret sharing schemes. We derive a lower bound on the communication rate and show that for a (t,n)-threshold partial broadcast secret sharing scheme the rate is at least 1/t and then we propose constructions with high communication rates. We also present the case of partial broadcast secret sharing schemes for general access structures, discuss possible extensions of this work and propose a number of open problems.