Generalized linear threshold scheme
Proceedings of CRYPTO 84 on Advances in cryptology
An optimal class of symmetric key generation systems
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Secret sharing homomorphisms: keeping shares of a secret secret
Proceedings on Advances in cryptology---CRYPTO '86
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
Fully dynamic secret sharing schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Interaction in key distribution schemes
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Perfectly-Secure Key Distribution for Dynamic Conferences
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Threshold Schemes with Disenrollment
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Secret sharing schemes with partial broadcast channels
Designs, Codes and Cryptography
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All known constructions of information theoretic t-out-of-n secret sharing schemes require secure, private communication channels among the parties for the reconstruction of the secret. In this work we investigate the cost of performing the reconstruction over public communication channels. A naive implementation of this task distributes O(n) one times pads to each party. This results in shares whose size is O(n) times the secret size. We present three implementations of such schemes that are substantially more efficient: - A scheme enabling multiple reconstructions of the secret by different subsets of parties, with factor O(n/t) increase in the shares' size. - A one-time scheme, enabling a single reconstruction of the secret, with O(log(n/t)) increase in the shares' size. - A one-time scheme, enabling a single reconstruction by a set of size exactly t, with factor O(1) increase in the shares' size. We prove that the first implementation is optimal (up to constant factors) by showing a tight 驴(n/t) lower bound for the increase in the shares' size.