How to share a secret with cheaters
Journal of Cryptology
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The detection of cheaters in threshold schemes
SIAM Journal on Discrete Mathematics
Perfectly secure message transmission
Journal of the ACM (JACM)
Size of shares and probability of cheating in threshold schemes
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
Robust sharing of secrets when the dealer is honest or cheating
Journal of the ACM (JACM)
A perfect threshold secret sharing scheme to identify cheaters
Designs, Codes and Cryptography
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Secret Sharing Schemes with Detection of Cheaters for a General Access Structure
Designs, Codes and Cryptography
On the Cost of Reconstructing a Secret, or VSS with Optimal Reconstruction Phase
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
t-Cheater Identifiable (k, n) Threshold Secret Sharing Schemes
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Provably Secure Metering Scheme
ASIACRYPT '00 Proceedings of the 6th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Optimum Secret Sharing Scheme Secure against Cheating
SIAM Journal on Discrete Mathematics
Almost Secure (1-Round, n-Channel) Message Transmission Scheme
Information Theoretic Security
Optimum secret sharing scheme secure against cheating
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Flaws in some secret sharing schemes against cheating
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Efficient (k, n) threshold secret sharing schemes secure against cheating from n - 1 cheaters
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Detection of algebraic manipulation with applications to robust secret sharing and fuzzy extractors
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Almost optimum secret sharing schemes secure against cheating for arbitrary secret distribution
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Brief announcement: optimal amortized secret sharing with cheater identification
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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In Crypto'95, Kurosawa, Obana and Ogata proposed a k- out-of-n secret sharing scheme capable of identifying up to t cheaters with probability 1 - ε under the condition t ≤ ⌊(k - 1)/3⌋. The size of share |νi| of the scheme satisfies |νi| = |S|/εt+2, which was the most efficient scheme known so far. In this paper, we propose new k-out-of-n secret sharing schemes capable of identifying cheaters. The proposed scheme possesses the same security parameters t, ε as those of Kurosawa et al.. The scheme is surprisingly simple and its size of share is |νi| = |S|/ε, which is much smaller than that of Kurosawa et al. and is almost optimum with respect to the size of share; that is, the size of share is only one bit longer than the existing bound. Further, this is the first scheme which can identify cheaters, and whose size of share is independent of any of n, k and t. We also present schemes which can identify up to ⌊(k- 2)/2⌋, and ⌊(k-1)/2⌋ cheaters whose sizes of share can be approximately written by |νi| ≈ (nċ(t+1)ċ23t-1ċ|S|)/ε and |νi| ≈ ((nċtċ23t)2ċ|S|)/ε2, respectively. The number of cheaters that the latter two schemes can identify meet the theoretical upper bound.