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
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
Conditionally secure secret sharing schemes with disenrollment capability
CCS '94 Proceedings of the 2nd ACM Conference on Computer and communications security
A perfect threshold secret sharing scheme to identify cheaters
Designs, Codes and Cryptography
Designs, Codes and Cryptography
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Secret Sharing Schemes with Veto Capabilities
Proceedings of the First French-Israeli Workshop on Algebraic Coding
The Detection of Cheaters in Threshold Schemes
CRYPTO '88 Proceedings of the 8th 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
A Generalized Secret Sharing Scheme With Cheater Detection
ASIACRYPT '91 Proceedings of the International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
Cheating Prevention in Linear Secret Sharing
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Optimum Secret Sharing Scheme Secure against Cheating
SIAM Journal on Discrete Mathematics
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
Dynamic threshold and cheater resistance for shamir secret sharing scheme
Inscrypt'06 Proceedings of the Second SKLOIS conference on Information Security and Cryptology
Secret-sharing hardware improves the privacy of network monitoring
DPM'10/SETOP'10 Proceedings of the 5th international Workshop on data privacy management, and 3rd international conference on Autonomous spontaneous security
Comments on Harn---Lin's cheating detection scheme
Designs, Codes and Cryptography
Cheater identification on a secret sharing scheme using GCD
ACM Communications in Computer Algebra
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In a (t, n) secret sharing scheme, a secret s is divided into n shares and shared among a set of n shareholders by a mutually trusted dealer in such a way that any t or more than t shares will be able to reconstruct this secret; but fewer than t shares cannot know any information about the secret. When shareholders present their shares in the secret reconstruction phase, dishonest shareholder(s) (i.e. cheater(s)) can always exclusively derive the secret by presenting faked share(s) and thus the other honest shareholders get nothing but a faked secret. Cheater detection and identification are very important to achieve fair reconstruction of a secret. In this paper, we consider the situation that there are more than t shareholders participated in the secret reconstruction. Since there are more than t shares (i.e. it only requires t shares) for reconstructing the secret, the redundant shares can be used for cheater detection and identification. Our proposed scheme uses the shares generated by the dealer to reconstruct the secret and, at the same time, to detect and identify cheaters. We have included discussion on three attacks of cheaters and bounds of detectability and identifiability of our proposed scheme under these three attacks. Our proposed scheme is an extension of Shamir's secret sharing scheme.