Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Minimum-knowledge interactive proofs for decision problems
SIAM Journal on Computing
How to share a function securely
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Perfect Homomorphic Zero-Knowledge Threshold Schemes over any Finite Abelian Group
SIAM Journal on Discrete Mathematics
Communications of the ACM
CRYPTO '89 Proceedings of the 9th 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
Non-Existence of Homomorphic General Sharing Schemes for Some Key Spaces (Extended Abstract)
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Multiplicative Non-abelian Sharing Schemes and their Application to Threshold Cryptography
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Existence of multiplicative secret sharing schemes with polynomial share expansion
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Randomness Required for Linear Threshold Sharing Schemes Defined over Any Finite Abelian Group
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Requirements for Group Independent Linear Threshold Secret Sharing Schemes
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Optimal Black-Box Secret Sharing over Arbitrary Abelian Groups
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Equitable Key Escrow with Limited Time Span (or, How to Enforce Time Expiration Cryptographically)
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Generalised Cumulative Arrays in Secret Sharing
Designs, Codes and Cryptography
Secret sharing schemes with partial broadcast channels
Designs, Codes and Cryptography
A sequence approach to linear perfect hash families
Designs, Codes and Cryptography
Explicit constructions for perfect hash families
Designs, Codes and Cryptography
Linear hash families and forbidden configurations
Designs, Codes and Cryptography
Redistribution of mechanical secret shares
FC'02 Proceedings of the 6th international conference on Financial cryptography
Robust information-theoretic private information retrieval
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Geometric constructions of optimal linear perfect hash families
Finite Fields and Their Applications
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Multiplicative threshold schemes are useful tools in threshold cryptography. For example, such schemes can be used with a wide variety of practical homomorphic cryptosystems (such as the RSA, the El Gamal and elliptic curve systems) for threshold decryption, signatures, or proofs. The paper describes a new recursive construction for multiplicative threshold schemes which makes it possible to extend the number of users of such schemes for a relatively small expansion of the share size. We discuss certain properties of the schemes, such as the information rate and zero knowledge aspects. The paper extends the Karnin-Greene-Hellman bound on the parameters of ideal secret sharing schemes to schemes which are not necessarily ideal and then uses this as a yardstick to compare the performance of currently known multiplicative sharing schemes.