Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Some improved bounds on the information rate of perfect secret sharing schemes
Journal of Cryptology
Journal of Combinatorial Theory Series B
An explication of secret sharing schemes
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Weighted threshold secret sharing schemes
Information Processing Letters
Communications of the ACM
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Shared Generation of Authenticators and Signatures (Extended Abstract)
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
New General Lower Bounds on the Information Rate of Secret Sharing Schemes
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
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
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
Monotone circuits for monotone weighted threshold functions
Information Processing Letters
Ideal Multipartite Secret Sharing Schemes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Ideal secret sharing schemes whose minimal qualified subsets have at most three participants
Designs, Codes and Cryptography
Monotone circuits for monotone weighted threshold functions
Information Processing Letters
On secret sharing schemes, matroids and polymatroids
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Any 2-asummable bipartite function is weighted threshold
Discrete Applied Mathematics
Multipartite secret sharing by bivariate interpolation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
On codes, matroids and secure multi-party computation from linear secret sharing schemes
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
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
On matroids and non-ideal secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Secured hierarchical secret sharing using ECC based signcryption
Security and Communication Networks
CT-RSA'13 Proceedings of the 13th international conference on Topics in Cryptology
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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. A secret sharing scheme is ideal if 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). The family of subsets authorized to reconstruct the secret in a secret sharing scheme is called an access structure. An access structure is ideal if there exists an ideal secret sharing scheme that realizes it. It is known that some weighted threshold access structures are not ideal, while other nontrivial weighted threshold access structures do have an ideal scheme that realizes them. 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, that we introduce here, 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.