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
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
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
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th 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 bipartite access structure
IEEE Transactions on Information Theory
Cryptanalysis schemes against batch verification signature
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
Study on ring signature and its application
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
Threshold signature scheme with subliminal channel
CCDC'09 Proceedings of the 21st annual international conference on Chinese Control and Decision Conference
Hyper-elliptic curves based group signature
CCDC'09 Proceedings of the 21st annual international conference on Chinese control and decision conference
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
Information-theoretic security without an honest majority
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and 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
Key management scheme with bionic optimization
IITA'09 Proceedings of the 3rd international conference on Intelligent information technology application
Hyper-elliptic curves based ring signature
IITA'09 Proceedings of the 3rd international conference on Intelligent information technology application
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
Approximate quantum error-correcting codes and secret sharing schemes
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
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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 benefit. 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.