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
Lower bounds for monotone span programs
Computational Complexity
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
A Linear Construction of Secret Sharing Schemes
Designs, Codes and Cryptography
Communications of the ACM
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
A Comment on the Efficiency of Secret Sharing Scheme over Any Finite Abelian Group
ACISP '98 Proceedings of the Third Australasian Conference on Information Security and Privacy
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
Society and Group Oriented Cryptography: A New Concept
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques 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
Robust and Efficient Sharing of RSA Functions
CRYPTO '96 Proceedings of the 16th 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
Optimal-resilience proactive public-key cryptosystems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Efficient multiplicative sharing schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
New bounds on the information rate of secret sharing schemes
IEEE Transactions on Information Theory
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In a t out of n threshold scheme, any subset of t or more participants can compute the secret key k, while subsets of t - 1 or less participants cannot compute k. Some schemes are designed for specific algebraic structures, for example finite fields.Whereas other schemes can be used with any finite abelian group. In [24], the definition of group independent sharing schemes was introduced. In this paper, we develop bounds for group independent t out of n threshold schemes. The bounds will be lower bounds which discuss how many subshares are required to achieve a group independent linear threshold scheme. In particular, we will show that our bounds for the n - 1 out of n threshold schemes are tight for infinitely many n.