On the optimization of bipartite secret sharing schemes
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Generalized oblivious transfer by secret sharing
Designs, Codes and Cryptography
SIAM Journal on Discrete Mathematics
Ideal secret sharing schemes for useful multipartite access structures
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Optimal complexity of secret sharing schemes with four minimal qualified subsets
Designs, Codes and Cryptography
Ideal hierarchical secret sharing schemes
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
On the optimization of bipartite secret sharing schemes
Designs, Codes and Cryptography
Natural generalizations of threshold secret sharing
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
Efficient integer span program for hierarchical threshold access structure
Information Processing Letters
| Hi-index | 0.00 |
Weighted threshold secret sharing was introduced by Shamir in his seminal work on secret sharing. In such settings, there is a set of users where each user is assigned a positive weight. A dealer wishes to distribute a secret among those users so that a subset of users may reconstruct the secret if and only if the sum of weights of its users exceeds a certain threshold. On one hand, there are nontrivial weighted threshold access structures that have an ideal scheme—a scheme in which the size of the domain of shares of each user is the same as the size of the domain of possible secrets (this is the smallest possible size for the domain of shares). On the other hand, other weighted threshold access structures are not ideal. In this work we characterize all weighted threshold access structures that are ideal. We show that a weighted threshold access structure is ideal if and only if it is a hierarchical threshold access structure (as introduced by Simmons), or a tripartite access structure (these structures generalize the concept of bipartite access structures due to Padró and Sáez), or a composition of two ideal weighted threshold access structures that are defined on smaller sets of users. We further show that in all those cases the weighted threshold access structure may be realized by a linear ideal secret sharing scheme. The proof of our characterization relies heavily on the strong connection between ideal secret sharing schemes and matroids, as proved by Brickell and Davenport.