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
Secret Sharing Schemes with Detection of Cheaters for a General Access Structure
Designs, Codes and Cryptography
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
Almost optimum secret sharing schemes secure against cheating for arbitrary secret distribution
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Detection and identification of cheaters in (t, n) secret sharing scheme
Designs, Codes and Cryptography
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
| Hi-index | 0.00 |
In (k, n) threshold secret sharing scheme, Tompa and Woll consider a problem of cheaters who try to make another participant reconstruct invalid secret. Later, the model of such cheating is formalized in some researches. Some schemes secure against cheating of these models are proposed. However, in these models, the number of colluding participants is restricted to k - 1 or less. In this paper, we consider k or more colluding participants. Of course, secrecy is not maintained to such participants. However, if considering detecting the fact of cheating, we need to consider a cheating from k or more colluding participants. In this paper, we propose a (k, n) threshold secret sharing scheme that is capable of detecting the fact of cheating from n - 1 or less colluding participants. A scheme proposed by Tompa and Woll can be proven to be a (k, n) threshold secret sharing scheme that is capable of detecting the fact of cheating from n - 1 or less colluding participants. However, our proposed scheme is much more efficient with respect to the size of shares.