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
How to avoid the cheaters succeeding in the key sharing scheme
Designs, Codes and Cryptography
An explication of secret sharing schemes
Designs, Codes and Cryptography
Geometric secret sharing schemes and their duals
Designs, Codes and Cryptography
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
Communications of the ACM
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
On the Information Rate of Secret Sharing Schemes (Extended Abstract)
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Optimum secret sharing scheme secure against cheating
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
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
InfoSecu '04 Proceedings of the 3rd international conference on Information security
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
An Efficient and Secure Self-Healing Scheme for LKH
Journal of Network and Systems Management
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
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Aperfect secret sharing scheme is a method of distributing sharesof a secret among a set P of participants in sucha way that only qualified subsets of P can reconstructthe secret from their shares and non-qualified subsets have absolutelyno information on the value of the secret. In a secret sharingscheme, some participants could lie about the value of theirshares in order to obtain some illicit benefit. Therefore, thesecurity against cheating is an important issue in the implementationof secret sharing schemes. Two new secret sharing schemes inwhich cheaters are detected with high probability are presentedin this paper. The first one has information rate equal to 1/2and can be implemented not only in threshold structures, butin a more general family of access structures. We prove thatthe information rate of this scheme is almost optimal among allschemes with the same security requirements. The second schemewe propose is a threshold scheme in which cheaters are detectedwith high probability even if they know the secret. The informationrate is in this case 1/3. In both schemes, the probabilityof cheating successfully is a fixed value that is determinedby the size of the secret.