Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
How to share a secret with cheaters
Journal of Cryptology
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Verifiable secret sharing and achieving simultaneity in the presence of faults
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Verifiable secret sharing for monotone access structures
CCS '93 Proceedings of the 1st ACM conference on Computer and communications security
Geometric Shared Secret and/or Shared Control Schemes
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
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Informally, a (t, W)-threshold scheme is a way of distributing partial information (shadows) to w participants, so that any t of them can easily calculate a key (or secret), but no subset of fewer than t participants can determine the key. In this paper, we present an unconditionally secure threshold scheme in which any cheating participant can be detected and identified with high probability by any honest participant, even if the cheater is in coalition with other participants. We also give a construction that will detect with high probability a dealer who distributes inconsistent shadows (shares) to the honest participants. Our scheme is not perfect; a set of t - 1 participants can rule out at most 1 +(w-t+1/t-1) possible keys, given the information they have. In our scheme, the key will be an element of GF(q) for some prime power q. Hence, q can be chosen large enough so that the amount of information obtained by any t - 1 participants is negligible.