How to share a secret with cheaters
Journal of Cryptology
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
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
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
Lower bounds for robust secret sharing schemes
Information Processing Letters
Robust vector space secret sharing schemes
Information Processing Letters
Communications of the ACM
Cryptography: Theory and Practice
Cryptography: Theory and Practice
Detection of Cheaters in Vector Space Secret Sharing Schemes
Designs, Codes and Cryptography
Optimum secret sharing scheme secure against cheating
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Unconditionally-Secure robust secret sharing with compact shares
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefits. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure.