Proceedings of CRYPTO 84 on Advances in cryptology
How to share a secret with cheaters
Journal of Cryptology
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Elements of information theory
Elements of information theory
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
A perfect threshold secret sharing scheme to identify cheaters
Designs, Codes and Cryptography
Communications of the ACM
Cheating Immune Secret Sharing
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
Constructions of Cheating Immune Secret Sharing
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Cheating Prevention in Secret Sharing over GF(pt)
INDOCRYPT '01 Proceedings of the Second International Conference on Cryptology in India: Progress in Cryptology
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A secret sharing scheme is a cryptographic protocol by means of which a dealer shares a secret among a set of participants in such a way that it can be subsequently reconstructed by certain qualified subsets. The setting we consider is the following: in a first phase, the dealer gives in a secure way a piece of information, called a share, to each participant. Then, participants belonging to a qualified subset send in a secure way their shares to a trusted party, referred to as a combiner, who computes the secret and sends it back to the participantsCheating-immune secret sharing schemes are secret sharing schemes in the above setting where dishonest participants, during the reconstruction phase, have no advantage in sending incorrect shares to the combiner (i.e., cheating) as compared to honest participants. More precisely, a coalition of dishonest participants, by using their correct shares and the incorrect secret supplied by the combiner, have no better chance in determining the true secret (that would have been reconstructed if they submitted correct shares) than an honest participant.In this paper we study properties and constraints of cheating-immune secret sharing schemes. We show that a perfect secret sharing scheme cannot be cheating-immune. Then, we prove an upper bound on the number of cheaters tolerated in such schemes. We also repair a previously proposed construction to realize cheating-immune secret sharing schemes. Finally, we discuss some open problems.