Communication-efficient anonymous group identification
CCS '98 Proceedings of the 5th ACM conference on Computer and communications security
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
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
On the Security of the Threshold Scheme Based on the Chinese Remainder Theorem
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Threshold cryptography based on Asmuth-Bloom secret sharing
Information Sciences: an International Journal
Practical Threshold Signatures with Linear Secret Sharing Schemes
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Homomorphisms of secret sharing schemes: a tool for verifiable signature sharing
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Efficient multiplicative sharing schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Efficient multi-party computation over rings
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Robust threshold schemes based on the Chinese remainder theorem
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
An efficient group-based secret sharing scheme
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
Threshold cryptography based on asmuth-bloom secret sharing
ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences
An efficient implementation of a threshold RSA signature scheme
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Algebraic geometric secret sharing schemes and secure multi-party computations over small fields
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Linear integer secret sharing and distributed exponentiation
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Circular and KDM security for identity-based encryption
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Efficient integer span program for hierarchical threshold access structure
Information Processing Letters
How to share a lattice trapdoor: threshold protocols for signatures and (H)IBE
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
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A threshold scheme is an algorithm in which a distributor creates $l$ shares of a secret such that a fixed minimum number ($t$) of shares are needed to regenerate the secret. A perfect threshold scheme does not reveal anything new from an information theoretical viewpoint to $t-1$ shareholders {about the secret}. When the entropy of the secret is zero all sharing schemes are perfect, so perfect sharing loses its intuitive meaning. The concept of {zero-knowledge sharing scheme} is introduced to prove that the distributor does not reveal anything, even from a computational viewpoint. New homomorphic perfect secret threshold schemes over any finite Abelian group for which the group operation and inverses are computable in polynomial time are developed. One of the new threshold schemes also satisfies the zero-knowledge property. A generalization toward a homomorphic zero-knowledge general sharing scheme over any finite Abelian group is discussed and it is proven that ideal homomorphic threshold schemes do not always exist.