How to share a secret with cheaters
Journal of Cryptology
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
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
Optimum Secret Sharing Scheme Secure against Cheating
SIAM Journal on Discrete Mathematics
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
A coding theorem for cheating-detectable (2, 2)-threshold blockwise secret sharing schemes
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
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
Cryptography and Communications
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
Identifying cheaters without an honest majority
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Recursive hiding of biometrics-based secret sharing scheme using adversary structure
Information Processing Letters
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
Practically efficient multi-party sorting protocols from comparison sort algorithms
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
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We consider the problem of cheating in secret sharing schemes, cheating in which individuals submit forged shares in the secret reconstruction phase in an effort to make another participant reconstruct an invalid secret. We introduce a novel technique which uses universal hash functions to detect such cheating and propose two efficient secret sharing schemes that employ the functions. The first scheme is nearly optimum with respect to the size of shares; that is, the size of shares is only one bit longer than its existing lower bound. The second scheme possesses a particular merit in that the parameter for the probability of successful cheating can be chosen without regard to the size of the secret. Further, the proposed schemes are proven to be secure regardless of the probability distribution of the secret.