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
Randomness in distribution protocols
Information and Computation
On the Dealer‘s Randomness Required in Secret Sharing Schemes
Designs, Codes and Cryptography
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
A Linear Construction of Secret Sharing Schemes
Designs, Codes and Cryptography
A note on the randomness in dynamic threshold schemes
Journal of Computer Security
Communications of the ACM
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Cryptography: Theory and Practice
Cryptography: Theory and Practice
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
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
A Randomnesss-Rounds Tradeoff in Private Computation
CRYPTO '94 Proceedings of the 14th 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
CRYPTO '97 Proceedings of the 17th 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
Improved Methods to Perform Threshold RSA
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: 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
Practical threshold signatures
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
IEEE Transactions on Information Theory
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
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Some secret sharingsc hemes can be used with only certain algebraic structures (for example fields). Group independent linear threshold sharing(GIL TS) refers to a t out of n linear threshold secret sharing scheme that can be used with any finite abelian group. Although group independent secret sharing schemes have long existed, here we formally introduce the definition of group independent linear threshold sharing. Using tools developed by [18], we develop some new necessary conditions for a GILTS. In addition, we develop lower bounds concerning the amount of randomness required within a GILTS.