Design theory
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
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
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
Cryptography: Theory and Practice
Cryptography: Theory and Practice
t-Cheater Identifiable (k, n) Threshold Secret Sharing Schemes
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Detection of Cheaters in Vector Space Secret Sharing Schemes
Designs, Codes and Cryptography
Secret Sharing Schemes with Detection of Cheaters for a General Access Structure
Designs, Codes and Cryptography
Secret Sharing Schemes with Detection of Cheaters for a General Access Structure
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
Cheating Prevention in Linear Secret Sharing
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Cheating in Visual Cryptography
Designs, Codes and Cryptography
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 t-cheater identifiable secret sharing schemes
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
A multi-stage secret sharing scheme using all-or-nothing transform approach
ICICS'09 Proceedings of the 11th international conference on Information and Communications Security
Practically efficient multi-party sorting protocols from comparison sort algorithms
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Symmetric Threshold Multipath (STM): An online symmetric key management scheme
Information Sciences: an International Journal
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Tompa and Woll considered a problem of cheaters in (k, n) threshold secret sharing schemes. We first derive a tight lower bound on the size of shares |νi| for this problem: |νi|≥ (|S|-1)/δ+1, where νi denotes the set of shares of participant Pi, S denotes thr set of secrets, and δ denotes the cheating probabilily. We next present an optimum scheme which meets the equality of our bound by using "difference sets."