Generalized linear threshold scheme
Proceedings of CRYPTO 84 on Advances in cryptology
Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
A protocol to set up shared secret schemes without the assistance of mutually trusted party
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Communications of the ACM
Asynchronous verifiable secret sharing and proactive cryptosystems
Proceedings of the 9th ACM conference on Computer and communications security
Remarks on the multiple assignment secret sharing scheme
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
APSS: proactive secret sharing in asynchronous systems
ACM Transactions on Information and System Security (TISSEC)
Secure multi-party computation made simple
Discrete Applied Mathematics - Special issue: Coding and cryptography
New efficient and practical verifiable multi-secret sharing schemes
Information Sciences: an International Journal
Verifiable secret sharing and achieving simultaneity in the presence of faults
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
A practical scheme for non-interactive verifiable secret sharing
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Mobile proactive secret sharing
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
The Round Complexity of Verifiable Secret Sharing Revisited
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
A threshold cryptosystem without a trusted party
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
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
Round-Optimal and efficient verifiable secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Space efficient secret sharing for implicit data security
Information Sciences: an International Journal
An ideal multi-secret sharing scheme based on MSP
Information Sciences: an International Journal
Efficient (n, t, n) secret sharing schemes
Journal of Systems and Software
Information Sciences: an International Journal
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A (t,n) secret sharing divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret; but fewer than t shares cannot reconstruct the secret. In this paper, we extend the idea of a (t,n) secret sharing scheme and give a formal definition on the (n,t,n) secret sharing scheme based on Pedersen's (t,n) secret sharing scheme. We will show that the (t,n) verifiable secret sharing (VSS) scheme proposed by Benaloh can only ensure that all shares are t-consistent (i.e. any subset of t shares defines the same secret); but shares may not satisfy the security requirements of a (t,n) secret sharing scheme. Then, we introduce new notions of strong t-consistency and strong VSS. A strong VSS can ensure that (a) all shares are t-consistent, and (b) all shares satisfy the security requirements of a secret sharing scheme. We propose a strong (n,t,n) VSS based on Benaloh's VSS. We also prove that our proposed (n,t,n) VSS satisfies the definition of a strong VSS.